Thermodynamics and kinetics of the quasibinary system Hg3 −3k In2kTe3—II. Investigations by electron microprobe measurements

J. Phys. Chem. Solids Vol. 49. No. Printed in Great Britain.

II,

pp.

1317-1327,

1988

$3.00 + 0.00 0022-3697188 0 1988 Pergamon Press plc

THERMODYNAMICS AND KINETICS OF THE QUASIBINARY SYSTEM Hg(, _ 3kJ In,,Te,-II. INVESTIGATIONS BY ELECTRON MICROPROBE MEASUREMENTS Institut

VOLKMAR LEUTE and HEINRICH MICHAEL SCHMIDTKE fiir Physikalische Chemie der Universitlt Miinster, Schlossplatz 4, D-4400 (Received

22 September

1987; accepted

in revised form

Miinster,

F.R.G.

19 April 1988)

Abstract-Measurements by means of an electron microprobe were used to investigate the reaction kinetics in the system Hg, _ r kjIn,, Te, The reactions were carried out between a HgIn, Te, -crystal as one reaction partner and a HgTe-crystal or a reactive gas phase containing Hg and Te as the other reaction partner. At temperatures T > 720 K only one reaction product with a continuously changing composition was formed. At lower temperatures a second reaction product in the form of a very thin layer could be detected. This product could be identified with the ordered p-phase (Hg,In,Te,). The cation interdiffusion coefficient in this layer is much lower than in the surrounding defect zincblende u-phase. To understand the diffusion mechanism, it must be considered that the structural vacancies in the ordered phases behave as interstitial sites, whereas in the cz-phase the association of these vacancies with the In-ions plays an

important part. Keywords: reactions.

Diffusion,

defect chemistry,

electron

microprobe

INTRODUCTION Quasibinary systems of II-VI and III-VI compounds are of interest because of the structural vacancies in their cation sublattice. The reaction kinetics depends on the concentration and on the degree of order of these vacancies. In a preceding paper [l] a phase diagram for the quasibinary system Hg,_,,,In,,Te, in the region 0
measurements,

phase

diagrams,

concentration dependence of coefficient should be expected.

solid state

the

interdiffusion

EXPERIMENTS The synthesis of the compounds HgTe, Hg, In,Te,, HgIn,Te, and In,Te,, and the conditions for growing crystals, were described in a previous paper [l]. Here we shall only give a description of the preparation of the reaction samples and of the conditions under which the reactions were carried out. Transport processes in solids are very sensitive to small variations in the defect concentrations. Therefore it is necessary to establish well-defined compositions for the reacting crystals by fixing their deviation from the stoichiometric composition. Compositions which can easily be reproduced are obtained by Te-saturation or by metal saturation of the crystals. The attempt to saturate In,Te, crystals with indium yields a new phase named a(I)-In,Te, [2], which shows a slightly higher indium content and a super structure which is completely different from the ordered structure of the Te-saturated a(II)-In,Te,. Reactions of In-saturated In,Te, crystals with Hg-saturated HgTe crystals leave the quasibinary section and yield reaction products such as InTe, which do not belong to the quasibinary section Hg,, _ 3kjIn, ,Te, Reactions with Te-saturated crystals, however, proceed along the quasibinary section. Moreover, chalcogen-saturated mixtures of II-VI and III-VI compounds have a maximum content of structural vacancies, and as we know from investi-

1318

VOLKMAR LEUTE

and

HEINRICH MICHAEL SCHMIDTKE

gations on Ga, Se, [3], the process of ordering of these vacancies in the cation sublattice is favoured by chalcogen saturation. Therefore. all reactions described in this paper are carried out with Te-saturated crystals.

