Hyperfine Interactions 60 (1990) 845-848 845

IMPURITY INTERACTIONS IN NiRh(In) A N D RhNi(ln) DILUTE ALLOYS

R DECOSTER, G. DE DONCKER, A.Z. HRYNKIEWICZ* and M. ROTS lnsliluut voor Kern- en Stralingsfysika, K.U Leuven, Celestijnenlaan 200 D, B-3030 Leuven

Impurity interactions in dilute ternary alloys NiRh(In) and RhNi(In) were studied by the TDPAC method. Binding energies +59.7(3.7)-meV and -a8.f~.9) meV and vibrational entropy contributions 0.81(5)k and --0.32(8)k were determined for Rhln impurity pairs in nickel and Niln pairs in rhodium respectively. The experimental values obtained are discussed in terms of existing models.

1. INTRODUCTION.

The TDPAC method is well suited for studies of the impurity interactions in dilute alloys and has been used for this purpose since 1977/1,2//. If the impurity (probe) atom has no impurities as nearest neighbours in a fcc lattice, the EFG at its position has a broad distribution centered around zero due to impurities located at various distant atomic positions. If the probe atom has an impurity a.s a nearest neighbour, an uniqve EFG acts on the probe nucleus and the TDPAC spectra reveal a pattern of well defined quadrupole interaction.

The perturbation factor takes the form

-n & G2(t ) = f ~ S2n cos(nWot ) + (1- f) ~ S2n e (1)

where f is a fraction of probe nuclei forming nearest neighbour pairs with other impurities. Measurements of the fraction f in a broad range of temperatures make possible the determination of the binding energy of nearest neighbour impurity pairs and of the preexponential entropy term in the Arrhenius law describing the interaction between impurities /3/.

In this work the interaction of impurities in NiI~h(ln) and l/hNi(ln) dilute alloys were

studied by the TDPAC method using l l l l n as a nuclear probe. In the specific case of a NiRh(In) alloy the ratio of the concentration of Rhln pairs to the concentration of isolated Rh and In impurities

c R h I n =/3 exp (-B/kT).

CRh cI n (2)

where B is tim binding energy of a Rhln pair and

fl = Z exp(AS/k) (a)

is the entropy factor. It describes the entropy change dt, e to the formation of Rhln pairs and consists of two contributions : Z and exp(AS/k) . The coordination number Z (Z=12 for a fcc lattice) is responsible for the configurational entropy change and AS represents the change of the nonconfigurational, mainly vibrational, entropy. Considering the crystal ,as a collection of harmonic oscillators one ob ta ins /4 /

AS = k ~. In ( Uio / uif ) (4) 1

gO .I.C. Baltzcr A.G., Scientific Publishing Company

846 P. Decoster et al., hnpurity interactions in NiRh(In) and RIANi(In ) alloys

where Uio and uif are lattice vibration frequencies before and after the formation of an

impurity pair.

2. EXPERIMENTAL DETAILS AND RESULTS.

Samples of binary NiRh alloys were prepared by melting tile appropriate amounts of the two constituents. Two Ni-based samples with Rh concentratioas of 1.6 at% and 2.9 at% and one Rh-based sample with 1.6 at% of Ni were used in tile experiments. Carrier free l l l i u in the form of l l l lnCl 3 was deposited on a NiRh foils and diffused for ca. all at 600C

in a I12 atmosphere. Then the samples were slowly cooled down. TDPAC measurements

were performed with a standard four detector set-up. The well-defined electric quadrupole frequencies were observed: 3t.I(4) Mc for NiRh(In) and 26.9(4) Mc for RhNi(In) alloy. Typical TDPAC spectra are shown in fig. 1. - -

-0.1

-41.2

- 0 . 3

- 0 . 1

-0.

r �9 ,,~ ~ �9 , N/

T r 773 K

; ,do 5o ~o ,do glnt~ (nsl

-0.0

"~'1 t

- 0 . 3

- 0 . 1'

- 0 . ~

- 0 . :3

T - |373 J~

.;o ~o ~o ,oo Tlgl~ I I'~ )

Fig.1. Typical TDPAC spectra measured at indicated temperatures for a) NiRh(ln) and b) Rt__ANi(In).

