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Thermophysical properties of HgTe and Hg0.9Cd0.1Te melts
Journal of Non-Crystalline Solids 391 (2014) 54–60
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Thermophysical properties of HgTe and Hg0.9Cd0.1Te melts C. Li a,1, Ching-Hua Su b,⁎, S.L. Lehoczky b, R.N. Scripa a, H. Ban c,2, B. Lin c,3 a b c
Department of Materials Science and Engineering, University of Alabama at Birmingham, Birmingham, AL 35294, USA Materials and Processing Laboratory, NASA Marshall Space Flight Center, Huntsville, AL 35812, USA Department of Mechanical Engineering, University of Alabama at Birmingham, Birmingham, AL 35294, USA
a r t i c l e
i n f o
Article history: Received 7 February 2014 Available online xxxx Keywords: II–VI semiconductor melt; Density; Electrical conductivity; Viscosity
a b s t r a c t Thermophysical properties, namely, density, viscosity, and electrical conductivity of HgTe and Hg0.9Cd0.1Te melts were measured as a function of temperature. A pycnometric method was used to measure the melt density in the temperature range of 948 to 1073 K for the HgTe melt and 1011 to 1131 K for the Hg0.9Cd0.1Te melt. The density results show a maximum at 1023 and 1020 K, respectively, for the HgTe and Hg0.9Cd0.1Te melts. The viscosity and electrical conductivity were simultaneously determined using a transient torque method from 944 to 1098 K for the HgTe melt and from 1016 to 1127 K for the Hg0.9Cd0.1Te melt. The measured electrical conductivity decreases as the mole fraction of CdTe, x, increases at a specific temperature, and increases as a function of temperature, which shows a semiconductor-like behavior. The measured viscosity decreases as the mole fraction of CdTe, x, increases at a specific temperature and decreases as the temperature increased. The analysis of the electrical conductivity of the melts and the relationship between the kinematic viscosity and density implied a structural transition in these melts. No relaxation phenomena were observed in the density, electrical conductivity, and viscosity of the HgTe and Hg0.9Cd0.1Te melts. Published by Elsevier B.V.
1. Introduction In our previous publications, the thermophysical properties, i.e., density, electrical conductivity and viscosity of pure Te melt [1] and Hg0.8Cd0.2Te melt [2] were determined as a function of temperature. The observed thermophysical properties in the Te melt was analyzed and the behavior was attributed to the transformation of a two-fold coordination structure to a three-fold coordination structure as the melt temperatures increase [1]. The analysis of the electrical conductivity of the Hg0.8Cd0.2Te melt and the relationship between the kinematic viscosity and density indicated a structural transition at the temperature of 1091 K [2]. In the published literatures on other compositions of the HgCdTe system, Chandra [3], Mokrovski [4], and Glazov et al. [5–7] observed a density increase in HgTe upon melting and they all observed a maximum in the density of the HgTe melt. Chandra [3], using the pycnometric method, observed a maximum in the density of Hg1 − xCdxTe (x = 0.05, 0.10) melts. Glazov [5,7] used the gamma radiation attenuation method to determine the density of Hg1 − xCdxTe (x = 0.05, 0.10, 0.15, 0.192) melts, which shows a
⁎ Corresponding author. Fax: +1 256 5448762. E-mail address: [email protected] (C.-H. Su). 1 Now at Eaton's Cooper Power System Business, 11131 Adams Road Franksville, WI 53126, USA. 2 Now at Mechanical and Aerospace Engineering, Utah State University, Logan, UT 84341, USA. 3 Now at Victory Energy LLC, 10701 E. 126th St., N., Collinsville, OK 74021, USA.
http://dx.doi.org/10.1016/j.jnoncrysol.2014.03.012 0022-3093/Published by Elsevier B.V.
behavior similar to those measured by Chandra [3]. Chandra adopted an inhomogeneous two-phase structure model for the melt to interpret the Hg1 − xCdxTe anomalous density changes [8]. Glazov [7] used an associate solution model by introducing a [Cd2−(Hg2Te4)2−] complex to explain the anomalous density change. Mazuruk et al. [9] observed a slow relaxation phenomenon in the measurement on the viscosity of Hg0.84Zn0.16Te melt. Two sets of viscosity relaxation data were obtained by cooling the Hg0.84Zn0.16Te melt from 1123 K to 1083 K and to 1063 K. It took a day for the viscosity of the Hg0.84Zn0.16Te melt to reach the equilibrium value at 1083 K. However, it took longer than a week for the viscosity of the Hg0.84Zn0.16Te melt to reach the equilibrium value after it has been cooled to the temperature of 1063 K, which is just 20 K above the liquidus temperature of 1043 K. Mazuruk [9] attributed the nature of this kind of timedependence effect to macroscopic and microscopic inhomogeneities in the melt. In this study, the thermophysical property measurements were extended to other compositions in the HgCdTe system. The density, electrical conductivity and viscosity were accurately determined for the HgTe and Hg0.9Cd0.1Te melts and the possible structural transition in the melts were analyzed. The density of the melts as a function of temperature was measured using a pycnometric method. The electrical conductivity and viscosity of the melt were simultaneously determined using the transient torque method developed recently [10,11]. The relaxation behavior of the thermophysical properties of the HgTe and Hg0.9Cd0.1Te melts was also investigated. These thermophysical properties were measured as a function of time after the melts was rapidly
C. Li et al. / Journal of Non-Crystalline Solids 391 (2014) 54–60
cooled to a lower temperature near the melting point or the liquidus temperature. 2. Experimental procedures 2.1. Sample preparation The ampules for thermophysical property measurements of the HgCdTe melts were made of fused silica tubes. A thermometer-shaped ampule, which had an approximately 10 cm long 15 × 9 mm “bulb” at the bottom and 10 cm long 6 × 3 mm “stem” at the top, was used for the density measurement. A 15 × 9 mm ampule was used for the electrical conductivity and viscosity measurement. Each ampule was baked in a vacuum of 5 × 10− 5 Torr at 1430 K for 16 h after it was cleaned by hydrofluoric acid, acetone, methanol, and distilled water. The Hg1 − xCdxTe, x = 0 and 0.10, samples for density, electrical conductivity and viscosity measurements were prepared by synthesizing directly from the pure elements. The starting materials were six nine grade Cd and Te from Johnson Matthey Co. and seven nine grade Hg from Bethlehem Apparatus. After the weighing by a Mettler AT201 electronic balance with an accuracy of 10−5 g, each element was loaded into the prepared ampule. Table 1 gives the weight of each element used in the HgTe, and Hg1 − xCdxTe samples for density measurements as well as for the electrical conductivity and viscosity measurements. After the ampules were sealed under a vacuum of approximately 5 × 10−5 Torr, they were placed in a rocking furnace and synthesized according to the following homogenization procedures. The HgTe samples for thermophysical property measurements were heated to approximately 773 K in the horizontal position and held for 1 h. The temperature was then raised to 973 K and the samples were held at the temperature for approximately 2 h to ensure that the reaction of Hg and Te was complete. Finally, the HgTe samples were heated to 1143 K, which was approximately 20 K higher than the maximum temperature used for the measurements of the thermophysical properties, and were held for 1 h. The Hg0.9Cd0.1Te samples were homogenized following the procedure developed previously at NASA/ MSFC [12]. The ampules containing the elements were heated in the rocking furnace to approximately 770 K and held at this temperature for 16 to 20 h. Then the temperature was raised to 935 K, which is about 30 K below the solidus temperature [13], and maintained there for 20 h to allow for the homogenization by the inter-diffusion of the elements. Finally, the temperature was increased to 1095 K, which is about 100 K above the liquidus temperature [13], and held there for 20 h with the furnace rocking to homogenize the melts. Before the sample was cast in the rocking furnace, the sample was heated to 1143 K, which is approximately 20 K above the maximum temperature used in the thermophysical property measurements. Both the HgTe and Hg0.9Cd0.1Te samples were solidified by turning off the power to the rocking furnace, with the furnace being held at 60° to its horizontal position during casting. 2.2. Density measurement The densities of the HgTe and Hg0.1Cd0.9Te melts as a function of temperature were measured by the pycnometric method. The Table 1 The weight of each element used in the HgTe, and Hg0.1Cd0.9Te samples for density, electrical conductivity and viscosity measurements. Sample
Hg (g)
Te (g)
Cd (g)
HgTea HgTeb Hg1 − xCdxTea (x = 0.1) Hg1 − xCdxTeb (x = 0.1)
32.70543 14.03774 25.31182 14.41327
20.80072 8.92898 17.89101 10.19109
– – 1.57609 0.89760
a b
Density measurements. Electrical conductivity and viscosity measurements.
