Knight shifts and bonding in liquid semiconductors

828

Journal of Non-Crystalline Solids 114 (1989) 828 North-Holland

KNIGHT SHIFTS AND BONDING IN LIQUID SEMICONDUCTORS $

K. OTT, M. Dt3RRW/~CHTER, M.A. HAGHANI, M. v. HARTROTT , B. SAUER, D. QUITMANN Institut ffir A t o m - und Festk6rperphysik, Freie Universitiit Berlin Arnimallee 14, D-1000 Berlin 33, FRG

The Knight shifts 3~of both atoms in liquid binary semiconducting alloys are derived, using the quasichemical model which had been developed for the thermodynamic properties, and plausible assumptions about the hyperfine interactions. An asymmetric shape for ~ v e r s u s concentration is obtained. Comparison is made with data for ..~(Te) in liquid Sn-Te. A strong reduction of J~on the minority side appears to be a general consequence, and a sign of local interaction, in strongly bound liquid alloys. Liquid semiconductor alloys Al-xBx show physical

Here we try and connect the Knight shift to indepen-

properties which are, in most cases, very different

dent information, viz to the major energetic effects in

indeed from their pure liquid metal constituents, and

the liquid alloys, which are the heat and entropy of mixing (AH(x), AS(x), respectively). - Establishing the

from the solid intermetallic compound(s) as well. A general description of these properties usually starts from the electronic density of states at the Fermi energy

connection between hyperfine interactions and energetic effects may also pave the way of understanding both, in

eF. This quantity is strongly reduced with respect to a free electron approximation1'2, by a factor 0 < g < l . But

terms of bonding. - Last not least it had been observed in a few cases that the Knight shift, if measured far

which microscopic information do we have about the

enough beyond xs, did deviate systematically from the

mechanisms which displace the occupied electronic

trend of ~/a(x,T) or magnetic susceptibility X(c,T).

levels from the region around eF to lower energies?

~(Cu) in 3 Cu-Te and K(Cs) in 8 Au-Cs are relevant

Among the most versatile local probes are the hyperfine

cases.

int eractions, as measured by NMR or related techniques on the nuclei of the constituent atoms (A,B). The most obvious change in properties is the reduc-

We shall use the quasichemical model for the description of energetic effects in liquid alloys with bonding, because it has proven very successful in thermody-

tion in "metallic character". The electrical conductivity

namics of alloys 7. It is based on a bimodal distribution

a(x,T) dips around a stoichiometric composition Xs. As

of states for each constituent, the two state assumption following from an assumed reaction

an indicator for the metallic character, the Knight shift ~ h a s been used extensively (see s for a survey). In fact, a relation K~~]a which is a consequence of the pseudogap

/tA + ~B ~ A # B

(1)

modell'3 does not hold for liquid Te alloys on the minority side of the probe. In order to describe the transition

where the stoichiometry Xs=#/(#+v) is that of the li-

between metallic and nonmetallic state more precisely,

quid semiconductor. The three species (free A, free B;

the percolation model was applied 4. However, when it comes to discussing experimental data like for III-Te alloys inS, the Knight shift (or its high temperature limit) is itself taken as th___eemeasure of metallic character. *)BESSY GmbH, Lentzeallee 100, D-1000 Berlin 33 0022-3093/89/$03.50 @ Elsevier Science Publishers B.V. North-Holland

and associates A # B ) have concentrations nl, nz n3 respectively, determined by a law of mass action. The energetic parameters are the heat of formation of A # B , AH03<0; the corresponding entropy ~S03<0; and the interaction between the free A and B, WI~<0. (W13 and W23 are often negligible). The solution of the system of

829

K. Ott et al./Knight shifts and bonding

nonlinear equations for nl, n2, n3, and the determination of the parameters from experimental data AH(x), AS(x) have been discussed thoroughly in s. The necessary data AH(x), AS(x) exist for the case which will be discussed here 9, Sn-Te. Curves of nl(X,T), n2(x,T), n3(x,T) for alloys which may be considered typical are presented inS: There is a peak of n3 at Xs, while nl(x) and n2(x) are low and roughly constant on their respective minority sides, and rise from Xs to their pure sides. We thus consider the relative concentrations of free A and B, and of associates A#B v as known (here: free Sn, nl, free Te, n~, and SnTe, n~). For obtaining the hyperfine interaction parameters of, say A, in the two states free A and A#Bv, we have at present no a priori method. Phenomenologically we start from the usual expression for the Knight shift 87r

