Figure 1: Low temperature isotherms Ln(Cp/R) vs Ln(N) of diamond-like phases with sphalerite structure. 1) 20, 2) 25, 3) 30, 4) 35, 5) 40, 6)45, 7) 50K
It is also convenient to use the form Cp vs Ln(N) above 50K
No |
Phase |
a |
b |
c |
T. K range |
n |
σMK |
Reference |
1a |
Si |
23.55 |
3.394 |
4.138 |
300-1500 |
31 |
0.04 |
[10] |
1b |
Si, AlP |
23.34 |
3.476 |
3.837 |
300-1500 |
66 |
0.23 |
[10] |
1c |
Si, AlP |
24.31 |
2.319 |
4.550 |
300-1500 |
31 |
0.08 |
This work |
2 |
GaP. (AlAs) |
23.53 |
3.369 |
2.182 |
300-1000 |
9 |
0.02 |
This work |
3a |
Ge |
23.45 |
3.740 |
1.162 |
324- 753 |
29 |
0.05 |
[10] |
3b |
Ge, (GaAs) |
23.45 |
3.813 |
1.185 |
300-1500 |
28 |
0.05 |
This work |
4 |
InAs. GaSb |
24.43 |
3.339 |
1.192 |
300-1000 |
9 |
0.02 |
This work |
5a |
a-Sn, (InSb) |
25.25 |
2.958 |
1.121 |
300-1000 |
9 |
0.01 |
This work |
5b |
a-Sn, InSb |
24.32 |
4.723 |
0.1776 |
800-1000 |
6 |
0.07 |
[10] |
6 |
HgS |
24.98 |
3.036 |
1.062 |
300-1000 |
12 |
0.02 |
This work |
7 |
HgSe |
25.88 |
2.506 |
1.061 |
300-1000 |
12 |
0.04 |
This work |
8 |
HgTe |
26.14 |
2.944 |
0.4395 |
300-1000 |
12 |
0.02 |
This work |
9 |
Pb |
27.25 |
2.414 |
0.3818 |
300-1000 |
12 |
0.02 |
This work |
Table 1: Parameters of Maier-Kelley equations CMKP= a + b10-3T - c105T-2 (J·(mole-atom)-1·K-1) at the high temperature region
No |
Phase |
n |
To |
A1 |
T1 |
A2 |
Θ2 |
A3 |
T2 |
a |
b |
σ 102 |
1 |
Si. AlP |
77 |
230 |
0.350 |
338.8 |
0.365 |
819.1 |
0.285 |
852.6 |
24.31 |
2.319 |
6 |
2 |
Ge |
137 |
313.7 |
0.358 |
187.7 |
0.330 |
467.2 |
0.311 |
504.2 |
23.45 |
3.813 |
11 |
3 |
a-Sn |
27 |
82.5 |
0.464 |
128.3 |
0.227 |
338.7 |
0.309 |
380.1 |
25.25 |
2.958 |
6 |
4 |
AlAs. GaP |
33 |
429.9 |
0.484 |
281.1 |
0.210 |
693.1 |
0.305 |
714.7 |
23.53 |
3.369 |
7 |
5 |
InAs. GaSb |
31 |
299.6 |
0.435 |
160.9 |
0.260 |
417.5 |
0.306 |
429 |
24.53 |
3.369 |
10 |
6 |
HgS |
27 |
64.9 |
0.451 |
133.3 |
0.242 |
356.1 |
0.307 |
380.1 |
24.96 |
3.060 |
7 |
7 |
HgSe |
27 |
220.8 |
0.428 |
98 |
0.267 |
272.7 |
0.305 |
315.4 |
25.88 |
2.506 |
8 |
8 |
HgTe |
27 |
52.7 |
0.523 |
83.7 |
0.204 |
265.8 |
0.273 |
287.3 |
26.32 |
2.401 |
7 |
9 |
Pb |
26 |
36.6 |
0.396 |
74.2 |
0.396 |
74.5 |
0.208 |
300.9 |
27.25 |
2.414 |
14 |
Table 2: Parameters of function (1) in the range 0.1 - Tm K
Phase |
Si. AlP |
AlAs. |
Ge. GaAs [10] |
InAs. |
Sn. |
HgS |
HgSe |
HgTe |
Pb |
5 |
0.00048 |
0.0018 |
0.0050 |
0.015 |
0.044 |
0.0365 |
0.10 |
0.269 |
0.300 |
10 |
0.00596 |
0.021 |
0.0667 |
0.213 |
0.450 |
0.4029 |
0.90 |
1.699 |
3.311 |
15 |
0.0300 |
0.117 |
0.330 |
0.711 |
1.432 |
1.255 |
2.53 |
4.100 |
7.544 |
20 |
0.0971 |
0.366 |
0.828 |
1.578 |
2.871 |
2.581 |
4.43 |
6.624 |
11.16 |
25 |
0.2383 |
0.707 |
1.528 |
2.711 |
4.443 |
4.075 |
6.21 |
8.625 |
13.83 |
30 |
0.4790 |
1.187 |
2.398 |
3.952 |
5.957 |
5.543 |
7.79 |
10.37 |
15.80 |
35 |
0.8199 |
1.790 |
3.359 |
5.193 |
7.356 |
6.914 |
9.23 |
11.86 |
17.31 |
40 |
1.165 |
2.484 |
4.348 |
6.385 |
8.445 |
8.180 |
10.54 |
13.2 |
18.51 |
45 |
1.589 |
3.234 |
5.327 |
7.511 |
9.842 |
9.358 |
11.77 |
14.42 |
19.50 |
50 |
2.061 |
4.010 |
6.277 |
8.573 |
10.97 |
10.46 |
12.91 |
15.52 |
20.34 |
55 |
2.567 |
4.791 |
7.190 |