55
technique has been described in detail elsewhere [1,2] and will be presented briefly here. The weight of the empty ampule and that of the ampule filled to each quartz mark on the ampule with distilled water as well as the water temperature were measured. The volume corresponding to each referenced mark was calculated from the weight difference and the water density vs. temperature data from CRC Handbook [14]. The density ampule was placed in the center of a two-zone (15 and 35 cm long) transparent furnace provided by Thermcraft, Inc. Four K-type thermocouples were attached along the outside of the ampule wall to record the temperature of the sample. The temperatures of the two zones were set with a positive temperature difference of 3 K (hot on top) to avoid bubble formation inside the melt during the density measurement. The temperature stability of the transparent furnace was better than 0.5 K at all of the measured temperatures. A silhouette of the curved melt surface was visible through the transparent furnace with the aid of a backlight. The distance between the silhouette and a reference mark was monitored and recorded using a digital camera and a VCR. The volume of the HgTe and Hg0.1Cd0.9Te melts was determined by measuring the distance from the meniscus of the melt to one of the reference marks. The resolution of the distance measurement in this pycnometric setup was 0.05 mm, corresponding to an uncertainty of approximately 0.15% in the measured density. 2.3. Electrical conductivity and viscosity measurement The viscosity and electrical conductivity of the HgTe and Hg0.9Cd0.1Te melts were measured by a transient torque viscometer (TTV) developed in our laboratory to determine the viscosity and electrical conductivity rapidly and simultaneously. The schematic setup and the principle of the TTV have been discussed in detail in our previous publications [15]. The essential feature of this method was the utilization of a rotating magnetic field (RMF) to interact with the melt and generate a rotating Lorentz force. This force in turn generated a rotational flow in the melt which caused the ampule to rotate along with the flow. The transient rotating angle of the ampule as a function of time after the RMF has been applied was measured to determine the electrical conductivity and viscosity of the melt. 2.4. Time dependence of thermophysical properties The time dependence of the thermophysical properties of the HgTe and Hg0.9Cd0.1Te melts was also investigated. The time relaxation behavior of the density of the HgTe melt was measured after the melt was cooled from 1073 K to 948 K, which is approximately 5 K above the melting point of HgTe. The time needed for the HgTe melt to cool from 1073 K to 948 K in the transparent furnace was approximately 15 min. The time “zero” of the relaxation measurement was started when the temperatures of the thermocouples attached to the outside of the ampule wall reached 948 K. The time relaxation behavior of the electrical conductivity and viscosity of the HgTe melt was measured after the melt was cooled from 1103 K to 950 K. Before cooling, the HgTe sample has been held at 1103 K for a week to ensure that it was in the equilibrium state. The thermocouple could not be attached to the outside of the ampule during the electrical conductivity and viscosity measurement in the TTV. The temperature of the sample was monitored using the reading of the TTV furnace controller and time “zero” was defined as when the controller thermocouple reads 950 K. The time needed for the temperature of the TTV furnace to decrease from 1103 K to 950 K was approximately 45 min. During the actual temperature calibration for the TTV furnace, it was observed that it took approximately half an hour after the time “zero” for the temperature inside the TTV furnace to be cooled down to the equilibrium temperature. The density of the Hg0.9Cd0.1Te melt as a function of time was measured after the melt was cooled from 1130 K to 1010 K, which is approximately 15 K above its liquidus temperature. Cooling time was approximately 15 min. The viscosity and electrical conductivity of the
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C. Li et al. / Journal of Non-Crystalline Solids 391 (2014) 54–60
Hg0.9Cd0.1Te melt as a function of time were determined after the melt was cooled from 1130 K to 1010 K in approximately 30 min. The time “zero” for the density, electrical conductivity, and viscosity measurements was determined in the similar methods as discussed earlier for the HgTe melt.
3. Results, analyses and discussions 3.1. Density 3.1.1. HgTe melt During the heat-up, an increase in the density of HgTe was observed upon the melting of the sample. The published value of the density of solid HgTe just below the melting point is 7.97 × 103 kg/m3. The density of the HgTe melt measured as a function of temperature is shown in Fig. 1. Previously published density results for the HgTe melt by Glazov [5,6] using the gamma radiation attenuation method and by Chandra [3] using the pycnometric method are also plotted in Fig. 1 for comparison. In the figure, “Temp. Up” and “Temp. Down” indicate that the measurements were taken while increasing and decreasing the temperature, respectively. There were over 200 data points reported in Refs. [5,6] in the temperature range of 943 K to 1080 K with the absolute error reported to be approximately ±0.01 × 103 kg/m3. The fitting curve of these density data of HgTe melt determined is thus shown as a solid line in Fig. 1. The density of the HgTe melt increased as a function of increasing temperature to a maximum value of 8.16 × 103 kg/m3 at about 1023 K and then showed a slight downward trend. The previous works by Glazov [5,6] and Chandra [3] show a similar trend. However, the values of Glazov were about 0.6% and that of Chandra were about 1.5 to 2% lower than the present results. In Glazov's work [5,6], the absorption coefficient of the HgTe melt in the gamma ray radiation attenuation method was calibrated using a solid HgTe sample, which might have contributed an additional error in the density measurements. The underestimation in the densities of the HgTe melt by Chandra [3] was suspected by Glazov [5,6] to be due to the possible formations of tiny Hg bubbles in the HgTe melt because of the non-uniform temperature distribution in the melt during the density measurements. The density trend of the HgTe melt shows the similar behavior to that of the Te melt [1] in that it goes through a maximum as a function of temperature. This behavior implies that there are likely two or more types of structures in the HgTe melt [5,6,8]. A quantitative description of the density of the HgTe melt as a function of temperature was attempted by both Chandra [8] and Glazov [5,6] by applying an effective-medium theory developed by Cohen and Jornter [16–19]. In Chandra's assumption, the HgTe melt structure was considered to be a
mixture of low- and high-coordination-number structures that have the same total number of Hg and Te atoms. The assumed lowcoordination-number structure of the HgTe melt has a lower density than that of the high-coordination-number structure. The increase in density of the HgTe melt with increasing temperature was attributed to its continuous transformation from the low-coordination-number structure to the denser, high-coordination-number structure. The decrease in the density of the HgTe melt after reaching its maximum is due to the thermal expansion of the two structures. In Glazov's assumption, which was based on an associated equilibrium solution theory [20], the structure of the HgTe melt consists of several kinds of structures namely, Hg, Te, HgTe, and Hg2Te3. The maximum in the HgTe melt density was attributed to the combined changes of the molar volumes and the volume fractions of the various structures as a function of temperature.
3.1.2. Hg0.9Cd0.1Te melt The measured densities of the Hg0.9Cd0.1Te melts as a function of temperature are shown in Fig. 2. Previous results for the Hg0.9Cd0.1Te melt measured by Glazov [5,7] and Chandra [8] are also plotted in the figure for comparison. The density of the Hg0.9Cd0.1Te melt measured by Glazov was scattered with the 2nd-order polynomial least rootmean-square fitting result shown as a curve. The density values of the Hg0.9Cd0.1Te measured by Chandra [8] and by Glazov are about 0.2% and 0.25%, respectively, lower than the results of the present study. The lower density values measured for the Hg0.9Cd0.1Te melt in those studies may be attributed to the same reasons as described earlier for the HgTe melt. A maximum in the density of the Hg0.9Cd0.1Te melt was observed in this study at a temperature of approximately 1020 K, as shown in Fig. 2. The temperature where the Hg0.9Cd0.1Te melt density reaches a maximum agrees with Chandra's results [8]. The density measured by Glazov (fitting curve in Fig. 2) shows a maximum at 1029 K. Fig. 3 includes the density data of the HgTe and Hg0.9Cd0.1Te melts as well as our previous results on the Hg0.8Cd0.2Te [2] melt for comparison. It clearly shows that the density of the Hg1 − xCdxTe melt decreases with an increase in the CdTe mole fraction in the melt. The temperatures of 1023 and 1020 K labeled in Fig. 3 are the temperatures where the density of the HgTe and Hg0.9Cd0.1Te melts, respectively, reaches the maximum. The approximately same temperature at which the maximum density of the HgTe and Hg0.9Cd0.1Te melts occurred implies that the density change in the Hg0.9Cd0.1Te melt is mainly due to its density change of its HgTe component. The reason that no maximum was observed in the density of the Hg0.8Cd0.2Te melt may be due to its liquidus temperature (approximately 1160 K [13]), which is higher than 1023 K.