J~= --~ Xp fl < [ ¢(0)] ~> F

(2)

where Xp is the spin susceptibility of the conduction electrons, f] an atomic normalization volume, and <[¢(0)]2> F the density at the nuclear site of those electrons which are energetically at eF. We assume that a splitting of ~ i n t o two factors, one mainly determined by the surrounding (Xp), and the other mainly by the

This factor dips symmetrically around Xs (where n,(xs)~0~n2(xs)). The quantity which describes the effective transfer of spin polarization from e=e F to the nucleus of interest, Ff~ in eq. (2), will however depend decisively on whether the atom is free or associated (i.e. left hand side or right hand side of eq. (1)). In the bound state those occupied energy levels which derived from the atoms A or B, and which used to be near eF in the liquid metal, have moved far below eF. It appears reasonable to assume therefore that the local density of states is strongly reduced, f]F~0 for A#B v. On the other hand, we use the metallic values of f]<[¢(0)[2> F for the left hand side of eq. (1). This completes the assumptions. For a full presentation of the ansatz sketched here, see11. Here we shall concentrate on an application to the liquid Sn-Te system. It shows moderate energetic effects 9, and also a moderate development of liquid semiconductor properties; for a, see 12. It has been discussed using a simple thermodynamic scheme in12. When the quasichemical ansatz is applied, without approximations, the interaction parameters obtain the following

values

(at

T=ll00K):

AHOSnTe=-55

kJ/mole, AS0SnTe=-12.6 J/mole/K, WSn_Te=-3.4

state of the NMR probe atom < [ ¢(0) [ 2>F, is basically correct even in the much more complicated situation of a liquid semiconductor, where there are certainly major corrections to eq. (2). ~, eq. (2), has now to be averaged over the states on both sides of eq. (1). In order to proceed practically, we assume that the spin susceptibility will follow essentially a nearly free electron behaviour, electrons being contributed only by

kJ/mole, Wsn_SnTe=19 k J/mole, WTe_SnTe=-10 k J/mole. The degree of association which is defined as (#+v)n3/((#+v)n3+nl+n2) reaches 0.9 in Sn-Te which expresses the moderate bonding referred to above. We have recently performed a measurement of ~ T e ) in liquid Snx-xTex, using the TDPAD-technique (see13). It allows one to measure hyperfine interactions at vanishingly low concentrations, like ~ T e ) at

the "free" species Zi, but volume by all three species

X=XTe<10-s. SnCl~ melt has been used as the reference setting ~ T e ) = 0 for it. The data, together with J~Te)

(Vi). Equivalent assumptions of compound formation in liquid alloys (but no quantitative calculations) are generally made in the discussion of Mott's g-factor (see e.g. 10). Then 2

3

i=l

i=1

xp~(z niZi/r~ nlVi)lp

(3)

at x = l from 14'15, are shown in fig.1. It is seen that J~Te) ~hows an asymmetric shape around Xs=0.5, not recovering on the Sn-rich side although liquid Sn is certainly a more metallic system than liquid Te (at 1100 K). This is, to our knowledge, the first case where the Knight shift of the electronegative partner has been followed far into its minority region.

830

K. O t t e t al./Knight shifts and bonding

In order to carry the analysis on quantitatively, we calculate )~p from eq.(3) using Zsn=4 and ZTe=6; (a choice of ZTe=2 as in ~2 will not change the general picture). Atomic volumes are used for V1, V2, and a volume reduction V3=(VI+V2)'0.7 is taken into account (seelS). The metallic value of f~F is adapted to the experimental ~ T e ) for x=l, T=ll00 K of Warren 14. For the right hand side state of eq.(1), the approximation 12< [ ¢(0)[ 2>FU0 leads to jd=0. 0.9

ation has been completed recently, covering successfully some 20 liquid metallic alloys 8. Magnetic susceptibility has been discussed by starting from the quasichemical model inlS. - Work is in progress on other liquid semiconductors and on the magnetic susceptibility.