Methods of preparation Te-saturation of a telluride crystal is carried out by annealing the crystal in an evacuated sealed quartz ampoule together with a fine powdered mixture of elementary tellurium and the relevant compound. It is difficult to react HgTe crystals with In,Te, or HgIn,Te, crystals because the usual methods of pressing the crystals together cannot be applied [4] without producing cracks in the rather brittle In,Te, or HgIn,Te, crystals. These cracks would create high diffusivity paths and would lead to porous reaction layers, which cannot be polished. Therefore, HgIn,Te, crystals were reacted with a vapour phase containing Hg and Te. Small crystal samples of about 3 x 3 x 2 mm3 are obtained by cleaving the grown crystal bars. The cleavage faces of these crystal pieces are smooth enough to be used without being further polished. The reactive vapour phase consists of a powdered solid solution Hgo _ 1kjInz,Te3 with k = 0.025 and of some Te in excess, which was added in order to maintain the Te-saturation during the reaction. The reaction was carried out by annealing the Tesaturated HgIn,Te, crystal together with the vapour source in an evacuated sealed quartz ampoule. The annealing temperatures ranged between 600 and 950 K. and the corresponding reaction times between 6 weeks and 1 h depending on temperature (Table 1). After the annealing procedure, the ampoules are quenched in ice water. The annealed crystals, together with small crystals of HgTe and In,Te, as standards, are soldered on a small brass cube by use of a silver suspension. They are then embedded using an electrically conductive synthetic resin. The resulting bars are ground and polished rectangularly to the surface of the annealed crystal. The composition profile in the diffusion zone is then investigated by an electron microprobe.

Measurements probe

by means of an electron micro-

The X-ray intensities, ZFmp’e,(i = In or Hg) which are measured by the electron microprobe in the solid solution regions or in the reaction products, are related to the X-ray intensities, Iytandard, which are measured in the standard substances HgTe or In,Te, (Fig. 1). The relative intensity R, is described as a function of the mass fraction M; of the corresponding binary component j. R,=Z:“mp”/l~~“d”‘d=A,.~//[l The calibration

coefficients

-(l

-AJ.w,].

(I)

Aj are determined

experi-

mentally. The so-called line scan profiles are obtained by measuring the X-ray intensities of In and Hg while shifting the sample relative to the stationary electron beam with an average velocity between 1 and 10 pm min-’ For all measurements the acceleration voltage for the electron beam was W = 25 kV. the absorbed electron current I(abs) E 4 nA and the beam diameter d Y 1 pm. In Fig. 1 two characteristic profiles for reactions between a HgIn,Te,-crystal and a reactive HgTecontaining gas phase are shown. Both profiles demonstrate that a region of solid solution is formed by exchange of In from the crystal against Hg from the gas phase and that a distinct phase boundary between the chalcopyrite phase HgIn,Te, and the solid solution region exists. At high temperatures (800 K) the metal concentrations change continuously in the region between this phase boundary and the crystal surface, whereas for temperatures T I 700 K an additional thin region with steep changing metal concentrations is observed. This region is situated in the midst of the solid solution region, giving the impression of a miscibility gap which is caused by a spinodal decomposition. For temperatures T 5 700 K the measured profiles extend from the composition of HgIn,Te,, down to k a0 at the crystal surface. If thermodynamic equilibrium is established between the powder mixture and the reactive vapour, as well as between the vapour phase and the crystal surface, the concentration at the crystal surface must be equal to the concentration k = 0.025 of the powder mixture. Because of the exchange of In and Hg across the crystal surface during the reaction, the overall composition of the polycrystalline source substance, however, is shifted somewhat to a lower

Table 1. Reaction conditions for the samples from which the phase boundary concentrations, plotted in Fig. 3. are determined Temperature ‘UK) 600 625 637 650 662 675 687 700 712 719 725 750 775 800 825 850 875 900 925 950

Annealing time t(h) 350.0 350.0 481.0 350.0 98.0 25.0 69.0 42.5 159.0 165.0 7.2 18.0 2.0 1.0 5.0 16.0 4.5 1.0 1.25 4.0

494.0 1004.0 470.0 980.0 621.0 470.0 930.0 192.0 358.0 99.0 235.0 330.0 98.0 59.5 41.5 45.0 6.5 2.0 25.0 22.25 5.0 2.0

90.0 91.0 14.0 4.0

3.75

168.0 234.0 161.5 142.0 24.5 16.0

46.0 32.0

92.5 50.5

Thermodynamics and kinetics

1319

64

(b)

Fig. 1. X-ray intensity profiles for Hg and In of samples which have been annealed at (a) 800 K for 32 h, (b) 700 K for 234 h.

