Electric quadrupole interaction at 181Ta probes in hexagonal TiNi3-type compounds

Journal oF

ALLOY5 AHD COMFOUHD5 ELSEVIER

Journal of Alloys and Compounds 219 (1995) 128--131

Electric quadrupole interaction at 181Ta probes in hexagonal TiNi3-type compounds B. Wodniecka, P. Wodniecki, M. Marszalek, A.Z. Hrynkiewicz H. Niewodniczahski Institute of Nuclear Physics', Radzikowskiego 152, 31-342 Cracow, Poland

Abstract

The perturbed angular correlation technique was applied to study the electric field gradient (EFG) in TiNi3-type compounds. HfPd3, Zro.98Hfo.02Pd3 and Tio.98Hfo.o2Pd3 samples were neutron irradiated in order to produce 181Ta probes. The perturbed angular correlation measurements performed in the temperature range 45 K-1100 K demonstrated the existence of two axially symmetric EFGs in each of the investigated compounds related to the 2(a) and 2(c) probe sites in the D024 structure. The temperature dependence of the quadrupole frequencies exhibits different slope parameters for each of the observed frequencies. Keywords: Intermetallic compound; Perturbed angular correlations; Electric field gradient

I. Introduction

The electric field gradient (EFG) at the probe sites in metals is generally considered to arise from two sources. The non-cubic arrangement of lattice ions causes a lattice field gradient V~'. In addition, an electronic contribution V~ is due to a non-uniform charge density of the conduction electrons. The V~' value can be obtained from lattice sum calculations and its enhancement by the quadrupole deformation of the closed electronic shells of the probe atom can be taken into account by the Sternheimer correction factor 1-7~. The conduction electron contribution is difficult to calculate since the conduction electron wavefunctions and the density of states must he known. In most simple metals the temperature dependence of the EFG is much stronger than expected from the lattice expansion and can be described by the T 3/2 relation

close packing of spheres of the same size, whereas their RA/RB values differ considerably from unity. This indicates that the atoms have effective sizes that are not consistent with their coordination number 12 (CN12) atomic radii. The lattice of TiNi3-type four-layer compounds consists of a coplanar layer sequence arranged like hexagonal tiles and stacked in abac sequence. A CN12 polyhedron is formed around the A atom which is composed entirely of B atoms. Fig. 1 shows the unit cell containing four molecules of HfPd 3 (Hf atoms in •

•

0

[1]. In the course of systematic study of quadrupole interactions in binary transition metal compounds we present our results for hexagonal D024 (space group D~, P63/mmc) TiNi3-type intermetallic compounds of Hf, Zr and Ti with Pd. At the AB3 composition six families of phases occur which can be classified according to various stacking schemes of ordered close-packed layers. The characteristics of these phases are reviewed in Ref. [2]. Combinations of a titanium group A element and a nickel group B element account for all the TiNi3type phases. The axial ratios of TiNi3-type hexagonal phases are usually very close to the ideal values for

0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reservcd SSDI 0925-8388(94)05066-X

Hf

2(a)

o,0

0

.

p

o

.

a,

o

•

•

I Q~

0 ~>

•

O

O ©

2(c)O

•

0

o

0

0 0

•

0

0

@ 0

©

© o

0

•

c

2(c) c:~ ,,~~ •

o

o

•

•

2(a) Fig. [. The unit cell of the Hfl?d3 compound and the nearest neighbourhood of Hf atoms in 2(a) and 2(c) lattice sites of the Hfl?d3 compound.

B. Wodniecka et aL / Journal of Alloys and Compounds 219 (1995) 128-131

129

2(a)-D3a and 2(c)-D3h positions with axial symmetry and Pd atoms in 6(g)--C2h and 6(h)--C2v positions with lack of axial symmetry) as well as the nearest neighbourhood of Hf atoms in 2(a) and 2(c) positions.

asymmetry parameters ~7~=0. The HfPd3 and ZrPd3 samples exhibited a non-random orientation of the crystallites. The same effect was observed in the case of Hf2Pd and Zr2Pd compounds [4]. The data were least-squares fitted with the perturbation factor

2. Experimental details and data analysis

G2(t) = ~ fi ~ {s2~ cos[6n(zd20)voit]