This work is supported by Bundesministerium for Forschung und Technologie.

0.0

0.4 ~"

"~" 0,6

0.0

~ 0,0 Sn

0,2

0,4.

0,6

0.8

Q.O ;.,0 Te

Figure 1 Knight shifts Jgin liquid Snl-xTex at ll00K. ~ T e ) : right hand scale and full squares. Experimental points from this work, point at x = l from~4; curve is calculated from the model. Left hand scale is the Sn Knight shift, the curve is the calculated prediction for ~ S n ) , using the value at x=9 from is. For thermodynamic parameters see the text. The calculated curve for ~ T e ) is really asymmetric, this asymmetry being caused by the low values of n2 on the Sn-rich side (Te is rarely in the free state where it is the minority) rigA. A mirror like curve is predicted

for ~(Sn). The scheme sketched here has been applied alsoU to the Knight shifts in liquid Cu-Te where Warren has pointed to the asymmetry between Cu and Te on the Te rich side 3, and to 17 liquid Au-Cs. In both cases, the thermodynamic model, together with the assumptions for the hyperfine parameters as presented here, give a good explanation of the Knight shift data. In both cases, the Knight shift of the electropositive partner stays low on its minority side. We mention here that a similar discussion for the quadrupolar part of nuclear spinrelax-

References 1. N.F. Mort and E.A. Davies, Electronic Processes in Non-Crystalline Materials (Clarendon Press, Oxford, 1971) 2. M. Cutler, Liquid Semiconductors (Academic Press, New York, 1971) 3. W.W. Warren, Conf. Prop. Liq. Met., Taylor & Francis, London, (1973) p. 395 4. M.H. Cohen and J. Jortner, Phys. Rev. B 13 (1976) 5255 5. Y. Tsuchiya, S. Takeda, S. Tamaki, E.F.W. Seymour, Sol. State Phys, 15 (1982) 2561 and 6497 6. R. Dupree, D.J. Kirby, W. Freyland, W.W. Warren, J. de Phys, 41 (1980) C8-16 7. F. Sommer, Z. Metallkunde, 73, (1982) 72 and 77, A.B. Bhatia, W.H. Hargrove, Phys. Rev. B10 (1974) 3186 E.A. Guggenheim, Mixtures (Clarendon Press, Oxford 1952) 8. K. Ott, M.A. Haghani, C.A. Panlick, D. Quitmann, Progress in NMR Spectroscopy, 21 (1989) 203 9. Y. Nakamura, S. Himuro, M. Shimoji, Ber. Buns. Phys. Chem., 84 (1980) 240 10. W.W. Warren, J. Non--cryst. Sol. 8-10 (1972) 241 11. K. Ott, M. Diirrw~ichter, M.A. Haghani, B. Sauer, D. Quitmann, Europhys. Lett., in the press 12. S. Takeda, T. Akasofu, Y. Tsuchiya, S. Tamaki, J. Phys. F 13 (1983) 109 13. G. Schatz und A. Weidinger, Nukleare FestkSrperphysik (Teubner, Stuttgart 1985) 14. W.W. Warren, Phys. Rev. B.__66,(1972) 2522 15. G.C. Carter, L.H. Bennett, D.J. Kahan, Metallic Shifts in NMR, Prog. Mat. Sci. (Pergamon Press 1977) 16. V.M. Glazov, S.N. Chizhevskaja, N.N. Glagoleva, Liquid Semiconductors (Plenum Press, New York 1969) 17. K. Ott, M. Diirrwgchter, M.A. Haghani, D. Quitmann, Int. Conf. Liq. and Am. Metals 1989, J. Non-Cryst. Sol. in the press 18. P. Terzieff, K.L. Komarek, E. Wachtel, J. Phys F. 16, (1971) 1071