HgTe-content, causing a decreasing equilibrium partial pressure of Hg and thus a slowly decreasing HgTe-mole fraction at the crystal surface. At temperatures T 2 800K the HgTe-concentration at the crystal surface is distinctly smaller than the expected equilibrium value. As the interdiffusion of In and Hg in the reacting crystal increases rather fast with increasing temperature, we suppose that for

T 2 800 K the equilibrium between the vapour source and crystal surface is no longer established and that the transport through the gas phase becomes the rate determining step. For each sample listed in Table 1 a series of at least five line scan profiles along different traces covering the whole reaction zone was measured. These profiles show slight differences because of crystal in-

1320

VOLKMAR

LEUTE and HEINRICH MICHAEL SCHMIDTKE

homogeneities such as dislocations, micropores or low angle grain boundaries. It it is known from the phase diagram that a high intensity gradient in a profile corresponds to a phase boundary, the X-ray intensities for both sides of this boundary are determined by positioning the discontinuity onto the site of maximum slope and by extrapolating the profiles on both sides of this discontinuity. Using a computer program, the smoothed intensity profiles are transformed into mass fraction profiles w(z) using the calibration function (1) and subsequently into mole fraction profiles k(z). The site of the phase boundary between the HgIn,Te, phase and the HgTe-rich a-phase is chosen as an arbitrary origin for the space coordinate Z, because in the profiles of all samples this phase boundary can be exactly localized by the discontinuity in the course of the absorbed electron current. The computer plots in Fig. 2(ac) show the In,Te, mole fraction profiles of three samples, which were annealed at 800, 750 and 700 K. Each of these figures is a superposition of several profiles k(z), which were determined at one and the same sample. From these diagrams the boundary concentrations at the interfaces within the reaction zone can be determined to within an accuracy of k = f0.02. In Fig. 3 these boundary concentrations are plotted as functions of the temperature. For the temperature region 720 K > T > 630 K two interfaces in the reaction zone have been detected, whereas outside this region only one interface could be found.

Growth kinetics The kinetic behaviour of the reaction between a HgIn,Te,-crystal and a reactive HgTe-containing gas phase was investigated by measuring the thickness I, of the whole reaction layer between the crystal surface on the one hand and the phase boundary between the HgIn,Te, chalcopyrite phase and the HgTe-rich a-phase on the other hand. These measurements were carried out for different annealing times in the region 650 K I T I 800 K. In Fig. 4(a) the square of the layer thickness is plotted vs the annealing time for the high temperature region (I), in which only one phase boundary could be detected. Figure 4(b) shows an equivalent plot for the low temperature region (II), in which the additional interface within the defect zincblende phase could be detected by the electron microprobe. As mentioned above, even in the low temperature region the composition at the crystal surface is not really independent of time and therefore one may assume that the ratio g = 1:/t is a function of time. The growth, however, obeys a parabolic rate law as long as the temperatures are not higher than 800 K. Thus, local thermodynamic equilibrium is established at the phase boundaries at least in this temperature region. In Fig. 5 the growth constant g is plotted logarithmically vs the reciprocal temperature. Obviously the slope of this curve increases with decreasing

temperature. The course of this function can be approximated by two straight lines: one for the higher temperature region (I), corresponding to Fig. 4(a), and the other for the lower temperature region (II), corresponding to Fig. 4(b). In region (I) all phase boundary concentrations depend only slightly on temperature yielding nearly constant boundary conditions. For temperatures lower than 720 K (II), however, the miscibility gap within the cc-phase increases perceptibly with decreasing temperatures. Therefore the linear approximation is much less justified for region (II) than for region (I). The following activation energies were determined from the Arrhenius plots: EL= E”=

DISCUSSION

144kJmol-‘; 175 kJmol_‘.