2

3

i=1

The HfPd3, Zro.gsHfo.02Pd3and Tio.9sHfo.02Pd3samples were prepared by argon arc melting followed by a 4 day anneal at 1100 K in evacuated and sealed quartz tubes. The powder X-ray diffraction patterns confirmed the D024 structure of the investigated compounds. The samples were neutron irradiated in order to produce the ~S~Hf(/~-)~S~Ta probes and annealed for 2 days at 1000 K prior to experiments in order to remove irradiation defects. The quadrupole interaction at the site of Hf atoms was measured by the time-dependent perturbed angular correlation (PAC) method. The experiments were performed with the 133-482 keV 7-3' cascade in lSlTa with an intermediate state of half-life 10.6 ns. A complete description of the technique can be found in the literature [3]. The PAC spectra were recorded in the temperature range 45 K-1100 K using a four BaF2 detector set-up with an instrumental resolution of 800 ps full width at half-maximum. For PAC measurements carried out below room temperature a closed cycle helium refrigerator was applied. For temperatures above 300 K a small resistive vacuum oven was used. The room temperature spectra for HfPd3, ZrPd3 and TiPd3 samples are presented in Fig. 2 together with the Fourier transforms of the data. The experimental PAC spectra for each sample exhibit two fractions of probe atoms exposed to different axially symmetric EFGs corresponding to quadrupole frequencies voi and

-R(t)~

TiPd3'

P(vo) 0'

TiPd3 VO1

v~

ZrPd3 Vm

0.00

exp[- 6n(Tr/20)8,t]}

vo(T) = ~Q(O)(1 - b T 3/2)

(2)

3. Results and discussion

The fitted quadrupole interaction parameters for HfPd3, ZrPd3 and TiPd 3 compounds are collected in Table 1. For all compounds two probe fractions in different environments are detected. The values of the fractions fl and f2 are equal for HfPd3, where the lSlHf probes (identical with compound constituent) occupy 2(a) and 2(c) crystallographic positions, and nearly equal for ZrPd3 and TiPd3 samples. The measured asymmetry parameters ~1 and ~2 equal to zero are in accordance with the symmetry of 2(a) and 2(c) sites in the D024 structure. For all compounds the frequency distributions are very narrow which indicates a welldefined nearest neighbourhood of the probe atoms. The substitution of Zr and Ti sites by probe atoms in ZrPd3 and TiPd3 compounds seems to be obvious. The fitted widths of the frequency distributions for higher vo values are close to zero (about 0.2(1)%) for HfPd 3 and ZrPd3. The somewhat larger 8 parameter observed Table 1 The fitted quadrupole interaction parameters of tStTa in nfPd3, ZrPd3 and TiPd3 (Eqs. (1) and (2))

HfPd3

Vo(300 K) (MHz)

"7

VOl

o.,ol~,Jl J~ ~ 2o

(1)

reflecting the existence of two non-equivalent axially symmetric 2(a) and 2(c) Hf sites in the D024 structure of the investigated samples. The values of fractions f , quadrupole frequencies Vo. widths 8i of assumed lorentzian shape frequency distributions, and coefficients s2~ were left as free parameters. The measured temperature dependence of quadrupole frequencies was fitted using the formula [1]

Compound ~

tm

o

n~0

vo(O) b (MHz) (×10 -5 K-3t2)

Attributed lattice site

,.I

40

sot

[nsleO

IO00vo[MHz]2000

Fig. 2. Room temperature PAC spectra (with corresponding Fourier transforms) of tStTa in TiPd3, ZrPda and HfPd3 samples. - - , leastsquares fits of the theoretical functions G2(t) (Eq. (1)).

HfPd3

0.51(1) 613(1) 0.49(1) 30(3)

0.0 614(1) 0.0 31(1)

0.02(1) 2(a) 0.9(1) 2(c)

ZrPd3

0.52(1) 692(1) 0.48(1) 29(1)

0.0 699(1) 0.0 27(1)

0.16(1) 2(a) --1.1(3) 2(c)

TiPd3

0.45(1) 476(1) 0.55(1) 55(2)

0.0 0.0

2(a) 2(c)

B. Wodniecka et aL / Journal of Alloys and Compounds 219 (1995) 128-131

130

for TiPd3 sample (about 1.0(1)%) can be connected with the oversized Hf probes (RHr/RTi= 1.08). Lower frequencies measured in each of the investigated compounds are determined much less precisely, as the short lifetime of the 482 keV intermediate state allows the observation of the time spectra to about 100 ns only. The computed values of the experimental field gradient