7.815
8.16
7.810
Density (103 kg/m3)
Density (103 kg/m3)
8.12 8.08 8.04 8.00 Solid Te
7.96
Present study (Temp. Up) Present study (Temp. Down)
7.92
Tm=943 K
Glazov (1997)
980
1000
1020
1040
7.795 7.790 7.785 Present study (Temp. Up)
7.780
Present study (Temp. Down)
7.775
Glazov (1998)
7.770
7.88 960
7.800
Fitting curve from Glazov
Chandra (1983)
940
7.805
1060
Temperature (K) Fig. 1. Density of HgTe as a function of temperature.
1080
1000
Chandra (1983)
1020
1040
1060
1080
1100
1120
Temperature (K) Fig. 2. Temperature dependence of density of Hg0.9Cd0.1Te melt.
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C. Li et al. / Journal of Non-Crystalline Solids 391 (2014) 54–60
8.2
HgTe (Temp. Up) HgTe (Temp. Down)
8.0
7.9
Hg
Cd Te (Temp. Up) 0.9 0.1
Hg
Cd Te (Temp. Down) 0.9 0.1
Hg
Cd Te (Temp. Up) 0.8 0.2
Hg
Cd Te (Temp. Down) 0.8 0.2
7.8
7.7
Electrical conductivity (104Ω-1m-1)
16
8.1
Density (103 kg/m3)
57
14
Hg Cd0.1Te (Temp. up)
12
Hg0.9Cd0.1Te (Temp. down)
0.9
10 8 6 4 2 T = 961 K
7.6 0 750
T=1020K T=1023K 7.5 930
960
990
1020
1050
1080
1110
900
950
1000
1050
1100
1150
1140 Fig. 5. Temperature dependence of electrical conductivity of Hg0.9Cd0.1Te.
Fig. 3. Density of the HgTe, Hg0.9Cd0.1Te, and Hg0.8Cd0.2Te melts.
3.2. Electrical conductivity In this study, the electrical conductivity measurement by the transient torque method started at 750 K, where the HgTe and Hg0.9Cd0.1Te samples were solids. The measured electrical conductivities for the HgTe and Hg0.9Cd0.1Te solids and melts as a function of temperature are shown in Figs. 4 and 5, respectively. Presently, no data are available in the literature on the electrical conductivities of the HgTe and Hg0.9Cd0.1Te samples at elevated temperatures for comparison. As shown in Fig. 4, the electrical conductivity of the HgTe changes drastically when the sample melts. By monitoring the change of the electrical conductivity as a function of temperature, the melting point of HgTe was determined to be 942 K, which is 1 K lower than the published value. Similarly, the solidus temperature of Hg0.9Cd0.1Te was estimated to be 961 K, which is 1 K higher than the results previously reported [13] using the precision differential thermal analysis. To compare the electrical conductivities of the HgTe and the Hg 1 − x Cd x Te solids, all data, including previously published results for the Hg0.8Cd0.2Te solid [2], are plotted together in the measured range of 750 to 940 K in Fig. 6. The decrease in electrical conductivity as a function x is most likely due to the increase in the energy gap of the Hg1 − xCdxTe solids. HgTe is a semimetal with an energy bandgap of 0 eV and an analysis of its electrical conductivity as a function of temperature from 300 K to the melting point will be given in detail
elsewhere. The bandgap, Eg, of Hg1 − xCdxTe increases with the increasing x and temperature. For instance, using the formula given by Hansen et al. [21], Eg = 0.20 and 0.30 eV for x = 0.1 and 0.2, respectively, at 750 K and Eg = 0.29 and 0.36 eV for x = 0.1 and 0.2, respectively, at 950 K. Fig. 7 shows the electrical conductivity of the HgTe and Hg1 − xCdxTe melts, including the previously published results for the Hg0.8Cd0.2Te melt [2], in the logarithm scale versus 1/T. At a specific temperature, the electrical conductivity of the melts decreases as the mole fraction of CdTe, x, increases. The measured electrical conductivity of HgTe and Hg1 − xCdxTe melts (x = 0.1, 0.2) increases as a function of temperature, which shows a semiconductor-like behavior. For an intrinsic nondegenerate semiconductor, the electrical conductivity, σ, can be approximated as a function of temperature T as: Eg σ ¼ σ 0 exp − 2kT
ð1Þ
where σ0 is related to carrier mobility in Ω−1 m−1, Eg is the energy gap for the semiconductor in eV, and k is the Boltzmann's constant of 8.62 × 10−7 eV/K. Assuming that the carrier mobility does not vary very much with the temperature, the plot of ln(σ) versus 1/T will give a straight line with a slope of −Eg/2k if the energy gap is a constant as a function of temperature. According to Gubanov's liquid model [22], the energy gap in liquid semiconductor melts is approximately constant as a function of temperature, assuming that no structural transition
16
2.7 HgTe (Temp. up) HgTe (Temp. down)
Electrical conductivity (104Ω-1m-1)
Electrical conductivity (104Ω-1m-1)
850
Temperature (K) Temperature (K)
14
800
12 10 8 6 4 2
HgTe (Temp. up) HgTe (Temp. down)
2.4
Hg
Cd
Te (Temp. up)
Hg
Cd
Te (Temp. down)
Hg
Cd
Te (Temp. up)
Hg
Cd
Te (Temp. down)
0.9
2.1
0.9 0.8
1.8
0.8
0.1 0.1 0.2 0.2
1.5 1.2 0.9 0.6 0.3
T = 942 K
0 750
800
850
900
950
1000
1050
1100
1150
Temperature (K) Fig. 4. Electrical conductivity of HgTe as a function of temperature.
0.0 720
760
800
840
880
920
960
1000
Temperature (K) Fig. 6. Electrical conductivity of HgTe and Hg1 − xCdxTe solids as functions of temperature.
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C. Li et al. / Journal of Non-Crystalline Solids 391 (2014) 54–60
100 s, compared with the approximately one hour measurement time needed in the oscillation cup method [23], which further reduced the possibility of additional measurement errors caused by the instability of the system. The viscosity of the Hg0.9Cd0.1Te melt, together with that of the HgTe and Hg0.8Cd0.2Te melts [2], as a function of temperature measured by the TTV is shown in Fig. 9. It can be seen that all of the three sets of data show the same trend as a function of temperature. The increase in the measured viscosity as a function of CdTe content is most likely due to the addition of the CdTe melt, which has a higher viscosity [24] than the viscosity of HgTe melt. Using Eyring's theory [25], the free activation energy of the viscous flow Fb can be expressed: F b ¼ RT ln
Fig. 7. Electrical conductivity of HgTe and Hg1 − xCdxTe melts as functions of temperature.
occurs in the melt. As shown in Fig. 7, the logarithm of the electrical conductivity of the HgTe and Hg1 − xCdxTe melts vs. 1/T deviates from a straight line. This may be due to the fact that the energy gap of the HgTe and Hg1 − xCdxTe melts changes as a function of temperature caused by the structure changes of the HgTe and Hg1 − xCdxTe melts as a function of temperature.