Measurements were performed in the temperature range of 400C - 1000C. Tile factor f (see formula (1)), obtained from the TDPAC spectra determines the concentration ratio of probe-impurity pairs and isolated probe atoms. Measurements of f for different temperatures and the application of the Arrhenius law (2) give the results listed in Table 1.

TABLE 1. Binding energies and entropy factors.

Alloy B (meV) In/3

NiRh(In) +59.7(3.7) 3.29(5)

RhNi([n) -38.1(6~9) 2.17(8)

Tile obtained values of B reflect tile repulsive interaction between the Rh and the In

R Decoster et aL, hnpurity interactions in N jiRh(ht) attd RlylNi(ln) alloys 847

impurities in nickel and tim attractive interaction between the Ni and In impurities in rhodium. A Iogaritmic plot of the normalized experimental fraction of probe atoms forming impurity-impurity pairs in the Ni - and ILh-matrix is shown in fig.2.

3 . 5 3

] . 0

2 . '5-

C

lO00 / l (K I

6 ~ - 38171 ,,,eV

b

0:6 ,?~- ,:~ ,:, 100011111

Fig.2. Plots of the normalized fraction of l l l I n probe atoms in In-Rh (nickel matrix) or In-Ni (rhodium matrix) pairs.

3. DISCUSSION.

3.1. Size effects in the Miedema-Krolas approach.

The binding energies obtained can be compared with the predictions based on tim correlation proposed by Krolas /5[ between microscopic bonds and beats of alloy formation calculated from the semi--empirical formulas of Miedema/6/ . In the case of the alloys with a transitional metal and a polyvalent metal with p--electrons, the Miedema heats of alloy formation differ for solid and liquid solutions. The question does arise which values give better fit to the experimental binding energies.

In order to improve the fig Alonso et al . /7/introduced the size correction in the form

ABsize= e (V A - VB) (V A - VC) , (5)

where V A , V B , and V C are atomic volumes of the host metat A and of the impurities B

and C, respectively. In table 2 the experimental binding energies are compared with the Miedema-Krolas

predictions B M-I( for solid and liquid cases. For both cases the size correct, ion was calculated as

ABsize= Bexp_ B M - K ,

and the c~ coefficients in formula (5) obtained in this way are also listed in Table 2. From the

B M-K lead to more consistent cr values. above evaluation it, can be concluded that I i quid

848 P.. Decoster et al., hnpurity interactions in N iRh(In) and Rl~Ni(In) alloys

TABLE 2. Comparison with the Miedema-Krolas predictions.

Alloy Bexp BM-K BM-I( s o 1. 1 i q. as01. aliq.

meV meV meV meV/(cm3/g.at) 2

NiRh(In) +60(4) -19 -31 4.7(3) 5.4(4)

RhNi(ln) -38(7) +48 +40 6.4(,5) 5.8(5)

3.2. Pre-exponential entropy term.

This term can be expressed as

I n / 3 = l n Z + AS/k.

In the case of a fee lattice Z= 12 and lnZ = 2.485. ltence from the measured In/? the AS/k can be calculated. For NiRh(In) we find AS/k =0.81(5) , while for RhNi(In) it equals --0.32(8). The sign of AS is consistent with the type of impurity int"~rraction observed. When impurities attract each other, which is the case with Niln in rhodium, the formation of a pair strengthens the bond and increases the vibration frequencies ( uif > Uio ), which

makes AS negative. In the case of the repulsive interaction the bond becomes weaker when a pair is formed and the vibrational entropy should increase.

On leave from the Institute of Nuclear Physics, Krakow,Poland

References.

I l l R. Butt, B. liaa.s and H. Rinneberg, Phys.Lett. 60A (1977) 323 K. Krolas, B. Wodniecka and P. Wodniecki, Hyp.Int. 4 (1978) 605

J 3/A.Z. ttrynkiewicz and K. Krolas, Phys.Rev. B28 (1983) 1864 4/. H.B. Huntington, G.A. Shrin and E.S. Wajda, Phys.Rev. 99 (1955)1085

/~/ K Krolas, Phys.Lett 85A (1981) 197 A.R. Miedema, P.F. Chatel and F.R. de Boer, Physica B100 (1980) 1

7/J.A. Alonso, T.E. Cranshaw and N.H. March, J.Phys.Chem.Solids 46 (1985) 1147