aim of this part ta+pxrd course - helsinki

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TA+PXRD coursePart 4, Phase analysis

November 2017, Mikko Heikkilä

2.12.2015TA+PXRD course - Part 4, Phase analysisNovember 2017, Mikko Heikkilä 1 www.helsinki.fi/yliopisto

Aim of this part

• XRD phase analysis, can be divided to two parts

• Qualitative XRD

• data reduction, representation, search and match

• Quantitative XRD

• Traditional methods• Quantitative Rietveld refinement

2.12.2015TA+PXRD course - Part 4, Phase analysisNovember 2017, Mikko Heikkilä 2


Introduction– Qualitative and quantitative XRD

Qualitative XRD

• What’s in my sample?

• Is there more than one phase?

• Is there something that wasn’t expected and if so, what’s that?

• Is it crystalline at all?


Introduction– Qualitative and quantitative XRD

Quantitative XRD

• after the qualitative questions are solved, one might want to know

what are the amounts of different phases

• while XRD usually probes for crystalline material, there are

methods for determining the amount of amorphous (or

unidentified!) material as well

• Phase transitions during or after heat treatments are nice

playground for qualitative and especially quantitative analyses



Introduction– Basics of phase identification

Diffractogram is a ”fingerprint” for each material

• Identification is based on positions and and intensity ratios of

observed reflections

• Position of the reflections depends on lattice dimensions (Bragg’s law)

• Intensity ratios of the reflections depend on chemical composition

(structure factor)

→ each material has a unique diffractogram


Introduction– Basics of phase identification

Identification of polymorphs is possible

• One of the more useful features of XRD is that materials with same

composition and different crystal structure can be identified

• As an example, diffractograms of three TiO2 phases

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from Whitfieldand Mitchell

TA+PXRD course - Part 4, Phase analysisNovember 2017, Mikko Heikkilä 6


Phase identification

Brief history (Adapted from Snyder & Jenkins, Introduction to X-ray Powder Diffractometry, 1996, Wiley)

Year Event1917-1919 P.J.W. Debye and P. Scherrer in Europe and A.W. Hull in the USA point out the potential advantages of

powder diffraction as a tool for qualitative analysis

1927 A. N. Winchell publishes first private collection of diffraction patterns

1935 A.W. Waldo publishes patterns for 51 copper ores

1938 J.D. Hanawalt, H.W. Rinn and L. Frevel publish a file of 1000 patterns with an indexing and search system

1938 The Institute of Mines in Leningrad tabulates powder data for 142 minerals

1941 Patterns produced on 3x5 cards by the National Research Council (NRC) and Committee AmericanSociety for Testing and Materials E4 of the (ASTM)

1941-1945 Other societies join the powder committee of ASTM

1969 The Join Committee on Powder Diffraction Standards (JCPDS) is incorporated as an independent non-profit organization

1977 JCPDS changes its name to International Centre for Diffraction Data (ICDD)

1994 The ICDD Powder Diffraction File grows to 60000 patterns

2015 The current PDF4+ from ICDD contains 365877 patterns (http://www.icdd.com/products/pdf4.htm)



Example of a PDF card for NaCl

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screen capture fromPCPDFWIN software




Other databases in addition to ICDD

• ICSD – Inorganic Crystal Structure Database

• http://www.fiz-karlsruhe.de/icsd.html

• ”At present (Dec 2015), the ICSD contains more than 181,000 entries,

including”

• 2,023 crystal structures of the elements

• 34,114 records for binary compounds

• 66,292 records for ternary compounds

• 62,666 records for quarternary and quintenary compounds

• About 143,500 entries (81%) have been assigned a structure type.

• There are currently 9,136 structure prototypes.



Other databases

• PCD – Pearson’s Crystal Data

• http://www.crystalimpact.com/pcd/Default.htm

• “Aims to create and maintain the world's largest critically evaluated

Non-organic database”

• “The current release 2015/16 contains about 274,000 structural data

sets”

• “about 157,000 different chemical formulas, roughly 17,900 experimental powderdiffraction patterns and about 255,000 calculated patterns (interplanar spacings,intensities, Miller indices)“

• “In addition over 45,200 figure descriptions for such as cell parameters as a functionof temperature, pressure or concentration are given.”




