M Ö S SBAU ER STUDY OF 57F E 2+ IONS IN SOME R H O M B O H E D R A L CRYSTALS

A thesis submitted for the degree of Doctor of Philosophy

of the

Australian National University

by

Batit iy V&nnit> Howza

J anuary 19 80

(i)

S T A T E M E N T

The research described in this thesis was

carried out while I was a full-time research scholar

at the Australian National University, and except where

due reference is made is my own.

This thesis contains no material that has been

accepted for the award of any other degree or diploma

in any university or similar institution.

6.B.D. HOWES

January 1980

A C K N O W L E D G E M E N T S

I wish to express my appreciation and gratitude

to my supervisor, Dr. D.C. Price, for stimulating discussions

and helpful guidance during this course of study. I am

also indebted to Dr. D. Creagh for offering his equipment

and time to carry out the X-ray study of the

(M. e^ ) ( Py NO ) g ( C104 ) 2 compounds and discuss the results of the analysis.

I am grateful to Dr. M. Wiltshire and Dr. D. Taylor

for their interest in my work and also to the technical staff of the Department, particularly Mr. G. Sampietro for his preparation of the Co^ ^Fe^Cl2 crystals.

Finally I would like to thank the Australian National University for offering me a Ph.D. scholarship

and also the Department of Solid State Physics for the provision of laboratory facilities.

(iii)

A B S T R A C T

The 57Fe Mössbauer spectra of Fe(PyNO)g(C104)2 ,

where PyNO is Pyridine - N - oxide [viz. C -H NO) , recorded l

at low temperature in zero applied magnetic field showed2. "f*effects of slow relaxation of the Fe ion between its

lowest two (quasi-degenerate) energy levels. The spectra

of small crystals display resolved paramagnetic hyperfine

structure which disappeared when the crystals were ground

to power. These spectra have been reproduced using a2 +model in which the Fe sites, which are trigonally distorted

octahedra, experience a small off-axial distortion. The

magnitude of the off-axial crystal field, represented by a

term B2^2 ’ ^s considered to be of the same order as the

hyperfine interaction, so the two were applied together as

perturbations to the coupled electron-nuclear quantum2 +system of the high spin Fe ion. Distributions of values

2 2 — 1 of the parameter centred at Bn = 0 or 0.03 cm enabled

simulation of the experimental spectra for the unground2 -1crystals whereas a distribution centred at B^ = 0.3 cm

was required for the ground crystals. One effect of

grinding the crystals thus appears to be a significant

increase in the average cation site distortion.2 +Substitution of Fe ions into the isomorphous

compounds M (PyNO)6 (C104)2 (M = Zn,Mg) provided a further

opportunity to study the cation site distortion thought to

(iv)

exist in Fe(PyNO)g(C104)2• The general trends of the2 +Mössbauer spectra of Fe ions doped into Zn(PyNO)g(C104)2

and Mg(PyNO)0(CIO4)2 were again reproduced using the site

distortion model mentioned above. The Mössbauer spectra

for the Zn-Fe series indicated that, for a certain2 -tconcentration range, the proportion of distorted Fe sites is

diminished with respect to Fe(PyNO)0(0104)2*

An unusual dependence on the iron concentration was

found for the Mössbauer spectra of the Zn-Fe series. An X-ray

powder diffraction analysis showed that the cell constants

of the Zn-Fe series also exhibit abnormal behaviour as a

function of iron concentration. No such behaviour was

observed for the Mg-Fe series in either the Mössbauer or

X-ray results. The dependences of the Mössbauer spectra and

cell constants on iron concentration in the Zn-Fe series

appear to be correlated and related to changes in the degree

of disorder in the crystal lattice. However, the origin of

this disorder is uncertain.

The solid solution series Co Fe Cl? has also1 -x x zbeen studied. This hexagonal layered system is of particular

interest because of the competing spin anisotropies of the2 +two cations. The Fe magnetisation direction and homogeneity

have been examined as functions of iron concentration at

4.2 K in zero applied field by observation of the hyperfine

interactions at the ferrous site. The results obtained to

date indicate that the hyperfine field direction, and thus

the spin, of the ferrous ion rotates, from its orientation

(v)

in the basal plane for very low iron concentrations

towards an alignment parallel to the c axis as

the iron concentration is increased. This behaviour is

thought to be a result of competition between the ferrous2 +spin anisotropy energy and the Co crystal field

anisotropy energy.

(vi)

TABLE OF CONTENTS

Page

S ta t emen t (ii)

Acknowledgements (iii)

Abstract (iv)

Chapter 1 General Introduction 1

1.1 5 7 Fe2+ Ions in the M(PyNO)g (CIO 4 I 2 3Compounds (M=Fe,Zn,Mg)

1.2 57Fe2+ Ions in CoCl 2 7

Chapter 2 Theoretical Review 1224-2.1 Electronic Level Structure of Fe 13

Ions in Sites of Trigonal Symmetry2.1.1 Crystal Field Interaction 142.1.2 Spin-Orbit Interaction 18

2.2 Hyperfine Interactions 19

2.3 Magnetic Hyperfine Interaction 21

2.3.1 Origins of the Magnetic 26Hyperfine Interaction

2.4 Relative Intensities of Absorption 29Peaks

2.4.1 Single Crystal Absorbers 292.4.2 Randomly Packed Polycrystalline 34

Ab s o rb e r s

2.4.3 Relative Intensities of 36Transitions between Coupled Electron-Nuclear States

2.5 Evaluation of Crystal Field Parameters 39 from Mössbauer Spectra

(vii)

Page

Chapter 3 Experimental Procedures 40

3.1 Sample Preparation 40

3.1.1 Crystal Growth 40

3.1.2 Absorber Preparation 42

3.2 Apparatus 4 4

3.2.1 Mössbauer Spectrometer 44

3.2.2 Variable Temperature Controller 46

3.3 Evaluation of Mössbauer Spectra 46Parameters

Chapter 4 Evidence for Cation Site Distortions 49in Fe (PyNO)6 (ClOy)2

4.1 Introduction 49

4.2 Crystal Sturcture 51

4.3 Results and Discussion 52

4.4 Model for the Distortion of the Cation 56Site in Fe (PyNO)s (C10y)2

4.4.1 Derivation of the Coupled 58Electron-Nuclear Basis States

4.5 Discussion 62

4.6 Conclusions 682 +Chapter 5 Further Studies of the Fe Ion in the 69

Isomorphous M(PyNO)g (CIO4)2 Compounds (M = Zn, Mg)

5.1 Introduction 69

5.2 Results 70

5.2.1 Mössbauer Data 70

5.2.2 X-ray Diffraction Analysis 71

(viii)

Page

5.2.3 Detailed Investigation of 71<Zno.2Feo.8> (PVN0) 6 (C10h) 2

5 . 3 Discussion 745.3.1 Mössbauer Data 745.3.2 Spin-Spin Coupling between 76

2 +Fe Ions in the M (PyNO) § (C101+) 2 Compounds

5.3.3 X-ray Analysis 785.3.4 Correlation of the Mössbauer 80

and X-ray Results5.3.5 Effects of Changes in the 82

Crystal Preparation Conditions5.3.6 Temperature Dependence of 83

the Spectral Features5.4 Future Work 845.5 Conclusions 85

2. ”4"Chapter 6 Magnetic Behaviour of the Fe Ion in 87C o C1 2

6.1 Introduction 876.2 Crystal Structure of Co, Fe Cl? 886.3 Theoretical Considerations 896.4 Results and Discussion 926.5 Future Work 976.6 Conclusions 98

References 99

( ix)

1

C H A P T E R 1

GENERAL INTRODUCTION

The emission and absorption of y-rays without

loss of energy due to recoil of the nucleus is known as

the Mössbauer effect as it was first observed by Rudolf

Mössbauer in 1957 (Mössbauer, 1958). Mössbauer spectroscopy

has since found applications in many diverse fields, such

as solid state physics and chemistry, biology and

archaeology. Its great value derives from the fact that

the width of the emission (or absorption) lines resulting

from transitions from metastable nuclear levels are often

smaller than the interactions between the nucleus and

atomic electrons, the so-called hyperfine interactions.— i 2This extremely high degree of resolution (ca. 10 )

has allowed the observation of phenomena which before the

discovery of the Mössbauer effect were considered to be

unmeasurable, for instance, a laboratory measurement of

gravitational red shift and observation of the Zeeman

splitting of nuclear levels. The strength and nature

of the hyperfine interations depend critically on the

electronic, chemical and magnetic state of the atom.

Mössbauer spectroscopy can thus provide considerable

information about the atom and its environment.

2

Many nuclides are known to be suitable for use as

Mossbauer nuclides but in the context of this thesis only

57Fe will be considered. Two distinct groups of high spin

ferrous compounds will be examined. Although they have

dissimilar properties they are linked by their common

rhombohedral crystalline structure and consequent

octahedrally coordinated cation sites with trigonal

symme try.

In a cubic octahedral field the free ion ground

multiplet (5D) of the high spin ferrous ion is split into

an orbital doublet and a lower lying orbital triplet

T . Spin-orbit coupling leads to further splitting of

the orbital levels resulting in a triplet ground state.

In the presence of a trigonal field this triplet is split

into a singlet and a doublet which, for the cases of

interest in the present study, is the lower. The

separation of the doublet and singlet is a key factor in

determining the appropriate description for the magnetic

properties of the ion and its characterisation (when

desired) by an effective (or psuedo) spin. These level

separations and hence the aforementioned characteristics

of the ion are dependent upon the relative magnitudes of

the trigonal field and spin-orbit interactions.

Two particular cases are pertinent to the present

work. In the first, the trigonal field is much larger

than the spin-orbit coupling, giving rise to a ground

doublet well separated (by ~ 100 cm ) from higher lying

states. In the second the trigonal field and spin-orbit

3

coupling are of the same order of magnitude which results

in a small separation (~ 10 cm ) between the doublet and

singlet. These cases are considered in Chapter 4 and

Chapter 6 respectively. It will be seen that the approach

chosen to analyse the experimental data is greatly-

influenced by the degree of separation of the s p in j 1 eve 1 s .

Further details of the electronic structure of a high spin

ferrous ion in a trigonal environment will be given in

Section 2.1.

1.1 57Fe2 Ions in the M (PyNO)6 (C104) 2 Compounds(M = F e , Zn, Mg)

2 +Paramagnetic Fe ions in Fe(PyN0)6(C104)2 , wherePyNO is Pyridine - N - oxide (viz. C^H^NO), and irondoped into the diamagnetic isomorphous structuresM (PyNO)e(C104)2 (M = Zn, Mg) constitute the first groupof materials studied. The interest in these compoundsoriginated from an investigation of high spin ferrous

substances designed to explore the possibility that someof them might display slow relaxation and, if so, to

understand the structural conditions required to allow

observation of such processes.

Before proceeding further it is of value to briefly

recall that the electronic relaxation rates of paramagnetic 2 “f"high spin Fe ions are normally fast compared to the

nuclear precession rates even at low temperatures. This

contrasts with the situation prevailing in magnetically

ordered systems where strong exchange interactions help

to decrease the relaxation rate. In paramagnetic systems

4

spin-lattice and spin-spin interactions tend to disorient

the electronic spin both in time and space. It is a

consequence of these interactions that relaxation rates

are fast in paramagnetic systems. The fast relaxation

causes the magnetic moment of the ion and the resultant

hyperfine field at the nucleus to fluctuate rapidly with the

result that the nuclear spin does not experience a unique

direction of the hyperfine field to precess around.

Consequently, the Mossbauer effect measures a time averaged

field of zero at the nucleus.

Observation of slow relaxation effects in the • • 2 "I-Mossbauer spectra for Fe ions in ZnC03 (Price et ai . ,

1977) and MgC03 (Srivastava, 1976) suggested that other2 ”{■substances in which the Fe ions have the same site

symmetry might also show slow relaxation effects. The

cations in these rhombohedral carbonates are coordinated

octahedrally with a trigonal distortion of the octahedron

(point symmetry C .). In the majority of cases for which* X

ferrous ions occur in distorted octahedral sites the ionic

ground state is an orbital singlet. Spin-orbit mixing

with excited states gives rise to a non-magnetic singlet

ground state and two excited doublets. At low temperatures

only the singlet is occupied and no hyperfine structure

will be visible in the spectra. At higher temperatures

one might expect that Raman relaxation processes within

the ground quintet will allow faster relaxation than is

expected for cases with doublet ground states and relatively

5

large excitation energies, A, to states above the ground

doublet. This is the result of a A-2 term in the

expression for the Raman relaxation rate (Price et al.,

1977). It follows that observation of hyperfine structure

in the Mössbauer spectra for such ions is less probable

than for cases with doublet ground states and relatively

large separations from higher lying states (if spin-spin

relaxation is unimportant). Such a system exists in the

carbonates mentioned earlier. A further example is found

in Fe(PyNO)6(C104)2•

In the absence of an applied magnetic field the

Mössbauer spectra for Fe(PyNO)6(C104)2 at low temperature

(Sams and Tsin, 1975a, b; 1976) do not exhibit the

we 11-reso1ved paramagnetic hyperfine structure evident

in the spectra of the carbonates. However, application

of small (~ 0.1 T) magnetic fields results in the appearance

of resolved hyperfine structure (Sams and Tsin, 1976). A

similar effect was observed by Price and Srivastava (1976)2 4“for Fe ions in CaC03 and CdC03. The site symmetry of

the ferrous ions in these carbonates is the same as in

ZnC03 and MgC03, but to observe resolved hyperfine structure

an applied magnetic field was necessary.

It was suggested by Price and Srivastava that the

doublet ground state was split by £ 0.5 cm and on

this assumption they were able to satisfactorily interpret

their data. Zimmermann et al. (1974a,b) discovered evidence

for slow relaxation in two other high spin ferrous compounds,

6

Fe(papt)2 •C 6H 6 and tetrakis-(1 ,8 -naphthyridine) iron

(II) perchlorate. Both substances have a doublet- lground state which is split by less than 1 cm . The

transition probabilities for spin-lattice relaxation

between the doublet ground states were determined by

Zimmermann to be very small thus enabling the observation

of resolved hyperfine structure in the presence of an2 +applied field. In the case of Fe ions in ZnCÜ3

the states of the unsplit ground doublet are magnetic

and resolved hyperfine structure is visible at sufficiently2 “I"low temperature whereas for Fe ions in CaCÜ3 the states

of the slightly split ground doublet are non-magnetic and

an external field is required to remagnetise them and allow

the observation of hyperfine structure.

The observations of Fe(PyNO)6 (C104)2 made by Sams

and Tsin ( 19 75a,b; 19 76 ) and the new results reported

in the following chapters may be well described by a

model in which the doublet ground state is slightly

split by a small off-axial distortion. The splitting is

considered to be of the same order of magnitude as the

magnetic hyperfine interaction and thus even in zero

applied field the split states will be remagnetised to a

small extent by the nuclear magnetic moment. This results

in the onset of hyperfine structure manifested as the

line broadening of the powder spectra of Sams and Tsin

(1975a,b; 1976) and the resolved structure of the many-

crystal samples reported in Chapter A.

7

The off-axial distortion mentioned above was for

reasons of simplicity assumed to be of rhombic form

resulting from random strain fields within the crystal.

Such a distortion is not expected to be an accurate

representation but within the limitations of the model

it was anticipated that it would provide a reasonable

insight into the system.

It appears evident from the foregoing that the2 +assumption of fast relaxation for high spin Fe ions

is not valid under certain conditions which result in a

doublet ionic ground state well separated from

higher states. In other words it is highly probable that2 ”4"the slow relaxation observable in high spin Fe ions

is a consequence of the site symmetry.

1.2 57Fe Ions in CoCl2

The randomly mixed two component systems of the

type R M X , where R and M are different magnetic cations1 “ X X

with competing spin anisotropies and X represents the

anions, have attracted much attention because the differing

characteristics of the constituent cations give rise to

interesting magnetic properties.

Fishman and Aharony (1978) have considered the

concentration versus transition temperature phase diagrams

of alloys of two materials which have competing anisotropies.

They have predicted three kinds of ordered phases and

also a tetracritica 1 point in such systems. The ordered

phases correspond to the ordering of each spin component

8

at either end of the concentration range and to a new

phase, which for a mixture of two antiferromagnets with

different anisotropies has been called oblique-

ant i f er romagnet (OAF)(Matsubara and Inawashiro, 1977), in

the intermediate concentration region. In the OAF phase

there is simultaneous ordering of the two spin components.

The spin of each species of cation has its own axis of

sublattice magnetisation which is directed obliquely to

the easy axis of the pure system. Such a phase is thought

to have been found in, e.g. Co Fe C12.2H20 (Katsumata

et al. , 19 79 ) and K2Mn^ x^ex^4 (Bevaart et al. , 19 78).

The solid solution series Co Fe Cl2 is a systeml -x xwhich has competing spin anisotropies and constitutes

the second group of materials investigated in this thesis.

Anhydrous FeCl2 and CoCl2 are hexagonal layered compounds

of the CdCl2 type in which layers of metal ions are

separated by two layers of halide ions (further details

of the crystal structures will be given in Section 6.2).

Magnetic susceptibility measurements (Starr et al., 1940)

showed that the susceptibilities of both compounds, from

room temperature to 75 K, obeyed the Curie-Weiss law

(viz. x = C/(T-0) where x is the susceptibility, 0 is the

Curie temperature and C a constant). Extrapolation of these

results gave rise to a positive value of the paramagnetic

Curie temperature which according to the Weiss theory

corresponds to a positive molecular field and indicates

9

the occurrence of a ferromagnetic transition. However,

susceptibility measurements at lower temperatures reveal

maxima at approximately the same temperatures as A-type

anomalies observed in the specific heat measurements (Trapeznikowa

and Shubtiikov , 19 35;Trapeznikowa e t al., 19 36 ) thus implying

antiferromagnetic transitions. Furthermore, for both compounds a

large fraction of the expected saturation magnetisation can be

produced by magnetic fields that are much smaller than

those usually associated with the exchange coupling in

an antiferromagnet which has a transition temperature

of ~ 24 K (Wilkinson et al., 1959). Materials which

exhibit these unusual magnetic properties are known as

metamagnets (Becquerel and van den Handel, 1939). Below

the ordering temperature of the compound (23.5 K for FeCl2 ,

24.9 K for C0 CI2 ) the cation spins are aligned ferro-

magnetically within any one layer while the spins in

alternate layers are aligned antiparallel resulting in an

overall antiferromagnetic structure. The spins are

oriented parallel and perpendicular to the trigonal axis

in FeCl2 and C0 CI2 respectively as a result of the dominant

crystal field anisotropy.

