Densities and electrical conductivities of liquid TlTe, InTe and GaTe systems

Materials Science and Engineering, 51 (1981) 213 - 222

213

Densities and Electrical Conductivities of Liquid T1-Te, In-Te and Ga-Te Systems DONG NYUNG LEE

Department of Metallurgical Engineering, College of Engineering, Seoul National University, Seoul (Korea) BARRY D. LICHTER

Department of Mechanical and Materials Engineering, Vanderbilt University, Nashville, TN 3 7235 (U.S.A.) (Received May 23, 1981 ; in revised form July 23, 1981)

SUMMARY

The densities of the liquid I n - T e and Ga-Te alloy systems were measured over the entire composition ranges, using fused silica pycnometers. The isothermal density results show a negative deviation from linear mixing, with the minimum relative density at 60 at.% Te for both systems. The density of alloys near the composition Ino.4Teo:6 rises immediately above the melting point, passes through a maximum and then falls with increasing temperature. For alloys with compositions near Gao.4Teo.6, the density shows only a very small temperature dependence. The electrical conductivities o f the liquid TlTe, I n - T e and Ga-Te systems were measured by the inductive coupling method. The results show positive temperature coefficients for most compositions and minima in the conductivity isotherms occurring at Tlo.67Teo.33, Ino.4Teo. s and Gao.4Teo.6. The results are analyzed and discussed in relation to theories and models of liquid metallic, semimetallic and semiconducting systems.

1. INTRODUCTION

Previous investigations of the properties of liquid metallic and semimetallic alloys [1 - 4] have attempted to show the existence of useful relationships between the electrical properties (e.g. resistivity and/or conductivity, Hall coefficient, thermoelectric power) and the solution thermodynamic properties (e.g. heat of mixing, partial molal free energy, excess free energy of mixing, compressibility) of these systems. The objective of the present work was to investigate similar properties of 0025-5416/81/0000-0000/$02.50

liquid III-Te systems. Investigations of the density and the electronic properties of the T1-Te, I n - T e and G a - T e systems in the liquid state have been carried out by many workers [ 5 - 21]. These systems are characterized by a negative Hall coefficient, a positive thermoelectric power in most composition ranges and a strong composition dependence of conductivity with the presence of minima at certain compositions. These properties have led many investigators to characterize the liquid III-Te systems as being semiconducting [5, 8 - 14, 16]. In the present work the density and the conductivity of these systems were measured to confirm the results of previous workers and to obtain additional data where experimental results were lacking.

2. EXPERIMENTAL METHODS

2.1. Density measurement The densities of liquid alloys were measured using fused silica pycnometers and a precision cathetometer. Samples were prepared from elements 99.999% pure. The constituents were weighed to 0.001 gf and placed in a calibrated fused silica pycnometer which was evacuated to 10-2 Torr and sealed. The sealed cell, suspended in a tube furnace with Nichrome wire, was heated above the liquidus temperature for about 12 h during which time the sample was vigorously shaken to remove entrapped gas bubbles before density measurements were made. The experimental set-up is shown in Fig. 1. Two Nichrome wire tube furnaces, each with independent temperature controllers, were used. The top furnace consisted of t w o splitcore sections with a small opening between © Elsevier Sequoia/Printed in The Netherlands

214

o

o o

l

o o

l

LIGHT

:i

0"::,?. !

o~:.'.::'! o .:-..;.-: o'f::':

CATHETOMETER

OmmlF [

MERCURYLEVEL~ r 7

o :.:y;: o .~ ;.::: o :.:'.'.:.

'2 ;2

o-::..?:i o.f"..2. o

Tz

? ~. ~ '.'

"rt

Fig. 1. The apparatus for density m e a s u r e m e n t : T1, T2, T3, thermocouples.

