V. P. KALANTARIAN and V. I. CHECHERNIKOV: NMR and Susceptibility Measurements 113

phys. stat. sol. (b) 76, 113 (1976)

Subject classification: 19; 13; 18; 21; 21.1

Institute of Radiophysics and Electronics, Academy of Sciences of the Armenian SSR, Ereflan ( a ) , and

Department of Physics, Moscow State University ( 6 )

Nuclear Magnetic Resonance and Susceptibility Measurements of Transition Metals and Alloys

V-Ta, V-Nb, and Nb-Ta Systems

BY V. P. KALANTARIAN (a) and V. I. CHECHERNIKOV (b)

The Knight shift of V51 and NbQ3 and the magnetic susceptibility have been measured in binary alloys of 3d, 4d, and 5d transition metals including vanadium, niobium, and tanta- lum. The experimental results and estimates of the various contributions to K and x show that the orbital contribution due to d-electrons is dominant in these alloys. In the cal- culations of the various contributions, both the electron-phonon interaction and s-d hybridization are taken into account.

B CTaTbe IIpMBeneHbI pe3yJIbTaTJd 3KClIepHMeHTanbHOrO HCCJIenOBaHHfI CnBHra HaiiTa K Ha finpax Vs1 M Nbg3 II MaI'HHTHOfi BOCnPkiHMqMBOCTH X B CmaBaX 3d-, 4d- 12 5d-IIepeXO~HbIX MeTaJInOB BaHanMH, HHOBIIH EI TaHTaJIa. Ha OCHOBaHHEl 3KCIIePHMeHTaJIbHbIX pe3yJIbTaTOB II IIpOBeAeHHbIX OgeHOK pa3JIIIqHbIX BKJIaAOB B K M X HeJIaeTCFl BbIBOA, 9 T O B HCCJIeAOBaHHbIX CHCTeMaX CIIJIaBOB npeo6nanae~ OpGHTaJIbHbIa BKJIaA, 06yCJIOBJIeHH61fi Op6HTaJIbHbIM KBHXeHHeM d-3jIeKTPOHOB. nPII paCq6TaX pa3JlMsHblX BHJIanOB y~HTbIBaJIOCb KBIC 3,rleKTPOH-@OHOHHOe B3aHMO- HeiicTsHe, TaK M s-d r ~ 6 p ~ n ~ 3 a q 1 1 ~ .

1. Introduction In order to interpret the magnetic properties of metals and alloys in terms

of their electronic structures, the Knight shift K and the magnetic susceptibility x are important quantities. We have investigated the nuclear magnetic resonance - the Knight shifts of V5I and NbQ3 and the magnetic susceptibility in 3d, 4d, and 5d transition metal alloys, namely, in V-Ta, V-Nb, and Nb-Ta binary alloy systems. The Knight shift observed in transition metals and alloys is it sum of contributions resulting from orbital and core polarization interactions with the d-band electrons, as well as the s-contact interaction. The purpose of this paper is to find the composition dependence of K and x and to estimate the relative importance of various contributions to them.

The first investigations of NMR properties and magnetic susceptibilities of the V-Nb system have been published in [l] but in their calculations and estima- tions of various contributions the electron-phonon interaction was not taken into account and measurements have been carried out only a t room temperature. In the present work the electron-phonon interaction is taken into account as well as the s-d hybridization. The two-band model, according to which in tran- sition metals there are two separate bands (a wide s-band and a narrow d-band with high density of states) is not correct. In fact, there is an s-d hybridization, which results in a broadening of the d-band. For example [2], it is shown that 8 physica (b) 76/1

114 V. P. KALANTARIAN and V. I. CHECHERNIKOV

the hybridized band states of Pe contain an appreciable amount of d-character over an energy range of about 0.6 Ryd which is larger than the unhybridized d-band width of 0.464 Ryd [Z ] .

2. Experimental Details

The alloys were prepared by arc melting required amounts of electrolytic vanadium and niobium or tantalum in an argon atmosphere. The vanadium was of 99.8% purity; those of the other metals are 99.9%. The alloy compositions reported here are those of the weighed charges before melting, since the loss of weight upon melting was negligibly small. Each specimen was homogenized at 1000 'C for 10 h in vacuum and was subsequently water quenched. Samples were prepared from the ingot by filing and then screening them with a 160 mesh sieve. The alloys were examined by X-ray and optical metallography to ensure the single phase. At room temperature V and Ta or Nb form body-centered cubic alloy systems as well as Nb and Ta. The lattice parameter of the alloys increases almost linearly from pure vanadium (a = 3.03 A) to pure niobium and tantalum (a = 3.30 A).

Knight shift measurements were performed with a wide-line NMR spectro- meter. The reference compound used for the VS1 Knight shift measurements was a saturated solution of KVO, dissolved in distilled water. At 77 K the shifts of V51 were measured relative to C d 3 from a copper coil of circuit pick-up and then are quoted relative to KVO,. The shifts of Nbg3 were relative to the solu- tion NbF, in hydrofluoric acid.