Other databases

• COD – Crystallography Open Database

• http://www.crystallography.net/

• ”>300,000 entries in crystallographic information file (CIF) format in 2014”

• Gražulis et al., Nucl. Acids Res., 40 (2012) D420

• Gražulis et al., J.Appl.Cryst., 42 (2009) 726

• as the name implies, it’s free of charge



Other databases

• CSD – Cambridge Structural Database

• http://www.ccdc.cam.ac.uk/products/csd/

• ”records bibliographic, chemical and crystallographic information for

organic molecules and metal-organic compounds”

• CRYSTMET

• https://cds.dl.ac.uk/cgi-bin/news/disp?crystmet

• “entries covering metals, alloys and intermetallics.”

• Nowadays Implemented to CSD




Historical Search and match software generations

• Alphabetic method

• Names of the substances in alphabetic order, followed by chemical

formula, d-values of the three strongest lines, PDF number and

sometimes RIR-value

2.12.2015TA+PXRD course - Part 4, Phase analysisNovember 2017, Mikko Heikkilä

From Snyder and Jenkins

13 www.helsinki.fi/yliopisto



• Hanawalt method

• Patterns are sorted according to the d-value of the 100% peak

• This list is broken into smaller groups

• First column is the strongest, but the group is sorted by the second

strongest line

• Before electric format, these were browsed manually in books

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• Fink method

• Problem with Hanawalt system is the dependency on intensities

• Fink method uses eight strongest lines and the creates cyclic

permutatios based on four strongest

• Example of Fink index is shown below

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TA+PXRD course - Part 4, Phase analysisNovember 2017, Mikko Heikkilä 15 www.helsinki.fi/yliopisto



• Boolean search methods

• Search against several different index keys such as Chemistry, Strong

lines, Journal CODEN, Author and Date, Physical properties, etc.

• 1st generation, mid-60’s

• Johnson-Vann approach used computer speed comparing each

reference pattern in PDF (60000 entries then) to the unknown data and

giving FOM for the best 50

• Approach by Nicholas took Hanawalt-type approach






• 2nd generation, 70’s

• Alfred university implemented a Hanawalt-type strategy in addition to a

Johnson-Vand or Fink-like exhaustive approach with hierarchical use of

databases

• Much better at identifying unknown multiphases

• Commercial version by Siemens used hierarchical approach

• First searched against smaller 300 phases database, then 2500 frequent

phases and finally the full PDF

• The key to success was the creation of reliable residual pattern after a

phase was found for further searching17 www.helsinki.fi/yliopisto



• 3rd generation, late 80’s

• In this approach the whole observed pattern with its background (not just

I-d –list) is searched and candidate phases are added together to

compose, rather than decompose, an observed multiphase pattern

• The results are now heavily influenced by where peaks do not occur

instead of only by where they are present

• Much faster searches against full database




Present Search and match softwares

• Modern softwares use previous or their own implementations with

different scoring (or FOM) schemes

• Hardware vendors usually provide a software for phase ID

• EVA (Bruker-AXS)

• Highscore (PANalytical)

• PDXL2 (Rigaku)

• Softwares by others

• Match! (Crystal Impact) http://www.crystalimpact.com/match/Default.htm



Database usage within search&match softwares

• latest version of Highscore can use multiple databases

• However, only NIST version of FIZ-ICSD

• Match! does that as well, also EVA

• although EVA don’t seem to be able to search against ICDD and free

COD database at the same time




Data preprocessing

• Background determination

• Conversion from ADS to FDS if necessary

• For proper comparison of intensities

• Smoothing might help if data is noisy, but it might add artifacts to the

data

• Ka2 stripping may help in determining peak positions in multiphase

mixtures where at higher angles Ka1 and Ka2 are more separated

• Peak search



Data preprocessing

• Peak profile fit if possible

• More accurate peak position

• Peak shape/width can be used as a parameter in searches with some

softwares (at least with Highscore Plus)