Fig. 2. The fused silica p y c n o m e t e r .

the sections in order to observe the sample inside the furnace. A stainless steel tube 25 mm in inside diameter and 30 cm long was introduced into the furnace to obtain a large uniform temperature region. The t o p half of this tube was machined to have t w o longitudinal slits through which the sample could be observed. The temperature of the specimens was measured using a chromel-alumel thermocouple placed at the b o t t o m of the specimen. The p y c n o m e t e r was a specially shaped ampoule made of fused silica (Fig. 2). The lower part of this ampoule had a fairly large volume while the middle part was precisionbore silica tubing 6.35 + 0.051 mm in inside diameter with a fiducial mark made with a diamond point. The volume of each p y c n o m e t e r was calibrated with mercury as follows. A known volume of pure mercury was poured into an ampoule, and the distance between the fiducial mark and the mercury level was measured to 0.01 mm using the cathetometer. After the mercury had been removed, the ampoule was cleaned with nitric acid, rinsed a few times with distilled water a n d dried using a vacuum pump. The sample was loaded into the calibrated ampoule, and measurements were carried o u t with the liquid samples. The density of the sample can be calculated by the following equation:

d-

W v + A ( x - - y)

where x and y are the distances between the fiducial mark and respectively the mercury and sample levels, w is the weight of the sample, v is the volume of mercury and A is the cross-sectional area of the precision-bore tube. The volume of the molten alloy was a b o u t 17 cm a. 2.2. Conductivity

measurement

The inductive coupling method described by Nyberg and Burgess [22] was applied in the present investigation. The first experimental application of this method to liquid metals and alloys was the work of Tomlinson and Lichter [2]. A detailed description of this technique is given by Lee and Lichter [1]. The electrodeless method avoids the difficulties associated with the selection of suitable contact materials as in conventional direct-contact methods: It also makes it possible to seal the ampoule containing the sample hermetically; this is particularly important for the volatile elements used in the present investigation. The present technique is particularly suitable for low conductivity materials because the problem due to inadequate skin depth is avoided; however, the m e t h o d requires the accurate determina-

215

tion of sample volume. Moreover, systematic errors are inherent in the inductive coupling method, especially in the conductivity range of typical liquid metals.

3. EXPERIMENTAL RESULTS

3.1. Results o f density measurement 3.1.1. I n - T e system The results of density measurements for 12 alloys of the In-Te system with 20.0, 33.4, 43.7, 50.0, 53.0, 57.2, 60.0, 62.5, 67.0, 71.5, 80.0 and 90.0 at.% Te are shown in Figs. 3 and 4. Glazov et al. [5] measured the densities of In0.sTe0.5 and In0.4Te0.6. Their I

l

I

i

[

I

I

I

I

data are respectively 0.6% lower and 0.3% higher than the data of the present work. The densities of most alloys (44 - 90 at.% Te) do not show a linear dependence on temperature. The densities of alloys with 53 - 90 at.% Te rise immediately above the melting point, pass through a maximum and then decrease with increasing temperature. Even though the densities of two alloys {43.7 and 50.0 at.% Te) do not show maxima, the negative temperature coefficient of density is smaller immediately above the melting point than at higher temperatures. In contrast with this behavior, the normal linear density change with temperature is observed for the indiumrich alloys with 20.0 and 33.4 at.% Te. The results of least-squares analyses for these two alloys are summarized in Table 1 in terms of the coefficients of the linear equation d =a--bt

6.6

~ 6.5 Te:

REF.6

~- 5.~

5.7 5.E 5.~ 400

6OO 7O0 TEMPERATURE(~)

8OO

9OO

where d (g cm-3) is the measured density and t (°C) the temperature. Results for pure indium [21] are also shown for comparison. The density isotherm at 700 °C shows a negative deviation from a linear combination of the component densities (a positive deviation for gram atomic volumes) and has the minimum relative density at 60 at.% Te (Fig. 5).

Fig. 3. The temperature dependence of the density of liquid I n - T e alloys: A, 71.5 at,% Te; $, 80 at.% Te; ©, 90 at.% Te.

i l l l l f l l i

6.6 6.4 6,2

~

6.2

6.0 6.1 0

5.8

6-0

-

\\\\

-

~

\\\\\\\

5.6

~5.9

5.8 A

qD

•

®

2Z-

5.7

~ 2o

5.6

5OO

600

700 800 TEMPERATURE(°C)

900

Fig. 4. The temperature dependence of the density of liquid I n - T e alloys: line A, Te [6] ; o, 20 at.% Te; e, 33.4 at.% Te; v, 43.7 at.% Te; o, 50 at.% Te;A, 53 at.% Te; e, 57.2 at.% Te; o, 60 at.% Te; A, 62.5 at.% Te; o, 67 at.% Te.