Magnetic susceptibility measurements were made by the Faraday method at temperatures 77 to 295 K. All measurements were performed under vacuum. The estimated accuracy is &1.5% relative to the susceptibility of Ta. The estimated accuracy of the shift of V51 is 0.01% and of Nb93 is 0.03%.

3. Results

Measured values of the V51 Knight shift and magnetic susceptibility for various compositions of V-Ta system are plotted in Fig. 1. The Knight shift of VS1 decreases from 0.56% for pure V to 0.45% a t 90 atyo Ta.

- 068 f 064

060 < 0 56

1 300 5 140 2 8 0 $ldo

'0 260

s F .p" 240 a51 - 055 i --

210

I80 047 $ 160 0 43

\

* zoo B 220 x

0 20 40 60 80 100 0 20 40 60 80 100 v 7i

composition (at yo) - V Nb cornposifion (of %] -

Fig. 1. Knight shifts of V51 K v and mag- netic susceptibility in V-Ta alloys as a

function of atyo Ta

Fig. 2. Knight shifts of V51 K v and mag- netic susceptibility in V-Nb alloys as a

function of atyo Nb

Nuclear Magnetic Resonance and Susceptibility Measurements 115

Fig. 3. Magnetic susceptibility data in V-Ta, V-Nb, Nb-Ta alloys and the partioning into (1) zmeas, (2) Xorb, and (3) xspin (see text for details). 0 V-Ta,

Nb-Ta, x V-Nb system

The line width of is about 15 Oe and is un- changed within the experimental error. The line is symmetric and its intensity decreases with the increase of Ta concentration and becomes almost twice a t 77 K. The magnetic suscepti- 0 20 40 60 80 100

V, Nb Nb, To bility in this alloy system monotonously de- creases with increasing Ta content. Within the experimental error no temperature dependence of the susceptibility and shift was found over the temperature range from 77 to 293 K.

In the V-Nb alloys K(V51) increases from pure V to a maximum near 50 at% Nb and then decreases with increasing Nb content (Fig. 2), and the magnetic susceptibility monotonously decreases with the increase of Nb con- centration.

In alloys of the Nb-Ta system there is no temperature dependence of K and x over the range 77 to 293 K. The measured magnetic susceptibility data in V-Ta, V-Nb, and Nb-Ta alloys and their resolved values of xorb and xBpin are shown in Fig. 3.

4. Interpretation and Discussion

40

composition ( a t % I -

In the transition metals and their alloys the susceptibility x and the Knight) shift K are usually expressed as follows:

and

= & X s + PXd + cxorb (1b) where xs and K , are the s-band contributions, xd and K , are the d-band contri- butions associated with core polarization, Xorb and Kerb are the contributions from the induced orbital paramagnetism, and IY, P, c are the constants of atomic hyperfine interactions. In order to calculate the various contributions to the Knight shift it is necessary to know the atomic hyperfine fields as well as susceptibilities [3]. The atomic hyperfine fields for V and Nb due to s-contact, d-core polarization, and orbital interactions are taken from [4]. It is assumed that these hyperfine fields do not change appreciably over the whole concen- tration range measured. xspin is calculated for the alloy systems from the relation

where ye is the gyromagnetic ratio, y the electronic specific heat coefficient, and Ic the Boltzmann constant. The electronic specific heat coefficient is enha.nced by 8'

116 V. P. KALANTARIAN and V. I. CHECHERNIKOV

a factor (1 + A) from the elect,ron-phonon interaction (A is the electron-phonon coupling constant) and hence the relation ( 2 ) should be written as

The density of states of a band NBs(0) is related to density of states N,(O) deduced from experimental values of y as

The values of y and 1 for V-Ta, n'b-Ta, and V-Nb systems are given in [ 5 ] . To estimate roughly xorb, one may use the approximate relation [ 2 ]

where no and nu are the numbers of occupied and unoccupied states in the d-band and A is the width of the d-band. From (5) one may quantitatively explain the decrease of xorh from V to Ta in the alloy system, because the d-band width of V is 0.4 Ryd and that of Ta is 0.81 Ryd. The s-d hybridization will result in d-band broadening and hence a decrease in Xorb. I n [6, 71 i t is shown that the effect on xorh of the hybridization between the b.c.c. d-band and the conduction band leads to a decrease in the value of Xorb a t maximum by about 25%. As the orbital susceptibility determines the value of the orbital contribution to the Knight shift, the account of s-d hybridization will result in the change of the orbital as well as the spin contribution to the shift and magnetic susceptibility.