3.3. Viscosity The temperature dependence of the viscosity measured for the HgTe melt is shown in Fig. 8 together with the previous results obtained by Mazuruk et al. [23] using the oscillation cup method. Both viscosity data show similar trends in that the viscosity of the HgTe melt decreased rapidly as the temperature increased. However, the present results were approximately 20% lower than that measured by Mazuruk from 1040 K to 1065 K. The two possible reasons for the discrepancies are: (1) the possible Hg bubble formation in the melt during viscosity measurement, as hypothesized by Mazuruk [23] and (2) the experimental error that is caused by the airflow around the cup in the hot furnace with the oscillation cup method adopted by Mazuruk. The unstable air not only causes high background noise but also changes the cup damping characteristics at each measurement. The TTV measures the viscosity with the ampule under a vacuum environment of 10−4 Torr, which eliminates the air convection caused by the hot furnace. Also, the measurement time with the transient torque method is only about
Mν ¼ Hb −Sb T; Nh
ð2Þ
where ν is the viscosity of the melt, M is the molecular weight, N is the Avogadro's number of 6.022 × 1023 mol−1, h is the Planck's constant of 6.626 × 10−34 J·s, T is the absolute temperature in K, and R is the molar gas constant of 8.314 J/mol-K. The free energy Fb can be expressed in terms of enthalpy Hb and entropy Sb. The values of Fb for the HgTe melt, which were calculated using the above equation, are shown in Fig. 10 as a function of temperature. The deviation of Fb from the linear function from the melting point, 943 K, to 980 K is considered to be due to the difference in the liquid structure at low temperatures and at high temperatures. The activation enthalpy of viscous flow for the HgTe melt above 980 K was determined to be 51.93 kJ/mol, and the entropy of viscous flow for the HgTe melt to be −6.435 J/mol. Similar result was obtained for the Hg0.9Cd0.1Te melt, i.e., the calculated Fb could not be treated as a linear function. Another theory, proposed by Bachinskii [26,27], can be used to obtain the structural information in the liquid phase. Bachinskii's equation, which is based on the assumption that the viscosity of a liquid is governed by the nature of the interaction between the atoms or molecules, states that the reciprocal of the kinematic viscosity is a linear function of its density ρ if the structure of a metallic or semiconductor melt is homogeneous. The equation proposed by Bachinskii can be expressed as: 1 1 b ¼ þ ρ ν c c
ð3Þ
where c and b are constants. The dependences of the reciprocal of the kinematic viscosity on the density of the HgTe and Hg0.9Cd0.1Te melts are shown in Figs. 11 and 12. In Fig. 11, a large deviation from a straight line 5.0 HgTe (Temp. up) HgTe (Temp. down) Hg0.9Cd0.1Te (Temp. up) Hg0.9Cd0.1Te (Temp. down) Hg0.8Cd0.2Te (Temp. up) Hg0.8Cd0.2Te (Temp. down)
Kinematicd Viscosity (×10-7 m2/s)
5.0
Kinematic viscosity (10-7m2/s)
Mazuruk (1995)
4.5
Fitting curve by Mazuruk Present study (Temp. Up) Present study (Temp. Down)
4.0 3.5 3.0 2.5 2.0
4.0 3.5 3.0 2.5 2.0 1.5
Tm 1.5 940
4.5
930 960
980
1000
1020
1040
1060
1080
1100
960
990
1020
1050
1080
1110
1140
Temperature (K)
Temperature K Fig. 8. Viscosity of HgTe melt as a function of temperature.
Fig. 9. Viscosity of the HgTe, Hg0.9Cd0.1Te, and Hg0.8Cd0.2Te melts as functions of temperature.
C. Li et al. / Journal of Non-Crystalline Solids 391 (2014) 54–60
59
46.8 6.0
1/(Kinematic viscosity) (106/(m2/s))
Free activation energy (kJ/mol)
46.6 46.4 46.2 46.0 45.8 Fb = -6.435 ×10 T+51.931 -3
45.6 45.4 45.2 45.0 Tm = 943 K
44.8 930
960
5.0 4.5 T=1066K
4.0 3.5 3.0
Temp up Temp down
1020
1050
1080
7.795
1110
of the 1/ν vs. ρ plot for the HgTe melt is an indication of a structural transition in the melt. A deviation of the similar plot for the Hg0.9Cd0.1Te melt from the linear function is also present as shown in Fig. 12. In other words, the analysis of viscosity implies a structural transition in the HgTe and Hg0.9Cd0.1Te melts as the temperature increased from the liquidus temperature to 1097 and 1127 K, respectively. 3.4. Time dependence of thermophysical properties On the relaxation measurements of the thermophysical properties, the measured density of the HgTe melt did not change, as the meniscus of the melt in the ampule remained at the same position, through the 8 h period after the temperature of the thermocouple readings has been cooled from 1073 K to 948 K. The time dependences of the electrical conductivity and the kinematic viscosity of the HgTe melt show that only the electrical conductivity and viscosity data taken at the initial 0.1 h after the furnace setting was cooled to 950 K were, respectively, higher and lower than their equilibrium values measured after holding at 950 K for approximately 7 h. With the rest of the data being within the experimental error of 1.6% for the electrical conductivity and 4.6% for the viscosity measurement associated with the TTV, the first set of measurements might have been taken when the temperature of the melts is still a little higher than the final equilibrium temperature. Thus, it is concluded that no relaxation behavior in the density, electrical conductivity, and kinematic viscosity of the HgTe melt was observed in this study.
1/(Kinematic viscosity) (106/(m2/s))
6.0
1
5.5
1 b c c
T=1097K T=1078K
4.5
T=1027K
4.0 3.5 3.0 Temp up Temp down T=944K
2.0 8.11
8.12
T=1016K
2.5 990
Fig. 10. Temperature dependence of the free activation energy for the HgTe melt.
2.5
1 b c c
5.5
8.13
8.14
8.15
8.16
Density (103kg/m3) Fig. 11. Dependence of the reciprocal of the kinematic viscosity on the density of the HgTe melt.
7.800
7.805
7.810
7.815
Density (103kg/m3)
Temperature (K)
5.0
1
T=1127K
Fig. 12. Dependence of the reciprocal of the kinematic viscosity on the density of the Hg0.9Cd0.1Te melt.
On the relaxation study of the Hg0.9Cd0.1Te melt, after the temperature of the thermocouples attached to the outside of the ampule wall decreased from 1130 to 1010 K, the density of Hg0.9Cd0.1Te melt did not change as a function of time. The measured electrical conductivity and viscosity of the Hg0.9Cd0.1Te melt as a function of time after the temperature was lowered from 1130 K to 1010 K show the similar behavior as that for the HgTe melt. The electrical conductivity measurement at a time of 0.25 h was 6.22 × 104 Ω− 1 m−1, which was higher than the equilibrium electrical conductivity value of 6.18 × 104 Ω−1 m−1 measured at 24.5 h. The value of the first viscosity measurement at 0.25 h was 3.36 × 10−7 m2/s, which was a little lower than the equilibrium viscosity value of 3.43 × 10−7 m2/s measured at 24.5 h. The high electrical conductivity value and the low viscosity value at approximately 0.25 h were probably due to the fact that the melt temperature was still higher than the final equilibrium temperature. It is concluded that, within the experimental error of the TTV, no relaxation behavior in the electrical conductivity and viscosity of the Hg0.9Cd0.1Te melt was observed in this study. 4. Conclusion Thermophysical properties, i.e., density, electrical conductivity and viscosity of HgTe and Hg0.9Cd0.1Te melts were determined as a function of temperature. The density results for both melts, measured by the pycnometric method, show maxima around 1020 K. The electrical conductivity and viscosity of the melts were simultaneously determined using the transient torque method. Comparing the present results for the HgTe and Hg0.9Cd0.1Te melts and previous results on the Hg0.8Cd0.2Te melt [2], the measured electrical conductivity decreases as the mole fraction of CdTe, x, increases at a specific temperature, and increases as a function of temperature, which shows a semiconductor-like behavior. On the contrary, the measured viscosity of the HgTe and Hg1 − xCdxTe melts (x = 0.1 and 0.2 [2]) increases as the mole fraction of CdTe, x, increases at a specific temperature and decreases as the temperature increased. The analysis of the electrical conductivity of the melt and the relationship between the kinematic viscosity and density implied a structural transition in these melts. No relaxation phenomena were observed in the density, electrical conductivity, and viscosity of the HgTe and Hg0.9Cd0.1Te melts. Acknowledgments The author would like to acknowledge the supports of the Advanced Capabilities Division, Exploration Systems Mission Directorate, NASA Headquarter.
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References [1] C. Li, Ching-Hua Su, S.L. Lehoczky, R.N. Scripa, B. Lin, H. Ban, J. Appl. Phys. 97 (2005) 83513. [2] C. Li, R.N. Scripa, H. Ban, B. Lin, Ching-Hua Su, S.L. Lehoczky, J. Non-Cryst. Solids 351 (2005) 1179. [3] D. Chandra, L.R. Holland, J. Vac. Sci. Technol. A 1 (1983) 1620. [4] N.P. Mokrovski, A.R. Regel, Zh. Tekh. Fiz. 22 (1952) 1281. [5] M. Glazov, L.M. Pavlova, Thermochem. Acta 314 (1998) 265. [6] V.M. Glazov, L.M. Pavlova, S.V. Stankus, J. Chim. Phys. 94 (1997) 1816. [7] V.M. Glazov, L.M. Pavlova, J. Cryst. Growth 184/185 (1998) 1253. [8] D. Chandra, Phys. Rev. Lett. B 31 (1985) 7206. [9] K. Mazuruk, C.-H. Su, Y.-G. Sha, S.L. Lehoczky, J. Appl. Phys. 79 (1996) 9080. [10] C. Li, R. Scripa, H. Ban, B. Lin, Ching-Hua Su, S.L. Lehoczky, S. Zhu, Rev. Sci. Instrum. 75 (2003). [11] Heng Ban, Bochuan Lin, Chao Li, Ching-Hua Su, S. L. Lehoczky, and Rosalia Scripa, “Theoretical basis for the transient torque viscosity measurement method”, submitted to J. Fluid Mech. [12] Ching-Hua Su, S.L. Lehoczky, F.R. Szofran, J. Appl. Phys. 60 (1986) 3777. [13] F.R. Szofran, S.L. Lehoczky, J. Electron. Mater. 10 (1981) 1131.