,~

ts

-

I

In

I

I

I

I

i

50 alornic % Te

I

i

I

Te

Fig. 5. The isothermal density and atomic volume of liquid I n - T e alloys at 700 °C: ©, this work; e, from ref. 5.

216 TABLE 1 Densities of two In-Te alloys showing normal linear density changeswith temperature (d = a -- bt) Alloy

In [21] In0.sTe0. 2 (20 at.% Te) Ino.67Teo.ss (33 at.% Te)

a (gcm -3 )

b × 104 ( g c m - 3 C-1)

Computed density at 700°C (gcm -3 )

Temperature range

7.15 6.703 ± 0.021 6.397 ± 0.011

8.36 6.98 ± 0.26 7.00 ± 0.14

6.34 6.21 5.90

150-300 660-950 490-990

3.1.2. G a - T e s y s t e m

Figure 6 shows the results of density measurements of the liquid Ga-Te system with 33.0, 40.0, 50.0, 60.0, 70.0, 75.0, 80.0 and 90.0 at.% Te. Density data have been reported for liquid Gao.4Te0.e and Ga0.sTe0.5 by Glazov et al. [ 5]. The present density data for the composition Gao.4Teo.6 are in excellent agreement with their published result. Their data for Gao.sTeo.5 are in agreement with those of the present work immediately above the melting point, while the expansion coefficient derived from their data is notably larger than that of the present work. Such a large expansion coefficient is suspect and suggests the possibility of bubble formation in their specimen. The density results show a linear dependence with temperature within the experimental error, except for the 90 at.% Te alloy which shows departure from linearity above 870 °C. The results of least-squares analyses are summarized in Table 2, which includes published

results for pure gallium [23] and pure tellurium [6]. The density isotherm at 850 °C shows a negative deviation from linear mixing (a positive deviation for gram atomic volumes) with the minimum value occurring at 60 at.% Te (Fig. 7). i

5.6

!

l

'

J

i

r

f

f

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!

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f

~5.4 ~ 5.2 a

5.0 P'"

22

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>o

~'J/ I8

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¢¢¢s

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(°c)

i

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;0

Go

I

I

I

I Te

otomic % T e

5,6

Fig. 7. The isothermal density and atomic volume of liquid G a - T e alloys at 850 °C: o, this work; A, ref. 5.

5.5 5.4

3.2. R e s u l t s o f c o n d u c t i v i t y m e a s u r e m e n t 3.2.1. Pure tellurium

5.~

~5.z 5.1 5.0

~ I

400

~

I

500

,

I

~

I

600 700 TEMPERATURE ('C)

i

I

800

~

I

900

t

Fig. 6. The temperature dependence of the density of liquid G a - T e alloys: line A, Te [6 ] ;line B, Ga [ 23 ] ; e, 33 at.% Te; ~, 40 at.% Te;A, 50 at.% Te; o, 60 at.% Te; • 70 at.% Te; e 75 at.% Te; A 80 at.% Te; o, 90 at.% Te.

As a check of the measuring technique used in this work the conductivity of pure tellurium was measured over the range 450 700 °C and compared with published results [7, 18 - 20]. The density data necessary for the conductivity calculation were taken from Lucas and Urbain [6]. The results are shown in Fig. 8. The present results are in good agreement with the other data. The

217 TABLE 2

Densities of Ga-Te liquid alloys showing normal linear density changes with temperature (d = a - - bt) Alloy

a

b X 104

Computed density

(g cm - 3 )

(g cm - 3 ° c - l )

at 8 5 0 °C

T e m p e r a t u r e range (°C)

(g cm - 3 ) Ga [23] Gao.67Teo.33 (33 at.% Te) Gao.6Teo. 4 (40 at.% Te) Gao.sTeo. 5 (50 at.% Te) Gao.4Teo. 6 (60 at.% Te) Gao.3Teo. 7 (70 at.% Te) Gao.25Teo.75 (75 at.%Te) Gao.2Teo. s (80 at.% Te) Gao.lTeo. 9 (90 at.% Te) Te [6]

