Liquid Te and its alloys

Journal of Non-Crystalline Solids 35 & 36 (1980) 1269-1275 ©North-Holland Publishing Company

LIQUID Te AND ITS ALLOYS J.E. Enderby and M. Gay H.H. Wills Physics Laboratory U n i v e r s i t y of B r i s t o l Royal Fort Tyndall Avenue B r i s t o l BS8 ITL U.K. Liquid Te is a l i q u i d whose e l e c t r i c a l properties are b o r d e r l i n e between m e t a l l i c and semiconducting. This f a c t is r e f l e c t e d in the c h a r a c t e r i s t i c form o f the r a d i a l d i s t r i b u t i o n function g ( r ) , f o r l i q u i d Te. When i m p u r i t i e s are added, two main types of change have been observed. Ni i m p u r i t i e s on the one hand r a p i d l y convert l i q u i d Te i n t o a metal, w h i l e Ag, Cu and Se enhance the semiconducting p r o p e r t i e s . ~ v e c a r r i e d out a series o f s t r u c t u r a l and ~ctronic measurements on a wide range of l i q u i d Te a l l o y s . In p a r t i c u l a r , the technique o f neutron d i f f r a c t i o n combined with i s o t o p i c s u b s t i t u t i o n has enabled us to f o l l o w the s t r u c t u r a l changes which occur in the l i q u i d f o r several systems. We shall explore the c o r r e l a t i o n between the changes in s t r u c t u r e and e l e c t r o n i c p r o p e r t i e s and show how the local bonding and conformations are c r u c i a l to a proper understanding of l i q u i d semiconductors. INTRODUCTION I t has long been recognised t h a t l i q u i d Te occupies a unique p o s i t i o n in discussions of the e l e c t r i c a l

properties o f l i q u i d conductors.

The e l e c t r i c a l

conductiv-

i ty (~), Hall c o e f f i c i e n t (R) and t h e r m o e l e c t r i c power (S), are beyond the l i m i t of what can be explained on the nearly free e l e c t r o n (NFE) theory but are only j u s t beyond.

Doubtless a theory based on pseudopotentials could be made to f i t

some of the data but i t

is doubtful whether any real physical i n s i g h t would be

gained from t h i s e x e r c i s e .

The essential p o i n t is t h a t s t r u c t u r a l l y l i q u i d Te is

c l e a r l y d i f f e r e n t from n e a r l y free e l e c t r o n metals, even those with comparatively short mean free paths.

We begin by reviewing the current status of the s t r u c t u r e

of l i q u i d Te by reference to the neutron d i f f r a c t i o n

studies made by the B r i s t o l

and Saclay groups. THE STRUCTURE OF LIQUID Te A full

account of the neutron method, the analysis of and c o r r e c t i o n s to the

experimental data and the estimation of random, systematic and computational errors has been given by North, Enderby and E g e l s t a f f (1968). which can be derived from the d i f f r a c t i o n the r a d i a l d i s t r i b u t i v e

The two q u a n t i t i e s

data are the s t r u c t u r e f a c t o r S(Q) and

function g ( r ) , defined and r e l a t e d by

1269

1270

J.E. Enderby, M. Gay / Liquid Te and its Alloys

1

( i ~ . ~ . ) 12>= 1 + - ~ ! L f ( g ( r ) - l )

S(Q) : ~ < l ~ e x p

r sin Qr dr

...(I)

where N is the number of atoms in the volume V, ~I is the position of the i

th

atom and ~ is a wave vector. A l t e r n a t i v e l y , the r a d i a l d i s t r i b u t i o n function can be w r i t t e n g(r)

=

1 + ~ 1 2~ nr

I ~o [ S ( Q ) - I ]

Q sin QrdQ

...(2)

where n is the number of atoms per u n i t volume.

For reasons which w i l l become

clear below, in our work a second radial d i s t r i b u t i o n function gw(r) is calculated f o r l i q u i d Te through 1 gw(r) = 1 + ~ [ o

IS(Q)-1] W(Q)Q sin QrdQ

where W(Q), a "window" function, is defined by W(Q)

=

½ (I + cos ~m)Q < Qm

=OQ~Q m and Qm is the maximum value of Q f o r which data were taken. The form of g(r) is dominated by the Q-space data beyond 2A-I (North, Enderby and E g e l s t a f f (1968)) so that the uncertainty in g(r) from c a l i b r a t i o n errors can be calculated d i r e c t l y .