There has been some conflict in the literature

concerning the relative magnitudes of the trigonal field

splitting 6 and the spin-orbit coupling parameter A for2 +F e C 1 2 • The magnetic properties of the Fe ion are

dependent upon the ratio 6/A and thus it is of importance

to resolve which assessment is more appropriate. Kanamori

( 1958 ) without interpretab 1e data assumed, with reservations,

10

that the trigonal field dominated the spin-orbit

interaction (i.e. 6 >> A) in F e C1 2 • Thus at low temperatures

a good approximation of the spin system can be given by

an Ising model. This means that the ground doublet of the 2 +Fe ion is well separated from the higher lying singlet

and consequently the transverse spin components are

completely quenched. Such a model was pursued by other

authors (e.g. Heap, 1962; Yomosa, 1960) to calculate a

number of properties. However, the results of a Mössbauer

study of FeCl2 (Ono et al. 1964) showed that 6/A ~ 1. In

systems which have 6/A ~ 1 the separation between the doublet

and singlet states is ~ 10 cm and the Ising model, as

described above, is not a valid representation of the magnetic2 +properties of the Fe ion. Hazony and Ok (1969) repeated

the Mössbauer analysis and their interpretation of the

measurements was found to support Kanamori’s contention.

Both sets of authors obtained almost identical temperature

dependences for the quadrupole splitting but their

interpretations of the data were quite different. Ono

et al. derived A = 95 cm 1, 6 = 119 cm 1 (6/A = 1.25)

whereas Hazony and Ok found A = 42 cm , 6 = 340 cm

(6/A = 8.4). Before proceeding further it should be pointed

out that it is possible to obtain such widely differing

deductions from two similar sets of data because the

temperature dependence of the quadrupole splitting does

not offer a reliable or unambiguous method for estimating

static crystal field parameters (see Section 2.5). The

evidence from a number of different techniques (vide infra)

11

indicates that the closest description of the magnetic2 +properties of the Fe ion in FeCl 2 is given in terms of

a model in which the effective spin is 1 and 6/A ~ 1,

in agreement with Ono's analysis of the Mossbauer data.

A model of this type has been used to interpret

measurements obtained from e.g. neutron-scattering, Raman

scattering, the para 1lei and perpendicular

susceptibilities and the specific heat of F e C12 by

Birgeneau et al. (1972), Johnstone et a l . (1978),

Bertrand et al. (1974) and Lanusse et al. (1972) respectively.

All achieved good agreement between theory and experiment.

Tawaraya and Katsumata (1979) have observed, using susceptibility measurements, three distinguishable

magnetically ordered phases in Co 1 ^Fe^Cl 2 • They associated these phases with the Fe-rich and Co-rich antiferromagnetic phases, and a phase at the intermediate

concentration region (viz. 0.75 £ x £ 0.65 at 5 K) they

identified with the OAF phase mentioned earlier. In the

present study of Co ^Fe^Cl 2 the behaviour of the ferrous spin as a function of iron concentration is observed via

the hyperfine interactions at the iron ion. Such an investigation might provide useful information concerning

the OAF phase thought to exist in this system, although

no measurements have yet been made in the appropriate

concentration range.

12

C H A P T E R 2

T H E O R E T I C A L R E V I E W

In this chapter outlines and definitions will be

given only of the essential theoretical aspects which are

relevant to the work of this thesis and that providepertinent background information. In particular the

derivation of the electronic energy level structure of 2 +Fe ions under the influence of a trigonal crystal field

and spin-orbit coupling will be discussed. Features of the hyperfine interactions will be considered with

particular reference to the description of the magnetic

hyperfine interaction by the effective field approximation. The relative intensities of Mössbauer absorption peaks

and the difficulties encountered in attempting to evaluate

static crystal field parameters from Mössbauer data are

also summarised. The general theory of the Mössbauer

effect has been described by many authors. The reader

is referred to well documented accounts by, for example,

Boyle and Hall (1962) and Greenwood and Gibb (1971).

13

2 T-2.1 Electronic Level Structure of Fe Ions in Sites of Trigonal Symmetry

The Mössbauer spectra of ions in a crystal latticedepend very strongly on the electronic energy level structure

of the ions in a particular crystalline environment. In thissection it is intended to provide an outline of the effects

of the various factors acting upon the free ion ground state 2 +of a Fe ion when it is located in a site of trigonal

2 - | -symmetry. This discussion will be restricted to Fe ions

in trigonal sites because of their particular relevance to

the work presented in this thesis.

The Hamiltonian which describes the splitting of the free ion ground term (5D) may be written:

X = X + W + X + X + X 2.1ct so ss m q

where X represents the crystal field interaction, X go is

the intraionic spin-orbit interaction, X is the interionicssspin-spin interaction, X is the nuclear magnetic dipoleminteraction and X represents the nuclear electric quadrupole interaction.

The intraionic spin-spin coupling will be neglected

because in the present context it will not lead to further splitting of the ionic states (the only non-zero matrix

elements are those derived from the spin operator S^) and

since it is expected to be small (< 1 cm 1; Abragam and

Bleaney , 19 70).

The last two terms of Equation 2.1 operate on

the nuclear and electronic components of the wavefunctions

and are included in calculations only when the electronic and

14

nuclear systems are treated as one coupled system. The

importance of such terms, particuarly in the context of

this thesis) will become apparent in Chapter 4. In this

section only purely electronic wavefunctions are considered

and thus these terms are ignored. The term 3Cs arises from

dipole-dipole coupling and exchange interactions between

the electron spins of neighbouring ions. Both of these

interactions may induce transitions between spin states,

leading to the well known spin-spin relaxation process. In a

paramagnetic compound the exchange interaction is expected

to be small and dipolar coupling between neighbouring electron

spins is not sufficiently strong to have any significant

effects on the electronic structure. Therefore, it is possible to omit these interactions from a discussion of the electronic structure of ions in a paramagnetic compound.When a compound which is magnetically ordered is considered, however, the degeneracy of the electronic levels may be lifted

by the exchange interactions. The form and implications of the presence of strong exchange interactions will be examined

in Chapter 6 for the particular case of the antiferromagnetic

Co Fe^ Cl^ compounds. In this section only those termsin the Hamiltonian 2.1 representing the crystal field and

spin-orbit interactions will be considered.

2.1.1 Crystal Field Interaction

An estimate of the electrostatic potential V(r,0,(|>)

experienced by a paramagnetic ion in a crystal may be made if it is assumed that the surrounding ions can be treated as

point charges. The form of such a potential is:

15

V ( r , 0 , <J>) lj

2 . 2

w h e r e i s t h e c h a r g e o f t h e j n e i g h b o u r i n g i o n l o c a t e d

a t a d i s t a n c e R f r o m t h e o r i g i n . The p o t e n t i a l may b e

e x p a n d e d i n s p h e r i c a l h a r m o n i c s u s i n g t h e s p h e r i c a l h a r m o n i c

a d d i t i o n t h e o r e m ( e . g . G r i f f i t h , 1 9 6 1 ) a n d w r i t t e n a s i n

E q u a t i o n 2 . 3 ( B l e a n e y a n d S t e v e n s , 1 9 5 3 , H u t c h i n g s , 1 9 6 4 ) :

V ( r , 0 , <J)) I Am < r n > Ym (0, (f)) 2 . 3n , m

w h e r e Ym ( 9 , d ) ) a r e s p h e r i c a l h a r m o n i c s , Am d e n o t e s a c r y s t a l l i n e n n

f i e l d p a r a m e t e r a n d < r n > i s t h e e x p e c t a t i o n v a l u e o f t h e n ^

p o w e r o f t h e d e l e c t r o n r a d i u s . T h e p r o d u c t s A™ < r n > a r e

n o r m a l l y d e t e r m i n e d b y f i t t i n g t h e c r y s t a l l i n e f i e l d H a m i l t o n i a n

t o e x p e r i m e n t a l d a t a . U s i n g o p e r a t o r e q u i v a l e n t s a n d

f o l l o w i n g O r b a c h ( 1 9 6 1 ) i t i s p o s s i b l e t o r e w r i t e E q u a t i o n

2 . 3 a s :

v , m n _ _ m, _ .) A < r > 6 0 ( L)L n n n —n , m

2 . 4

T Bm 0 m( L) u n n — n , m

w h e r e 0 (_L) a r e o p e r a t o r e q u i v a l e n t s , t h e f o r m o f w h i c h i s

g i v e n by O r b a c h ( 1 9 6 1 ) , a n d B™ = A™ < r n > 0 ^ . The m u l t i p l i c a t i v e

f a c t o r s 0^ a r e t a b u l a t e d b y H u t c h i n g s ( 1 9 6 4 ) .

p -j-Th e Fe i o n s c o n s i d e r e d h e r e i n a r e i n c u b i c -

o c t a h e d r a l c r y s t a l f i e l d s w i t h a t r i g o n a l d i s t o r t i o n a l o n g

t h e [ 1 1 1 ] d i r e c t i o n o f t h e o c t a h e d r o n . I f t h e q u a n t i s a t i o n z

a x i s i s t a k e n t o be t h e [ 1 1 1 ] d i r e c t i o n o f t h e o c t a h e d r o n ,

16

which is a three-fold symmetry axis, then because in the

present case many of the terms in Equation 2.3 have zero

matrix elements the general form of V showing a distortion

along the [111] direction is (Bleaney and Stevens, 1953):

V B°0° + B°0° + B^O* 2 . 5

Equation 2.5 is a summation of cubic and axial

crystal field terms.

It is assumed that the crystal field interaction

is much weaker than the intra-atomic Coulomb interactions,

so that no admixture of spectroscopic terms by the crystal

field is considered. It is also assumed that the cubic

component of the crystal field interaction is much larger

than any of the other perturbing effects. In fact, for 2 *4"Fe ions in octahedral symmetry in crystals such as those

of interest here the splitting due to the cubic field is

~ 10 cm whereas that for the trigonal field is < 10J- lcm . On this basis it is possible to make the

approximation that the ground state in the cubic field can

be used to calculate the states resulting from other

smaller perturbations. In other words, admixtures with

the excited cubic state may be ignored in some

circumstances. In this case the ground 5T state is2gconsidered to be equivalent to a 5P state with the

replacement of by an effective orbital angular momentum

a jL where £ = 1 and a = -1 (Griffith, 1961; Abragam and

Pryce, 1951). Calculations performed by Sams and Tsin

(1975b), which allowed for admixture of the excited state

17

i n t o t h e g r o u n d s t a t e ( 5T ) , i n d i c a t e d t h a t s i g n i f i c a n t2 8

e r r o r s w e r e n o t i n t r o d u c e d b y t h i s a p p r o x i m a t i o n .

T h e t e r m f o r n = m = 0 h a s b e e n o m i t t e d i n t h e

e x p r e s s i o n f o r t h e c r y s t a l f i e l d p o t e n t i a l 2 . 5 b e c a u s e

i t i s a n a d d i t i v e c o n s t a n t a n d d o e s n o t g i v e r i s e t o

s p l i t t i n g o f s t a t e s .

5 2 +Th e D g r o u n d s t a t e o f t h e Fe i o n ( c o n f i g u r a t i o n

3 d 5 ) i s s p l i t b y t h e c u b i c - o c t a h e d r a l f i e l d i n t o a g r o u n d

s t a t e o r b i t a l t r i p l e t ( 5T ) a n d a n o r b i t a l d o u b l e t ( 5 E )2g g

s e p a r a t e d t y p i c a l l y by ~ 1 0 4 cm ( A b r a g a m a n d B l e a n e y ,

1 9 7 0 ) ( F i g u r e 2 . 1 ) . Th e a n g u l a r p a r t s o f t h e 5T2 8

w a v e f u n c t i o n s may b e w r i t t e n a s ( B l e a n e y a n d S t e v e n s , 1 9 5 3 )

4>i = ~ (2 / 3 >2 Y ~ 2 - ( i / 3)2 y '2

K -h h

<t>-1 = ( 2 / 3 ) y\ - ( 1 / 3) Yj

T h e s e s t a t e s a r e s p l i t b y t h e t r i g o n a l f i e l d i n t o

a n o r b i t a l d o u b l e t (<{) + ^) a n d a n o r b i t a l s i n g l e t ( ( j )^) . Th e

3 - 1s e p a r a t i o n b e t w e e n w h i c h i s t y p i c a l l y < 10 cm ( A b r a g a m

a n d B l e a n e y , 1 9 7 0 ) ( F i g u r e 2 . 1 ) . T h e M o s s b a u e r

q u a d r u p o l e i n t e r a c t i o n d a t a o f Sams a n d T s i n ( 1 9 7 5 a ) a n d2 -f-

Ono et al. ( 1 9 6 4 ) h a v e s h o w n t h a t f o r Fe i o n s i n a l l t h e

c o m p o u n d s s t u d i e d i n t h e p r e s e n t w o r k t h e o r b i t a l d o u b l e t

i s l o w e r t h a n t h e s i n g l e t .

18

2.1.2 Spin-Orbit Interaction

Each of the orbital states have five-fold spin

degeneracy. These degeneracies are partially lifted when

account is made of the coupling between the spin and

orbital angular momenta. For the free ion this coupling

has the form A L-S where A = - 103 cm 1 . The effects of o— — ocovalency on an ion situated in a crystal must be

considered, however, and may be approximated by a fractional

decrease in Aq (Ingalls, 1964). Thus the spin-orbit

coupling may now be written:

A L-S = a 2 A [L S + h (L,S + L S.)]— — o z z + - - +

where a 2 is a factor which accounts for the decrease in

2 . 7

A odue to covalency effects.

Application of successive perturbation calculations,

which introduce successively smaller terms of the Hamiltonian

2.1 to the free ion ground state, result in the electronic

level structure shown in Figure 2.1. It is noted that the

spacings shown are illustrative only and do not accurately2 m\~ #represent either of the Fe systems studied in this thesis.

It should be stressed that the above discussion

of the electronic level structure has assumed that the

trigonal field interaction is much larger than the spin-

orbit interaction which can thus be applied as a

perturbation to the trigonal states. This is, however,

very often not the case. In such instances the same state

degeneracies will result as are indicated for the spin-

orbit split states in Figure 2.1. The wavefunctions and

:.. — - — -

\ 1000 cm*1

XL.S

Fig. 2.1 Schematic diagram of the electronic energylevels of the high spin Fe2 + ion in a crystal field of trigonal symmetry as in Fe(PyNO)5 (CIO4)2 and FeCl2 . (a) The effect of the cubic andtrigonal crystal fields the 5D free ion state.(b) The effect of the trigonal crystal field component and the spin-orbit coupling on the 5T orbital triplet. The values of the parametersused were for illustrative purposes onlyo2

2g

Bu = - 55.56 cm 1 , B° = - 125 cm 1 and- 19 4.4 cm

19

splittings between states will, of course, be modified

depending on the relative magnitudes of the trigonal field

and spin-orbit interactions. In anhydrous ferrous chloride, for instance, the trigonal field interaction is of the same

order as the spin-orbit interaction (Ono et a l ., 1964).

In this case the trigonal field and spin-orbit interactions

are applied jointly to the cubic states to determine the

energy level structure pertinent here.

2 . 2 Hyperfine Interactions

The hyperfine interactions which originate from the

coupling between the nucleus and the atomic electrons contribute terms to the total Hamiltonian for the atom which may be written:

Jf = JC + (E + M, + E, + higher order terms) 2.8o o 1 z

represents all terms in the Hamiltonian for the atom

except the hyperfine interactions. is the electricmonopole interaction, M x is the magnetic dipole interaction

and E2 is the electric quadrupole interaction.

The hyperfine interactions E ^ , M 1 and E2 constitute

only the first few terms of a multipole expansion (terms

within the brackets of Equation 2.8) which expresses all

of the hyperfine interactions. Terms of higher order than

those specified are not detectable by the Mossbauer effect

and will not be considered further. All of the hyperfine

interactions can be expressed as the product of a multipole

moment of the nucleus and a corresponding multipole field

20

produced by the electrons which surround the nucleus.

The electric monopole term E , which represents theo

Coulomb interaction between the electrons and a point

nuclear charge is not a hyperfine interaction. However,

the correction to this interaction, required to account for

the overlap of the electrons with a nucleus of finite

dimensions, is a hyperfine interaction and determines the

so-called isomer shift. As a consequence of the differing charge radii of the ground and excited levels of the nucleus

the Coulomb interaction with the electronic charge is different for the two states. The y-ray energy is thus

changed relative to its value for a point nucleus by an amount proportional to the total electron density at the nucleus. If the chemical environments of the Mössbauer ions in the source and absorber differ, the total s electron densities at the source and absorber nuclei will also be

different. The subsequent difference in transition energies, the isomer shift AE, has been derived by, for example,

Wertheim (1964):

AE = f1- Z e2 [R2-R2][ 14» <0) I 2 - I tjj(o) I 2 ] 2.95 e g ' 1 a 1 's

where R and R are the effective radii of the excited ande gground nuclear states, | ip (0 ) | and | ip ( 0) | are the total s electron densities at the absorber and source nuclei.

The electric quadrupole interaction, E 2 , denotes

the coupling of the nuclear electric quadrupole moment of

a given nuclear energy level, Q, with the electric field

gradient (e.f.g.) at the nucleus. The nuclear quadrupole

21

moment reflects the deviation of the nucleus from spherical

symmetry and nuclei whose spins are 0 or \ have a zero

quadrupole moment. The Hamiltonian which describes this

interaction is written in Equation 2.10 in the form

determined by Abragam (1961) and Cohen and Reif (1957).