6.00 5.985 5.373 5.320 5.087 5.231 5.265 5.413 5.489 6.04

6.5 6.62 0.39 1.89 0.04 1.20 0.48 1.27 0.45 5.3

± 0.041 ± 0.020 ± 0.113 ± 0.005 ± 0.006 ± 0.006 ± 0.009 ± 0.005

I ,

,

,

,

,

i

I

'

'

'

'

840 950 990 960 990 960 920 920 870 750

I

I

@--

~0~

560 760 860 820 810 770 520 460 540 575

5.45 5.42 5.34 5.16 5.08 5.13 5.22 5.30 5.45 5.59

± 0.49 ± 0.21 ± 1.27 ± 0.05 ± 0.22 ± 0.08 ± 0.12 ± 0.07

7000

@ @ 600(

X~X

o

xx x~ 7E

500(

I-

7~ 4000 ~200C

N N 3000 o

,~c,

'

I 500

,

J

,

,

I

I

i

600

,

,

I

,4r

2000

700

TEMPERATURE( °C )

Fig. 8. T h e t e m p e r a t u r e d e p e n d e n c e o f the

conduc-

of liquid tellurium: o, this work; ~, ref. 7; ~, ref. 1 8 ; $ , ref. 19; [], ref. 20. tivity

conductivity increases with increasing temperature within the experimental range. However, Busch and Guntherodt [7] measured the conductivity up to 1100 °C, and their results show that the conductivity starts to decrease from about 900 °C. 3.2.2. TI-Te system This system has been studied by many investigators because of its unusual properties [ 8 - 12]. Previous results are compared with the present data, and agreement is very good (Fig. 9), again demonstrating the reliability of the inductive coupling technique. Conductivity data show positive temperature coefficients in most composition ranges. The isothermal

1000

0

I 400

I I 500 600 TEMPERATURE(~C)

I 700

800

Fig. 9. The temperature dependence of the conductivity of liquid T1-Te alloys: n 14 at.% Te; ×, 16 at.% Te; o, 20 at.% Te; A e, 50 at.% Te; e, 70 at.% Te; ~, O, 80 at.% Te;/% e, 90 at.% T e ; e , 100 at.% Te;±, }, A, ref. 8.

conductivity data at 600 °C (Fig. 10) show that the minimum value occurs at Tlo.67Te0.38. The density data for conductivity calculations were taken from Dahl [13]. 3.2.3. In-Te system

Conductivity data for I n - T e alloys (50 80 at.% Te) have been published previously [14, 15]. In the present work the conduc-

218

000 - ! I I I 1 I I l

I t' 3000

o

~ 2000

-

> P

2000

~ o~"

1500--

I000 q 000

TI I

I

I 5 0I I I I I Te atomic % Te

Fig. 10. The isothermal conductivity of liquid TI-Te alloys at 600 °C; o, this work; zx, ref. 8; e, refs. 9 - 12.

tivities of In-Te alloys were investigated for the entire composition range excluding the two-melt region (0- 28 at.% Te). The results show positive temperature coefficients of conductivity (Fig. 11). The minimum conductivity value at 700 °C occurs at 60 at.% Te (Fig. 12). Previously published data are compared with the present results in Fig. 12. The results by Chizhevskaya and Glazov [14] are far different from the present results in absolute magnitude while Blakeway's data [15] are close to the present data. Our previous study [ 1 ] shows that systematic errors may occur with the rotating magnetic field method as applied by Chizhevskaya and Glazov [14], leading to higher than true values for the conductivity. 3.2.4. Ga-Te system Chizhevskaya and Glazov [16] measured this system using a rotating magnetic field method. The density data in Section 3.1.2 were used to calculate the conductivity of the system in the present work. The conductivities of 12 alloys with 40.0, 43.8, 50.0, 57.1, 60.0, 62.5, 71.4, 75.0, 80.0, 86.0 and 95.0 at.% Te were measured (Fig. 13), and in all cases the conductivity increases with increasing temperature. The isothermal conductivity at 850 0(3 shows the minimum at 60 at.% Te and is compared with the previously published data in Fig. 14. The present results show a lower conductivity than the

o

400

,

eJ9 ° 1

,

8oo

~

I

6oo

,

?~1

7~o

,

TEMPERATURE('C)

,

I

coo

,

,

900

Fig. 1 I. The temperature dependence of the conductivity of liquid In-Te alloys: e, 28.8 at.% Te; e, 33.4 at.% Te; D, 43.75 at.% Te;4, 46 at.% Te; ¢, 50 at.% Te; A, 53 at.% Te; o, 60 at.% Te; ×, 62.5 at.% Te; v, 71.43 at.% Te; o, 80 at.% Te; o, 90 at.% Te.