[14] D.R. Lide, CRC Handbook of Chemistry and Physics, CRC Press LLC, Boca Raton, London, New York, Washington, D.C., 2002. [15] C. Li, H. Ban, R.N. Scripa, Ching-Hua Su, S.L. Lehoczky, Rev. Sci. Instrum. 75 (2004) 2810. [16] M.H. Cohen, J. Jortner, Phys. Rev. B 13 (1976) 5255. [17] M.H. Cohen, J. Jortner, Phys. Rev. Lett. 30 (1973) 699. [18] M.H. Cohen, J. Jortner, Phys. Rev. Lett. 30 (1973) 696. [19] M.H. Cohen, J. Jortner, Phys. Rev. A 10 (1974) 978. [20] R.F. Brebrick, A.J. Stauss, J. Phys. Chem. Solids 26 (1965) 989. [21] G.L. Hansen, J.L. Schmit, T.N. Casselman, J. Appl. Phys. 53 (1982) 7099. [22] A.I. Gubanov, Quantum Electron Theory of Amorphous Conductors, Consultants Bureau, New York, 1965. [23] K. Mazuruk, Ching-Hua Su, S.L. Lehoczky, F. Rosenberger, J. Appl. Phys. 77 (1995) 5098. [24] V.M. Glazov, S.N. Chizhevshaya, N.N. Glagoleva, Liquid Semiconductors, Plenum Press, New York, 1969. [25] S. Glasstone, K.J. Laidler, H. Eyring, Theory of Rate Processes, McGraw-Hill, New York, 1941. [26] A.I. Bachinskii, Mremennik ob-va im. Ledentsova, prilozhenie, 3 (1913). [27] A. I. Bachinskii, Izd. An SSSR, Moscow (1960).
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/ locate/ jnoncrysol
Thermophysical properties of HgTe and Hg0.9Cd0.1Te melts C. Li a,1, Ching-Hua Su b,⁎, S.L. Lehoczky b, R.N. Scripa a, H. Ban c,2, B. Lin c,3 a b c
Department of Materials Science and Engineering, University of Alabama at Birmingham, Birmingham, AL 35294, USA Materials and Processing Laboratory, NASA Marshall Space Flight Center, Huntsville, AL 35812, USA Department of Mechanical Engineering, University of Alabama at Birmingham, Birmingham, AL 35294, USA
a r t i c l e
i n f o
Article history: Received 7 February 2014 Available online xxxx Keywords: II–VI semiconductor melt; Density; Electrical conductivity; Viscosity
a b s t r a c t Thermophysical properties, namely, density, viscosity, and electrical conductivity of HgTe and Hg0.9Cd0.1Te melts were measured as a function of temperature. A pycnometric method was used to measure the melt density in the temperature range of 948 to 1073 K for the HgTe melt and 1011 to 1131 K for the Hg0.9Cd0.1Te melt. The density results show a maximum at 1023 and 1020 K, respectively, for the HgTe and Hg0.9Cd0.1Te melts. The viscosity and electrical conductivity were simultaneously determined using a transient torque method from 944 to 1098 K for the HgTe melt and from 1016 to 1127 K for the Hg0.9Cd0.1Te melt. The measured electrical conductivity decreases as the mole fraction of CdTe, x, increases at a specific temperature, and increases as a function of temperature, which shows a semiconductor-like behavior. The measured viscosity decreases as the mole fraction of CdTe, x, increases at a specific temperature and decreases as the temperature increased. The analysis of the electrical conductivity of the melts and the relationship between the kinematic viscosity and density implied a structural transition in these melts. No relaxation phenomena were observed in the density, electrical conductivity, and viscosity of the HgTe and Hg0.9Cd0.1Te melts. Published by Elsevier B.V.
1. Introduction In our previous publications, the thermophysical properties, i.e., density, electrical conductivity and viscosity of pure Te melt [1] and Hg0.8Cd0.2Te melt [2] were determined as a function of temperature. The observed thermophysical properties in the Te melt was analyzed and the behavior was attributed to the transformation of a two-fold coordination structure to a three-fold coordination structure as the melt temperatures increase [1]. The analysis of the electrical conductivity of the Hg0.8Cd0.2Te melt and the relationship between the kinematic viscosity and density indicated a structural transition at the temperature of 1091 K [2]. In the published literatures on other compositions of the HgCdTe system, Chandra [3], Mokrovski [4], and Glazov et al. [5–7] observed a density increase in HgTe upon melting and they all observed a maximum in the density of the HgTe melt. Chandra [3], using the pycnometric method, observed a maximum in the density of Hg1 − xCdxTe (x = 0.05, 0.10) melts. Glazov [5,7] used the gamma radiation attenuation method to determine the density of Hg1 − xCdxTe (x = 0.05, 0.10, 0.15, 0.192) melts, which shows a
⁎ Corresponding author. Fax: +1 256 5448762. E-mail address: [email protected] (C.-H. Su). 1 Now at Eaton's Cooper Power System Business, 11131 Adams Road Franksville, WI 53126, USA. 2 Now at Mechanical and Aerospace Engineering, Utah State University, Logan, UT 84341, USA. 3 Now at Victory Energy LLC, 10701 E. 126th St., N., Collinsville, OK 74021, USA.
http://dx.doi.org/10.1016/j.jnoncrysol.2014.03.012 0022-3093/Published by Elsevier B.V.
behavior similar to those measured by Chandra [3]. Chandra adopted an inhomogeneous two-phase structure model for the melt to interpret the Hg1 − xCdxTe anomalous density changes [8]. Glazov [7] used an associate solution model by introducing a [Cd2−(Hg2Te4)2−] complex to explain the anomalous density change. Mazuruk et al. [9] observed a slow relaxation phenomenon in the measurement on the viscosity of Hg0.84Zn0.16Te melt. Two sets of viscosity relaxation data were obtained by cooling the Hg0.84Zn0.16Te melt from 1123 K to 1083 K and to 1063 K. It took a day for the viscosity of the Hg0.84Zn0.16Te melt to reach the equilibrium value at 1083 K. However, it took longer than a week for the viscosity of the Hg0.84Zn0.16Te melt to reach the equilibrium value after it has been cooled to the temperature of 1063 K, which is just 20 K above the liquidus temperature of 1043 K. Mazuruk [9] attributed the nature of this kind of timedependence effect to macroscopic and microscopic inhomogeneities in the melt. In this study, the thermophysical property measurements were extended to other compositions in the HgCdTe system. The density, electrical conductivity and viscosity were accurately determined for the HgTe and Hg0.9Cd0.1Te melts and the possible structural transition in the melts were analyzed. The density of the melts as a function of temperature was measured using a pycnometric method. The electrical conductivity and viscosity of the melt were simultaneously determined using the transient torque method developed recently [10,11]. The relaxation behavior of the thermophysical properties of the HgTe and Hg0.9Cd0.1Te melts was also investigated. These thermophysical properties were measured as a function of time after the melts was rapidly
C. Li et al. / Journal of Non-Crystalline Solids 391 (2014) 54–60
cooled to a lower temperature near the melting point or the liquidus temperature. 2. Experimental procedures 2.1. Sample preparation The ampules for thermophysical property measurements of the HgCdTe melts were made of fused silica tubes. A thermometer-shaped ampule, which had an approximately 10 cm long 15 × 9 mm “bulb” at the bottom and 10 cm long 6 × 3 mm “stem” at the top, was used for the density measurement. A 15 × 9 mm ampule was used for the electrical conductivity and viscosity measurement. Each ampule was baked in a vacuum of 5 × 10− 5 Torr at 1430 K for 16 h after it was cleaned by hydrofluoric acid, acetone, methanol, and distilled water. The Hg1 − xCdxTe, x = 0 and 0.10, samples for density, electrical conductivity and viscosity measurements were prepared by synthesizing directly from the pure elements. The starting materials were six nine grade Cd and Te from Johnson Matthey Co. and seven nine grade Hg from Bethlehem Apparatus. After the weighing by a Mettler AT201 electronic balance with an accuracy of 10−5 g, each element was loaded into the prepared ampule. Table 1 gives the weight of each element used in the HgTe, and Hg1 − xCdxTe samples for density measurements as well as for the electrical conductivity and viscosity measurements. After the ampules were sealed under a vacuum of approximately 5 × 10−5 Torr, they were placed in a rocking furnace and synthesized according to the following homogenization procedures. The HgTe samples for thermophysical property measurements were heated to approximately 773 K in the horizontal position and held for 1 h. The temperature was then raised to 973 K and the samples were held at the temperature for approximately 2 h to ensure that the reaction of Hg and Te was complete. Finally, the HgTe samples were heated to 1143 K, which was approximately 20 K higher than the maximum temperature used for the measurements of the thermophysical properties, and were held for 1 h. The Hg0.9Cd0.1Te samples were homogenized following the procedure developed previously at NASA/ MSFC [12]. The ampules containing the elements were heated in the rocking furnace to approximately 770 K and held at this temperature for 16 to 20 h. Then the temperature was raised to 935 K, which is about 30 K below the solidus temperature [13], and maintained there for 20 h to allow for the homogenization by the inter-diffusion of the elements. Finally, the temperature was increased to 1095 K, which is about 100 K above the liquidus temperature [13], and held there for 20 h with the furnace rocking to homogenize the melts. Before the sample was cast in the rocking furnace, the sample was heated to 1143 K, which is approximately 20 K above the maximum temperature used in the thermophysical property measurements. Both the HgTe and Hg0.9Cd0.1Te samples were solidified by turning off the power to the rocking furnace, with the furnace being held at 60° to its horizontal position during casting. 2.2. Density measurement The densities of the HgTe and Hg0.1Cd0.9Te melts as a function of temperature were measured by the pycnometric method. The Table 1 The weight of each element used in the HgTe, and Hg0.1Cd0.9Te samples for density, electrical conductivity and viscosity measurements. Sample
Hg (g)
Te (g)
Cd (g)
HgTea HgTeb Hg1 − xCdxTea (x = 0.1) Hg1 − xCdxTeb (x = 0.1)
32.70543 14.03774 25.31182 14.41327
20.80072 8.92898 17.89101 10.19109
– – 1.57609 0.89760
a b
Density measurements. Electrical conductivity and viscosity measurements.