“ frfej C3Iz - I(I+1) + n<i* - i;>] 2-10

where eq = 9 2V/3z2 (i.e. the z component of the electric

field gradient) and r\ is the asymmetry parameter of the

e.f.g. defined by

n = (32V / 3 x 2 - 32V/3y2y 3 2V/3z 2

where the x,y and z axes are normally chosen so that

3 2 V / 3z 3 2 V/3x 3 2 V / 3y

and hence 0 < n < 1.

The magnetic dipole interaction, Mi, is the coupling

of the nuclear magnetic dipole moment with the electrons.

It is possible, following Abragam and Pryce (1951), to

represent this interaction in a spin-Hamiltonian form:

S • A- I 2.11

where A is known as the magnetic hyperfine tensor. This

interaction will be discussed in some detail in the

following section.

2 . 3 Magnetic Hyperfine Interaction

The magnetic dipole hyperfine interaction will now

22

be discussed further with the view to understanding when one

is justified in describing it by the effective field

approximation.

The effective field approach is a simplified

description of the interaction that is valid under certain

circumstances which will be clarified below. One considers

that the electrons interact with the nucleus via a magnetic

field at the nucleus produced by the electrons. As a

consequence of treating the interaction in this way the

back effect of the nuclear magnetic moment on the electronic

system is ignored. This means that the electronic system

is assumed to be unaffected by the interaction and any

admixture of electronic states is negligible. The

fundamental approximation may be obtained from the

generalised Hamiltonian (Equation 2.11) and is written:

K = < S •A> . Im — = —

2.12and H < S • A>— e f f — =

where _H ^ is the magnetic hyperfine field (effective

field). The coupling between the nuclear magnetic moment,

p , and the electrons may be rewritten:— n

" H r :e f f2.13

g 3 I * Hn n— — eff

where g is the nuclear g-factor and 3 denotes the nuclear n nmagne ton.

The effective field approximation may be stated in

23

the following manner: the magnetic hyperfine interaction

does not couple eigenfunctions of the electronic Hamiltonian.

In other words the hyperfine operators do not cause admixture

of the electronic states because the only non-zero matrix

elements of the electronic component of the hyperfine

interaction are the diagonal ones and these are equivalent

to an effective field acting on the nucleus. In this

approximation the electronic and nuclear systems are treated

independently of each other and the wavefunctions for the

combined quantum system of the open shell electrons and the

nucleus of the ion can then be written in the product

form:

<J> (e , n) ^i(e) Xj(n)

where e,n represent the electron and nuclear coordinates

respectively. X^(n ) can be written in terms of the basis

states I I , m > .

If the electronic level separation is large compared- 2 - 1with the magnetic hyperfine interaction energy (~ 10 cm )

this approximate treatment is perfectly valid. However,

if they are of the same order of magnitude there may be

mixing of the electronic states by the hyperfine operators

and the approximation will then not be applicable. Under

such circumstances the electronic and nuclear systems must

be considered as one coupled quantum system with basis

states defined by lL,m ,S ,m ,I,m >.' L s I

It is immediately apparent that the sizes of the

matrices which must be diagonalised to obtain the states

24

of the coupled electron-nucleus system are much larger than

in the corresponding cases for which the effective field

approximation may be applied and only the nuclear matrix

elements are required. Nevertheless, for cases in which

the hyperfine coupling between well separated electronic

states may be ignored the computational difficulties can

be eased and relatively small matrices obtained if basis

states of the type ijj (e) [l,m >, where the are only those

eigenfunctions of the electronic Hamiltonian that are

degenerate or nearly degenerate, are used. This procedure

will be employed to derive the eigenfunctions of the

coupled electron-nucleus quantum system in Fe(PyN0 )6 (C1 0 4 ) 2

(Section 4.4).

The compounds studied in the present work will now

be examined with a view to determining whether the effective

field approximation of the magnetic hyperfine interaction is2 -f-valid for the lowest electronic states of the Fe ion.

2 -f-The states of the ground doublet of the Fe ion

in Co Fe Cl2 are highly magnetically anisotropic (g = 0)1 X X J_

and for this reason they are not mixed by the hyperfine

interaction (i.e. the hyperfine Hamiltonian within the

ground electronic doublet is diagonal). Thus, matrix

elements of the hyperfine Hamiltonian may be written in

the form:

<^i (e) |3C(e) I \p± (e) ><x. 15C ( n ) | , >

where i[i (e) represents electronic states of the type |a >

or |°> shown in Figure 2.1, and:

25

<a|JC(e)|si> is non-zero for some of the forms

of 3f(e) (e.g. L ,S ) butz z<a 13C( e) I b> is zero always. These matrix

elements ensure that the electronic and nuclear wavefunctions

may be determined separately since the hyperfine Hamiltonian

cannot mix these electronic states. In (M Fe )(PyNO)G~l -x x(0104)2? however, the magnitude of the splitting of a

similar ground electronic doublet by the presence of a

site distortion is of the same order as the magnetic

hyperfine interaction. The resultant non-magnetic rhombic

states, \fj i and ip 2 , have the form:

« 1 2 - — (|a> ± |t> >)’ Jl

The trigonal wave f unc t ions |3-> and |b> of Figure 2.1 (for

Fe(PyN0)6(C104)2) are of the form:

|a> 0 .994»! I - 2 > - 0.104» I - 1 > + 0 1—* 0 -©- 1 0 V11A

0 .104)! I o> - 0.104) I i> +0 0 * 9 9 4)_ 1 1 2>

w h e r e <j) , (J) a r e t h e w a v e f u n c t i o n s of t h e g r o u n d o r b i t a l

t r i p l e t ( 5T 2 ) •g

It is c l e a r t h a t the r h o m b i c s t a t e s m a y

be mixed by the magnetic hyperfine interaction, i.e.:

|3Cj^ > + 0

It follows that the effective field approximation is not

applicable in this instance.

26

2.3.1 Origins of the Magnetic Hyperfine Interaction

There are three major contributions to the magnetic

dipole hyperfine interaction. The first arises from the

isotropic Fermi contact interaction produced by the direct

overlap of unpaired electrons with the nucleus. These

electrons are mainly ionic core s electrons which have a

net density at the nucleus due to exchange interactions

with the open shell electrons. The two other terms result

from the orbital and spin moments of the ion. Both of the

latter contributions are anisotropic and cause the anisotropy

which may be observed in the magnetic hyperfine interaction.

In detail, the three contributions originate as follows:

(a) When the total orbital angular mo m e n t u m L is

non-zero there is a coupling with the nucleus arising from

the orbital motion of the open shell electrons (the 3d

electrons for the ferrous ion case). The orbital c ontribution

to the magnetic hyperfine H amiltonian may be expressed

(A b ragam and Bleaney,1970):

d C = 2g 33 < r _ 3 >(L. I) 2. 14L n n — —

where 3 is the Bohr mag n e t o n and r is the 3d electron radial

c o o r d i n a t e .

(b) The c o n t r ibution from the dipole moment of the

electronic spin distr i b u t i o n is given by:

( 3 S • r ) ( r • I )2g 33 < r 3 >n n - S . I 2.15

This contribution is non-zero only when the orbitals

are such that there is an aspherical spin density. It is

27

related to the valence electric field gradient which results

from an aspherical charge density (Abragam and Bleaney,

1970). Using equivalent operators Equation 2.15 may be

written in the more convenient form (Abragam and Bleaney,

19 70) :

K = - 2g ßß <r~3>C[|(L-I)(L-S) + 4 (L-S)(L-I)-L(L+1)(S .I)]D n n z — — — — l — — — — — —2 . 16

where £ is a constant dependent upon the electronic1 2 +configuration of the ion (- for Fe ).

(c) The coupling between the nuclear magnetic

moment and the unpaired electron density at the nucleus,

the so-called Fermi contact interaction, has the form (Abragam and Bleaney, 19 70) :

K I 6 (r.) (s . • I) 2.17c 3 n n V i l —lwhere the delta function represents the electron density at the nucleus. In transition metal ions this interaction arises predominantly because of polarisation of the inner

s electrons by the 3d electrons. Different exchange interactions experienced by electrons of opposite spin

orientation produce a resultant difference in density for

s electrons at the nucleus (viz. |ijj^(0)|2-|i|^(0)|2).

Through the Fermi contact interaction this net spin

density at the nucleus contributes to the hyperfine

interaction. Equation 2.17 can be rewritten using operator

equivalents in the form (Abragam and Bleaney, 1970):

28

K c = - 2§n3ßn<r 3> *(£•!) 2.18

where K is a numerical factor which measures the p olarisation

To summarise, the magnetic dipole hyperfine

i nteraction between a nucleus and its surrounding electrons

may be expressed by the Hamiltonian:

3C = 2g ßß Im n n . — - ri ri

3(r. •s .)(r . • JO7 'I + ---1--- — ---

+ 6 ( r . ) ( s . • I )3 l i — 2.19

where the index i refers to the electrons of the ion.

C ontributions from electrons in closed shells vanish

leaving terms from only the 3d electrons, except of course

for the delta function term. Equation 2.19 may be rewritten

using operator equivalents as:

U = 2g ßß <r 3>{L-I - C [ | ( L . I ) ( L - S ) + 4 ( L . S ) ( L . I ) - L ( L + 1 ) ( S . I ) ] m n n — — 2 — — — — 2 — — — — — —

- K(S_.I_)} 2.20%

It is possible to consider this interaction, under

certain circumstances, in terms of a magnetic field at the

nucleus, produced by the e l e c t r o n s , c o u p l i n g with the nuclear

magnetic moment - the effective field approximation.

Recalling the form of Equation 2.13 the effective field ü e f£

may be written:

H = - 23< r _ 3 >{L - £ [ | l (L.S)+ | ( L •S )L - L ( L + l )S ]— eft — 2— — — i — — — —- K 8} 2.21

29

The field is considered to result from three major

constituent fie1ds ■ (Marsha11 and Johnson, 1962)

corresponding to the orbital, dipolar and Fermi contact

interactions. The relative magnitudes of the contributions

are determined by the electronic configuration and the

environment of the ion.

2 •4 Relative Intensities of Absorption Peaks

In the presence of a magnetic field and/or an

electric field gradient the nuclear states will, in general,

not be pure states (i.e. there will be mixing of nuclear

substates). This is evident from an examination of the

magnetic dipole and electric quadrupole Hamiltonians

(Equations 2.20 and 2.10) for systems in which the principal

axis of the e.f.g. is not along the magnetic field direction

and r) is non-zero. Transitions between these states for5 7 Fe allow the observation of eight line Mossbauer spectra.

The intensity formalisms appropriate to magnetic dipole

transitions for single crystal and randomly packed

po1ycrysta11ine absorbers will be described in this section.

Reduction of the generalised expression to some simpler

commonly occurring situations will also be discussed.

2.4.1 Single Crystal Absorbers

The system under consideration is one in which

transitions occur between generalised states (of the type

shown in Equation 2.22) arising from a nuclear spin I = —e 2and a spin I = ~ manifold, as for 57Fe, with I values of

g z *

30

n'e and respectively, i.e. between states of the form:

3/2 1/2l3> ■ C (3/2,i)l3/2>3/2> + C (3/2,i)|3/2’1/2>

-3/2+ C

- 1 / 9 ^7 I 3/2 , — l/2> + C I 3/2,-3/2>(3 /2 ,1) (3/2 , i )

2 . 22

/ 2 -1 / 2■ c (1/2 ,j)|1/2’1/2> + c (1/2>j)l1/2.-i/2>

m m2 ewhere C , ° ~ N and C , „ , _ . . are coefficients of normalised0 / , J ) (3/2,i)eigenvectors, |l,m^.> are the nuclear basis states and

i = 1, ...4; j = 1,2.The probabilities of absorption of a y-ray whose

propagation direction is (0 , c f )) with respect to the

quantisation axis (z axis) for single crystal absorbers may be obtained from (Kündig, 196 7) :

m * m

P(0,(f); 3/2, i; 1/2,j) = I C (1 /2 , j ) C (3/2 , i ) M (m ,m )m , m e ge g2 .23

M, s = <1/2,m ;L,m|3/2,m > X(me »m ) 6 1 e

where the symbol <1> denotes the C1ebsch-Gordan coefficient

coupling the angular momentum vectors jt , L_ and I_ . The

vector X is perpendicular to the direction of y-ray

propagation and specifies the angular dependence of the

intensity. Kündig (1967) gives expressions for its components in the directions of increasing 0 and increasing

(j), (x™,x™). The allowed transitions for magnetic dipole

31

radiation are m = Am^ = 0, ±1. Hence, the intensity of

transition between the generalised nuclear states results

from an aggregate of the six possible transitions. To

illustrate the calculation procedure more explicitly the

intensity of a particular line, resulting from transitions

between levels j and i, is determined.

Equation 2.23 may be rewritten:

P(0,(J>;3/2,i;l/2, j) =

*m m 2g e m0m , me g

m , m e g

2

A I 2 + I B I 2 2 . 24

32

3 /: 3 / 2 / 2A = C , . ;<1 . . C , , /n . s ( - c o s 0 s i n (J) + i c o s 0 c o s 4>)0 / 2 , 3 ) ( 3 / 2 , i ) 2

1 / 2 1 / 2

+ C ( . 1 / 2 >j ) C ( 3 / 2 , l ) ^ ) ( i S i n 0)

1 / 2 - 1 / 2 / 2 ,+ C ( \ / 2 j ) c (3 / ' ) i ) 0 1 / 3 ( - — ) ( c o s 0 s i n $ + i c o s 0 c o s ({>)

- 1/2 1/2 /2+ C ( i / . , j c (3 / 2 i ) ^ 1 / 3 ~ ( - c o s 0 s i n ({) + i c o s 0 c o s (}))

- 1 / 2 - 1 / 2

+ C ( l / 2 , j ) C ( 3 / 2 , i ) ( - / I 7 T ) ( i S i n 6)

- 1 / 2 - 3 / 2/ 2 ,

+ 0 ( i / 2 . ) C ( 3 / 2 i ) “ ^ ) ( c o s 0 s i n 4> + i c o s 0 c o s fy)

a n d

1 / 2 3 / 2 / 2 ,B = C ( 1 / 2 >j ) C ( 3 / 2 , i ) ( - T ) ( c o s * + 1 s l n <|,}

1 / 2 1 / 2

+ C ( l / 2 , j ) C ( 3 / 2 , i ) ( 0 2 / 3 ) ( 0 . 0 )

1 / 2 - 1 / 2/ 2

+ 0 / 1 / O .N 0 / 0 / 0 • \ Ol / 3 —5- ( - c o s (j) + i s i n <t>)( 1 / 2 , 3 ) ( 3 / - , 1 ) 2

- 1 / 2 1 / 2 / 2 ,+ C , , , , l r i / 9 . v Ol / 3 ( - — ) ( c o s <f) + i s i n (J))( 1 - / 2 , 3 ) ( / 2 , i ) 2

- 1 / 2 - 1 / 2

+ C ( 1 / 2 , j ) C ( 3 / 2 >i ) v/2 7 3 ) ( 0 . 0 )

- 1 / 2 - 3 / 2/ 2

+ C ( 1 / 2 , j ) C ( 3 / 2 , i ) i ( " COS ^ + 1 s i n

33

Evaluation of this expression for all of the allowed

transitions between levels j and i leads to the possibility

of an eight line Mossbauer spectrum. Equation 2.23 may be

readily reduced to a simpler form when there is no admixture

of nuclear substates. It then becomes:

P ( 0 ; 3 / 2 , m ; 1 / 2 , m ) e g M (m , m ) e g

2

<1/2,m ;L ,mI 3/2,m > g 1 e

+ <1/2,m ;L ,mI 3/2,m > g 1 e 2 . 25

The angle 0 determines the direction of the y-ray with

respect to the crystal axis. The transition probabilities

are independent of (p when the electric field gradient has

axial symmetry (i.e. q = 0) and the magnetic field is

parallel to the e.f.g. z axis.

Using Equation 2.25 the relative intensities for

transitions between pure nuclear states are found to be:

P (0 ; 3/2 , ±3/2 ; 1 / 2 ,±1/2) = 1/2 (1 + cos2 0)

P (0; 3/2 ,±1/2;1/2,±1/2) = 2/3 sin2 0 2 . 26

P (0;3/2,±1/2;1/2,+1/2) = 1/6 (1 + cos2 0)

5 7If the Fe nuclei experience an axially symmetric

electric field gradient the Mossbauer spectrum will exhibit

a doublet with an intensity ratio, easily derived from

34

Equation 2.26, of:

P (± 3/2) 1 + co s 2 Bp (± i / 2) y / T ^ T ö s ^ e

In the presence of a magnetic field parallel to the

crystal axis the degeneracies of the nuclear excited and

ground states are completely lifted. The six allowed

transitions between the resulting levels have the following intensity ratios:

3 : x : 1 : 1 : x : 3

where x = 4 sin20/(l + cos20). In other words the relative intensities of the transitions |±3/2> |±l/2> andI ± 1 / 2 > |+l/2> are in the ratio 3:1 and the ratio is

angular independent, whereas the transitions | ± 1 / 2 > ■ + | ± 1 / 2 >are a function of 0 and have values in the range 0 - 4 . A

fuller discussion of such non-genera1ised situations is given by Greenwood and Gibb (1971).