~0 A

28002400

1

TE~

,x

U 8OO

4OO

I

In

f

l

I 5O

atomic % Te

Te

Fig. 12. The isothermal conductivity of liquid I n - T e alloys at 700 °C; o, this work;A, ref. 14; e, ref. 15.

data of Chizhevskaya and Glazov [16] whose results are suspect for reasons discussed in our previous work [ 1 ], as mentioned above.

219 25oc

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~

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J

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~E

m

,/ / 4

I000

o

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,

i

i

soo

~

i 600

, ,~'i

, 4.~e~-, ,

~oo

soo

9oo

TEMPERATURE( ~C )

Fig. 13. The temperature dependence of the conductivity of liquid Ga-Te alloys: o, 40 at.% Te; o, 43.75 at.% Te; e, 50 at.% Te;O, 57.14 at.% Te; ×, 60 at.% Te; A, 62.5 at.% Te; o, 71.43 at.% Te; ¢, 75 at.% Te; A, 80 at.% Te;V, 86 at.% Te; ", 95 at.% Te. ~00o

4OO0

b-

§

20oo

I000

I

I

Ga

I 50 atomic %

Te

Te

Fig. 14. The isothermal conductivity of liquid Ga-Te alloys at 850 °C: o, this work; A, ref. 16.

4. DISCUSSION

4.1. Density The density data for the T1-Te [13] and for In-Te and Ga-Te systems show positive volumes of mixing in the liquid state, which suggests that directionality of bonding persists after fusion, leading to a structure that is

"open" relative to that of the components. For most compositions the systems In-Te and Ga-Te display exceptionally small temperature coefficients of the density, compared with the magnitude of the normal linear decrease of density with temperature shown by the pure liquid elements (see Tables 1 and 2 and Figs. 3, 4 and 6). Only the most indium-rich (20 and 33 at.% Te) and galliumrich (33 at.% Te) alloys display such "normal" behavior. For the composition In0.4Te0.6 and most neighboring alloys, soft maxima are seen in the temperature variation in the density, and there is a tendency for the coefficients of alloys to increase in magnitude (to become more negative) with increasing temperature. Although maxima were not observed for Ga-Te alloys the (negative) coefficients are, to within experimental error, an order of magnitude lower than the normal values for the liquid elements. For both systems the lowest density values are observed for the composition III0.4Te0.6, and these alloys are the most resistant to density change with temperature. Also, for both systems the alloys containing as much as 90 at.% Te fail to display normal behavior, even showing a soft maximum in the In-Te case; however, at higher temperatures, both alloys appear to approach the behavior of pure liquid tellurium (see Figs. 3 and 6). Such anomalies in the temperature dependence of the density may be attributed to structural changes in the molten state. Solid In2Tea and Ga2Te3 have ZnS-type defect structures. Compounds with the normal ZnS-type structure have a low packing density and a low coordination number (CN) (CN = 4), and the packing density for defect structures is even lower (CN < 4). It is therefore assumed that the short-range order of liquid In0.4Te0.6 and Ge0.4Te0.6 changes above the melting point, and the change results in some increase in the packing density. Thus the temperature dependence of the density can be explained by two competing processes occurring in the molten state: (i) changes in the short-range order, producing a closer packing of the structural units in the melt; (ii) the occurrence of the usual increase in the interatomic spacings, making the structure looser. Immediately above the melting point the changes in the short-range order play the predominant role. They alter the carrier