• if unknown mixture has phases with very different crystallite sizes, the

reflections belonging to certain phase can be estimated from similar peak

widths




Thin films

• No sample preparation possibility

• If large preferential orientation or texture is present, it’s useful to

use multiple measurement modes for phase identification

• In the example, only two peaks

are present in q-2q scan

making identification difficult

• When measuring in grazing

incidence, more peaks appear



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Several round robins have been conducted on this, example

below was published in 2003

• Very useful info here:

http://www.nist.gov/mml/upload/6-1_NScarlett_APD_IV.pdf



Phase identification- CuOX example

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• Highscore Plus

software is used for

these examples,

since our version of

EVA is so outdated

• the example is a thin

film sample that was

supposed to be Cu2O

• first, the background

is determined



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• next part is the peak

search

• different parameters

can be used for

finding peaks

• closer examination

of the diffractogram

is usually in order to

add missing peaks

or remove ones that

don’t belong thereTA+PXRD course - Part 4, Phase analysisNovember 2017, Mikko Heikkilä 26



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• after peaks are

found, database

search&match is

next

• in this case

multiphase was

preferred and small

shift was accepted

(sometimes caused

by GIXRD geometry)



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• elemental restrictions

were applied, so that

Cu has to be in the

sample and O is a

possibility

• quality restricitions

may also be used




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• it was found that film

consisted mainly of

copper and some

oxide in the form of

cuprite (Cu2O) was

also present


Phase identification- YSZ example

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• another example is a

yttrium stabilized

zirconia (YSZ)

substrate that was

delivered to us

• the diffractogram

seemed to contain

too many peaks,

what might be the

cause for that?

• peak search firstTA+PXRD course - Part 4, Phase analysisNovember 2017, Mikko Heikkilä 30



2.12.2015

• elemental

restrictions are

applied next

• oxygen was made

compulsory since

the material is most

likely all oxides

• in case Y and Zr

oxides are both

there, ”at least one

of” was selectedTA+PXRD course - Part 4, Phase analysisNovember 2017, Mikko Heikkilä 31 www.helsinki.fi/yliopisto


2.12.2015

• yttrium content of

YSZ was given by

supplied as 15 %

• pattern with that

composition fits well,

but explains only

small part of the

features




2.12.2015

• the second

candidate on the list

was monoclinic ZrO2

which explains most

of the remaining

features


°2Theta302928272625242322

Tem

pera

ture

(°C

)

1 000900800700600500400300200100

Phase identification- non-ambient examples

Non-ambient measurements

• Peak shift due to thermal expansion has to be taken into account

• thermal expansion complicates phase identification at high

temperatures

• Reference cards are usually measured at room temperature

• Anisotropic thermal expansion makes things even worse

• In the figure, Nb2O5 crystallizes

at 575 °C, above that the

29°2q peak shifts 0.3°2q

when heated to 1075 °C

• No shift with 22.7°2q peak 2.12.2015TA+PXRD course - Part 4, Phase analysisNovember 2017, Mikko Heikkilä 34


End of qualitative part

Time for questions.


Quantitative phase analysis- Introduction

• Quantitative phase analysis (QPA) is one of the most important

industrial applications of powder XRD, often taking place in quality

control

• most often used approach in industry quality control is to measure

the chemical composition alone (easy, accurate, often XRF)

• Even when crystal phase is used for plant optimization, it is often derived

from bulk chemical analysis

• However, the most direct method to obtain phase related

information is diffraction since the information is acquired straight

from the crystal structure instead of deriving from secondary

information2.12.2015




• Relationships between diffracted peak intensity and the quantity of

phase in a mixture producing the peak are well established

• In industry quality control these analyses are most often very

automatized with batch measurements from sample changers

• To keep things simple, softwares often compare only single peaks

• Many factors complicate the analysis

• Experimental sample and instrument related effects, like counting errors,

preferred orientation etc.