2.4.2 Randomly Packed Polycrystalline Absorbers

In the generalised case for po1ycrysta11ine samples

the relative intensities may be found by integrating Equation 2.23 over 0 and (j) :

it 2 7TP(0,4>;3/2,i; l/2,j) sin 0 d0 d(j)P(3/2,i;l/2, j)

0 = 0 <b = 02.28

35

The integration has been done algebraically by Kündig (1967)

and may be expressed as:

P(3/2,i;l/2,j) 4 TT 3

r 1 / 2X 3/2 ___ 1/2* -3/2C (l/?,j)C (3/2,i)+ 1/1/3 C (l/2,j)C (3/2,i)

- 1 / 2* - 1/2 _______ - 1/2 1/2 2+ C (l/2, j)C (3/2,i)+ /l-/3 C (l/2,j)C 3/2,i)

1/2* 3/2 ___ 1/2* -1/2C (1/2,j)C (3/2,i)‘ ‘/l/~3 C (l/2, j)C (3/2,i)

&-1/2 -3/2 ___ -1/2 1/2C (1/2,j)C (3/2,i)+ 1/1/3 C ( 1 / 2 , j ) C ( 3 / 2 , i )

♦ !*1 / 2 1 / 2 *-1/2 -1/2 2 3

C (l/2, j)C (3/2,i) + C (l/2,j) C (3/2,i) >

When the electric field gradient has axial s ymme try

with respect to the z axis and the magnetic field is parallel

to this axis the nuclear states are pure states and the

intensities are given simply by the squares of the appropriate

Clebsch-Gordon coefficients:

P (3/2,m ;1/2,m ) = <1/2,m ;L,m|3/2,m > 2e g g e

Under these circumstances it is clear that in the

presence of an electric field gradient alone the Mössbauer

spectrum would be a symmetric doublet. However if the

nuclei experience a magnetic field only an intensity pattern

3 : 2 : 1 : 1: 2: 3 would be observed.

36

2.4.3 Relative Intensities of Transitions between Coupled Electron-Nuclear States

In some cases it is necessary to treat the electronic

and nuclear systems as one coupled system (Section 2.3).

This section outlines the calculation procedure for

determining the relative intensities of transitions

between coupled states for powder absorbers. This is in

fact the most general case from which the simpler ones

described previously can be derived. To illustrate the

problem the case of particular interest for the work on

the perchlorate compounds presented in this thesis will

be described.In this example the ferrous ion has a ground

electronic doublet well separated from higher levels (see Chapter 4). The coupled system basis states of the form

ij^(e) |l,m >, where \p^(e) are the states of the ground

electronic doublet |a> and |"k> (Figure 2.1), consist of a quartet ground state and an octet excited state. These

basis states are mixed and split by the combined perturbations of the rhombic crystal field and the hyperfine

interaction to give four eigenstates (i) associated with the

nuclear ground state and eight eigenstates (f) derived

from the 14.4 keV excited state of the form:

37

3/2 1 / 2 -1/2f > = 1 ( 3/ 2) f ) I a> I 3 / 2 > + 1 ( 3 / 2 > f ) I a> I 1 / 2 > + I(3/2t£) la > I — 1 / 2 >

+ I-3/2 ( 3 / 2 , f ) la > I - 3 / 2 >

3 / 2 1/2 - 1/2 + J (3/2,f)lb > l3/2> + J (3/2,f) I1/2> + 3/2,f) lb>I-l/2>

-3/2

1/2 - 1/2

+ J ( J/2jf)!b>|-3/2>

1/22.29

- I (l/2,i)la > l1/2> + I (l/2,1 )la > |-l/2> + J (1/2;i)l^>|l/2>

- 1 / 2

+ J(l/2,i)tb>|-l/2>

where the symbols I and J denote the coefficients appropriate

to the componentsof the eigenstates which contain the

electronic states |&> and ["b > respectively.

The relative intensities P(f,i) of the 32 possible

transitions between these states are obtained from the

transition probability per unit time:

P(f,i) ^ I < f I (7CI i > 2 . 30

where 5C is the magnetic dipole operator governing the

absorption of radiation. It is clear that using states of

the type given in Equation 2.29 with the above expression

for the peak intensities one obtains a sum of products of

an electronic overlap (<i|i^(e) |i|; (e)> = 6 _ ) with a

nuclear transition matrix element employing the normal

selection rules for magnetic dipole transitions. Thus

38

Equation 2.30 becomes:

P(f ,i) I 8(1/2 , i)

I 6 <1/2,m ;1,mI 3/2,m >(3/2,f) 8 6

+ I j 8m , m (1 / 2 , i ) e g

J e <1/2,m ;1,mI 3/2,m >(3/2,f) 8

2.31

where m and m denote the nuclear sublevels of the ground g eand excited nuclear states, and <1/2,m :1,mI 3/2,m > areg ethe Clebsch-Gordon coefficients coupling the angular

momentum vectors _I ,_L and (L=l for a magnetic dipole

transition) .

It is to be noted that in the present example the

lifting of the coupled state degeneracies is incomplete ndeven to 2 order perturbation. The form of the trigonal

s tstates |a > and |^> (Section 4.4) means that to 1 order

only operators of the electric quadrupole interaction can

mix the coupled states. However, in spite of such coupling,

which might be expected to enable a complete lifting of the

coupled states degeneracies to occur, the resultant

eigenfunctions consist of two doubly degenerate ground

states and four doubly degenerate excited states. Transitions

between these states give only eight peaks in the Mossbauer

spectrum. As a consequence of the large separation of the

ground electronic doublet from the first excited level the

splitting of these doublets, expected from symmetryndconsiderations, is still negligible to 2 order.

39

2.5 Evaluation of Crystal Field Parameters from Mossbauer Spec tra

ZThe high spin Fe ion is frequently found in a

slightly distorted octahedral environment. Thermal electron

excitation in the resultant close lying energy levels

produces a temperature dependent electric field gradient

(e.f.g.) at the ion nucleus. This temperature dependence

causes a variation in the quadrupole splitting observed in the Mossbauer spectra. Experimental and theoretical studies

(e.g. Gibb et a l ., 1972; Bacci, 1978; Price, 1978) have

indicated the importance of incorporating the effects of

vibronic coupling in an interpretation of the temperature dependence of the quadrupole splitting data. As a consequence of such effects and the inherent temperature dependence of the crystal field, the conventional derivation

of static splitting parameters from experimental data relating to the temperature dependent population of electronic levels (Ingalls, 1964) is seen to be an inadequate procedure, unless it is known that the above effects can be

reasonably neglected. In addition, it is often the case that there are too many unknown parameters involved in the fitting of the quadrupole splitting data to allow

their unambiguous determination from such a set of

Mossbauer data. The possible ambiguity resulting from all

of the above influences is illustrated in Chapter 1 by the

conflicting interpretations given by Ono et al. (1964)

and Hazony and Ok (1969) of the quadrupole splitting data

for FeC12 •

40

C H A P T E R 3

E X P E R I M E N T A L PROCEDURES

It is intended in this chapter to describe the techniques for crystal preparation and absorber fabrication from these crystals. In addition, a background to the Mossbauer spectrometer and auxiliary equipment used in the present work for data accumulation will be provided. Finally, the computational procedures for analysing the data will be detailed.

3.1 Sample Preparation

All the reagents employed in the synthesis of the following samples were 98+% pure and were obtained from commercial sources. They were used without further purification except where stated.

3.1.1 Crystal Growth

(a) Fe (Py NO) 6 (C10 ) 2 • This compound was preparedby mixing stoichiometric methanolic solutions of the hydrated metal perchlorate (ca. 0.06M) and pyridine-N-oxide (ca. 0.4M) (Quagliano et a l., 1961). A small amount of 2,2dimethoxypro pane was added to the solutions as a dehydrating agent. It was necessary to reduce the perchlorate solution

41

(using reduced iron powder) before the reagents were3 +combined in order to remove the Fe ions from solution.

Small dark red rhombohedral crystals (with < 1 mm. sides)

separated when the solution was left to stand for a few

hours .

(b) (M Fe ) (PuNO) & (C10u) 2 • Here M represents i - x x__________________Zn or Mg. Compounds of this type, for values of x in the

range 0 < x < 1, were prepared by mixing the metal perchlorates

in the appropriate stoichiometric amounts and then reacting

them with pyridine - N-oxide in a manner identical to that

described for Fe(PyN0)6 (0104)2* Crystals of (M^ Fe^)~

(PyNO)6(C104)2 formed when the solution was left to stand

for a few hours.

The relative solubility in methanol of the two

perchlorates (Zn, Fe(PyNO)e(CIO 4)2) was an important factor

in determining the final composition of the crystals. Clearly,

if there is a significant difference in solubilities there

would be preferential crystallisation resulting in an incorrect

composition. Although the solubilities were unknown standard

X-ray fluorescence observations demonstrated that in all cases

the final composition was within ± 2% of that desired.

Thus in this instance any difference in solubility appears

to be of little consequence. The crystal colour was observed

to change continuously across the series from light red for

low iron concentrations to the dark red characteristic of

Fe (PyNO)6(CIO4)2• X-ray powder diffraction studies using a

Rigaku SG-7 diffractometer revealed that crystals formed

across the entire series were all of the same rhombohedral

structure. Evidence from the X-ray spectra also indicated

that the crystals were good stoichiometric mixtures.

(c) Col Fex Single crystals of thesecompounds were prepared by initially heating the hydrated

metal chlorides, mixed in the appropriate amounts, in vacuo

for one day and then in a stream of dry HC1 gas for three

hours to remove any residual water. The purified material

was then transferred to a glass ampoule sealed under vacuum

and placed in a Bridgman furnace. The furnace was activated

and after the material had become molten it was lowered, at

a rate of 0.5 mm/hr, through the "hot zone" of the furnace (held at 40°C above the melting point of the material) into

the, "cool zone" (held at 40°C below the melting point).When the entire ampoule was in the cool zone the furnace was

allowed to cool to room temperature. The compositions of the samples were checked by atomic absorption. The analyses were carried out by Ms. B. Stevenson, Research School of

Chemistry, A.N.U. The above procedure is described in greater detail by Meglino and Kostiner (1976).

3.1.2 Absorber Preparation

(a) Fe(PyNO)e (CIO4)2 and (Ml_x Fex) (pyN°)6 (C10k)2 .

For both types of sample the method of absorber

preparation adopted was the same. In this work both many- crystal absorbers and powdered crystal absorbers were used.

The many-crystal absorbers were prepared by placing a

randomly oriented matrix of small (< 0.5 mm) crystals

between mylar sheets. Powder absorbers were prepared by

43

mixing ground crystals with boron nitride and then placing

the mixture in a brass sample holder between mylar sheets.

Dimensionless effective thickness parameters which

are extremely useful in the determination of the optimum

thickness of a source and an absorber can be defined, for

sources and absorbers in which the resonant nuclei are

randomly distributed, by

T = f n a 0 ts s s s o s

T = f n a a ta a a a o a

where the subscripts s and a indicate the following source

and absorber quantities

f = probability of resonance absorption without

recoiln = number of atoms per unit volume

a = fractional abundance of atoms which can

absorb resonantly

t = thickne s s

O o is the resonance absorption cross-section of

the Mössbauer nuclei.

The quantity of a sample used in a particular

powder absorber and the thickness of a many-crystal

absorber were defined by the criterion that the effective

thickness of the absorber T , should be less than unity.’ a ’If this condition is satisfied then, assuming that the

effective thickness of the source, T , is << 1, thes ’transmitted peak has a Lorentzian shape and a full width

44

at half height which is the sura of the emission and

absorption peak widths (Margulies and Ehrman, 1961).

(b) Co Fe Cl9. The layer-like structure ofi -x x z

these compounds (see Section 6.2) enables axial single

crystal absorbers to be readily obtained by the sellotape

stripping technique of Campbell (1978). The orientation

of the crystal slice was confirmed by Laue photographs.

Crystals were thinned by successive stripping to a thickness

~ 0.06 mm, which was required to achieve an effective

isotopic thickness of less than unity. The crystal slice

so obtained was glued onto a lead plate with G.E. varnish.

The entire preparation procedure was carried out in a dry nitrogen atmosphere because of the hygroscopic nature of

the samples. The compounds were found to be hydrated by silicone vacuum grease which is often used to protect materials. However, subsequent tests showed that if the exposure time of an unprotected absorber to the atmosphere

was kept to an absolute minimum no detectable hydration occurred.

3.2 Apparatus

3.2.1 Mössbauer Spectrometer

The Mössbauer spectrometer used for this work is

based on a mini-computer (Window et a l ., 1974). It

utilises a constant acceleration source drive waveform

and a transmission geometry arrangement of the source,

45

absorber and detector. The mini-computer, a PDP 11/10

with 8k of core store, generates a very smooth drive

waveform and also may accumulate up to a maximum of eight

spectra simultaneously. The velocity reference signal was

a linear ramp during the period of data accumulation

followed by a fly-back period (Cranshaw, 1964), with an

overall sweep frequency of 13 Hz. In normal operation

eight spectra can be accumulated, each with 256 channels.

It is possible, however, to combine these groups to obtain

spectra with 512 or 1024 channels, thereby achieving greater

resolut ion.

A conventional electromechanical transducer

(loudspeaker type) was used. In this type of design two

loudspeaker magnets are mounted back to back. Two coils

are wound on a former which has its axis coincident with

the common axis of the magnets. One of the coils, the

pick-up coil, develops an emf proportional to the velocity

of the transducer. The signal from this monitoring coil

is compared with the reference signal generated by the

computer and a correction signal derived from this

comparison drives the transducer via the drive coil. A

more detailed account of such transducers is given by

Kalvius and Kankeleit (1972).

A commercially available 57Co Rh source was used

and for all the spectra recorded the source was maintained

at room temperature. The absorber was kept stationary and

the transmitted y-rays were detected by an argon-10%

methane filled proportional counter.

46

The spectrometer was calibrated using the spectrum

of a natural iron foil absorber at room temperature and

the data of Violet and Pipkorn (1971) . Zero velocity was

taken to be at the centroid of the iron foil spectrum.

To facilitate observation of low temperature effects

on the Mossbauer spectra a cryostat of the type described

by Cranshaw (1974) was used.

3.2.2 Variable Temperature Controller

Absorber temperature in the range 10-300 K could

be attained by the use of a bridge balancing type of

temperature controller (Window, 1969). This arrangement

consists essentially of balancing the resistance of a

temperature sensor against an external resistance, with

which the temperature may be varied. The temperature sensor

was a carbon resistor (15 ohm at R.T.) for temperatures

below 30 K and a copper resistor (100 ohm at R.T.) above

30 K. A given temperature could be maintained to within

0.1 K for long periods by heating against a thermal leak

to a cryogenic bath. In this system the heater was the

temperature sensor itself, with the possibility of using

an auxiliary constantan resistance element connected in

parallel with the sensor.

3.3 Evaluation of Mossbauer Spectra Parameters

The interpretation of a Mossbauer spectrum requires

the derivation of certain parameters from the spectrum.

47

The number and type of parameters depends on the particular

spectrum in question and the evaluation of these parameters

is done by fitting the spectrum to a number of Lorentzian

or psuedo-Lorentzian lines using a least squares fitting

routine. A general introduction to least squares fitting

procedures is given by Bevington (1969).

In the present work a computer program, provided

by Dr. Price, Solid State Physics Department, A.N.U.,

performs a least squares fit of a spectrum to a sum of

analytical functions which define the parameters that are

to be determined.

The least squares fitting procedure provides an

optimum description of the data by minimisation of the

weighted sum of squares of the deviations of the data points

from the fitting function. This is achieved by minimisation

of a quantity called the goodness of fit parameter which

is de fined as :

NX2 = I £Y. - Y(X.,a)]2 W. 3.1

i= 1

where are the data points, Y(X ,_a) denotes the fitting

function, and a_ define the values of the fitting functiont hcorresponding to Y^, is the weight ascribed to the i

data point and N is the number of data points. The process

of y-ray emission is a random event hence, is the inverse

of the square of the standard deviation of the i*'*1 point

(i.e. W = 1/Y ). Y^ represents the number of y-photons

counted at a known channel number X., which is related tol

the Doppler velocity. The components of the M-dimensional

48

vector a_ represent M parameters which define Y(X^) and

w h ich are to be determined. The parameters a^ do not all

occur linearly in the fitting function and thus m i n i misation

of x 2 cannot be achieved by solving Equation 3.2

a n a l y t i c a l l y with respect to a^.

ax3 a m i = 1

N 1I [Y. - Y(X. ,a)]2 -

where m

= - 2 Y(X.,a) ]3Y(X ,a)

Y . 3a l m0 3 . 2

2 , M .

Expansion of Y(X^,ji) in a Taylor series with respect

to increments in a enables Equation 3.2 to be solvedmwith respect to the linear parameters 5 a^ (viz. the

i n c r ements in a ). The m i n i m i s a t i o n of X 2 now consists mof solving Equation 3.2 with respect to 6 a^ iteratively

to obtain successively better values of a^. Examples of

the iteration techniques used to solve this problem have

been given by Powell (1964, 1965).

The fitting procedure is iterative in the non-linear

parameters, e . g . line widths, line positions and initial

estimates of the parameters have to be supplied. Linear

parameters, e.g. line areas, however, are calculated

exactly for each set of values of the non-linear parameters

and no initial estimates are required for them. Further

details of the fitting procedure can be found in Price

( 19 7 7 ) .

49

C H A P T E R 4

E V I D E N C E F O R C A T I O N S I T E D I S T O R T I O N S IN F e ( P y N O ) 6 ( Cl 0 J 2

4 . 1 Introduc tion

Recent studies of the relaxation processes of

Fe + ions in ZnC0 3 (Price et al., 1977 ) and MgC03

(Srivastava, 1976), in which the cations are coordinated

to six oxygen ions in an octahedral configuration with a

trigonal elongation (point symmetry C ), have revealedwell resolved paramagnetic hyperfine structure in zero

applied field at low temperatures. It is somewhatsurprising therefore that the Mössbauer spectra ofF e (PyN0)c(C10 4) 2 reported by Sams and Tsin (19 75a,b;1976) do not exhibit such resolved hyperfine structure,since the site symmetry of the iron in this compound is

the same as in the carbonates. As discussed in Section 2.1

high spin Fe ions in sites of symmetry which have anorbital doublet lowest, when spin-orbit coupling is

considered, result in a doublet ground state. The states

of this ground doublet are highly magnetically anisotropic

and consequently spin-spin relaxation between them is

expected to be very slow. The dominant relaxation

mechanisms are thought to be two-phonon processes

involving excited electronic states within the trigonal

5E multiplet, as described by Price et al. (1977). The S

50

relaxation rate of these processes is strongly temperature

dependent and is very slow at low temperatures.