The random e r r o r s , though generally small at any given value

of Q, give rise to cumulative errors in the transform which appear as increasingly v i o l e n t o s c i l l a t i o n s in g(r) as r tends to zero. There i s , however, a f u r t h e r major source of e r r o r which is p a r t i c u l a r l y severe f o r the l i q u i d chalcogens, namely, the need to truncate the integral in equation 2 at Qm (12]~-I in our experiments and somewhat less in those by Tourand and Breuil(1970)) Truncation errors w i l l depend on the damping of S(Q) at high Q.

To quantify this

e f f e c t l e t us consider the value of [S(Q)-I] at successive extrema f o r a l i q u i d metal and the three chalcogens Te, Se and S.

The data show c l e a r l y that the

approximation [S(Q)-I] = O for Q ~ 12A-I is reasonable f o r l i q u i d metals, less reasonable f o r l i q u i d Te and not at a l l s a t i s f a c t o r y f o r l i q u i d Se and S.

We

must therefore expect spurious structure in g(r) f o r a l l three chalcogens. illustration

we r e f e r to an e a r l i e r paper

(Hawker, et a l . (1975))

As an

in which the

r e s u l t of i n v e r t i n g data f o r which Qm : 12A-I f o r l i q u i d Se at 230°C was described. The problem of deciding which of the many features in g(r) were due to truncation errors and which represented real structures was c l e a r l y apparent. I d e a l l y , measurements should be continued out to much higher values of Q using, f o r example, a LINAC f a c i l i t y .

Although experiments along these lines are in

progress (see e s p e c i a l l y the work of Misawa and Suzuki (1977)), i t w i l l s t i l l some time before r e l i a b l e results are available f o r a l l three Chalcogens.

be

In the

1271

J.E. Enderbg, M. Gay / Liquid Te and its Alloys

meantime, we have adopted a scheme which enables those features in g(r) which are associated with true s t r u c t u r e to be r a p i d l y i d e n t i f i e d . modified by the window function and transformed.

F i r s t , the data are

A comparison of g(r) with gw(r)

reveals that c e r t a i n features do not survive the a p p l i c a t i o n of W(Q).

This

strongly suggests that they arise because of premature truncation and we therefore eliminate them in g ( r ) , transform back to S(Q) and i t e r a t e this l a s t step u n t i l the experimental data are reproduced.

The idea of extending s t r u c t u r a l data

beyond the measured l i m i t by repeated Fourier inversions is a well documented one (see, f o r example, Kaplow et a l . (1966)) and is a technique widely used in other branches of experimental science. first

Our method of using a window function in the

step of the process f a c i l i t a t e s

rapid convergence.

For l i q u i d Se, this

approach can be tested since high Q data due to Misawa and Suzuki (1977) are a v a i l a b l e ; the comparison shows that our numerical methods do in f a c t c o r r e c t l y i s o l a t e those features in g(r) which are spurious.

Accordingly, we present in

f i g u r e 1 the radial d i s t r i b u t i o n functions f o r l i q u i d Te calculated by t h i s method -1.6 1,4 1.8

1.2

1.6

1.0 g(r) (800"O 0.8

1.4 1.2 g(r) 1.0 (500'C) 08

O-& 0-2

06 0 0.4 0.2 0

i

~

I

,

I

I

I

J

r(A) Fig. 1:

The radial d i s t r i b u t i o n f o r l i q u i d Te at 500°C and 800°C

The results of the inverse transformation to S(Q) compare s a t i s f a c t o r i l y with the experimental S(Q) and i t is not necessary to invoke features in g(r) additional to those shown in order to reproduce the measured S(Q).

Our conclusions therefore

d i f f e r from those of Tourand and Breuil (1970) who argue that the three peaks found at 3.01, 3.82 and 4.52 A in g(r) a l l represent real s t r u c t u r e . We consider

1272

J.E. Enderby, M. Gay / Liquid Te and its Alloys

i t dangerous to assume that truncation errors are unimportant in the region of 4A f o r l i q u i d Te.

A numerical inversion shows that S(Q), consistent with the data of

Tourand and B r e u i l , can be regenerated from a g(r) in which the only peaks resolved are at 3.O1 and 4.52.