55
technique has been described in detail elsewhere [1,2] and will be presented briefly here. The weight of the empty ampule and that of the ampule filled to each quartz mark on the ampule with distilled water as well as the water temperature were measured. The volume corresponding to each referenced mark was calculated from the weight difference and the water density vs. temperature data from CRC Handbook [14]. The density ampule was placed in the center of a two-zone (15 and 35 cm long) transparent furnace provided by Thermcraft, Inc. Four K-type thermocouples were attached along the outside of the ampule wall to record the temperature of the sample. The temperatures of the two zones were set with a positive temperature difference of 3 K (hot on top) to avoid bubble formation inside the melt during the density measurement. The temperature stability of the transparent furnace was better than 0.5 K at all of the measured temperatures. A silhouette of the curved melt surface was visible through the transparent furnace with the aid of a backlight. The distance between the silhouette and a reference mark was monitored and recorded using a digital camera and a VCR. The volume of the HgTe and Hg0.1Cd0.9Te melts was determined by measuring the distance from the meniscus of the melt to one of the reference marks. The resolution of the distance measurement in this pycnometric setup was 0.05 mm, corresponding to an uncertainty of approximately 0.15% in the measured density. 2.3. Electrical conductivity and viscosity measurement The viscosity and electrical conductivity of the HgTe and Hg0.9Cd0.1Te melts were measured by a transient torque viscometer (TTV) developed in our laboratory to determine the viscosity and electrical conductivity rapidly and simultaneously. The schematic setup and the principle of the TTV have been discussed in detail in our previous publications [15]. The essential feature of this method was the utilization of a rotating magnetic field (RMF) to interact with the melt and generate a rotating Lorentz force. This force in turn generated a rotational flow in the melt which caused the ampule to rotate along with the flow. The transient rotating angle of the ampule as a function of time after the RMF has been applied was measured to determine the electrical conductivity and viscosity of the melt. 2.4. Time dependence of thermophysical properties The time dependence of the thermophysical properties of the HgTe and Hg0.9Cd0.1Te melts was also investigated. The time relaxation behavior of the density of the HgTe melt was measured after the melt was cooled from 1073 K to 948 K, which is approximately 5 K above the melting point of HgTe. The time needed for the HgTe melt to cool from 1073 K to 948 K in the transparent furnace was approximately 15 min. The time “zero” of the relaxation measurement was started when the temperatures of the thermocouples attached to the outside of the ampule wall reached 948 K. The time relaxation behavior of the electrical conductivity and viscosity of the HgTe melt was measured after the melt was cooled from 1103 K to 950 K. Before cooling, the HgTe sample has been held at 1103 K for a week to ensure that it was in the equilibrium state. The thermocouple could not be attached to the outside of the ampule during the electrical conductivity and viscosity measurement in the TTV. The temperature of the sample was monitored using the reading of the TTV furnace controller and time “zero” was defined as when the controller thermocouple reads 950 K. The time needed for the temperature of the TTV furnace to decrease from 1103 K to 950 K was approximately 45 min. During the actual temperature calibration for the TTV furnace, it was observed that it took approximately half an hour after the time “zero” for the temperature inside the TTV furnace to be cooled down to the equilibrium temperature. The density of the Hg0.9Cd0.1Te melt as a function of time was measured after the melt was cooled from 1130 K to 1010 K, which is approximately 15 K above its liquidus temperature. Cooling time was approximately 15 min. The viscosity and electrical conductivity of the
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Hg0.9Cd0.1Te melt as a function of time were determined after the melt was cooled from 1130 K to 1010 K in approximately 30 min. The time “zero” for the density, electrical conductivity, and viscosity measurements was determined in the similar methods as discussed earlier for the HgTe melt.
3. Results, analyses and discussions 3.1. Density 3.1.1. HgTe melt During the heat-up, an increase in the density of HgTe was observed upon the melting of the sample. The published value of the density of solid HgTe just below the melting point is 7.97 × 103 kg/m3. The density of the HgTe melt measured as a function of temperature is shown in Fig. 1. Previously published density results for the HgTe melt by Glazov [5,6] using the gamma radiation attenuation method and by Chandra [3] using the pycnometric method are also plotted in Fig. 1 for comparison. In the figure, “Temp. Up” and “Temp. Down” indicate that the measurements were taken while increasing and decreasing the temperature, respectively. There were over 200 data points reported in Refs. [5,6] in the temperature range of 943 K to 1080 K with the absolute error reported to be approximately ±0.01 × 103 kg/m3. The fitting curve of these density data of HgTe melt determined is thus shown as a solid line in Fig. 1. The density of the HgTe melt increased as a function of increasing temperature to a maximum value of 8.16 × 103 kg/m3 at about 1023 K and then showed a slight downward trend. The previous works by Glazov [5,6] and Chandra [3] show a similar trend. However, the values of Glazov were about 0.6% and that of Chandra were about 1.5 to 2% lower than the present results. In Glazov's work [5,6], the absorption coefficient of the HgTe melt in the gamma ray radiation attenuation method was calibrated using a solid HgTe sample, which might have contributed an additional error in the density measurements. The underestimation in the densities of the HgTe melt by Chandra [3] was suspected by Glazov [5,6] to be due to the possible formations of tiny Hg bubbles in the HgTe melt because of the non-uniform temperature distribution in the melt during the density measurements. The density trend of the HgTe melt shows the similar behavior to that of the Te melt [1] in that it goes through a maximum as a function of temperature. This behavior implies that there are likely two or more types of structures in the HgTe melt [5,6,8]. A quantitative description of the density of the HgTe melt as a function of temperature was attempted by both Chandra [8] and Glazov [5,6] by applying an effective-medium theory developed by Cohen and Jornter [16–19]. In Chandra's assumption, the HgTe melt structure was considered to be a
mixture of low- and high-coordination-number structures that have the same total number of Hg and Te atoms. The assumed lowcoordination-number structure of the HgTe melt has a lower density than that of the high-coordination-number structure. The increase in density of the HgTe melt with increasing temperature was attributed to its continuous transformation from the low-coordination-number structure to the denser, high-coordination-number structure. The decrease in the density of the HgTe melt after reaching its maximum is due to the thermal expansion of the two structures. In Glazov's assumption, which was based on an associated equilibrium solution theory [20], the structure of the HgTe melt consists of several kinds of structures namely, Hg, Te, HgTe, and Hg2Te3. The maximum in the HgTe melt density was attributed to the combined changes of the molar volumes and the volume fractions of the various structures as a function of temperature.