Behaviour quite different from this was found for

Fe(PyNO)6 (C104 ) 2 by Sams and Tsin (1975b). They observed

line broadening consistent with a slowing down of the

relaxation rate as the sample temperature was decreased

below 30 K. Nevertheless below ~ 15 K the rate appeared

to remain constant and no resolved hyperfine structure was

observed. They did find, however, that resolved hyperfine

structure appeared when small (~ 0.1 T) magnetic fields

were applied to powder samples at 4.2 K (Sams and Tsin,

19 76) .

The relaxation behaviour of Fe" ions in CaC0 3 and

CdC0 3 has also been studied by Price and Srivastava (1976),

and although these compounds are isomorphous with ZnCO 3

and MgC0 3 no magnetic hyperfine structure was observed in

zero field even at temperatures of 1.6 K. It was suggested2that this could result from the Fe site suffering a small

distortion from symmetry.

In this chapter a distortion model similar to that

proposed by Price and Srivastava (1976) will be developed

and shown to provide an explanation which is both

consistent with the results reported previously for

Fe(PyNO)6 (C104 )2 by Sams and Tsin ( 19 7 5 a , b ; 19 76) , and with

the new results to be presented here.

51

4.2 Crystal Structure

A detailed crystal structure analysis of the

compound Ni (PyNO)6(BF4)2, which is isomorphous with

Fe(PyNO)g (C104)2 has been carried out by van Ingen

Schenau et al. (1974) using X-ray powder diffraction

techniques. Their determination showed the crystal

structure to be rhombohedral with the trigonal space group

R3. The cation coordination with the aromatic rings

(i.e. the PyNO groups) via the oxygen atoms is almost

octahedral. The M-O-N angles, where M represents the

cation, are approximately 120° and this non-linear geometry

lowers the symmetry of coordination by the PyNO groups to

C, . ( S )• Figure 4.1 shows a projection of one layer of 1 6the unit cell of Fe(PyN0) g (C104)2 (reproduced from Bergendahl

and Wood) 1975). The lattice parameters of Fe(PyNO)6(C104)2,

for hexagonal indices, have recently been accurately determined

as a = 12.515 X and c = 19.501 ^ (see Table 5,1),

An analysis of the temperature dependence of the

quadrupole splitting for Fe(PyNO)6(C104)2 has enabled Sams

and Tsin (1975b) to show that the oxygen octahedron

surrounding the cation is distorted by a trigonal elongation

along the [111] direction.

The structural features described above have recently

been confirmed by a single crystal X-ray study of

Fe(PyNO)6(CIO4)2 (Taylor, 1978).

Fig . 4.1 A [001] projection of one layer of the unit cell in Fe(PyNO)ß(C104)2 (Bergendahl and Wood, 1975).

52

4.3 Results and Discussion

The Mossbauer study of samples consisting of a large

number of randomly oriented small F e (PyNO)6(C104)2 crystals and of powder samples obtained by the mechanical grinding of

crystals grown from the same solution produced a number of

interesting observations. Figure 4.2 shows typical Mossbauer spectra for these two different physical states

of F e (PyNO)6(C104)2 , both recorded at 4.2 K in zero applied field .

The salient features of these spectra are, firstly,the striking differences between the spectra of the two

different physical states. The spectrum of the ground

crystals is essentially identical to the spectrum ofFe(PyNO) 6(CIO 4)2 j recorded under similar conditions, reportedby Sams and Tsin (1976). Secondly, the appearance of peaks

in the spectrum of the unground crystals is reminiscent of

the well resolved hyperfine structure observed in 2 +Fe :ZnC03 (Figure 4.2). The disappearance of this hyperfine

structure as a consequence of grinding the crystals indicates that lattice distortions or defects are of some importance in causing the modification. In the next section a simple

model for the effects of such a distortion will be described.

It will be shown that the spectra for Fe(PyNO)6(C104)2 (Figure 4.2) can be explained quite well in terms of such a

mod e1 .

Clearly one must ascertain that the hyperfine

structure present in the spectrum for the unground crystals

TRRN

5MI 55

iDN

C R )

1 V*wifrwi»mTwi«M iiunMii

C B )

V B L D C I T Y ( M M / 5 )Fig. 4.2 Mössbauer spectra of (a) a large number of

small, uncrushed F e (PyNO)g (C104)2 crystals and (b) a powder produced by mechanical grinding of similar crystals. (c) and (d) are the spectra of powder samples of -20% FerZnCOg and 3.6% Fe2 + :C a C 0 3 reproduced from Price et ai. (1977) and Price and Srivastava (1976) respectively. All spectra were recorded with the samples at 4.2 K and in zero applied field.

53

is a real and consistent feature of Fe (PyNO)6(C104)2

crystals and not merely a spurious result of sample

preparation conditions. In other words, it was necessary

to verify that the structure observed was hyperfine

structure and not due for example to chemical impurities.

To resolve the uncertainty x-ray measurements were taken

and the crystal preparation conditions varied. The latter

could also elucidate further the properties of this

compound.The molar ratio of the initial reagents, pyridine-N-

oxide and ferrous perchlorate, normally used in the

preparation of Fe(PyNO)6 (C104)2 was 6:1. When this ratio was progressively changed between the two extremes of 12:1

and 3:1 the Mössbauer spectra for the resulting crystals remained essentially unchanged. The same invariance was

also observed when the concentrations of methanolic

solutions of pyridine-N-oxide and ferrous perchlorate were changed. The exception to this behaviour was material

which precipitated immediately after combination of the reagents plus a small amount of acetone (added as a crystallisation inducing agent) and whose Mössbauer

spectrum was an asymmetric doublet closely resembling that

for ground crystals of F e (PyNO)6(C104)2 (Figure 4.2b).

The ranges of solution concentrations investigated were :

0.5 - 7.0 molar for pyrid ine-N-oxide and 0.1 - 1.3 molar for ferrous perchlorate. The first rhombohedral crystals of Fe(PyNO)6(CIO 4)2 began to crystallise after ~ 30 minutes

54

for the lowest solution concentrations and immediately for

the highest solution concentrations plus acetone. It is

worthy of note that the form of the F e (PyNO)6(C104)2 obtained

from solutions of initial reagents containing acetone was

different from that found for all other preparations. In

this particular preparation F e (PyNO)6(C104)2 precipitated

from solution immediately after the reagents were combined

and appeared to have little crystalline character, whereas

in all other preparations conducted the Fe(PyNO)6(C104)2

was of a definite rhombohedral crystalline form. X-ray measurements, however, confirmed that it was the desired compound.

It is apparent from the foregoing that the hyperfine

structure is an inherent feature of F e (PyNO)6(C104)2 crystals. It has also been confirmed from X-ray measurements that samples prepared in the standard manner, as described in

Section 3.1, are indeed Fe (PyNO)6(C104)2 •The Mossbauer spectra for ground crystals of

F e (PyNO)6 (C104)2 recorded through the temperature range 4.2 - 35.5 K in zero applied field (Figure 4.3) are of

identical form to the spectra of F e (PyNO)6(C104)2 >

observed under equivalent conditions, reported by Sams and

Tsin (1975b). The symmetric (vide infra) quadrupole doublet of the 35.5 K spectrum becomes progressively asymmetric

as the temperature is decreased. This asymmetry, however,

becomes only slightly more pronounced upon decreasing from

9.0 K to 4.2 K .

The marginal inequality of intensities remaining in

7RHN

5M!5

5!ON

35.5 K

21.7 K

15.0 K

4.2 K

2 - 1 0 4* l + 2 + 2V E L O C I T Y ( M M / 5 )

Fig. 4.3 Mössbauer spectra for ground crystals of Fe(PyNO)ß(CIO4 )2 recorded at selected temperatures. The temperature is indicated for each spectrum. All spectra were recorded in zero applied field.

55

the 35.5 K spectrum (Figure 4 .3) is still observable at

much higher temperatures. A similar inequality is also

present in the high temperature spectra of (ZnQ 2^e o o^~

(PyNO)6(C104)2 (Figure 5.4). In both instances the areas

of the two peaks in the doublet differ by an amount greater

than the experimental error and thus it is unlikely that

slow relaxation processes are the origin of the inequality.3 + jThe difficulty of obtaining samples free from Fe ions and

absorbers that consisted of a randomly oriented matrix of

crystals suggests that the inequality originates from either

texture effects or the coincidence of an absorption line (or3 +lines) resulting from disordered Fe ions with the low

velocity line of the doublet. However, the occurence of

the effect for both ground and unground crystals indicates

that texture is the less probable of these two suggestions.

Table 4.1 Mossbauer parameters forground crystals of Fe(PyNO) $(C1O 4)2

Tempera t ure (K)

Isomer (mm

*Shifts-1)

Quadrupole(ram

Splitting s- 1 )

9 .0 1 .28 (0.02) 1 . 86 (0.02)

79.0 1.27 (0.02) 1 . 79 (0.02)

196.0 1.23 (0.02) 1 .66 (0.02)

The isomer shift is measured relative to iron metal.The figures in parentheses represent the standard deviations of the quantities.

56

The measured values of the isomer shifts and

quadrupole splittings for ground crystals of F e ( P y N 0 ) e ( C 1 0 4 ) 2

at selected temperatures are listed in Table 4.1. The

results are in good agreement with those obtained by Sams

and Tsin (1975b). Values are not quoted for the unground

crystals because difficulties experienced in obtaining good

fits of the plainly more complicated spectra precluded an

accurate evaluation of the parameters.

4.4 Model for the Distortion of the Cation Site in Fe (PyNO) 6 (CIO*) 2

The distortion model presented here is similar

to that used by Price and Srivastava (1976). A small

rhombic distortion, described by a term of the form

B * 1 2 (L2- L 2), is added to the single ion H a m i l tonian for a1 x y2 +Fe ion in a site of C symmetry (Equation 2.1). This

particular form of the distortion model was chosen because

it was the simplest way of introducing a non-axial

distortion. It is to be expected that only an approximate

r e presentation can follow from such a description.

The rhombic crystal field term, V , may be written

in the form:

B 2 0 2 (L) 4 . 1

2The parameter B z determines the m a g n itude of the splitting,

A, caused by this rhombic crystal field. Such a distortion

will mix and split the states of the ground doublet, labelled

57

|a > and |b> in Figure 2.1, producing two non-magnetic r rsinglets ip and ip 2 given by (to first order):

< ■1 ( |a> -/2

, r ^21 (|a> +/2

| b > )

|b>)4 . 2

2 +If this were the situation for Fe ions in F e ( P y N O ) 6 (CIO4 )2

and the rhombic field splitting was much greater than the

magnetic hyperfine inte r a c t i o n then no hyperfine structure

would be observable in the M ö s s bauer spectra. However, if

the splitting is c omparable in m a g n itude with that of the

magnetic h y p e rfine i n t e r a c t i o n then the non-magnetic r reigenstates ip x and ip 2 would tend to be remagnetised through

interaction with the nuclear magnetic moment. Thus in the

limit of large ( c f . d C ) A the basis electronic states aremhere denoted by Equation 4.2 and in the limit A = 0 by

the purely trigonal w a v e f u n c t i o n s (viz. | a> and |b>). For

instances other than these two limits the basis w a v e f u nctions

must be represented by coupled electronic and nuclear

quantum numbers.

The line broa d e n i n g observed in the 4.2 K spectrum2 +for ground crystals (Figure 4.3) indicates that for Fe

ions in F e ( P y N O ) e ( C 1 0 4 )2 the rhombic field splitting may be

comparable with the m a g n i t u d e of the magnetic hyperfine

interaction.

The rhombic d i s t o r t i o n and the magnetic hyperfine

interaction were applied together as a p erturbation to

coupled electron-nuclear states derived from the ground

58

doublet (viz. the trigonal states |a > , |b>) of Figure 2.1.

This can be justified because the excitation energy of the

lowest excited state is ~ 100 cm , whereas the perturbations

are < 1 cm 1, rendering the ground doublet essentially

isolated from higher lying states. The perturbing Hamiltonian

and the mode of synthesising calculated spectra using the

distortion model will now be described in more detail.

The perturbing Hamiltonian 3C ’ may be written:

3C ’ = V + 3C + If 4.3r q m

where is the rhombic crystal field potential. JC and

«H* represent the nuclear electric quadrupole interaction and magnetic hyperfine interaction which were discussed in

Section 2.2.

4.4.1 Derivation of the Coupled Electron-Nuclear Basis States

It is recalled from Section 2.1 that the orbitaltriplet (5T ) is split by a trigonal field into a doublet8 te'UC.(<j)+1) and a singlet ((j) ) . The ground y doublet states |a > and |b > are represented by linear combinations of these

states .

The pertinent electronic states are the d states

with £ = 2. Thus the angular parts of the ground bT2gorbital wavefunctions of importance here may be written in

the form (Bleaney and Stevens, 1953):

59

<(1, = - (2/3)!s y 22 - anf v*

*0 ■ Y °

<t>_, = (2/3)'"2 Y2 - (1/3)*5 Y~‘ 4.4

where Y™ (m = 0, ±1, ±2) represent spherical harmonics oforder 2 .

As was mentioned in Section 2.1 the trigonal field and

second order spin-orbit interaction produce small admixtures

of the ground 5E state and the 5E state at ~ 10,000 cm 1 .8 gHowever, neglecting these interactions and term mixing

Griffith (1961) has shown that the 5T state is equivalent2g5 2 +to a P state. Taking into account now the spin of the Fe

ion the electronic components of the basis function arelinear combinations of the fifteen |m ,m > states, where1 s L

0, ±1, ±2 and m. 0 , ±1s ' ' L

It must be pointed out here that, in view of thecomments made in Section 2.5 concerning the difficulty ofderiving static crystal field parameters from the temperaturedependence of the quadrupole splitting data, the estimatesof Sams and Tsin (1975b) obtained in this way are open

to criticism. In addition the intraionic spin-spin coupling- lparameter determined by Sams and Tsin to be 24 cm is

thought to be unrealistically large (see Section 2.1).

These considerations place in some doubt the electronic

energy level structure derived by them. Nevertheless, for

the reasons given below the assumption of a ground doublet

essentially isolated from excited states is believed to be valid.

60

The sign of the electric field gradient and the

magnitude of the quadrupole splitting enabled Sams and Tsin

(1975b) to deduce that in Fe(PyNO)6 (0 1 0 4 ) 2 the distortion

from octahedral symmetry corresponds to an elongation of

the octahedron along the trigonal axis. As described in

Section 2.1 such a distortion results in an orbital

doublet ground state which when spin-orbit coupling is

accounted for results in a doublet ground state. The

small variation in the magnitude of the quadrupole splitting

over a large temperature range means that one may qualitatively

conclude that the ground doublet is well separated from

higher lying states. A high degree of magnetic anisotropy

(g II ~ 10, g^ = 0) was found for the doublet ground state of

Fe(PyNO)6 (CIO4 )2 by Sams and Tsin (1976). From this

observation, recalling that g = 0 for doublet states of

even electron systems (Griffith, 1963), one may conclude

that the ground doublet is sufficiently well separated from

higher energy states that mixing of these states into the

ground doublet is negligible.

As a consequence of the lack of accurate information

on the crystal field parametersof Fe(PyNO)6 (C104 ) 2 the

eigenfunctions of the ground doublet, being the only

wavefunctions of interest for the present study, which

were used are:

a > 0.99 d), I - 2 > - 0.10 d> |-1> + 0.10 <b I 0> 1 ' o - 1

|u> 0.10 <t>,|0> - 0.10 * |1> + 0.99 <|> ,|2>1 1 T n 1 - 1 1

where d) , d) , 1 are the orbital wave f unc t ions of the 5T cubic Yo ± 1 2 g

61

ground state and lms> are the spin components of the

electronic wavefunctions. The above eigenfunctions are

believed to be reasonable representations of a doublet

ground state well separated (~ 100 cm *) from excited states.

Inaccuracies in these wavefunctions will be reflected by

discrepancies in the line positions and intensities. Any

deviation from the free ion value of <r 3> used in these2 *4*calculations as a result of the Fe ion being located in a

lattice would also be expected to contribute to discrepancies

in the line positions.

The formulation of the coupled electron-nuclear basis

states can now be finalised. If the nuclear and electronic

systems of the ion are treated as one quantum system then

one has basis states consisting of electron orbital and

spin quantum numbers and nuclear spin quantum numbers

(i.e. a coupled wavefunction has the form Il ,L , S,S , I,I >).1 z z zThus, in the present system the levels associated with the

nuclear ground state and the electronic states |a> and Jt) >

are doubly degenerate and those with the 14.4 keV nuclear excited state have four-fold degeneracy. Specifically, the

coupled electron-nuclear wavefunctions are lj; (e ) | I , m . >

where i[i (e) represents the electronic component of the

wavefunction (viz. |a> or |b>), m . = ±h for the ground state

and ± \ , ±3/? for the excited state. These particular

wavefunctions constitute the basis states for dealing with

the perturbing interactions described in Equation 4.3 .Diagonalisation of the resulting 4 x 4 ground state matrix

and the 8 x 8 excited state matrix produces the eigenvectors

62

and eigenvalues for the system. Utilisation of the normal

selection rules for magnetic dipole transitions between

nuclear states (viz. Am . = 0 , ±1) and of the hyperfine

constants derived from the work of Sams and Tsin (1976)

yields the spectra shown in Figure 4.4. Figure 4.5

shows, in graphical format, the variation of the spectral

line positions and intensities as a function of the rhombic2distortion parameter B2 . As will be discussed further in

the next section it was found necessary to calculate spectra

using distributions of values of the distortion parameter B2.

The computational procedure employed for calculating spectra

of a single distortion value, with slight modification, was

able to accommodate this. Spectra calculated in this way

are shown in Figure 4.6.