We conclude that neither the S(Q) data reported here, nor

those due to Tourand and Breuil support the existence of a c l e a r l y defined peak at 3.82A. To resolve t h i s discrepancy requires S(Q) data to be taken out to at l e a s t 20A-I but a l l the evidence points against the existence of a well defined peak at 3.82A. This means that the disorder in l i q u i d Te is greater than is usually supposed and that the i d e n t i f i c a t i o n of bond numbers with f i r s t

shell coordination numbers

(which we find at be 3 in agreement with the values quoted by Tourand (1975)) may not be acceptable.

The disorder is c e r t a i n l y s u f f i c i e n t to produce a pseudogap in

the density of states N(E) of the sort described by Cutler (1977)but the existence of mixed m e t a l l i c and covalent bonding implied by our g(r) makes i t impossible to say a p r i o r i whether EF is in a region of ~ (Cabare and F r i e d e l , 1971).

< 0 (Cutler, 1977) or ~ > 0

The evidence from e l e c t r i c a l measurements favour the

former and in our view is not inconsistent with the s t r u c t u r a l studies h i t h e r t o reported. TELLURIUM BASED ALLOYS Liquid alloys in which the pure components are m e t a l l i c (e.g. Mg-Bi, Cs-Au or Li-Pb) show semiconducting behaviour i f t h e i r e l e c t r o n e g a t i v i t y difference is appreciable and a minimum in the c o n d u c t i v i t y at (chemical) stoichiometry.

For

these systems a model based on ionic bonding seems capable of explaining most of the observations; t h i s model, f i r s t

e x p l i c i t l y proposed by Enderby (1973), has been

more f u l l y j u s t i f i e d by Roth (1977) and seems to have gained general acceptance (Robertson, 1979).

We therefore have studied the s t r u c t u r a l and e l e c t r i c a l proper-

t i e s of a range of Te based alloys where the bonding is l i k e l y to be d i f f e r e n t and w i l l r e f l e c t the nature of l i q u i d Te i t s e l f . Structural studies based on the method of i s o t o p i c s u b s t i t u t i o n have been completed by our group f o r CuTe and Cu2Te and Ag2Te and the data have been reported elsewhere (Enderby, 1978).

Four conclusions are worthy of note:

( i ) the data

f o r CuTe and Cu2Te rule out the existence of large scale f l u c t u a t i o n s of the sort proposed by Cohen and Sac (1972).

(ii)

the data f o r Ag2Te are s i m i l a r to those

f o r Cu2Te and do not contain any of the c h a r a c t e r i s t i c s established f o r 2-I i o n i c melts (Enderby and Neilson, 1979).

( i i i ) there is no evidence

f o r d i s t i n c t Cu2Te

molecules of l i f e t i m e long enough to be s t r u c t u r a l l y s i g n i f i c a n t . ( i v ) Ag2Te appears to have rather more of a covalent nature than CuTe, as judged by the form of gAgTe(r).

We therefore conclude that a homogeneous network structure

]273

J.E. Enderby, M. Gay / Liquid Te and its Alloys

a r i s i n g from mixed bonds is the proper s t r u c t u r a l d e s c r i p t i o n f o r the s t o i c h i o m e t r i c composition.

A purely i o n i c d e s c r i p t i o n is i n c o r r e c t , and we now discuss each of

the systems separately. ( i ) Ag2Te This l i q u i d is characterised by an e l e c t r o n e g a t i v i t y difference which is s u f f i c i e n t l y high to give rise to local bonding, but not high enough to produce ions. The chemistry of Ag probably excludes complexing so that the e f f e c t i v e i o n i c i t y need not be corrected in the way described by Cutler (1977).

A well defined

pseudogap is to be expected because of the low coordination number (4 according to our experiments) associated with bonding which is somewhat covalent in character. (ii)

Cu2Te and CuTe

The form of gcuTe(r) shows c l e a r l y that than Ag2Te.

CuTe

is less molecular in character

A suggestion by Cutler (1977) that the tendency of Cu to form

complexes a r i s i n g from i t s chemistry could increase the e f f e c t i v e i o n i c i t y from 0.02 to ~ 0 . 5 , studies.

and would lead to the higher coordination number found in our

We have shown that the structure factors f o r l i q u i d Cu2Te can be well

reproduced by a q u a s i - l a t t i c e m o d e l based on the NiAs structure. i n c i d e n t a l l y , that l i q u i d TI2Te is

I t appears,

s t r u c t u r a l l y intermediate between Ag2Te and

Cu2Te and this fact is in accord with the observed e l e c t r i c a l properties. In order to explore f u l l y the connection between s t r u c t u r e , bonding and e l e c t r o n i c p r o p e r t i e s , we have carried out a new series of experiments on a range of Ni-Te alloys.