V~P=huo/eQ

(3)

where Q = 2.51 b [5] is the quadrupole moment of the 482 keV 181Ta excited state, are summarized in Table 2. The exact calculations of the EFG in a crystal can be extracted, in principle, from self-consistent field calculations of the total wavefunction. This has been done in metals with nearly all approximations of wavefunctions and potentials. To our knowledge, no selfconsistent field calculations of the EFG at t81Ta sites have been performed so far for the compounds discussed in this paper and the point charge model (PCM) is the only access to the theoretical predictions. The results of PCM calculations of the ionic contribution

V,~" = ( 1 - ,,/,~)V~'

(4)

where 1 - y~ = 62, with the assumption of + 4 charge on Hf, Ti and Zr atoms and 0 charge on Pd atoms, are collected in Table 2. Pure metallic bonding was assumed and any local distortions caused by the 18~Ta probe were neglected. In calculating the lattice sum ~k l k 3XkiXkj- 6i'ir2 v,~a,= e ' 4~'eo r~

thermodynamic properties [7] of Pd binary alloys with monovalent metals it can be concluded that 4d states of the Pd atoms can be completely filled in the compounds discussed in this paper. This leads to an effective charge Zpd = 0 and thus no contribution to the lattice EFG. The accuracy of the calculated ionic EFG contribution crucially depends on the proper choice of ionic charges and the experimental errors of the adopted crystal parameters. The corresponding lattice parameters used in these calculations were taken from Ref. [2]. The higher values of the ionic contribution V~n are obtained for the probe location in sites 2(a) of lower symmetry and thus the high frequency component in PAC spectra is attributed to these lattice sites. Raghavan et al. [8] gave an empirical expression (neglecting open shell effects) V==

V~"(1-K),

with K = +3

(6)

which describes a universal correlation between the effective EFG and its ionic contribution observed in most metallic systems. The calculated factor a = [V~Xp/Vi°"[ (see Table 2), related to the electronic enhancement factor K (Eq. (6)) so that a = [ 1 - / ~ , differs from the expected value 2, especially in the case of TiPd3. Variations might arise, for example, from the inappropriate choice of the lattice ionic charges. The measured temperature dependence of quadrupole frequencies in HfPd 3 and ZrPd3 samples is shown in Fig. 3, whereas the fitted parameters are listed in Table 1. It turned out that the slope parameters b (see Eq. (2)) for quadrupole frequencies attributed to different probe lattice locations are different. A similar

(5)

the contributions of all ions k in a sphere with radius securing the convergence were taken into account. Here, Zk denotes the ionic charge, xki the coordinates and rk the distance for the kth ion to the probe. Usually the ionic charge of pure metals is set equal to the nominal valence of the element forming the lattice. From magnetic susceptibility measurements [6] and the study of

vo[MHz]

o ZrPd3 • HfPd3

7OO

650 - - - 0

600 i

Table 2 The calculated values of the experimental I ~ Xp (Eq. (3)) and the ionic contribution V'°" (Eq. (4)) at ZatTa in HI'Pd3, ZrPd3 and TiPd3 (a denotes the IV~P/V~"I ratio)

40

AB 3

30

Ira=xp

V '°"

( X 10 t7

V cm -2)

( × 1017 V cm -2)

HfPd3

± 10.10(2) -t-0.50(5)

ZrPd3

± 11.40(2) +0.47(2)

TiPd3

± 7.84(2) ± 0.90(3)

,a

Lattice site

Site symmetry

+4.85 -0.15

2.08(1) 3.3(3)

2(a) 2(c)

3m ~un2

+4.78 -0.13

2.38(1) 3.6(2)

2(a) 2(c)

3m (-Jm2

+5.24 -0.21

1.50(1) 4.3(2)

2(a) 2(c)

3m (~-n2

I

i

I

~

I

20 *

0

500

T[K]

I

1000

Fig. 3. The temperature dependence of quadrupole interaction frequencies measured at XatTa in HfPd3 and ZrPd3 samples. - - , leastsquares fits of Eq. (2).