The constituent lines of the calculated spectra were

taken as Lorentzians each with a line width that was the

minimum obtainable with the equipment used (0.24 ram s ).

4.5 Discussion

2The spectra calculated with a single value of B2,

shown in Figure 4.4, indicate that a good representation of

the experimental spectrum for ground Fe(PyNO)e(CIO4)2 crystals2 - 1is given with a value for B2 ~ 0.5 cm . As was stated in

the previous section the onset of hyperfine structure (viz.

line broadening) visible in these spectra is observed

because interaction with the nuclear magnetic moment tendsr rto remagnetise the non-magnetic rhombic states and ip 2

when their splitting is sufficiently small to be of the same

RAN

SMIS

SIO

N B '= O- 0 8 cm

B~ = 5 0 cm

VELOCITY (MM/S)F i g . 4 . 4 M ö s s b a u e r s p e c t r a c a l c u l a t e d u s i n g t h e d i s t o r t i o n

m o d e l d e s c r i b e d i n t h e t e x t f ^ r d i f f e r e n t v a l u e s o f t h e d i s t o r t i o n p a r a m e t e r B^ . N o t e t h a t t h e c e n t r e s h i f t h a s n o t b e e n i n c l u d e d i n t h e s e s p e c t r a .

LINE

PO

SITI

ONS

(MM/

S)

0.04 0.08 0.12 0.16 0.20 0.242 _ lDistortion Parameter (cm )

Fig. 4.5 A plot of the variation of the spectral line positions and intensities, calculated using the cation site distortion model, as a function of the rhombic distortion parameter B^ •

TRAN

SMIS

SION

0.03 cm

0.07 cm

0.0 cm

0.15 cm

0.3 cm

0.45 cm

VELOCITY ■ (MM/S)Fig. 4.6 Mössbauer spectra calculated using Gaussian^

distributions of the distortion parameter B2 * The centre point and half width of each distribution are indicated for each spectrum. Note that the centre shift has not been included in these spectra.

63

order of magnitude as the hyperfine interaction. In

principle this is similar to the effect of a small applied2 "4“magnetic field on Fe :CaC03 reported by Price and

2Srivastava (1976). However, in that instance the B2

value is sufficiently large that it is impossible for the

nuclear hyperfine interaction alone to produce line

broadening. It was not found possible to reproduce well

the experimental spectrum for unground F e (PyNO)s (C104)22crystals with a single value of the distortion parameter B 2 .

Spectra calculated from a Gaussian distribution2 -1of B2 values centred at zero with a half-width of 0.15 cm

and from a Gaussian distribution centred at 0.03 cm 1 witha half-width of 0.07 cm , shown in Figure 4.6, both givea good description of the spectrum obtained for the unground

crystals, within the limitations of the model. It cannotbe unreservedly stated that a Gaussian distribution accuratelyrepresents the physical situation but it is clear that a

distribution of some character is essential to an understanding

of the data. A spectrum calculated from a Gaussian2 2 - 1distribution of B2 values centred at B 2 = 0.3 cm with a

half-width of 0.45 cm , which is shown in Figure 4.6 ,

describes the data for the ground F e (PyNO)6(C104)2 crystals

equally as well as a spectrum (an asymmetric doublet)2 -1calculated with the single B 2 value of 0.5 cm . It is

not unreasonable that both of these representations are

able to describe the data equally well. The spectrum2calculated from a broad distribution of B 2 values centred at

-1 20.3 cm is a superposition of spectra of differing B2

64

values and the spectra resulting from the most probable

values in the distribution have essentially the form of an

asymmetric doublet. It is not possible to resolve which

of these representations is the more accurate but an

important deduction can still be made. The change in the

spectra produced by mechanical grinding can at least

qualitatively be reproduced by a model in which one effect

of this treatment is to significantly increase the average

cation site distortion.

It is emphasised that this analysis is the simplest

possible model that could represent the physical situation

and its limitations must be borne in mind. It is almost

certainly not an accurate representation. The rhombic

distortion discussed in the preceding section, forming the

basis of the model, is the simplest non-axial crystal field

term that could be considered but this may not be the only

non-axial crystal field activated by the distortion or,

indeed, the rhombic term may not be present at all. Spin-

lattice relaxation effects have not been incorporated into

the model. However, this is not considered to be an

important limitation while the study is restricted to the

very low temperature region, which is the case here. The

possibility that spin-spin relaxation might, at least for 2 ~f"some Fe ions, be fairly rapid has not been taken into

account. As noted in Section 4.1 the ground doublet,

states |a > and |t>>, are highly magnetically anisotropic

but in the presence of a distortion the values of g^ forr rthe singlet states ijj 1 and ifj 2 are non-zero. Consequently,

quite rapid spin-spin relaxation is possible. This point will

65

be pursued further in Chapter 5 where the effects of2 +doping Fe ions into isomorphous host lattices will be

described. A further limitation of the extent to which

the model can aid the understanding of the unground crystals

spectrum is that the sample cannot be definitely

characterised as a matrix of randomly oriented crystals.

Although every effort was made to ensure a random

arrangement, the form of the crystals could possibly result

in some degree of preferred orientation. This would

certainly produce an effect on the relative intensities

of the peaks in the experimental spectrum. The spectra

calculated using the model assumed a random orientation

of crystals.

The uncertainties inherent in both the samples and

the model raise doubts about any quantitative deductions

which might be made from this study. Nevertheless, it is

believed that the qualitative conclusions are correct;

namely that there is a distribution of cation site

distortions present in the unground crystals and almost

certainly in the ground crystals too, that there is a

significant proportion of sites in the former sample that

have effectively no distortion and that the average site

distortion is increased markedly by mechanical grinding.

These conclusions tend to indicate that the distortions

are due to lattice strains rather than to point defects.

The magnetic field results of Sams and Tsin (1976)

appear to be at least qualitatively consistent with these

conclusions. For large applied magnetic fields (> 1.0 T)

66

the Zeeman interaction is greater than both the non-axial

crystal field and the magnetic hyperfine interaction, so

a reasonable description of the spectra can be obtained

assuming all sites are identical, albeit with g^ 0 as

expected for distorted sites. That they did not detect

any departure from axial symmetry in the electric quadrupole

interaction is not surprising in view of the very small2values of the distortion parameter B2 that are introduced

above. Their spectra in small applied fields, however,2 +indicate a non-uniqueness of the Fe sites, but rather

than this being due to a difference in spin-lattice

relaxation rates as they suggest their spectra could equally

well result from a distribution of distortions as proposed

here. In fact, their spectra in the smaller applied fields

closely resemble the zero field spectrum, shown in Figure

4.2, for the unground crystals sample. This similarity

can be explained qualitatively in terms of the Zeeman

interaction dominating the distortion and producing a2 +spectrum that appears to show that the Fe ions are in

undistorted sites. In other words the application of a

magnetic field has a similar effect to a shift towards2zero of the distribution of B2 values.

It is not possible to make any quantitative

deductions concerning the origin of the mechanism which

may be responsible for such a static distortion. It is

possible only to state that the increase in the average

cation site distortion produced by mechanically grinding

the sample implies that the distortion may be due to lattice

67

strains. In more general terras the lattice appears to be

in a slightly disordered state which is magnified by

grinding the sample. The disorder may result from

imperfections in the crystal growth, the presence of3 +impurities (for example Fe ions) or an inherent instability

of the R3 crystalline structure as is found for example in

the isomorphous fluoborate compounds (van Ingen Schenau et a 1 .,

1974). In these compounds the anions are disordered in

such a way as to give the structure an element of R3

character in addition to R3.

The 4.2 K Mossbauer spectrum of the Fe(PyNO)e(C10 4 )2

sample which precipitated immediately after the ferrous

perchlorate and pyridine-N-oxide (with acetone) were

combined was found to be very similar to that of the ground

crystals grown very slowly (Figure 4.2b). This indicates

that extremely rapid formation of Fe(PyNO) 6 (C10 4 ) 2 renders

it more susceptible to defects (or disorder).

Another mechanism which should be considered as a

potential origin of the distortion is the Jahn-Teller

effect. It is believed that an inherent effect such as a

Jahn-Teller distortion can be discounted here since the2 +site distortion is not present in all of the Fe ions. In

2 "taddition to this it is very unlikely that Fe ions in

octahedral coordination would undergo a static distortion

due to the Jahn-Teller effect, because the Jahn-Teller

coupling in the 2 * * 5 T 2 ground state is too weak to cause a

static distortion (Ham, 1967).

68

It is of value to note two important observations

from the work presented in this chapter. Firstly, that

doublet ground states appear to be highly sensitive to a

small off-axial distortion. Secondly, mechanical grinding

of samples to powder form is a routine procedure in

Mössbauer spectroscopy. However, these results attest

that spectra of samples treated in this manner should be

interpreted with care. The latter observation is further

emphasised by the work of Morimoto and Ito (1977). Theyc o •Ihave reported that the Fe Mossbauer spectra of KFeF3

are also sensitive to the effects of the mechanical

treatment, particularly grinding, of crystals during sample

preparation» Random strains arising as a result of the

mechanical treatment were found to be the cause of the spectral sensitivity to the mode of sample preparation.

4 .6 Conclusions

2 +The Mossbauer spectra of Fe ions in F e (PyNO)6(C104)2

have been well reproduced in terms of a model which introducesa small off-axial distortion into the perturbing Hamiltonian

2 4*of the coupled electron-nuclear quantum system for the Fe ions. It has been qualitatively demonstrated that mechanical

grinding of F e (PyNO)6(C104)2 crystals results in a significant increase in the average cation site distortion.

The origin of such a distortion remains in doubt. However,

it appears likely that it is due to the ions coupling with

4

lattice strain fields.

69

C H A P T E R 5

F U R T H E R S T U D I E S O F T H E F e 2 + I ON IN T H E I S O M O R P H O U S M ( P y N O ) 6 ( C 1 0 4 h C O M P O U N D S (M = In, M g )

5 . 1 Introduction

The work to be presented in this chapter was carried

out with the aim of further elucidating the results for

Fe (PyNO)6 (C104>2 reported in the last chapter. The solid solution series (Mj ^Fe )(PyNO)s (C104)2 , where M = Zn, Mgand 1 > x > 0 , was examined in order to investigate the

2 + 2 +effects on the Fe ion site symmetry of doping Fe ionsinto isomorphous host lattices, and to obtain informationon the importance of spin-spin relaxation processes for

2 -f-Fe ions in these compounds. Such a study would be

expected to provide information concerning the off-axial

site distortion of the ferrous ions in Fe(PyNO)6(C104)2

proposed in Chapter 4.

Mössbauer spectra for many-crystal absorbers of

the Zn-Fe and Mg-Fe series recorded at 4.2 K for selectedcompositions will be presented. To gain a fuller

understanding of the effects on the host lattices of 2 +introducing Fe ions into the structures an X-ray powder

diffraction analysis of the variation in the lattice

parameters as a function of composition was undertaken in

collaboration with Dr. D. Creagh of the Royal Military

70

College, Duntroon. The unusual dependence on the Fe

concentration displayed by both the Mossbauer and X-ray

results will be shown to be correlated. Unfortunately

the nature and origin of the disordering of the lattice

which appears to be present in these perchlorate

compounds remains unclear.

5.2 Results

5.2.1 Mossbauer Data

Mossbauer spectra of crystal samples with compositions

at regular intervals throughout each of the series correspond­

ing to M = Zn and Mg were recorded at 4.2 K. The spectra

for the Zn^ ^Fe^(PyNO)6(C104)2 samples (Figure 5.1) exhibit

unusual behaviour. On the basis of spectral features the

series may be divided into three regions, viz. 0 < x < 0.4,

0.4 < x < 0.8 and 0.8 < x < 1.0. Within the first region

(0 < x < 0.4) the degree of resolved magnetic hyperfine

structure is observed to increase as a function of increasing

iron content (i.e. increasing x). The spectra of the

central region (0.4 < x < 0.8) appear essentially independent

of iron content while those of the final region (0.8 < x Z

1.0) show the degree of hyperfine structure decreases with

increasing iron content. This may be contrasted with the

Mossbauer spectra for (Mg ^Fe^) ( PyNO)6(CIO 4)2 which were

invariant over the whole range of x (0 < x < 1). The example

reproduced in Figure 5.2 is typical of the spectra observed

for the series and bears a strong resemblance to the

Mossbauer spectrum for Fe(PyNO)6(C104)2 (Figure 4.2).

TRRN

SM!5

5!GN

0.90

0.60

0.40

I0.S5J' x*fL**0 j V » *

0.26

V E L D C t T Y C M M / 5 )Fig. 5.1 Mössbauer spectra for many-crystal

absorbers of the (Zn^_ Fe )(PyNO)ß(CIO4 ) 2 series at 4.2 K in zero applied field.The value of x is indicated for each spectrum.

TRHN

5M!55 I

DN

C R >

Fig. 5.2 Typical Mössbauer spectra observed for the (Mg^_xFex)(PyNO)ß(CIO4 ) 2series at 4.2 K in zero applied field (a) a many-crystal absorber (b) a powder absorber produced by mechanical grinding of similar crystals.Por the example shown x = 0.80 .

71

The effects on the Mössbauer spectra of varying the

preparation conditions are presented later in the section.

All of the spectra were recorded at 4.2 K in zero applied

field.

5.2.2. X-ray Diffraction Analysis

The results of an X-ray powder diffraction analysis

of the variation in the lattice parameters of (M Fe )-l -x x(PyNO)6 (C1 0 4 ) 2 as a function of iron concentration are

presented in Table 5.1 and also shown as the dependence

of the unit cell volume on iron content for both the Zn - Fe

system (Figure 5.3a) and the Mg-Fe system (Figure 5.3b).

The analysis revealed a non-linear dependence of unit cell

volume on composition for the Zn-Fe system. Indeed, it is

quite clear from Figure (5.3a) that the unit cell volume

passes through a minimum at x ~ 0.50. However a roughly

linear dependence of unit cell volume on iron content was

found for the Mg-Fe system (Figure 5.3b). The deviation

from linearity observed in the unit cell volume for the

Zn-Fe system is a reflection of the marked deviation from

Vegard's law (Barrett and Massalski, 1966) exhibited by the

c parameter of the series.

5.2.3 Detailed Investigation of ('An Fe ) (PyNO) 6 (C10 4) 2 __________________________________ o . z 0.8_________________

The behaviour of the hyperfine structure, visible

in some of the Mössbauer spectra for the (Zn^^Fe )-

(PyN0 )6 (C1 0 4 ) 2 series, under various conditions was examined

in more detail using the compound (Zn^ 2^eo 8 )(PyNO)6 (C1 0 4 )2 •

The grounds for selecting this particular compound were its

I—9—i

CN (N4 0 4

COCD

ctf* . 2

COQ) CO

i— 1

Ou

• H CM

O ✓ —s

- ____/ J t

or H

oCM

/■---s CD

J " ^ “ N

O oi— i zc_>

X ^ P - i

4 -) CD '— ,✓

•H -•— \-

S ö Xz 0)

X a j Ph pHe p - i X

* G lc r H /**-\ r-H

o O X D O

•H p> QJ SX Pm v—✓

CQ r H X /---- S

5-i r H 1 XI4-1 CL) r-H v__ /

C a c0) CNl TJO 4-1 ^ cc • H CQo C

o G cQ ✓ --- sv__/ QJ

c QJ >o X P4 5-4 •

5-i 4-1 O G ^

M 4 -1 O QJ4 -1 >

O C CO 5-i

o G P

G * H o uO 4-4 3

•H -H G X4-4 CO •H QJcQ O x X

• h a , G CO

>-• e O CQcQ o

> oa ro

ro

m

bo•H

( e $ ) au inx o a J T^ O I j u n

Table 5.

1 Cell constants of

th

e i

(My

Fe )(PyNO)6(C10h) 2

72

*to

o•o

oE0to

to'aco04EO0

/ '“ 'so<v_/a

/—\ /■— s S N /—V /—N -—\ /<—\ /■--N /•—XCO CTi Hi­ L(0 o U0 U0 uoo UO CsJ r-H n t r—1 r-H r-H »—l r-Ho o o o o o o o o o

o o o o o o o o o oN_✓ V_✓ V---' V_' 'w ' V_'

o o < r o r-H vD VO uo r-Hoo CN vO vo o n t O oCO r-H o 00 CNJ UO O r—H n t uo

O'. OV 00 o \ Ov O'* Ov O'. Ovt-h i—1 *—H 1—1 t—H r— i r-H r-H 1—1 r-H

* Figu

res

in pa

rent

hese

s re

pres

ent

one

stan

dard

de

viat

ion

in th

e un

cert

aint

y of

th

e qu

anti

ty.

73

large proportion of iron, which enabled statistically good

spectra to be obtained fairly rapidly, and the well-

resolved paramagnetic hyperfine structure observed in its

s pe c t rum.

Figure 5.4 demonstrates that there is a trend for

the hyperfine structure present in the Mössbauer spectrum

of (Zn^ 2 ^ e 0 8 ) (PyNO)6 (CIO4 )2 to collapse, from the well-resolved structure visible in the 10 K spectrum to the

quadrupole doublet observed in the 72 K spectrum, as the

absorber temperature is raised. The spectra recorded at

temperatures below 10 K showed no perceptible differences

from the 10 K spectrum, even at a temperature of 1.2 K. As was mentioned in Chapter 4 the high temperature spectra of

(Zn^ 2 Fe o B) (PyNO)6 (CIO 4 )2 display the same slight intensity inequality in the quadrupole doublet as those of Fe(PyNO)6 (C10 H )2 (Figure 4.3). In both instances it is considered highly probable that the inequality results

from either a small degree of texture or from the coincidence3 “f”of a peak produced by disordered Fe ions with the low

velocity peak of the doublet.

It was found that, as for the case of Fe (PyNO) 6 (C10 4) 2

(see Chapter 4), grinding (Zn Fe )(PyNO) 6 (C10 4) 2 crystalsO • 2 0 . 8

to powder produced gross changes in the Mössbauer spectrum.