Ni is a favourable case f o r neutrons, because by using an appropriate

mixture of 60Ni and 62Ni, the coherent s c a t t e r i n g length of Ni can be made to be zero.

I t is therefore possible to i n v e s t i g a t e gTeTe(r) d i r e c t l y .

Furthermore,

the tendency f o r Ni to be coordinated by six atoms or molecules is well known in a v a r i e t y of s o l i d state compounds.

Thus, as Ni is added to Te, a substantial

change in the structure of Te might be expected.

This is indeed the case as the

example in f i g u r e 2 shows and is accompanied by a rapid decrease in r e s i s t i v i t y ( f i g u r e 3). The essential clue seems to be that the a b i l i t y of nickel ions to increase the coordination number reinforces the m e t a l l i c character of l i q u i d Te.

The e a r l i e r

work on l i q u i d NiTe 2 quoted in the book by Mott and Davis (1971) grossly underestimated the c o n d u c t i v i t y . HoWever, both our group (Newport, Howe and Enderby, (1979)) and Takeda, e t a l . (1976) agree in the observation that Ni in l i q u i d Te g r e a t l y enhances the c o n d u c t i v i t y .

We therefore conclude that the mixed bond

picture of l i q u i d Te forms an e x c e l l e n t s t a r t i n g point f o r describing the e f f e c t of impurities.

The t r a n s i t i o n to m e t a l l i c regime or one of a more covalent

character depends on the local conformation which in turn can best be understood from a molecular bonding point of view (Cutler (1977), Robertson (1979))

1274

J.E. Enderby, M. Gay / Liquid Te and its Alloys

tE g ( r ) 1~ ~C OB O@ 04 O; OC

P

................................ i~ 1

2

3

4

5

6

7

I Present work

(Liquidus Temperature)

Present work

(I150°C)

Perron

4O0 Ni

9

Fig. 2: TeTe radial Distribution Function in NiTe2

(~-~ cm)

5OO

8

r(X)

(1967)

I

I

I

I

20

30

40

80

3O0

20O

Fig. 3:

Resitivity of liquid Ni-Te

Te

J.E. Enderby, M. Gag / Liquid Te and its Alloys

1275

REFERENCES (I)

Cabane, B. and Friedel, J.,

J. de Physique, 32 (1971) 73.

(2)

Cohen, M.H. and Sac, J.,

(3)

Cutler, M., Liquid Semiconductors (Academic Press, New York, 1977).

(4)

Enderby, J.E., Band Structure Spectroscopy of Metals and Alloys (Academic Press, London, 1973) p.609.

(5)

Enderby, J.E., The Metal Non-Metal Transition in Disordered Systems (SUSSP, 1978) p. 425.

(6)

Enderby, J.E. and Neilson, G.W., Advances in Physics (in press).

(7)

Hawker, I . , Howe, R.A. and Enderby, J.Eo, Proc. Liquid Metals Conf., Mexico (1975).

(8)

Kaplow, R., Strong, S.L. and Averbach, B.L., Phys. Rev. 138 (1965) A1336.

(9)

Misawa, M. and Suzuki, K., Trans. J.I.M. 18 (1977) 427.

Jnl. Non-Crystalline Solids, I0 (1972) 696.

(I0) Mott, N.F. and Davis, E.A., Electronic Processes in Non-Crystalline Materials (Clarendon Press, Oxford, 1971). ( I I ) Newport, R., Howe, R.A. and Enderby, J.E. (to be published). (12) North, D.M., Enderby, J.E. and Egelstaff, P.A., (13) Robertson, J., (14) Roth, L.M.,

Phil. Mag. 39 (1979) 479-499.

Liquid Metals (Institute of Physics, London, 1977) p.206.

(15) Takeda, S., Ohno, S. and Tamaki, S. (16) Tourand, G.,

J. Phys. C. 1 (1968) 784.

J. Phys. Soc., Japan 40 (1976) 113.

Phys. Letts. A54 (1975) 209.

(17) Tourand, G. and Breuil, M.,

C.R. Acad. Sci. Paris B270 (1970).