• Largest errors most likely caused by the operator…




Quantification of powder diffraction data can be divided in two

different methods

• Single peak methods

• measurement of a certain peak(s) for each phase of interest and

assumes that the intensity of the peaks are representative of their

amount in the mixture

• Whole pattern methods

• comparison of diffraction data with a calculated pattern formed

from the summation of individual phases that have been either (i)

measured from pure phase samples or (ii) calculated from crystal

structure38



Some dates worth mentioning (Adapted from Snyder and Jenkins)

)Year Event1919 Hull suggested the possibility of quantitative phase analysis using powder

XRD

1925 Navias quantified the amount of mullite in fired ceramics

1936 Clark and Reynolds used fluorite as internal standard for determining quartzin mine dusts

1948 Alexander and Klug described the theoretical background for the absorptioneffects on diffraction intensities in quantitative analysis

1978 The practice of quantitative analysis was described in comprehensive bookon X-ray powder diffraction by Klug & Alexander

A lot has happened later, most importantly the rise of Rietveldrefinement as the most used method for quantitative phase analysis


Quantitative phase analysis

Mathematical background for single peak methods

• The integrated intensity I of reflection hkl for phase a in a multi-

phase mixture measured on a flat-plate sample of infinite

thickness can be calculated from

• The first square bracket is constant for used experimental setup

and the second a constant for reflection hkl for phase a

( ) ( ) ( )3 4 2 22

02 4 2 2 *

1 cos 2 cos 2 132 2 sin cos

hkl mhkl hkl

e m

I e M XI Frm c V

aa a

a a

l q qp q q r m

é ùé ù é ùæ ö+= ´ ´ê úç ÷ê ú ê ú

è øë û ë ûë û



Quantitative phase analysis

2.12.2015

Mathematical background for single peak methods

• The Eq.1 can now be presented in simplified form:

where Cia = constant for reflection i of phase a

• The fundamental problem lies in the mass absorption coefficient

of the mixture

• Since there are two unknowns in single equation

• It is possible to estimate the mass absorption coefficient of the mixture by

either calculating or measuring it

( )* 2i im

XI C aa a

ar m=

* *

1m m

=

= ån

m i ii

X


Quantitative phase analysis– Absorption – diffraction method

• equation (2) is written twice, once for the line i of phase a in the

unknown and again for the same line of a pure sample of phase a

• This simplification applies if the mass attenuation coefficients of the

mixture and the phase to be analyzed are the same

• useful for a mixture of polymorphs, e.g. TiO2 or ZrO2

( )*

0 * 3i

m

mi

XCI X XXI C

aa

a a aa a

aaa

a a

r m mm

r m

= = »



Quantitative phase analysis– Spiking method

Method of standard additions, a.k.a. spiking method

• Based on adding known amounts of phase a which has a

diffraction line not overlapping by any line in the mixture and similar

mass absorption as the mixture

• Phase β is not analyzed and does not even need to be an identified

phase

• For a mixture containing phases a and β, the ratio of intensities

becomes

2.12.2015

( )4i

ii

j jj

XCC XI

XI C XC

aa

a b aa a a

bb b a bb

b b

rr mr

r m

= »



Method of standard additions, a.k.a. spiking method

• After adding mass Ya to the mixture containing an unknown

amount of a, the equation can be written

• plotting Ia/Iβ vs.Ya will produce a straight-line, where the slope is K

and Xa is the negative x-axis intercept

( ) ( ) ( )5ii

j j

C X YI K X YI C X

a b a aaa a

b b a b

rr

+= = +




• Example shown below

• Problems will occur if addition of the phase a significantly changes

the mass absorption of the sample

• Because of tedious sample preparation and data errors

encountered at low concentrations of

both phases, this is seldom

applied in quantitative

analysis. From Snyder & Jenkins


Quantitative phase analysis– Internal standard method

2.12.2015

• the problems caused by µm* can be eliminated by adding a known

amount of Xs of internal standard s to the mixture

• K is a calibration constant determined by plotting Iia/Ijs vs. Xa/Xs

• to avoid microabsorption effects, the mass absorption coefficients

and the particle size of the internal standard should be a close

match to the mixture

( )*

*

6i

i m

sjs sjs

s m

XCI XKXI XC

aa

a a ar m

r m

= »