220

density and mobility, and they are responsible for these properties in the temperature dependence and the composition dependence of electrical conductivity as discussed subsequently. It should be noted that at any particular temperature both the minimum relative density and the minimum electrical conductivity of the G a - T e and I n - T e systems occur at the composition of IIIo.4Teo.s, whereas the corresponding minima in the system T1-Te occur at Tlo.67Teo.33. 4.2. Electronic properties Mott and Davis [24] classified liquid conductors into four broad categories: (a) typical metals; (b) liquids of intermediate type; (c) semimetals or narrow gap semiconductors; (c) semiconductors. (a) Typical metals have a conductivity o greater than 5000 ~2-1 cm -1 . The mean free path L is such that kFL ~ 1 where k F is the wavenumber at the Fermi surface. Ziman's theory [25] is applicable, and the temperature coefficient d p / d T of resistivity is usually positive (but may be negative for some divalent metals). The Hall coefficient RH is given by R H = 1/nec where n is the freeelectron concentration, e is the electronic charge and c is the velocity of light. (b) Liquids of intermediate type, where kFL ~ 1, have a conductivity which is in the range 300 - 5000 ~-1 cm-1 and is due to non-activated diffusive motion. The conductivity is given by [ 24] S F e 2 ag 2

o-

121r2h

where SF = 4 ~ k F 2, g = N(E)/N(E)~,ee ~ 0.3 - 1 and a is the interatomic distance. The thermoelectric power Q is given by

normally negative and can be larger (about llnecg) than the free-electron value. (c) Semimetals or narrow gap semiconductors in the liquid phase are likely to have a deep pseudogap (0 in the range 1 100 ~2-1 cm-1). In liquids the atoms are in constant motion so that the positions of the localized states will continually change;thus it is possible that, when states are (instantaneously) localized, conduction is by diffusion rather than by hopping. (d) Semiconductors have a (hopping) conductivity which is negligible for energies n e a r EF, SO that the current must be carried by excited electrons with energies just above Ec or by holes just below Ev. The present conductivity results in this work suggest that materials studied here belong to class (b). Therefore, experimental results will be discussed on the basis of the properties of class (b), which will be further explored. Ziman [ 27 ] suggested that RH/Ro is inversely proportional to the ratio of N ( E F ) to the free-electron value, i.e. RH

_ N(EF)free _ l

"Ro N(EF) g where R a is the measured Hall coefficient and R0 is the calculated Hall coefficient based on the free-electron model. Since a strong decrease in the density of states is associated with strong interactions between the ions and electrons, it is expected that the density of states will vary with the temperature, as schematically shown in Fig. 15. Therefore, as the temperature rises it is expected that

dlQI dT

< 0

dlRHI

and

~

dT

< 0

[24] 2~r 2 k 2 T (d[ln { N(E)} ]1

This equation was also suggested by Lee [ 26 ]. The thermoelectric power of a p-type conductor is obtained when E F is on the low energy side of the pseudogap [24, 26]. As the temperature is raised, the pseudogap may be smeared out. Since L ( ~ l / k F ) remains constant, a is proportional to g~. Since the Knight shift K is proportional to g; o is also proportional to K 2. The Hall coefficient is

N(E)

/

i

Ef

E

Fig. 15. T h e d e n s i t y o f states for a liquid m e t a l at diff e r e n t temperatures: T 3 ~ T 2 ~ T 1.

221

since R0 is insensitive to temperature. These phenomena are observed for most materials in class (b). Since the Hall coefficient R H is inversely proportional to g and a is proportional to g2, a is expected to be inversely proportional to RH 2 .

4.3. Tellurium The conductivity of liquid tellurium is of the order of 2000 ~2-1 cm -1 and rises with temperature. The Hall coefficient is two to three times larger than expected from the formula R H = 1/nec, with n corresponding to 6 electrons atom -1, and RH decreases with increasing temperature [ 2 8 ] . Since the thermoelectric power is positive, the Fermi energy must be displaced towards the valence band, and it decreases with increasing temperature. Therefore the density of states of liquid tellurium would be similar to Fig. 15. The mean free path is short ( k F L .~ 1), so that in this case a ~ g2 and should be inversely proportional t o RH 2. This follows from the results in Fig. 16. The present conductivity data and available Hall coefficient data [28] were used to obtain the result.