3.1.2. Hg0.9Cd0.1Te melt The measured densities of the Hg0.9Cd0.1Te melts as a function of temperature are shown in Fig. 2. Previous results for the Hg0.9Cd0.1Te melt measured by Glazov [5,7] and Chandra [8] are also plotted in the figure for comparison. The density of the Hg0.9Cd0.1Te melt measured by Glazov was scattered with the 2nd-order polynomial least rootmean-square fitting result shown as a curve. The density values of the Hg0.9Cd0.1Te measured by Chandra [8] and by Glazov are about 0.2% and 0.25%, respectively, lower than the results of the present study. The lower density values measured for the Hg0.9Cd0.1Te melt in those studies may be attributed to the same reasons as described earlier for the HgTe melt. A maximum in the density of the Hg0.9Cd0.1Te melt was observed in this study at a temperature of approximately 1020 K, as shown in Fig. 2. The temperature where the Hg0.9Cd0.1Te melt density reaches a maximum agrees with Chandra's results [8]. The density measured by Glazov (fitting curve in Fig. 2) shows a maximum at 1029 K. Fig. 3 includes the density data of the HgTe and Hg0.9Cd0.1Te melts as well as our previous results on the Hg0.8Cd0.2Te [2] melt for comparison. It clearly shows that the density of the Hg1 − xCdxTe melt decreases with an increase in the CdTe mole fraction in the melt. The temperatures of 1023 and 1020 K labeled in Fig. 3 are the temperatures where the density of the HgTe and Hg0.9Cd0.1Te melts, respectively, reaches the maximum. The approximately same temperature at which the maximum density of the HgTe and Hg0.9Cd0.1Te melts occurred implies that the density change in the Hg0.9Cd0.1Te melt is mainly due to its density change of its HgTe component. The reason that no maximum was observed in the density of the Hg0.8Cd0.2Te melt may be due to its liquidus temperature (approximately 1160 K [13]), which is higher than 1023 K.
7.815
8.16
7.810
Density (103 kg/m3)
Density (103 kg/m3)
8.12 8.08 8.04 8.00 Solid Te
7.96
Present study (Temp. Up) Present study (Temp. Down)
7.92
Tm=943 K
Glazov (1997)
980
1000
1020
1040
7.795 7.790 7.785 Present study (Temp. Up)
7.780
Present study (Temp. Down)
7.775
Glazov (1998)
7.770
7.88 960
7.800
Fitting curve from Glazov
Chandra (1983)
940
7.805
1060
Temperature (K) Fig. 1. Density of HgTe as a function of temperature.
1080
1000
Chandra (1983)
1020
1040
1060
1080
1100
1120
Temperature (K) Fig. 2. Temperature dependence of density of Hg0.9Cd0.1Te melt.
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8.2
HgTe (Temp. Up) HgTe (Temp. Down)
8.0
7.9
Hg
Cd Te (Temp. Up) 0.9 0.1
Hg
Cd Te (Temp. Down) 0.9 0.1
Hg
Cd Te (Temp. Up) 0.8 0.2
Hg
Cd Te (Temp. Down) 0.8 0.2
7.8
7.7
Electrical conductivity (104Ω-1m-1)
16
8.1
Density (103 kg/m3)
57
14
Hg Cd0.1Te (Temp. up)
12
Hg0.9Cd0.1Te (Temp. down)
0.9
10 8 6 4 2 T = 961 K
7.6 0 750
T=1020K T=1023K 7.5 930
960
990
1020
1050
1080
1110
900
950
1000
1050
1100
1150
1140 Fig. 5. Temperature dependence of electrical conductivity of Hg0.9Cd0.1Te.
Fig. 3. Density of the HgTe, Hg0.9Cd0.1Te, and Hg0.8Cd0.2Te melts.
3.2. Electrical conductivity In this study, the electrical conductivity measurement by the transient torque method started at 750 K, where the HgTe and Hg0.9Cd0.1Te samples were solids. The measured electrical conductivities for the HgTe and Hg0.9Cd0.1Te solids and melts as a function of temperature are shown in Figs. 4 and 5, respectively. Presently, no data are available in the literature on the electrical conductivities of the HgTe and Hg0.9Cd0.1Te samples at elevated temperatures for comparison. As shown in Fig. 4, the electrical conductivity of the HgTe changes drastically when the sample melts. By monitoring the change of the electrical conductivity as a function of temperature, the melting point of HgTe was determined to be 942 K, which is 1 K lower than the published value. Similarly, the solidus temperature of Hg0.9Cd0.1Te was estimated to be 961 K, which is 1 K higher than the results previously reported [13] using the precision differential thermal analysis. To compare the electrical conductivities of the HgTe and the Hg 1 − x Cd x Te solids, all data, including previously published results for the Hg0.8Cd0.2Te solid [2], are plotted together in the measured range of 750 to 940 K in Fig. 6. The decrease in electrical conductivity as a function x is most likely due to the increase in the energy gap of the Hg1 − xCdxTe solids. HgTe is a semimetal with an energy bandgap of 0 eV and an analysis of its electrical conductivity as a function of temperature from 300 K to the melting point will be given in detail
elsewhere. The bandgap, Eg, of Hg1 − xCdxTe increases with the increasing x and temperature. For instance, using the formula given by Hansen et al. [21], Eg = 0.20 and 0.30 eV for x = 0.1 and 0.2, respectively, at 750 K and Eg = 0.29 and 0.36 eV for x = 0.1 and 0.2, respectively, at 950 K. Fig. 7 shows the electrical conductivity of the HgTe and Hg1 − xCdxTe melts, including the previously published results for the Hg0.8Cd0.2Te melt [2], in the logarithm scale versus 1/T. At a specific temperature, the electrical conductivity of the melts decreases as the mole fraction of CdTe, x, increases. The measured electrical conductivity of HgTe and Hg1 − xCdxTe melts (x = 0.1, 0.2) increases as a function of temperature, which shows a semiconductor-like behavior. For an intrinsic nondegenerate semiconductor, the electrical conductivity, σ, can be approximated as a function of temperature T as: Eg σ ¼ σ 0 exp − 2kT
ð1Þ
where σ0 is related to carrier mobility in Ω−1 m−1, Eg is the energy gap for the semiconductor in eV, and k is the Boltzmann's constant of 8.62 × 10−7 eV/K. Assuming that the carrier mobility does not vary very much with the temperature, the plot of ln(σ) versus 1/T will give a straight line with a slope of −Eg/2k if the energy gap is a constant as a function of temperature. According to Gubanov's liquid model [22], the energy gap in liquid semiconductor melts is approximately constant as a function of temperature, assuming that no structural transition
16
2.7 HgTe (Temp. up) HgTe (Temp. down)
Electrical conductivity (104Ω-1m-1)
Electrical conductivity (104Ω-1m-1)
850
Temperature (K) Temperature (K)
14
800
12 10 8 6 4 2
HgTe (Temp. up) HgTe (Temp. down)
2.4
Hg
Cd
Te (Temp. up)
Hg
Cd
Te (Temp. down)
Hg
Cd
Te (Temp. up)
Hg
Cd
Te (Temp. down)
0.9
2.1
0.9 0.8
1.8
0.8
0.1 0.1 0.2 0.2
1.5 1.2 0.9 0.6 0.3
T = 942 K
0 750
800
850
900
950
1000
1050
1100
1150
Temperature (K) Fig. 4. Electrical conductivity of HgTe as a function of temperature.
0.0 720
760
800
840
880
920
960
1000
Temperature (K) Fig. 6. Electrical conductivity of HgTe and Hg1 − xCdxTe solids as functions of temperature.
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100 s, compared with the approximately one hour measurement time needed in the oscillation cup method [23], which further reduced the possibility of additional measurement errors caused by the instability of the system. The viscosity of the Hg0.9Cd0.1Te melt, together with that of the HgTe and Hg0.8Cd0.2Te melts [2], as a function of temperature measured by the TTV is shown in Fig. 9. It can be seen that all of the three sets of data show the same trend as a function of temperature. The increase in the measured viscosity as a function of CdTe content is most likely due to the addition of the CdTe melt, which has a higher viscosity [24] than the viscosity of HgTe melt. Using Eyring's theory [25], the free activation energy of the viscous flow Fb can be expressed: F b ¼ RT ln
Fig. 7. Electrical conductivity of HgTe and Hg1 − xCdxTe melts as functions of temperature.
occurs in the melt. As shown in Fig. 7, the logarithm of the electrical conductivity of the HgTe and Hg1 − xCdxTe melts vs. 1/T deviates from a straight line. This may be due to the fact that the energy gap of the HgTe and Hg1 − xCdxTe melts changes as a function of temperature caused by the structure changes of the HgTe and Hg1 − xCdxTe melts as a function of temperature.