• After the calibration of K, the concentration of phase a can be

obtained using the equation

and the weight fraction of phase a if the original sample using

equation

2.12.2015

( )7i s

js

I XXI K

aa

´=

´

( ). 81

orig

s

XXXa

a =-



Notes on internal standard method

• the use of peak heights instead of integrated intensities can be

unreliable

• Since the internal standard is often very crystalline, the ratio of peak

intensities will be affected by possible peak broadening behaviour if

sample crystallinity is low




Notes on internal standard method

• Peak overlap between the standard and the sample should be

avoided

• Chosen standard should have strong reflections to avoid the need

to add large quantities of it

• e.g. NIST SRM674 was designed for this purpose

• 10g of each ZnO, TiO2, Cr2O3 and CeO2 packed under argon

• 714 $


Reference intensity ratios (RIR)

• The concept behind the most common RIR method is to provide a

intensity ratio of the 100% intensity peak of a phase a to the 100%

(113) peak of corundum in a 50:50 mixture

and defining K as RIR

• PDF2 database contains RIR-values for many materials, but unfortunately in most

cases only peak intensity instead of integrated area is used

Quantitative phase analysis– Reference Intensity Ratios (RIR)

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( )9cor cor

I XKI X

a a=



• This can be generalized for other reference materials as well:

• The Irel term ratios the relative intensities of the peaks used

• if the 100% peaks of both phases are used, the value of this term is 1

• RIR is still the slope of the calibration curve for phase a with

internal standard β but now has been normalized so that it may be

computed from any pair of diffraction lines in a mixture


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( ), 10relji irel

j i j

I X XI IRIRI I X I X

b b ba aa b

b a a b a

æ ö æ öæ öæ ö æ ö= =ç ÷ ç ÷ç ÷ç ÷ ç ÷ç ÷ç ÷ ç ÷è ø è øè øè ø è ø


• Rearranging the previous equation one gets

• The RIR value in this equation can be obtained through careful

calibration, by determining the slope of the internal standard plot,

or by derivation from other RIR values via


2.12.2015

( ),

11i

j

XIXI RIR

baa

b a b

æ öæ ö= ç ÷ç ÷ç ÷ç ÷

è øè ø

( ),,

,

12RIR

RIRRIR

a ga b

b g

=




• For a system consisting of n phases in which all components are

crystalline and included in the analysis, the following constraint can

be used:

• The effects of sample attenuation can be removed by applying this so-

called matrix flushing (or normalized RIR) method

• Using this in combination with equation (11) one gets

and the weight fraction of phase a is

2.12.2015

( )1

1 13n

kk

X=

=å

1

1

ns ik

kjs ks

X II RIR

-

=

æ ö= ç ÷

è øå

( )1

114

nik

ks ks

I IXRIR RIR

aa

a

-

=

æ ö= ´ç ÷

è øå



• The application of equation (14) assumes that all phases are

crystalline

• By adding internal standard allows calculation of the absolute

amount of each phase:

• Then for the unknown part:

2.12.2015

( )( )

( )( )15std known

absstd meas

XX X

Xaa = ´

( ) ( ) ( )1

1 16n

unknown k absk

X X=

= - å



Quantitative phase analysis– Rietveld methods

Rietveld methods

• more accurate than conventional single line methods because

• all of the peaks in the pattern contribute to the analysis, regardless

of the degree of overlap

• some sample effects, such as preferred orientation, are minimized

(or at least can be taken into account) when using all reflections

• Elemental analysis (e.g. XRF data) can be used as a restriction

in quantitative analysis

• mineral samples with >10 phases quantified surprisingly well


Quantitative phase analysis– Rietveld methods

• originally developed for structure solution

• in addition, one can get useful, non-structural information from

observed and calculated patterns

• peak width and shape contain information about microstructure

• scale factor (in multiphase mixture) relates to the amount of the phase

present

• gets a bit more complicated, enough to talk for some hours

→ I’ll skip it now




2.12.2015

Interesting newcomer in this field is Full Profile Search Match

(FPSM) by Luca Lutterotti

• http://cod.iutcaen.unicaen.fr

• ” The "FPSM method" uses a Rietveld like fitting procedure to test all

possible crystal structures from a Database, rank them and find the more

probable in your diffraction pattern. In the end a Rietveld phase

quantification is done with the phases identified. Be aware that if a phase is

not present in the database (COD is used here), it cannot be found nor

quantify”



2.12.2015

Example test data below

• You just give the data and elemental

composition, software does quantitative

Rietveld refinement automatically



End of quantitative part

Questions, comments?


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