9.578 |
12.00 |
11.49 |
13.96 |
16.53 |
21.07 |
60 |
3.095 |
5.563 |
8.067 |
10.53 |
12.97 |
12.45 |
14.92 |
17.44 |
21.70 |
65 |
3.635 |
6.319 |
8.908 |
11.42 |
13.88 |
13.35 |
15.80 |
18.26 |
22.25 |
70 |
4.180 |
7.054 |
9.715 |
12.27 |
14.72 |
14.19 |
16.61 |
19.00 |
22.74 |
75 |
4.725 |
7.766 |
10.48 |
13.07 |
15.49 |
14.98 |
17.33 |
19.66 |
23.17 |
80 |
5.266 |
8.456 |
11.22 |
13.82 |
16.21 |
15.70 |
17.99 |
20.25 |
23.56 |
85 |
5.802 |
9.122 |
11.93 |
14.52 |
16.86 |
16.37 |
18.59 |
20.78 |
23.90 |
90 |
6.331 |
9.766 |
12.60 |
15.18 |
17.46 |
16.98 |
19.13 |
21.26 |
24.20 |
95 |
6.852 |
10.39 |
13.23 |
15.80 |
18.02 |
17.55 |
19.62 |
21.68 |
24.47 |
100 |
7.366 |
10.85 |
13.84 |
17.40 |
18.53 |
18.08 |
20.07 |
22.07 |
24.72 |
110 |
8.369 |
12.02 |
15.07 |
17.04 |
19.43 |
19.00 |
20.84 |
22.73 |
25.14 |
120 |
9.338 |
13.04 |
15.90 |
18.29 |
20.20 |
19.79 |
21.49 |
23.27 |
25.48 |
130 |
10.269 |
13.98 |
17.00 |
19.07 |
20.85 |
20.46 |
22.03 |
23.72 |
25.77 |
140 |
11.161 |
14.84 |
17.90 |
19.74 |
21.41 |
21.03 |
22.49 |
24.09 |
26.01 |
150 |
12.010 |
15.63 |
18.50 |
20.32 |
21.89 |
21.52 |
22.89 |
24.41 |
26.21 |
160 |
12.817 |
16.36 |
19.12 |
20.83 |
22.31 |
21.95 |
23.23 |
24.68 |
26.39 |
170 |
13.579 |
17.02 |
19.67 |
21.28 |
22.67 |
22.33 |
23.53 |
24.92 |
26.54 |
180 |
14.297 |
17.63 |
20.16 |
21.67 |
22.99 |
22.65 |
23.79 |
25.12 |
26.68 |
190 |
14.973 |
18.19 |
20.59 |
22.01 |
23.27 |
22.94 |
24.03 |
25.3 |
26.80 |
200 |
15.606 |
18.69 |
20.97 |
22.32 |
23.52 |
23.20 |
24.23 |
25.46 |
26.91 |
220 |
16.753 |
19.58 |
21.62 |
22.85 |
23.94 |
23.63 |
24.59 |
25.72 |
27.09 |
240 |
17.753 |
20.33 |
22.15 |
23.27 |
24.23 |
23.99 |
24.86 |
25.94 |
27.24 |
260 |
18.625 |
20.95 |
22.58 |
23.62 |
24.58 |
24.28 |
25.13 |
26.12 |
27.37 |
280 |
19.390 |
21.49 |
22.94 |
23.92 |
24.78 |
24.53 |
25.35 |
26.28 |
27.49 |
Table 3: The recommended Cp(T) of like-diamond phases at low temperature in (J·(mol-at)-1·K-1)
T.K |
Si.AlP |
GaP. |
Ge. |
GaSb. |
Sn. |
HgS |
HgSe |
HgTe |
Pb sphalerite |
298.15 |
19.90 |
21.99 |
23.22 |
24.15 |
24.92 |
24.73 |
25.52 |
26.40 |
27.58 |
350 |
21.25 |
22.88 |
23.90 |
24.68 |
25.37 |
25.19 |
25.92 |
26.70 |
27.81 |
400 |
22.22 |
23.51 |
24.40 |
25.07 |
25.72 |
25.53 |
26.22 |
26.92 |
28.00 |
450 |
22.96 |
23.99 |
24.76 |
25.38 |
26.02 |
25.82 |
26.47 |
27.12 |
28.16 |
500 |
23.53 |
24.37 |
25.05 |
25.66 |
26.28 |
26.07 |
26.69 |
27.29 |
28.31 |
600 |
24.39 |
24.99 |
25.57 |
26.13 |
26.74 |
26.50 |
27.07 |
27.60 |
28.60 |
700 |
25.00 |
25.49 |
26.01 |
26.54 |
27.16 |
26.88 |
27.40 |
27.88 |
28.87 |
800 |
25.47 |
25.93 |
26.42 |
26.93 |
27.55 |
27.23 |
27.70 |
28.15 |
29.12 |
900 |
25.86 |
26.34 |
26.81 |
27.30 |
27.93 |
27.57 |
27.99 |
28.41 |
29.38 |
1000 |
26.19 |
26.72 |
27.19 |
27.65 |
28.30 |
27.90 |
28.27 |
28.66 |
29.63 |
1100 |
26.49 |
27.10 |
27.53 |
28.01 |
28.66 |
28.22 |
28.54 |
|
|
1200 |
26.76 |
27.47 |
27.94 |
28.36 |
|
|
|
|
|
1300 |
27.02 |
27.83 |
28.31 |
28.70 |
|
|
|
|
|
1400 |
27.26 |
28.19 |
28.68 |
29.04 |
|
|
|
|
|
1500 |
27.49 |
28.55 |
29.04 |
29.38 |
|
|
|
|
|
Table 4: The recommended Cp(T) of like-diamond phases at high temperature in (J·(mole-at)-1·K-1)