OF THE EXPERIMENTAL

RESULTS

Comparison with earlier measurements In a preceding paper [I] the phase diagram of the quasibinary system Hgo _ 3k)In,,Te, for the region 0 < k < 0.75 was determined from X-ray diffraction measurements. The full lines in Fig. 6 correspond to these measurements and the full circles to the microprobe results reported here. Comparing these results one can conclude that the single phase boundary, which was detected by microprobe in the samples for T > 720 K and T < 620 K, corresponds to the phase boundary between the defect zincblende phase, a, and the chalcopyrite phase, y. For the temperature region 720 K > T > 630 K the miscibility gap, which separates two regions of one and the same a-phase, could also be detected by the microprobe measurements. But the /?-phase which was established from X-ray diffraction measurements [l], could not be unambiguously identified by electron microprobe. The layer, which corresponds to the steep part of the cation profiles, is too thin, even at long reaction times, to allow a decision between the case of a real product layer of phase 8, bordered by two phase boundaries, and the case of a single phase boundary which is blurred as a result of the folding of the boundary with the electron beam. If, however, the product phase /l is really formed during the reaction, the growth rate of this layer will have to be very small compared with the adjacent regions of the solid solution a. In order to test if such a behaviour can be explained by suitable interdiffusion coefficients, we shall try to reproduce the observed concentration profiles by calculation.

Calculation of diffusion projiles The cation transport occurring during a reaction in the quasibinary system Hgo _ 3k)In,,Te, can be treated as an interdiffusion process of Hg and In. This interdiffusion is described generally by a composition

Thermodynamics

1.0 J A I 1 V17 I / 0.8~

1321

and kinetics

800

HGIN2TEC+HGTE_GflS

16

K

HI

x g-

0.6:

L g IL 0.c: w d = 0.2: I I I Il 0.0 40

-20

I

<---A 1 I I ;

I 80

I 60

I 40

I 20

I 0

SPFlCE COORDINFITE (4

F I I I I I 100 120 1’+0 160 180 200 Z /

(10-6

MI

----->

80

100

120

lC0

( 1 0-6

Ml

---->

1 .0

0.8

Y 5- 0.6 L k? Ll_ 0.c W d

0.2

= I I I I l

0.0 40

-20 <----

A I

0

20

SPFKE

40

60

COORD I NFITE Z / @)

160

1 .0

I j

0.8

x 5- 0.6 L z? L 0.L W d

0.2

= I I I I ’

0.0 -20

-10 <----

Fig. 2. Superposed

0

10

20

30

SPQCE COORDINQTE

Co, Z /

50

60 (10-6

70 Ml

80

90

----->

In,Te,-mole fractions profiles, k(z), as calculated from X-ray intensity profiles: (a) 8OOK, 16.0h; (b) 750K, 45.0h; (c) 7OOK. 98.0 h.

1322

VOLKMAR

.I000 I I I 950 I ’ 900 Y + 850 -

LEUTEand HEINRICHMICHAEL SCHMIDTICE

I

I

I

I

I

I

I

I

I

L

11

I 0

0 0 0 0 Cn @ m

: 800 2 $ 750 w

------

MOLE

FRACTION

K

r l-

-------->

Fig. 3. Boundary concentrations for several temperatures as calculated from mole fraction profiles for the set of samples listed in Table 1.

dependent diffusion coefficient d(k). At phase boundaries this diffusion coefficient changes discontinuously, except within a homogeneous phase. Nevertheless, a solid solution region can formally be subdivided into a series of slabs, si, with constant diffusion coefficients D, Provided that the boundary concentrations cl and c: of such a slab are independent of time, the differential equation &(z, t)/cYt = D,.d*c(z,

t)/az*

(2)

has the general solution: c(z, 1) = Ai + B,.erf[z/2,/(D;t)]

with Ai= {c:l.erf[zj/2.J(Di.t)]

- c;.erf[z:/2.,/(D;t)]}/N

(da)

Bi = [c; - c;]/N

(4b)

N =erf[zi/2.J(Di.t)]-

(4c)

erflz:‘/2.J(D;t)].

Since the concentrations within a solid solution must change continuously, the boundary concentrations of adjacent slabs, provided they belong to the same phase, must satisfy boundary conditions of the following type:

(3)

6

m ---

0.0

5’m

100 ANNEFILING TIME (4

1;0 T/H

2m0 ---->

0

100 ---

200

RNNEALING

300 TIME

600 T/H

----->

(b)

Fig. 4. Growth kinetics for the whole reaction zone. (a) For the high temperature region (725 K-800 K). (b) for the low temperature region (650 K-700 K).

500

1323

Thermodynamics and kinetics <-----

10-08

800 I

775 I

TEMPERFITURE 750 I

725 I

-

HIGH 800

_; VI N 5

10-09

T / K 675 I

TEMP.