B. Wodniecka et al. / Journal of Alloys and Compounds 219 (1995) 128-131

temperature behaviour was noticed also in some other intermetallic compounds [9,10]. It should be noted that the b values are relatively low for the higher frequency component in the case of ZrPd3 and, especially, of the HfPd3 compound. The strength of the EFG temperature dependence is attributed to thermal vibrations of the probe and lattice atoms which tend to reduce the EFG at high temperatures. Therefore, the EFG becomes related to the Debye-Waller factor of the system. In a simple picture where the crystal is considered as an array of harmonic oscillators, the "spring constant" of the oscillator is proportional to M ~ , M being the atomic mass and OD the Debye temperature of the crystal. So one would expect the temperature dependence of the EFG to be related to (MO2D)- 1. For pure metallic systems a correlation between the strength of the EFG temperature dependence and (MO~)-1 seems to be quite obvious. The slope parameter values b measured for impurity systems follow roughly a general trend of proportionality. Because the experimental data were not available, the mean Debye temperatures for HfPd3 and ZrPd3 were calculated according to the Lindemann equation: ~)D = K ( Tm/M)I/2(1/V) 1~

(7)

where M is the mean atomic weight, V the mean atomic volume, Tm the melting temperature and K a constant. The lattice parameters, melting temperatures and the K value of 145.1 used in the calculations were taken form Refs. [2,11-13]. The estimated (MO~) -1 values (equal to 0.94×10 -7 K -2 for HfPd3 and 1.04×10 -7 K -2 for ZrPda) are very low and can explain the observed very weak temperature dependence of the EFG. The low values of quadrupole frequencies corresponding to the 2(c) probe site and the observed texture of the samples reduce the accuracy of their temperature dependence determination. Nevertheless, a rising character of the temperature variation of the low quadrupole frequency in ZrPda sample seems to be unquestionable. For metals with large densities of states at the Fermi level, as in transition metals, the Fermi surface contribution to the EFG seems to be important. Our results suggest that electrons at the Fermi surface, where

131

thermally induced repopulation can occur, play a dominant role. A comparison of the temperature dependences with the variation in lattice contribution to the EFG cannot, unfortunately, be made because of the lack of experimental data on the anisotropy of thermal expansion in the compounds studied. To shed more light on the obtained results studies of the temperature dependence of electric quadrupole interaction in TiPd3 are under way and experiments concerning compounds of the same crystallographic structure with Pt and Ni are planned.

Acknowledgments The authors would like to express their appreciation to Dr. A. Bajorek for X-ray analysis of the samples. This work was supported by the State Committee for Scientific Research (Grant 2 0457 91 01).

References [1] J. Christiansen, P. Heubes, R. Keitel, W. Klinger, W. Loefler, W. Sandner and W. Witthun, Z. Phys. B, 24 (1976) 177. [2] M.V. Nevitt, in P.A. Beck (ed.), Electronic Structure and Alloy Chemistry of the Transition Elements, Wiley, New York, 1963, p. 101. [3] J. Christiansen, Hyperfine Interactions of Radioactive Nuclei, Springer, Berlin, 1983. [4] B. Wodniecka, M. Marszalek, P. Wodniecki, H. Saitovitch, P.R.J. da Silva and A.Z. Hrynkiewicz, J. Alloys Comp., 219 (1995) 132. [5] G. Netz and E. Bodenstedt, Nucl. Phys. ,4, 208 (1973) 503. [6] D.J. Lam and K.M. Myles, Z Phys. Soc. Jan., 21 (1966) 1503. [71 J.B. Darby, K.M. Myles and N.J. Pratt, Acta Metall., 19 (1971) 7. [8] R.S. Raghavan, E.N. Kaufmann and P. Raghavan, Phys. Rev. Left., 34 (1975) 1280. [9] P. Wodniecki, B. Wodniecka, M. Marszalek and A.Z. Hrynkiewicz, Hyperfine Interaction, 80 (1993) 1033. [10] M. Marszalek, B. Wodniecka, P. Wodniecki and A.Z. Hrynkiewicz, Hyperfine Interact., 80 (1993) 1029. [11] K.A. Gschneider, in F. Seitz and D. Turnbull (eds.), Solid State Physics, Voi. 16, Academic Press, New York, 1964, p. 275. [12] Landolt-Brrnstein, Strukturdaten der Elements und lntermetalischen Phasen, Springer, Berlin, 1971. [13] E.A. Brandes, Smithells Metals Reference Book, Butterworths, London, 1983.