4.4. TI-Te system The T1-Te system has been studied much more extensively by many investigators. Cutler and his coworkers [9 - 12, 29] assumed that T1-Te liquid alloys have a band structure similar to that of a solid semiconductor of composition T12Te. The p-type alloys (tellurium rich) are explained by assuming that a small fraction of the excess tellurium atoms introduce deep acceptor levels and that these dominate the conductivity and thermoelectric power. The n-type alloys (thallium rich) are explained by assuming that excess thallium creates donor states which are fully ionized. The temperature dependences of conductivity, thermoelectric power and Hall coefficient of tellurium-rich alloys are similar to those of liquid tellurium. Figure 16 shows that the relation a ~ IRH1-2 is valid for these alloys. The present conductivity data together with data for T10.67Te0.3s [9] and Hall coefficient data [8] were used to obtain the results shown in Fig. 16. For the thallium-rich alloys (e.g. less than 33 at.% Te), a depends little on temperature; these alloys display the electrical properties of a metal.

4.5. In-Te and Ga-Te systems

3./~,~

[

I

I

I

32I-~&'~"
22

I o"~

'

2.0I- ~ Io

~Te~1.2

1.~

16

18

20

,og I~* ~o'1 Fig. 16. The relation between the conductivity and the Hall coefficient for liquid tellurium and I I I - T e alloys, obtained using conductivity results from the present work and from Cutler and Malon [9] for Tlo.67Te~3a and using Hall coefficient data of Enderby and Simmons [8 ]. The slope of the full lines is --2 and R H is in electromagnetic units.

The composition dependences for the conductivities of the I n - T e and G a - T e systems are similar. The minimum conductivities occur at 60 at.% Te, whereas the minimum conductivity occurs at 33.3 at.% Te in the T1Te system. For all compositions the I n - T e system has a positive thermoelectric power which decreases with increasing temperature [15]. The work by Zhuze and Sheykh [17] indicates that the thermoelectric power of liquid Gao.4Te0.6 behaves like that of liquid Ino.4Te0.6. The Hall coefficient of liquid In0.4Te0.6 is negative and not very large in absolute magnitude, and dlR~l/dT< 0 [15]. It is noted that there is no p - n transition in the thermoelectric power near the minimum conductivity value in the G a - T e system. Warren [30] has investigated the Knight shift K of liquid Ino.4Teo. 6 and Gao.4Teo.s and found that K2/o is constant. The above facts together with the conductivity values indicate that these liquids are semimetals in class (b). The relation between o and RH is shown in Fig. 16. For smaller values of 0 (at lower temperatures) the relation o ~ IRH1-2 holds b u t it

222 is n o t true at higher temperatures. This deviation at higher temperatures cannot be explained. The Hall coefficient data may be erroneous in view of difficulties o f measurem e n t at elevated temperatures.

5. C O N C L U S I O N S

(1) The densities o f I n - T e and G a - T e in the liquid state were measured t h r o u g h o u t the entire composition region. The isothermal density results show a negative deviation f r om linear mixing with the m i ni m um relative density at 60 at.% Te in b o t h systems. The densities o f alloys near In0.4Te0.e rise immediately above the melting point, passing through a m a x i m u m and t hen falling with increasing t e mp er atu r e. The densities o f alloys near the composition Gao.4Te0.e show only a very small t e m p e r a t u r e dependence. Such anomalies in the t e m p e r a t u r e d e p e n d e n c e o f t he densities o f I n - T e and G a - T e systems suggest strong structural changes in the m ol t en state with changing t e m p e r a t u r e . (2) The conductivities of I I I - T e systems (i.e. T1-Te, G a - T e and I n - T e systems) show positive t e m p e r a t u r e coefficients in most compositions with minima in t he conductivity occurring at In0.4Te0.6, Gao.4Teo.6 and T10.87Te0.33. Considering o t h e r properties such as Hall coefficient and thermoelectric power, we feel th at these systems m e e t the requirem e n t o f Mott and Davis' second category of intermediate-type systems for w h i c h k F L ~ 1 where k F is the w a ve num ber at the Fermi surface and L is the mean free path o f charge carriers.

ACKNOWLEDGMENTS The authors wish t o express their sincere appreciation to Dr. W. F. Flanagan, Vanderbilt University, and Dr. J. L. Tomlinson, California State Polytechnic University, f o r their interest in this work and for valuable discussions and also t o Mr. H. I. Kim, Korea Institute of Science and Technology, for drawing the figures. The financial s uppor t f or this investigation was provided by the National Science F o u n d a t i o n Research Grant GK-18697.

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