REGION

K

< T <

Elll

\

=

I I I I I c ’

ICC

650 I

I

725

K

KJAIOL

5.10-‘0

\ L1 2

-----

700 I

.\

0.1 *.\ .\

2*‘0-‘0 10-10

2.‘ ****** LOW

TEMP.

700K Etlll

S-10-”

REGION


175

II .*'\

650K

;$

KJ/tlOL

?'\ *.

\

** 2.10-1’

I 1.25

I 1.30 _______

I 1.35 ,000

I I.60

I I.45

K , T

__.

I 1.55

I .50 >

Fig. 5. Temperature dependence of the growth constant g.

The concentrations at real phase boundaries are taken from the phase diagram (Fig. 6). Moreover at all boundaries, both between the same phase and between different phases, the flux of matter across these boundaries must run continuously, i.e. div (J) = 0:

If the reaction zone of the crystal is subdivided by this procedure into n regions there are (n - 1) boundary conditions of type (6). Using these stationary flux conditions together with eqns (3) and (4) a system of (n - 1) equations can be formulated, from which the positions of all interfaces for a given reaction time can be derived. For this purpose, of course, it must be required that the terms Ai and B, in eqn (3) are independent of time and position. This condition is only fulfilled if all interfaces are shifted during the reaction with a rate proportional to l/,/r. From the experimentally determined parabolic rate law (Fig. 4) it can be concluded that this condition is satisfied with a good approximation for temperatures T I 800 K. If for a set of n given diffusion coefficients the positions of (n - 1) interfaces have been determined by solving the equation system, the constants Ai and B, can be calculated using eqn (4). Subsequently the concentration profiles for each slab can be calculated using eqn (3). In Table 2 is listed the set of diffusion coefficients which was used to calculate the In, Te, -mole fraction profile for an annealing time of 32 h at a temperature of 800 K (Fig. 7). There is full accordance between

the calculated values and the profile which was derived from the X-ray intensities measured by means of an electron microprobe. Now a typical mole fraction profile for the low temperature region will be calculated. From X-ray diffraction measurements we know that at temperatures T < 720 K a new reaction product, called p-phase, should occur [l]. At the stoichiometric composition yHg,In,Te,, (k = 3/8), the structural vacancies v of this phase are strictly ordered. Between this phase and the surrounding a-phase, miscibility gaps of perceptible extension occur (Fig. 6). It should be assumed that these gaps are expressed by two steps in the X-ray intensity profiles. But in the profiles shown in Fig. l(b) these two steps cannot be resolved. Instead, there can be observed only a relatively unsharp step extending over a distance of a few pm. In order to calculate the mole fraction profile for T = 700 K from diffusion coefficients the miscibility gaps, shown in the phase diagram (Fig. 6), are taken as natural interfaces for a subdivision of the reaction zone into different slabs. The equilibrium concentrations at the phase boundaries in the phase diagram are used as boundary concentrations for these slabs. We know from the calculation of the profile for T = 800 K (Table 2) that the values for the interdiffusion coefficient in the chalcopyrite phase and in the HgTe-rich zincblende phase are nearly equal. The behaviour near the phase boundary, however, can only be adequately described if the interdiffusion coefficient on the zincblende side is distinctly smaller than on the chalcopyrite side. This would lead to a minimum of the interdiffusion coefficient near k x 0.5. Therefore, as a first approximation, the interdiffusion coefficient for the In,Te,rich region of the a-phase was taken as 40% of the

mole

hvction k ____*

Fig. 6. The phase diagram of the system Hgo _ )kJIn,, Te, for the range 0 I k 5 0.75 as determined in [I] including the phase boundary concentrations from Fig. 3.