As the composition dependence of the orbital susceptibility is known from the experiment, the shift Kerb has been calculated for all compositions and Kspin is obtained as Kspin = K,,,, - Kerb. In all three systems Kerb has been calculated for three cases : a) neglecting the electron-phonon interaction, b) taking into account the electron-phonon interaction on y and, hence on x, i.e. for 1 = 0 and A $. 0, and c) taking into account both the s-d hybridization and electron- phonon interaction. In our calculations of the orbital contribution to the Knight shift it was assumed that the value of the orbital hyperfine interactionconstant c

-.w 1 LO 40 60 80 100

V To composition (o f%) ----

-mO V Nb

cornposition id%) -

Nuclear Magnetic Resonance and Susceptibility Measurements 117

does not depend on alloy composition in V-Ta and Nb-Ta systems, because the constants of atomic hyperfine interactions usually are assumed to be indepen- dent of alloy composition and temperature. In the V-Ta alloys we took the value c = 5.2 x lo3 mol%/e.m.u. for vanadium. (The estimates for c by various authors, on the basis of the average of the d-electron radii over the Fermi surface (T-~),, or Hhf(orb), are c = (4 to 5.6) x lo3 niol%/e.m.u.). For niobium we take c == 5.1 x lo3 mol%/e.m.u. But this assumption will not be valid for V-Nb alloys. As shown in [l], the values of the square root of the nuclear spin- lattice relaxation rate increases for the VS1 nuclei with increasing Nb concentration. These results suggest that the d-electron density of states in- creases from pure V with increasing Nb concentration, according to the relation

= C,Ni(EF) + CdN:(EF). This is contrary to the well-known results [5] that y decreases from V to Nb in this alloy system. In order to solve this contradiction, the coefficient c must be changed with composition. Calculations of the contact contribution K, in pure vanadium and niobium, by using the value of the atomic hyperfine contact interaction coefficient for s-electrons according to the free-electron model, give 0.047 and 0.28%, respectively. To calculate the exchange polarization contribution from the d-electrons K , we must know the value of the hyperfine interaction coefficient f l for the d-electrons [8], which con- tains (@)),. ((@(())), is the net spin density a t the nucleus caused by one d-electron averaged over the d-states a t the Fermi surface.) Taking the value of (e(O)>, from [8], we have obtained p = -2.52 x 103 mol%/e.m.u. In the same way we can calculate ,3 for niobium. In our calculations the value of /3 = -3.2 x 103 moly,/e.m.u. for Nb was taken. The theoretical estimates of the atomic hyperfine interaction constants a and ,3 lead to the spin contribution Kspin = K, + K, which is compared with experimenta1Kapin = K,,,, - Kerb. Theoretical values of coefficients (Y and f l well explain the obtained experimental results. The best coincidence is obtained when both the electron-phonon inter- action (A=+ 0) and s-d hybridization are taken into account. In order to get reasonable agreement with experiments in the V-Nb alloy system, it is necessary to assume that p varies with composition. The spin contribution of the Knight shift, Kspln, may be estimated also from the relation Kspiu = bxspin, using the values of the coefficient b [9, 101. The best agreement is obtained in the V-Ta alloy system.

Nb Nb Fig. 6. K m e a s (o), Kgk (0), Kspin ( A ) versus at% Nb in Nb-Ta alloys. 8) Bothelectron- phonon interaction and s-d hybridization is taken into account; b) s-d hybridization is

not taken into account

118 V. P. KALANTARIAN and V. I. CHECHERNIKOV: NMR and Susceptibility Measurements

The coefficient b for Nb in the Nb-Ta alloy system has been calculated by using experimental results, €J = 1.2 x lo3 mol%/e.m.u. (in contrast to [lo], where i t is negative). Calculated values of various contributions to the V61 and Nb93 Knight shift in the V-Ta, V-Nb, and Nb-Ta binary alloy system are plot- ted in Fig. 4 to 6.

On the basis of experimental results of the Knight shifts and magnetic sus- ceptibilities as well as the estimated values of various contributions to K and x, we assume that in the Knight shift of VS1 in V-Ta and V-Nb alloys and in the Knight shift of Nb93 in Nb-Ta alloys the contribution due to the orbital motion of d-electrons is dominant. It is also supported by the measured values of the g-factor in some alloys of these systems, which have been obtained by the method of electron paramagnetic resonance. The measured values of the g-factor considerably differ from 2 and are equal to 3.2 to 3.35.

References [I] D. J. LAM, J. J. SPOKAS, and D. 0. VAN OSTENBURG, Phys. Rev. 156, 735 (1967). [2] C. M. PLACE and P. RHODES, phys. stat. sol. (b) 47, 475 (1971). [3] R. E. WATSON and A. J. FREEMAN, Phys. Rev. 133, 1630 (1964). [4] Y. MASUDA, If. NISHIOKA, and N. WATANABE, J. Phys. SOC. Japan 22, 238 (1967). [5 ] J. M. CORSAN and A. J. COOK, phys. stat. sol. (b) 40, 657 (1970). [6] C. M. PLACE and P. RHODES, J . appl. Phys. 39, 1282 (1968). 171 M. YASUI and M. SHIMIZU, J. Phys. SOC. Japan 31, 378 (1971). [8] J. BUTTERWORTH, Proc. Phys. SOC. 83, 71 (1964). [9] M. SHIMIZU, T. TAKAHASHI. and A. KATSUKI, J. Phys. SOC. Japan 18, 1192 (1963).

[lo] D. 0. VAN OSTENBURG, D. J. LAM, M. SHIDIIZU, and A. KATSUKI, J. Phys. Soc. Japan 18, 1744 (1963).

(Received March 26, 1976)