3.3. Viscosity The temperature dependence of the viscosity measured for the HgTe melt is shown in Fig. 8 together with the previous results obtained by Mazuruk et al. [23] using the oscillation cup method. Both viscosity data show similar trends in that the viscosity of the HgTe melt decreased rapidly as the temperature increased. However, the present results were approximately 20% lower than that measured by Mazuruk from 1040 K to 1065 K. The two possible reasons for the discrepancies are: (1) the possible Hg bubble formation in the melt during viscosity measurement, as hypothesized by Mazuruk [23] and (2) the experimental error that is caused by the airflow around the cup in the hot furnace with the oscillation cup method adopted by Mazuruk. The unstable air not only causes high background noise but also changes the cup damping characteristics at each measurement. The TTV measures the viscosity with the ampule under a vacuum environment of 10−4 Torr, which eliminates the air convection caused by the hot furnace. Also, the measurement time with the transient torque method is only about
Mν ¼ Hb −Sb T; Nh
ð2Þ
where ν is the viscosity of the melt, M is the molecular weight, N is the Avogadro's number of 6.022 × 1023 mol−1, h is the Planck's constant of 6.626 × 10−34 J·s, T is the absolute temperature in K, and R is the molar gas constant of 8.314 J/mol-K. The free energy Fb can be expressed in terms of enthalpy Hb and entropy Sb. The values of Fb for the HgTe melt, which were calculated using the above equation, are shown in Fig. 10 as a function of temperature. The deviation of Fb from the linear function from the melting point, 943 K, to 980 K is considered to be due to the difference in the liquid structure at low temperatures and at high temperatures. The activation enthalpy of viscous flow for the HgTe melt above 980 K was determined to be 51.93 kJ/mol, and the entropy of viscous flow for the HgTe melt to be −6.435 J/mol. Similar result was obtained for the Hg0.9Cd0.1Te melt, i.e., the calculated Fb could not be treated as a linear function. Another theory, proposed by Bachinskii [26,27], can be used to obtain the structural information in the liquid phase. Bachinskii's equation, which is based on the assumption that the viscosity of a liquid is governed by the nature of the interaction between the atoms or molecules, states that the reciprocal of the kinematic viscosity is a linear function of its density ρ if the structure of a metallic or semiconductor melt is homogeneous. The equation proposed by Bachinskii can be expressed as: 1 1 b ¼ þ ρ ν c c
ð3Þ
where c and b are constants. The dependences of the reciprocal of the kinematic viscosity on the density of the HgTe and Hg0.9Cd0.1Te melts are shown in Figs. 11 and 12. In Fig. 11, a large deviation from a straight line 5.0 HgTe (Temp. up) HgTe (Temp. down) Hg0.9Cd0.1Te (Temp. up) Hg0.9Cd0.1Te (Temp. down) Hg0.8Cd0.2Te (Temp. up) Hg0.8Cd0.2Te (Temp. down)
Kinematicd Viscosity (×10-7 m2/s)
5.0
Kinematic viscosity (10-7m2/s)
Mazuruk (1995)
4.5
Fitting curve by Mazuruk Present study (Temp. Up) Present study (Temp. Down)
4.0 3.5 3.0 2.5 2.0
4.0 3.5 3.0 2.5 2.0 1.5
Tm 1.5 940
4.5
930 960
980
1000
1020
1040
1060
1080
1100
960
990
1020
1050
1080
1110
1140
Temperature (K)
Temperature K Fig. 8. Viscosity of HgTe melt as a function of temperature.
Fig. 9. Viscosity of the HgTe, Hg0.9Cd0.1Te, and Hg0.8Cd0.2Te melts as functions of temperature.
C. Li et al. / Journal of Non-Crystalline Solids 391 (2014) 54–60
59
46.8 6.0
1/(Kinematic viscosity) (106/(m2/s))
Free activation energy (kJ/mol)
46.6 46.4 46.2 46.0 45.8 Fb = -6.435 ×10 T+51.931 -3
45.6 45.4 45.2 45.0 Tm = 943 K
44.8 930
960
5.0 4.5 T=1066K
4.0 3.5 3.0
Temp up Temp down
1020
1050
1080
7.795
1110
of the 1/ν vs. ρ plot for the HgTe melt is an indication of a structural transition in the melt. A deviation of the similar plot for the Hg0.9Cd0.1Te melt from the linear function is also present as shown in Fig. 12. In other words, the analysis of viscosity implies a structural transition in the HgTe and Hg0.9Cd0.1Te melts as the temperature increased from the liquidus temperature to 1097 and 1127 K, respectively. 3.4. Time dependence of thermophysical properties On the relaxation measurements of the thermophysical properties, the measured density of the HgTe melt did not change, as the meniscus of the melt in the ampule remained at the same position, through the 8 h period after the temperature of the thermocouple readings has been cooled from 1073 K to 948 K. The time dependences of the electrical conductivity and the kinematic viscosity of the HgTe melt show that only the electrical conductivity and viscosity data taken at the initial 0.1 h after the furnace setting was cooled to 950 K were, respectively, higher and lower than their equilibrium values measured after holding at 950 K for approximately 7 h. With the rest of the data being within the experimental error of 1.6% for the electrical conductivity and 4.6% for the viscosity measurement associated with the TTV, the first set of measurements might have been taken when the temperature of the melts is still a little higher than the final equilibrium temperature. Thus, it is concluded that no relaxation behavior in the density, electrical conductivity, and kinematic viscosity of the HgTe melt was observed in this study.
1/(Kinematic viscosity) (106/(m2/s))
6.0
1
5.5
1 b c c
T=1097K T=1078K
4.5
T=1027K
4.0 3.5 3.0 Temp up Temp down T=944K
2.0 8.11
8.12
T=1016K
2.5 990
Fig. 10. Temperature dependence of the free activation energy for the HgTe melt.
2.5
1 b c c
5.5
8.13
8.14
8.15
8.16
Density (103kg/m3) Fig. 11. Dependence of the reciprocal of the kinematic viscosity on the density of the HgTe melt.
7.800
7.805
7.810
7.815
Density (103kg/m3)
Temperature (K)
5.0
1
T=1127K
Fig. 12. Dependence of the reciprocal of the kinematic viscosity on the density of the Hg0.9Cd0.1Te melt.
On the relaxation study of the Hg0.9Cd0.1Te melt, after the temperature of the thermocouples attached to the outside of the ampule wall decreased from 1130 to 1010 K, the density of Hg0.9Cd0.1Te melt did not change as a function of time. The measured electrical conductivity and viscosity of the Hg0.9Cd0.1Te melt as a function of time after the temperature was lowered from 1130 K to 1010 K show the similar behavior as that for the HgTe melt. The electrical conductivity measurement at a time of 0.25 h was 6.22 × 104 Ω− 1 m−1, which was higher than the equilibrium electrical conductivity value of 6.18 × 104 Ω−1 m−1 measured at 24.5 h. The value of the first viscosity measurement at 0.25 h was 3.36 × 10−7 m2/s, which was a little lower than the equilibrium viscosity value of 3.43 × 10−7 m2/s measured at 24.5 h. The high electrical conductivity value and the low viscosity value at approximately 0.25 h were probably due to the fact that the melt temperature was still higher than the final equilibrium temperature. It is concluded that, within the experimental error of the TTV, no relaxation behavior in the electrical conductivity and viscosity of the Hg0.9Cd0.1Te melt was observed in this study. 4. Conclusion Thermophysical properties, i.e., density, electrical conductivity and viscosity of HgTe and Hg0.9Cd0.1Te melts were determined as a function of temperature. The density results for both melts, measured by the pycnometric method, show maxima around 1020 K. The electrical conductivity and viscosity of the melts were simultaneously determined using the transient torque method. Comparing the present results for the HgTe and Hg0.9Cd0.1Te melts and previous results on the Hg0.8Cd0.2Te melt [2], the measured electrical conductivity decreases as the mole fraction of CdTe, x, increases at a specific temperature, and increases as a function of temperature, which shows a semiconductor-like behavior. On the contrary, the measured viscosity of the HgTe and Hg1 − xCdxTe melts (x = 0.1 and 0.2 [2]) increases as the mole fraction of CdTe, x, increases at a specific temperature and decreases as the temperature increased. The analysis of the electrical conductivity of the melt and the relationship between the kinematic viscosity and density implied a structural transition in these melts. No relaxation phenomena were observed in the density, electrical conductivity, and viscosity of the HgTe and Hg0.9Cd0.1Te melts. Acknowledgments The author would like to acknowledge the supports of the Advanced Capabilities Division, Exploration Systems Mission Directorate, NASA Headquarter.
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