1324

VOLKMAR

LEUTEand HEINRICHMICHAELSCHMIDTKE

Table 2. Boundary mole fractions and diffusion coefficients for the slabs, into which the reaction zone is subdivided (T = 800 K, r =32h) Interdiffusion coefficient 6 (cm* s-‘)

Mole fraction 0.130~k 0.285 s k 0.393 I k 0.473 s k 0.740 I k

1.95. 1o-9 1.95’ 1o-9 1.70. 1o-9 1.00.10-9 2.00. 1o-9

~0.285 I; 0.393 5 0.473 5 0.529 5 0.750

values in the other slabs [Table 3 (l)]. A mole fraction profile, which was calculated under these conditions (Fig. 8), revealed that the thickness of phase B should grow with a rate comparable to the In,Te,-rich region of the a-phase, whereas in the experimental profiles [Fig. l(b)] the b-phase cannot be found. Lowering the value of the interdiffusion coefficient in the slab representing the b-phase, the profile in this part of the reaction zone gets steeper and steeper. If the interdiffusion coefficient for this region is decreased to 5% of the value in the adjacent HgTe-rich a-phase [Table 3 (2)], the profile (Fig. 8) gets so steep that a clear distinction between the b-phase and the adjacent miscibility gaps is no longer possible. Thus the experimental findings can be explained by a very low growth rate of the ordered j-phase.

Considerations concerning the difusion anism

mech -

The a-phase. The a-phase is a solid solution of HgTe and In,Te, which crystallizes in the so-called defect zincblende lattice. If In,Te, is alloyed to HgTe, one vacancy yM, will be created for every two In-atoms being incorporated into the zincblende lattice:

as defects in the cation sublattice. As the pattern of the X-ray reflections for the a-phase is the same as for the zincblende phase, it could be supposed that the Hg-ions, the In-ions, and the vacancies are statistically distributed over the cation sublattice. But thermodynamic investigations in similar systems, as for example in CdTe/Ga,Te, [5], have shown that specific interactions between the structure elements must be considered in order to explain the real thermodynamic behaviour of such solid solutions. These interactions will result in a deviation from the ideal statistical distribution of vacancies. In the frame of a defect model, deviations from the ideal thermodynamic behaviour at high defect concentrations can be attributed to an association of defects. Indium, substitutionally incorporated into HgTe, will have some positive effective charge and the vacancies in the metal sublattice some negative effective charge, as described for example by the simple ionization equations: In,, *InMe f e’;

(ga)

-_Vh, + h’. VMle

(8b)

The attracting Coulombic force between these defects will lead to the formation of associates: In,, + VL+(In,,V,,)*.

If local thermodynamic equilibrium is established, the concentrations of the defects involved will be correlated by ](InM,VM,)*l =

3 Te, + 2 InMe + yMe.

(7)

that

*I< PGI

wEI, 4 NLeI

0.8 ooeeeadcq

LL

5

r 0

0.L-

E IL w

$0.2,I I I ’ 0.0

III -60 -30 0 <----

30

SPRCE

(10)

(114

and

These so called structural vacancies must be regarded h

KAs~bdK.d

If it is assumed additionally [In,,

In,Te, a

(9)

II 60 90 COORDlNFlTE

I

I

I

I

I

120 150 180 210 2L0 2 0 Z /

cl06

Ml ---->

Fig. 7. Comparison between a calculated (-) and a measured (0) In,Te, mole fraction profile (800 K, 32 h); boundary concentrations and interdiffusion coefficients for the individual slabs of the calculated profile are listed in Table 2.

(1lb)

Thermodynamics Table 3. Boundary mole fractions and diffusion coefficients for the slabs, into which the reaction zone is subdivided (T=7OOK, f=16h) Interdiffusion coefficient d (cm2 s-l) (2) (1)

Mole fraction 0.051 Sk 0.195 I k 0.351 I; k 0.426 I k 0.744 I k

10.195 I 0.300 I 0.401 IO.500 5 0.750

1.00. IO-‘0 1.00~IO-‘0 1.00~10-‘0 0.40~10-‘0 1.00~10-‘0

1.00~lo-‘O l.OO~lo-‘” o.05~10-‘” o.40.10-‘” l.OO~lo-‘”

then the total content

of Indium, [In], and that of vacancies, v], can be described by:

[InI= bM,l + KbeYMe)*l

(124

El = DW + KInM,VMJ*l.

Wb)

Because of the stoichiometric condition of a II-VI/III-VI solid solution the total concentrations of indium and vacancies are correlated by: [In] = 2. w].