This is shown in Figure 5-5 in which only slight remnants

of the hyperfine structure are visible after mechanical

grinding of the crystals.The effects on the Mössbauer spectrum for

(Zn Fe ) (PyNO) 6 (C10 4 ) 2 of increasing the rate of 0 . 2 0 . 8

TR

RN

5M

1 55

!D

N

77 K

19 K

^ rtWurnriuMTiifilnii f

16 K

10 K

V E L O C I T Y ( M M / 5 5

Fig. 5.4 Mössbauer spectra for a matrix ofrandomly oriented (Zn^ ^Fe^ Q ^ 6 (CIO4 ) 2

crystals at selected temperatures. All spectra were recorded in zero applied field.

TRRN5M ! 5

5 I EIN

C R !>

V E L O C I T Y C M M Y R ^

Fig. 5.5 Mössbauer spectra for (a) a matrix ofrandomly oriented (Zn^ Q ß(CIO4 )crystals and (b) a powder produced by mechanical grinding of similar crystals.All spectra were recorded at 4.2 K in zero applied field.

74

crysta 11isaLion is clear from Figure 5.6. The salient feature

of such treatment is the increasing dominance of an

asymmetric doublet superimposed upon the well split hyperfine pattern.

5 . 3 Discussion

5.3.1 Mössbauer Data

The distortion model presented in Chapter 4, which

gave a good qualitative representation of the data for

Fe (PyNO)6(C104)2 > will also be used here to describe the2 "t"experimental results for Fe ions doped into host lattices

isomorphous with Fe (PyNO) 6 ( C104)2 •

The increased resolution of the hyperfine structureevident in some of the Mössbauer spectra for (Zn Fe ) —1 -x x(PyN0)g(Cl04)2 (Figure 5.1) indicates that the proportion

2 +of Fe ions situated in sites of strict symmetry ismuch greater than in F e (PyNO) 6(C104)2 • The modifications which must be made to the theoretical representations of

the F e (PyNO)6(C104)2 spectra (Figure 4.6) to describe the

spectra for (Zn^_^Fe^XPyNO)6(C104)2 demonstrate such a change in the cation site distortion. Figures5.7 and 5.8

show that the width of the Gaussian distribution centredat zero must be reduced, and the distribution centred at2 — 1 2B2 = 0.03 cm must be combined with a spectrum for B2 = 0,

2 -f-in a proportion reflecting the percentage of Fe ions

at sites of trigonal symmetry, in order to reproduce the

experimental spectra. It is noted that there are

discrepancies in the line positions and intensities between

TRFIN5M I 55

I DN

C F O

C C >

V E L D C I T Y C M M / 5 )Fig. 5.6 Mössbauer spectra for many-crystal absorbers

of (Zn^ 2 ^eo 8 ^^PyNO)g(CIO4 )2 grown at selectedrates. A measure of the rate is given for each spectrum in terms of the elapsed time after combination of initial reagents before crystals first appeared. (a) immediately (b) 1 min.(c) 30 min.

TRAN

SMIS

SION

0.15

VELOCITY (MM/S)Fig. 5.7 Mössbauer spectra calculated using the

distortion model described in Section 4.4 for Gaussian distribution^ of the distortion parameter centred at B2 = 0 cm- 1 . The halfwidth of the distribution is indicated for each spectrum. Note that the centre shift has not been included in these spectra.

TRAN

SMIS

SION

VELOCITY (MM/S)Fig. 5.8 M össbauer spectra calculated using the

distortion model of Chapter 4 for a combination of the curves: B „ = 0.0 cm“2 2plus the distribution centred at =0.03 cm-1, ö = 0.07 cm“ 1 in differing proportions, (a) 60% B2 = 0.0 (b) 20%B^=0.0 (c) 0% B2 = 0.0. The centreshift has not been included in these spectra.

75

these calculated spectra and the corresponding experimental

spectra. However, in view of the uncertainties inherent

in the distortion model (see Section 4.4) and the paucity

of evidence concerning the influence of spin-spin relaxation

processes (vide infra) and texture effects on the spectra

such discrepancies are not to be unexpected. The Mossbauer

spectra for crystal matrices of (Mg^ Fe )(PyNO)6 (C104 ) 2

(Figure 5.2) closely resemble the spectrum for Fe(PyNO)6 (C104) 2

(Figure 4.2a) which may be represented by the distortion

model using a Gaussian distribution of values centred at

either 0.0 cm or 0.03 cm (Figure 4.6).

The above considerations do not allow an accurate

description of the results but it is believed that a2 -f*qualitative insight into the effects on the Fe ion site

2 +of doping Fe ions into the isomorphous Zn ( PyNO)6 (C104 ) 2

and Mg(PyNO)6 (C104 ) 2 lattices has been gained. It is apparent 2 +that doping Fe ions into Zn(PyNO)6(CIO 4 ) 2 considerably

reduces, for certain percentage concentrations, the proportion 2 "f*of Fe ions which experience a small off-axial distortion,

when comparison is made with Fe(PyNO)6 (C104 )2 • However, the

proportion of undistorted sites is observed to vary in an

unusual manner as a function of iron concentration. This2 “f"behaviour may be contrasted with that for Fe ions doped

into M g (PyNO) 6 (C104 ) 2 which showed no detectable change in

the Fe ion site distortion for any concentration. The above

points will be considered further later in the discussion.

76

5.3.2 Spin-Spin Coupling between Fe 2+ Ions in the M ( PijNO ) 6 (C10 4 ) 2 compounds

The variation observed in the Mössbauer spectra

for the (Zn Fe )(PyNO)6 (C 10 4)2 series as a function of 1 -x xcomposition (Figure 5.1) does not give conclusive evidence

concerning the importance of spin-spin relaxation processes

in these compounds. It may be argued that the contrast

between the spectra for F e (PyNO) g (C 1 0 4)2 and (Zn^ ^Fe^ 8^~

(PyNO) 6 (C 104)2 is much more pronounced than could be expected2 +from a change in the concentration of Fe ions and the

resultant decrease in spin-spin relaxation rate. The

ferrous ion should still have ~ 5 iron nearest neighbours

in (Zn Fe )(PyN0 )e(C104)2 enabling spin-spin relaxation0 * 2 O • 8

to proceed fairly rapidly and thereby precluding the

observation of we 11-reso1ved hyperfine structure. However,

the omission of any reference to other factors which may

also be varying as a function of iron concentration or

influencing the relaxation rate is a serious flaw to the

argument. From the foregoing it is clear that one such

factor is the magnitude of the off-axial distortion. It

is worthwhile at this stage to consider how a change in the

off-axial distortion may affect spin-spin relaxation.

Spin-spin relaxation is largely the result of

dipolar and exchange interactions between electronic spins2 -f-at different sites. If one considers two identical Fe

ions, A and B, with eigenstates ip and then direct

relaxation may occur at a rate proportional to:

<i|< . (A)|J>. (B) |3f J 1 ss \ty. (B)ip± (A) > p(i)p (j) A B

2

77

/ • \ / • \

where P, and P„ are the probabilities that the ions A Bare in the required states initially. The ground doublet

states are highly magnetically anisotropic (g « 10, g^ = 0),

consisting essentially of = -2> and l(l)_ 1>m s = 2>,which at low temperatures results in a zero probability of

direct relaxation. Nevertheless, there exists the

s s^ i X s I V ’ °r 3 com inat i°n of spin-spin and spin-lattice processes. In the latter case one of a pair of coupled

spins is flipped by spin-lattice relaxation which, via the

spin-spin coupling, then flips the other spin. However,

for the temperatures of interest here this process can be

ignored. It is plain that in the absence of an off-axial

distortion spin-spin relaxation should be very slow at low

temperatures because of the restriction to indirect processes. This has been observed in Fe + :ZnCÜ3 (Price et al ., 19 7 7 ). In the

presence of a distortion, however, g^ for the singlet rhombic states is non-zero and could possibly give rise to fairly rapid spin-spin relaxation as direct relaxation

processes are now possible. The above discussion illustrates that spin-spin relaxation is possible in these perchlorate

compounds and the average rate may even vary as a function

of iron concentration because of its dependence on the

magnitude of the site distortion. This variation would be

in addition to any normal decrease in the rate as the number

of magnetic ions is decreased.

Thus any changes which might be expected to be

induced in the Mössbauer spectra by decreasing the iron

concentration, and consequently the relaxation rate, may be

possibility of indirect relaxation, e . g . < ip . 13C

78

c o m p l e t e l y o b s c u r e d by c o n c u r r e n t c h a n g e s i n t h e n u r a h e r o f

2 ”f"Fe i o n s w h i c h a r e d i s t o r t e d f r o m t r i g o n a l s y m m e t r y ,

2Th e d i s t r i b u t i o n o f B2 v a l u e s r e q u i r e d i n a l l c a s e s

b y t h e d a t a w o u l d p r o d u c e a c o r r e p o n d i n g d i s t r i b u t i o n o f

s p i n - s p i n r e l a x a t i o n r a t e s w h i c h c o n c e i v a b l y m i g h t i n f l u e n c e

t h e t y p e o f s p e c t r u m o b s e r v e d . S u c h a d i s t r i b u t i o n i f

i n c o r p o r a t e d i n t o t h e d i s t o r t i o n m o d e l c o u l d , f o r i n s t a n c e ,

i m p r o v e t h e a g r e e m e n t b e t w e e n t h e t h e o r e t i c a l s p e c t r u m f o r

a d i s t r i b u t i o n o f d i s t o r t i o n p a r a m e t e r s c e n t r e d a t

2 - 1B 2 = 0 . 0 3 cm ( F i g u r e 4 . 6 ) a n d t h e e x p e r i m e n t a l s p e c t r u m

f o r F e ( P y N O ) 6 ( C 1 0 4 ) 2 ( F i g u r e 4 . 2 a ) . T h i s may b e a p p r e c i a t e d

b y s u p e r i m p o s i n g u p o n t h e s p e c t r u m p r e s e n t e d i n F i g u r e 4 . 6

s p e c t r a f o r m e d f r o m t h e a v a i l a b l e t o t a l i n t e n s i t y o f t h e

s p e c t r u m s h o w n a n d h a v i n g d i f f e r i n g l o w e r d e g r e e s o f

h y p e r f i n e r e s o l u t i o n ( i . e . s p e c t r a a t v a r i o u s s t a g e s o f

t r a n s f o r m a t i o n t o t h e a s y m m e t r i c q u a d r u p o l e d o u b l e t ) .

5 . 3 . 3 . X - r a y Ana l y s i s

The l a t t i c e p a r a m e t e r s f o r t h e Zn-Fe s e r i e s d e t e r m i n e d from

t h e x - r a y powder d i f f r a c t i o n a n a l y s i s a r e g iv e n i n T a b le 5 . 1 . The

h e x a g o n a l a p a r a m e t e r i s n o t s t r o n g l y d e p e n d en t on i r o n c o n c e n t r a t i o n :

i t i s s c a t t e r e d a bou t a weak ly d e c r e a s i n g t r e n d w i t h i n c r e a s i n g x.

However , t h e h e xa gona l c in d ex p a s s e s t h r o u g h a d e f i n i t e minimum as

a f u n c t i o n o f i r o n c o n c e n t r a t i o n . T h i s i l l u s t r a t e s t h a t t h e r e i s a

p r o c e s s (o r p r o c e s s e s ) o p e r a t i v e which p r i m a r i l y a f f e c t s t h e s p a c i n g

o f t h e c a t i o n l a y e r s which l i e p e r p e n d i c u l a r t o t h e t r i g o n a l a x i s .

I t i s o f i n t e r e s t t o r e c a l l a t t h i s p o i n t t h a t t h e

s t r u c t u r e o f F e ( PyNO) 6 ( C1 0 4 ) 2 wa s d e t e r m i n e d b y T a y l o r ( 1 9 7 8 )

79

to be R) with a quoted R value of 3,2%. This factor gives

a measure of the disagreement between the experimental data

and a theoretical fit of the data using a model structure.

Consequently this raises the possibility that some

kind of disorder, resulting from a small deviation from

the R3 structure, may be present in the crystal lattice.

The crystals of Fe(PyNO) 5 (C104 ) 2 (and also (M Fe )-1 -x x

(Py NO) 6 ( C10 4 ) 2 where M = Zn,Mg) grown for the present study

were all thought to be of poorer quality than those of

Taylor. Preliminary single crystal X-ray diffraction

photographs revealed that the crystals were multiply-twinned.

The uncertainty present in the structure determination and

the poor quality of the crystals, which might be expected

to indicate enhanced disorder within the lattice since

the external form of a crystal reflects the internal

structure, makes it plausible that disorder exists within

the crys tals.

To clarify the meaning of disorder as used here

consider a perfect crystal lattice in which all of the atoms

are at their appropriate locations as dictated by the

crystal structure. In such a system there would be no static

stresses. However, if the crystal were imperfect then not

all of the atoms would be positioned as demanded by the

crystal structure and there would be resultant strain

fields within the lattice. As a result of these effects

the structure would be in a disordered state.

80

The doping of Fe ions into the isomorphous

structures of Zn(PyNO)6(0104)2 and Mg(PyNO)6(0104)2 isliable to cause additional disordering of the lattice

because of the effects due to mismatch of cation ionic

radii (ionic radii of Fe2+ = 0.74 Zn2+ = 0.74 X,

Mg + = 0.66 ; Weast, 1976). This is to be expected for2 "f“ 2 "f"the Zn-Fe series even though the radii of Fe and Zn ions

are nominally the same because, as indicated by the different

lattice parameters of the pure compounds, the two ions are

different in other respects.

5.3.4 Correlation of the Mossbauer and X-ray Results

The existence of a minimum in the unit cell volume

of the Zn-Fe series (Figure 5.3a) at approximately the same

composition that the Mossbauer results indicate corresponds2 •+■to the least proportion of Fe ions experiencing an

off-axial distortion implies that the two observations are

correlated. Such a correlation leads one to the deduction,

albeit speculative, that the minimum in the unit cell

volume is related to the lattice being in a less disordered

state possibly resulting from the structure being able to

pack together better, at least for some compositions. It

is pertinent to this point to note that the results of a

single crystal X-ray analysis of Zn(PyN0)6(C104)2 (O'Connor

et a 1 . , 1977) revealed that the oxygen octahedron in this

compound is slightly compressed. The mixing of compressed and

elongated octahedra in the Zn-Fe series may possibly give

rise to better packing of the structure at certain

compositions and be a cause of the observed behaviour.

81

The absence of any unusual behaviour, both in the

Mössbauer spectra and the lattice parameters, for the Mg-Fe

series may be a consequence of the significantly different• • 2 -f- 2 +ionic radii of the Fe and Mg ions. The disruption of

the lattice caused by the mismatch of the ionic sizes

seems unlikely to allow less disorder of the lattice for

the mixed Mg-Fe system than is present in the end members

of the series.

No mention has been made up to this point of the

effects which give rise to the disordering of the lattice

or why the degree of disorder appears to change as a

function of iron concentration. The suggestions put forward

in Chapter 4 as mechanisms which might be responsible for

causing an off-axial cation site distortion may equally

well be applicable here as potential origins of the observed

disorder. In other words the disorder may result from a

small inherent instability of the R3 crystalline structure

or be a consequence of random strain fields due to defects

in the lattice caused by imperfect growth. Although there

is an apparent correlation between the changes in the

Mössbauer spectra and the change of the c parameter for the

Zn-Fe series which seems to be related to a differing amount

of disorder within the lattice, a critical interpretation

of the correlation based on the experimental information

currently available is not possible. One may only repeat

the speculation that the changes induced in the lattice

packing through the introduction of ferrous ions enables

the lattice to form a more stable state, for certain iron

82

concentrations, rendering the cations less susceptible

to distortion.

5.3.5 Effects of Changes in the Crystal Preparation Conditions

The increasing dominance of an asymmetric doublet

(peak positions 0.35 and 2.20 mm s 2) in the Mössbauer

spectra (at 4.2 K) for (Zn Fe )(PyNO)6(C104)2 as a0 . 2 0 . 8

function of increasing crystallisation rate (Figure 5.6)

indicates an enhanced tendency for the cations to experience

an off-axial distortion. Crystals which were grown

relatively slowly (~ 30 min. elapsed before small crystals

became visible) exhibit only a weak asymmetric doublet in

their 4.2 K Mössbauer spectrum whereas crystals which were

formed rapidly (immediate crystallisation) show a relativelystrong asymmetric doublet. Increasing the width of the

2distribution of the distortion parameters (B2) centred at 2 -1 -1B 2 = 0.0 cm from 0.02 cm (which reproduced the spectrum

of crystals formed slowly) to 0.07 cm 1 allows a goodrepresentation of the Mössbauer spectrum of crystals produced

immediately to be made in terms of the distortion model2(Figure 5.7). Lowering the proportion of B 2 = 0.0 in the

2combined theoretical spectrum for B2 = 0.0 plus the distribution

centred at B 2 = 0.03 from 60% to 20% (Figure 5.8) also provides

a good description of the data. It thus appears that progressively increasing the crystallisation rate gives rise

to the occurrence of larger off-axial site distortions.

This result apparently reflects increased disorder within

the lattice as the substance is compelled to form too rapidly

83

to enable optimum growth of the crystal, The above

behaviour is not evident in Fe(PyNO)g(C104 ) 2 (Chapter 4)

which remains apparently unaffected by such changes in

preparation procedures, except for immediate crystallisation.

However, this may not be unexpected because the distortion

model shows that the Mössbauer spectra for Fe(PyNO)6(C104 )2

are insensitive to relatively small changes in the magnitude

of the cation site distortion. The theoretical spectrum2 — 1of a distribution centred at B2 = 0.0 cm with a half­

width of 0.15 cm 1 bears a close resemblance to a similar

distribution with half-width of 0.2 cm 1. The modifications

caused in the Mössbauer spectrum for Fe(PyN0 )6 (C1 0 4 ) 2 by

immediate crystallisation suggest that the lattice is being

affected by changes in the crystallisation rate, but the

relative insensitivity of the spectra to small changes in

the site distortion precludes observation of the progressive

modifications which is possible for the (Zn Fe )-0 .2 0 . 8

( PyNO)6 (C1 0 4 ) 2 case.