(13)

From this simple defect model, described by eqns (10)-(13), the concentration of the mobile vacancies [1’L,] can be expressed as a function of the total indium content [In]

P!be12+ WKA,,+ [IW) x l%A - [In]/(2. KAsr) =

0.

and kinetics

and Table 2, however, show that d is approximately constant for k c 0.4 and even decreases for higher k-values. Therefore, in the frame of this model, either the mobility of the free vacancies has to decrease or the association constant KAsshas to increase as [In] increases. If one changes from the phenomenological model describing the thermodynamic equilibrium between point defects to a microscopic model describing the statistical distribution of structure elements, one has to consider that the characteristic building unit of the zinblende lattice is a tetrahedron in which the central Te-ion is surrounded by four cation sites. These cation sites can be occupied by Hg-ions, In-ions or by vacancies. If a vacancy and an In-ion belong to the same tetrahedron they have to be treated as an associate. If ideal statistical distribution within the cation sublattice is assumed, the most probable tetrahedra including associates are those with the arrangements HgHgInV (a) and HgInInV (b). Tetrahedra of type (a) have maximum probability of p = 0.167 at k = 0.5, those of type (b) of p = 0.188 at k = 0.75 [5]. The real probabilities for these special tetrahedra will be even higher than the purely statistical probabilities, because the interaction energies for these tetrahedra are lowered by the association energy. Free vacancies, which can contribute to the interdiffusion process must be attributed to the tetrahedra of type HgHgHgV. Provided there is an ideal statistical distribution, the probability for the occurence of this type of tetrahedron is given by

(14) p(HgHgHgV)

According to this equation the concentration of mobile vacancies increases as the fraction of In,Te, in the solid solution increases, and the lower this fraction the higher the gradient. On the other hand, the interdiffusion coefficient d should increase with increasing concentration of mobile vacancies. Figure 7 .8

1325

= - (4/3)k4 +4k3-4k2+(4/3)k.

The probability for tetrahedra of type InInInV, which also represent free vacancies, can be neglected because their probability increases very slowly with

,

-10

<-----

I

I

0

10

SPRCE

(15)

I

20

I

30

I

L0

si

COOROlNFlTE Z / (l0-6 Ml ------>

Fig. 8. Calculated In,Te,-mole fraction profiles (700 K, 20 h); boundary concentrations and interdiffusion coefficients for the individual slabs are listed in Table 3 (I) and (2).

1326

VOLKMARLEUTEand HEINRICHMICHAELSCHMIDTKE

2 loeg

I

a 1.10-g

dl

012 mole

Oj3 traction

OjL k

0.5

016

__*

Fig. 9. The probability for HgHgHgV-tetrahedra as a function of the mole fraction k compared with the calculated cation interdiffusion coefficient D(k) for the a-phase at T = 800 K. increasing In-content and stays below p = 0.03 even at k = 0.5. In Fig. 9 the probability for free vacancies, according to eqn (15) is compared with the diffusion coefficient of Table 2. Function (15) correlates fairly well with the course of the interdiffusion coefficient, which was calculated by fitting the measured concentration profile of Fig. 7. As mentioned above, the probability for tetrahedra with In and v must be higher than the statistically calculated one. Consequently the probability for the tetrahedra with free vacancies must become even smaller than calculated from eqn (15) and this deviation must increase as the concentration of the tetrahedra comprising v and In increase. In the high temperature region, T 2 720, the activation enthalpy, E’ = 144 kJ molV’ , which was determined from the temperature dependence of the growth constant (Fig. 5) represents a mean value for the activation enthalpy for the interdiffusion of In and Hg. Since the concentration of mobile vacancies is mainly determined by the degree of association, the measured activation enthalpy will comprise contributions by the enthalpy of association and of mobility. The /I-phase. In a preceding paper [l] it was shown that the /I-phase with the stoichiometric composition Hg,In,Te, crystallizes in a tetragonal super structure belonging to space group 14m2. According to the phase diagram (Fig. 6) this p-phase exists only at T < 720 K. In the frame of a point defect model, the small value of the interdiffusion coefficient which causes the low growth rate of the ordered P-phase, can be understood if one considers that the structural vacancies in this super structure must be treated as interstitial sites and not as defects in the cation sublattice. Therefore, in spite of the high content of structural vacancies, the concentration of mobile defects should be very small, as long as the b-phase can be considered as a compound with the strict stoichiometry Hg, In2 Te, , corresponding to the mole fraction k = 0.375. The phase diagram, however, indicates that at 700 K the existence region of the B-phase extends from k = 0.35 to k = 0.38. In the region k < 0.375

some interstitial sites will be occupied by excess Hg-ions acting as Hg,, whereas in the region k > 0.375 some Hg-sites in the cation sublattice of the super structure will be vacant. These vacancies will act as real defects in contrast to the structural vacancies of the stoichiometric compound. Therefore, if the cation interdiffusion coefficient for the j-phase could be detected more accurately, one should obtain a minimum for B at the stoichiometric composition k = 0.375. As concerns the concept of tetrahedra, the super structure of the stoichiometric compound Hg,In,Te, can be constructed by use of only two types of tetrahedra. From X-ray diffraction experiments it could be shown [l] that in this structure there are only two different Te-positions, one corresponding to tetrahedra of type HgHgIny the other to those of type HgHgHgIn. As none of these tetrahedra correspond that the to a free vacancy, it is reasonable interdiffusion coefficient in this ordered /?-phase is much lower then in the surrounding cc-phase. The higher activation enthalpy (E’i = 175 kJ mol-’ , Fig. 5) in the low temperature region (II) compared with that in the high temperature region (I) is most probably caused by the thin /I-phase layer. In the ordered p-phase the fraction x* of the HgHgInytetrahedra with a strong bonded vacancy is much higher than in the ideal a-solid solution with the same composition. For k = 0.375 one obtains: .x*(/I) = 0.500;

x*(a)

=

0.146.

For this reason the mean dissociation enthalpy for the Iny-associates will be much higher in the ordered b-phase than in the a-phase. Consequently the transport through the thin p-phase layer will be the rate determining step and the activation enthalpy for interdiffusion in this layer will dominate the apparent activation enthalpy for the growth of the whole product layer. For temperatures higher than 720 K there are also indications that Hg and In are not statistically distributed, but that some partial order in the cation sublattice is preserved [l]. On the other hand, the diffusion experiments in this temperature region have

Thermodynamics not shown any irregularities in the concentration profiles which could indicate phase boundaries. Therefore the transition from this partially ordered high temperature region to the solid solution with defect zincblende structure must be a continuous one, probably according to a second order phase transition. The chnlcopyrite phase. In a completely disordered solid solution with the composition k = 0.75 the HgInIny-tetrahedron is the most probable one. Moreover, the composition of a single tetrahedron of this type reflects the stoichiometry of the chalcopyrite phase. Thus this tetrahedron appears to be particularly stable. It is reasonable that a structure, such as the chalcopyrite structure, which is constructed of only these tetrahedra, is energetically more favourable than the disordered solid solution. As concerns the nature of the structural vacancies in this compound the same arguments apply as for the /?-phase, i.e. the structural vacancies cannot act as defects. Nevertheless, some interdiffusion of In and Hg in the chalcopyrite phase can be observed. This is enabled by the deviation from the stoichiometric

PCS.

4911 I-0

1327

and kinetics

composition. Additional HgTe can be alloyed to HgIn,Te, until a mole fraction of k z 0.72 is reached. The Hg-ions in excess, act as interstitial cations in the chalcopyrite lattice and can contribute as defects to the interdiffusion.

Acknowledgemenfs-Financial support of this work by the Minister fiir Wissenschaft und Forschung des Landes Nordrhein-Westfalen and by the Fonds der Chemischen Industrie is acknowl&ged.

REFERENCES 1. Leute V. and Schmidtke H. M., J. Phys. Chem. Solids 49, 409 (1988). 2. Leute V. and Spalthoff U., Forschungsberichte aks L.anaks Nordrhein- Westfalen, No. 2914, Westdeutscher Verlag (1979). 3. Liibbers D. and Leute V., J. Solid Sr. Chem. 43, 339 (1982). 4. Leute V., Schmidtke H. M. and Stratmann W., Eer. Bunsenges. Chem. 86, 132 (1982). 5. Bred01 M. and Leute V., Ber. Bunsenges. Phys. Chem. 90, 714 (1986).