5.3.6 Temperature Dependence of the Spectral Features

The collapse of the we11-reso1ved hyperfine

structure present in the low temperature spectra for

(Zn Fe ) (PyNO)6 (CIO 4 ) 2 as the absorber temperature is 0 . 2 0 . 8raised (Figure 5.4) is consistent with an increasing

spin-lattice relaxation rate. Below 10 K the spectrum

did not perceptibly change, even at 1.2 K. At such a

temperature spin-lattice relaxation effects should be

negligible and thus cannot be the source of the finite

intensity between the two highest velocity peaks still

84

visible in the spectra below 10 K. A static effect such

as a distribution of distortion parameters or a distribution

of spin-spin relaxation rates must apparently be the origin

of this intensity.

5.4 Future Work

The explanations given concerning the nature and

origin of the lattice disorder which appears to be present

in the perchlorate salts of the transition metal hexakis

( pyridine-N-oxide) compounds examined in Chapters 4 and 5

are far from being firmly founded or explicit. There is

a need for much more direct experimental evidence to enable

a clear understanding of the disorder to be obtained.

Further studies which may prove helpful are suggested here.Before attempting further work the quality of the

crystals must be improved. This may be achieved by increasing the purity of the commercially obtained reagents and employing ethyl orthoformate as the dehydrating agent instead of 2,2 dimethoxypropane because of its greater effectiveness. Recrysta11isation might also aid the

production of improved crystals.A detailed single crystal X-ray diffraction study

of Fe(PyNO)6 (CIO4 )2 and selected compositions of the Zn-Fe and Mg-Fe series could be carried out with a view to

observing the source of the disorder. This might be

possible, in spite of comments made earlier emphasising

the smallness of the site distortion, since the slight

modification to the trigonal crystal field of the cation

85

site need not necessarily result from an equally small

effect depending on whether the distortion is local or

non-local. If all of the cations which are distorted

suffer a distortion of the same symmetry an investigation

of its form and magnitude would be possible using electron

paramagnetic resonance. Under conditions other than

these the EPR lines would be too broad to offer anything

useful. Another technique that would be expected to

provide interesting information is nuclear magnetic

resonance. Its sensitivity and ability to examine the

environment of atoms other than the central atom makes

this the most potentially rewarding approach. However,

line broadening due to the distributions of distortions

may prove a serious limitation to the effectiveness of

the latter two techniques because of their sensitivity

and the fact that derivative lineshapes are generally

observed.

5 . 5 Conclusions

•• 2The general trends of the Mossbauer spectra of Fe

ions doped in the isomorphous compounds Zn(PyN0)6(C104)2

and Mg(PyNO)6(C104)2 have been well represented using the

off-axial site distortion model outlined in Chapter 4.

However, the relative importance of spin-spin relaxation

in determining the form of the spectrum for these perchlorate

compounds could not be separated from that of distortion

effects.An unusual dependence on the iron concentration

found for both the Mossbauer spectra and the cell constants

86

for the Zn-Fe series appear to be correlated and related

to changes in the disorder of the lattice. Such abnormal

behaviour was not displayed by the Mg-Fe series. A full

understanding of the lattice disorder, which is apparently

present in the (M^_^Fe^)(PyNO)g(C104)2 compounds studied,

and why it changes as a function of iron concentration,

is still lacking.

8 7

C H A P T E R 6

MAGNETIC BEHAVIOUR OF THE Fe2 + ION IN CoCl 2

6.1 Introduction

The mixed a n t i f e r romagnetic solid solution series

COj ^Fe C 1 2 is expected to display interesting magnetic

properties as the relative proportions of the cations are

varied because of the competing magnetic anisotropies of

the two end members. The end members of the series

crystallise with similar hexagonal layer-type structures

(see Section 6.2) and both exhibit strong exchange

interactions which produce a n t i f e r r o m a g n e t i c ordering

below ~ 24 K. Exchange coupling within the layers of

cations, which lie pe r p e n d i c u l a r to the trigonal axis of

the crystal, results in f e rromagnetic alignment of the

spins. However, there is an additional, relatively weak,

exchange coupling between layers which gives a resultant

anti f e r r o m a g n e t i c ordering. Crystal field anisotropy leads2 ~f"to orientation of the Fe spins parallel to the c axis

2in F e C l 2 and of the Co spins perpe n d i c u l a r to the c axis

in C o C 1 2 .

In this chapter m e a s u r e m e n t s of the hyperfine

88

interactions at the iron sites in the mixed Co Fe Cl?1 -x x *-

system will be presented and used to determine the

homogeneity and behaviour of the site magnetisation direction

as functions of iron concentration. An indication of the

relative strengths of the Co anisotropy and Co-Co exchange

coupling will also be given.

Tawaraya and Katsumata (1979) identified a

magnetically ordered phase in the concentration range

0.75 > x >, 0.65 (at 5.0 K) of Co, Fe Cl? with the so-called

ob1ique-antiferromagnetic (OAF) phase (Matsubara and

Inawashiro, 1977). In this type of phase there is

simultaneous ordering of the two spin components. Each spin

component has its own axis of magnetisation directed

obliquely to the easy axis of the pure system. Information

concerning this phase might be obtainable from the present

study, but at this stage no measurements have been made in

the appropriate concentration range. Time has not permitted

completion of the investigation.

The results obtained by Fujita et al. (1969) and

the predictions of Oguchi and Ishikawa (1977) for the

special case of very low concentrations of iron in CoCl2

will be shown to be in agreement with the conclusions

reached in the present study.

6.2 Crystal Structure of Co. Fe Clo _______________________ 1 -x x

Anhydrous FeCl2 and CoCl2 have the crystal structure

of CdCl2 (Wyckoff, 1963). They are rhombohedral structures

with one molecule per unit cell in the trigonal space group

89

R3m, but for convenience they are considered here using

hexagonal indices. The hexagonal unit cell contains three

molecules. It can be seen from Table 6.1 that the two

compounds have similar lattice constants (Wilkinson et al . ,2 +1959) and ionic radii. Hence Fe substitutes readily

2 -ffor Co

Table 6.1 Cation ionic radii and lattice constants of the hexagonal unit cells.

Compound a ( X ) * c ( i b * Cation ionic radius ( X )

F eC 1 2 3.603 17.536 0.74

C o C1 2 3.553 17.359 0.72

After Wilkinson et al. (1959).

The ionic arrangement in these compounds consists

of layers of metal ions and Cl ions with alternate metal

ion layers missing (Figure 6.1). The metal ions are located

at the centre of chlorine octahedra (site symmetry D 3 ) .

The main part of the crystalline field experienced by the

cations is consequently of cubic symmetry. However, the

cations have a non-cubic arrangement which gives rise to an

additional crystalline field of trigonal symmetry, the

principal axis being perpendicular to the ionic layers.

6.3 Theoretical Considerations

For materials in which there are strong exchange

Fig. 6.1 Crystal structure of the CdCl- 2

type compounds (after Ono et a l . , 1964) .

90

interactions between magnetic ions leading to alignment of

spins below the ordering temperature, one must modify the

Hamiltonian describing the state of the atom under crystal

field and spin-orbit coupling effects (Equation 2.1) to

account for these interactions. If one considers a simple molecular field (Heisenberg) model for the exchange inter­

actions between the spins of a given ion i and its

neighbours, a term of the form shown in Equation 6.1 is

added to the Hamiltonian 2.1.

= - 2J I S.-S. 6.1ex - i iJ

where J is the exchange integral. In the present context Jmay be divided into two components, one arising from theexchange interaction between nearest neighbour pairs (i.e.interactions within a layer) and the other is the interlayerexchange coupling which is relatively weak and neglected

here (Ono et al . , 1964). J may take the value J_ _ ,Lo-loJ „ or J „ according to whether the coupling is Co-Fe Fe-Fe ö e öbetween a Co-Co, Co-Fe or Fe-Fe nearest neighbour pair

respec tively.

In the absence of an exchange interaction the

ground doublet electronic state of the Fe ion shown in

Figure 2.1 is ~ 10 cm-1 below a singlet state (see pp. 9-11).

However, the doublet state will be split by the exchange

interaction. In FeCl2 this splitting is ~ 21 cm-1 (Ono

et clI . , 1964). Thus in the presence of exchange the ground

singlet has two excited singlets in its close vicinity.

It is worthwhile to consider here the importance of the relative strengths of the Co anisotropy energy and

91

Co-Co exchange coupling in determining the homogeneity of2 +the exchange fields experienced by the Fe ions.

If the Co-Co exchange interaction is much stronger than2 +the crystal field anisotropy of the Co ions all of the

2 4*Co spins would lie in the direction of the Co-Co exchange

field. Thus at low iron concentrations, where there are2 “f~no complications from Fe-Fe coupling, the Fe ions would

experience a uniform exchange field. This was observed for 2 ”f"the case of Fe :MnCC>3 (Price et al . , 1974 ). However, if

the Co anisotropy is of the same order or greater than2 "f"the Co-Co exchange interaction the spin of a Co nearest

24-neighbour of an Fe ion may still be changed from its

orientation perpendicular to the c axis by the Fe-Co exchange24-coupling. But as the distance from the Fe ion increases

the strength of the Fe-Co exchange would decrease causing a

progressive realignment of the Co spins towards an

oreintation perpendicular to the c axis. This would result2 +in a distribution of Co exchange fields at the Fe sites

2 “f*because of the random separations of Fe ions.

It is interesting to speculate upon the behaviour

of the ferrous spin as a function of iron concentration.

For very low concentrations of iron ( ~ 1%) in C0CI2 one

might expect that the crystal field anisotropy energy of 2 "f"the Fe ions would be completely dominated by the anisotropy

2 +energy of the Co spins so that as a consequence of the2 "I“Fe-Co exchange interaction the Fe spins will be

perpendicular to the c axis. The results of Fujita et al .

(1969) and the predictions of Oguchi and Ishikawa (1977)

92

support such a speculation. However, assuming that the

exchange interaction is isotropic, competition between the2 "I- - 2 *4*crystal field anisotropy energies of the Fe and Co

systems, which becomes more pronounced as the iron2 “I“concentration increases, causes the Fe spin to be lifted

out of the basal plane. The balancing of these anisotropy

energies as the iron concentration increases further would2 +be expected to result in a continuous rotation of the Fe

spin until it is oriented parallel to the c axis.

Calculations are currently being carried out to illustrate

the effects on the hyperfine field of varying the angle of

the exchange field with respect to the trigonal axis. Such

calculations will place any speculations concerning the

behaviour of the ferrous spin on a firmer basis.

6.4 Results and Discussion

Mössbauer spectra for single crystal absorbers ofCo, Fe Cl? are shown in Figure 6.2 as a function of x. Care 1 -x xwas taken to ensure that as far as was possible the y-ray

propagation direction was parallel to the c axis for all

the spectra, which were recorded at 4.2 K in zero applied

field. These spectra were fitted, by the least squares

procedure described in Section 3.3, to spectra calculated

as detailed by Kündig (1967), with modifications to the

intensity calculations to account for the absorbers being

single crystals. The hyperfine parameters derived from such

fittings are given in Table 6.2. The parameters shown were

NDI SS!WSNBH1

Fig. 6.2 Mössbauer spectra for single crystals of Co Fe Cl2 at 4.2 K with the y-ray1 X Xpropagation direction parallel to the trigonal axis. The value of x is indicated for each spectrum. The calculated curves were obtained using the parameters listed in Table6.2 .

93

deduced from the "best" fits although in all cases a range

of parameters gave reasonable fits to the data. This range

is indicated for each sample in Figure 6.3. In one case (x = ö-l7?j an improved fitting was obtained by the use of two delta

functions, as an approximation to a distribution. It is

noted that the parameters given in Table 6.2 for x = 0.247

only reproduce some of the spectral features. As a

consequence, at this stage it is not possible to indicate

the range of parameters which reproduce the spectrum for

this sample. Uncertainties are not quoted for the derived

parameters because of the inherent uncertainties in the

fitting of the spectra discussed above. It is emphasised

that as a result of the poor fittings only approximate

representations of the spectra can be expected.

The ambiguity concerning the hyperfine parameters2 *4“derived for a particular spectrum implies that the Fe

ions experience a distribution of interactions. Atomic

absorption analysis of the composition of samples taken from

different parts of the same parent crystal revealed that

the iron concentration varied by ~ 3% over the length (~ 3 cm)

of the crystal. The samples examined in the Mössbauer study

were rectangular with sides ~ 7 mm by 4 mm. It was not

possible to assess accurately the degree of inhomogeneity

within these samples but if one assumes a linear variation

of iron concentration over the length of the crystal a

reasonable estimate may be obtained. Such an assumption

gives a variation of iron concentration within the sample of

~ 0.7%. One may conclude from the gradual change in the

(deg.)

H (kG)

concentration, *

Fig.6.3 The variation as a function of iron concentration of (a) the hyperfine field magnitude (b) the orientation of the hyperfine field with respect to the e.f.g. axes 0 ^ (c) the asymmetry parameter of the e.f.g. p. Also shown are the parameter ranges which gave reasonable fits to the data.

Table 6.2

Hyperfine parameters for selected compositions of the Co

Fe Cl

2 series

94

-U4-1 / - v• H <— 1 X I cn w5 eQJ £e ^ocnM

cr

00C•H4-14-1•Hi—IO j /— v CD r-l

Ia) cn!-Ho eCu £ 3 ^>4 XI cO 3 O'

4-4 Ö0, 3 <u

CD X)"— '

X IrHo;•H

4-4

X

o o

00

0 0 ON

o o

O LO

95

average value of the parameters for low iron concentrations

that such a variation in the sample contributes to, but is

not the primary source of the observed distribution of

parameters .

What is presumably the main contribution to the

width of the distribution may be visualised if one recalls

the comments made in the last section about the importance

of the relative strengths of the Co-Co exchange and Co

anisotropy energies in determining the homogeneity of the2 “I“exchange fields experienced by the Fe ions. When the

Co anisotropy energy is of the same order or greater than

the Co-Co exchange coupling there will be a distribution

in both the magnitude and direction of the Co exchange fields

at the ferrous sites.

At iron concentrations high enough to give a

significant probability of having Fe-Fe nearest neighbour

pairs there will exist strong Fe exchange fields, but due2 +to the random positioning of the Fe ions in the lattice

these exchange fields will not be uniform. This gives rise

to an additional source of inhoraogeneity in the magnetic2 "I"properties of the Fe ions.

It is not clear from Figure 6.3 whether the

orientation of the hyperfine field , in the range o < * £

0.40, exhibits a dependence on the iron concentration because

of the rather large range of 9 ^ which resulted in reasonable

reproductions of the data for each value of x. However,

preliminary crystal field calculations that include a simple

molecular exchange term have indicated that the decreasing

trend of the hyperfine field magnitude (Figure 6.3) is

expected from a rotation of the exchange field that results

in a rotation of the ferrous spin. In addition Ono et a l .

(1964) derived the following parameters for FeCl^-ö^^ - 0 ,

p = 0, hyperfine field strength ~ 0 kG which are also shown

• in Figure 6.3. The results in this figure therefore indicate

that the most significant changes in these parameters must occur

for x > 0.40. The rotation of the hyperfine field is

a reflection of a rotation of the ferrous spin as a function

of iron concentration, which may be understood in terms of

the arguments presented in the last section as a balancing

of the total crystal field anisotropy energies for the crystal.

It is noted here that, in general, the hyperfine field and

the ferrous spin direction are not collinear. This is a

consequence of there being contributions to the hyperfine

field other than that which is proportional to the ionic

spin, i.e. the* contact field, (see Section 2.3).

The results of Fujita et al . (1969) are in

agreement with those presented here for very low iron

concentrations. However, they reported that in 30% Fe:CoCl2

samples the ferrous spin lies almost parallel to the c

96

axis. On the basis of the evidence from the current

investigation of Co, Fe Clo and the neutron diffraction1 -x x ^results given by Tawaraya and Katsumata (1979) this

observation is believed to be incorrect.

Figure 6.3 also shows that the average value of

the asymmetry parameter (i.e. n) descreases as a function

of iron concentration. The non-zero value of the asymmetry

parameter is a consequence of the so-called magnetically

induced quadrupole interaction (Greenwood and Gibb, 1971).

As the orientation of the exchange field changes so will

the perpendicular components of the orbital angular

momentum which give rise to the asymmetry. This follows

because a non-axial exchange field will induce perpendicular

spin components which through the spin-orbit coupling leads

to perpendicular orbital components. At the higher doping

levels where the hyperfine field is parallel to the

trigonal axis and there are no non-zero perpendicular

components the electric field gradient is expected to be

axially symmetric.

6 . 5 Future Work

The incomplete state of the present investigation

of Co^ Fe CI2 makes further work on this system clearly

desirable. Observations of the dependence of the hyperfine

interactions on the iron concentration and an investigation

of the temperature dependence of these interactions will

enable an estimate of the strength of the Fe-Co exchange

coupling to be derived. Combination of these results with

98

those of the Fe-Fe exchange in FeCl2 (Ono et al., 1964)

and with measurements of the Co-Co exchange interactions,

perhaps obtained from bulk magnetisation studies, will give

a complete picture of the dominant exchange interactions

in the syst em.

6 . 6 Conclusions

A study of the hyperfine interactions at the iron2 +sites in Co., Fe Cl? has enabled the rotation of the Fe1 -x x

spin, resulting from competition between the ferrous spin anisotropy

energy and the Co crystal field anisotropy (that interact via

the Fe-Co exchange interaction)3 to be followed as a function

of iron concentration. From the poor fittings of the data

obtained using a single set of parameters it was deduced2 ”4"that the Fe ions experience a distribution of exchange

fields. Such a deduction also implies that the Co

anisotropy energy is not much smaller than the Co-Co

exchange coupling.

99

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