Phase |
Si |
AlP |
AlAs |
GaP |
Ge |
InP |
a-Sn Ttr |
InSb |
CdTe |
HgS |
HgSe |
HgTe |
Pb |
TmK |
1688 |
2800 |
2013 |
1790 |
1210.3 |
1344 |
287.15 |
795.35 |
1269 |
1098 |
1072 |
943 |
600.58 |
Cp |
27.90 |
30.03 |
28.57 |
28.14 |
28.46 |
29.06 |
24.91 |
27.57 |
29.40 |
28.67 |
28.91 |
28.87 |
28.76 |
Table 5: Maximal temperature of the existence of sphalerite phases and their ultimate Cp (J·(mole-at)-1·K-1) in solid state [20]
Figure 1: Low temperature isotherms Ln(Cp/R) vs Ln(N) of diamond-like phases with sphalerite structure. 1) 20, 2) 25, 3) 30, 4) 35, 5) 40, 6)45, 7) 50K
It is also convenient to use the form Cp vs Ln(N) above 50K
Figure 2: Cp vs Ln(N). Isotherms Cp= ax3 +bx2 +cx +d +ex-1; (x=Ln(N) of the like-diamond phases 1) 298, 2) 350, 3) 400, 4) 500, 5) 600, 6) 700, 7) 800, 8) 900, 9) 1000K [9]
Figure 3: Re-optimized description of the heat capacities of Si and AlP using a combination of this model and multiparameter family of functions [10]. Experimental points: ?[18], ?[19], +[21], x[15], ?[23], ?[16], The points + [21] were used only in the range 298 - 700K
Figure 4: The independent curve Cp(T) for GaP calculated using a combination of this model and multiparameter family of functions [10]. The experimental points: ?[30], x[29], ?[31], ?[32] were superposed after the calculation
Figure 5: The independent description of the heat capacities of the GaSb and InAs phases by a combination of this model and multiparameter function [10]. Experimental points: ?[33], x[24], +[34], +[35], ?[33], ?[24] were superposed after description
Figure 6: The independent optimized description of the heat capacities of the a-Sn phase using a combination of this model and multiparameter family of functions [10]. The experimental points: x[36], +[25], ?[38], ?[37], and complied data ?[39] were superposed after re-optimized description.
Figure 7: Comparison of two descriptions of the heat capacities of the a-Sn phase (blue line) and HgSe (rad line) using a combination of this model and multiparameter family of functions [10] in the range 0-300K. The all experimental points: ?[44], x[39], +[36], ?[25], ?[38] and ?[37] were superposed after descriptions. Notes: The descriptions of (a-Sn) and (HgSe) (blue and red) curves were accomplished independently from the experiment points.
Figure 8: Comparison of two descriptions of heat capacities of the HgTe phase (blue line) and diamond like Pb (rad line) using a combination of this model and multiparameter family of functions [10] in the range 0-600K. The all experimental points: x[44], +[17], ?[46], ?[31] and ?47] were superposed after the descriptions
Figure 9: The optimized curve Cp(T) for HgTe using a combination of this model and multiparameter family of functions [10] and the superposed experimental points ?[45] and x[47]
Figure 10: The heat capacities of diamond-like phases at the region of temperature 0-1000K. 9- Pb, 8-HgTe, 7- HgSe, 6-a-Sn (green), 5-HgS (red), 4-GaSb, 3-Ge, 2- GaP, 1-Si; The Cp(T) of diamond-like phases are localized at the point ?? = 30.5 J mol-at-1 K-1= 3.67 R or Ln (Cp/R) = 1.3 for Ln (114Fl) = 4.7362 [9]
Figure 11: The low temperature heat capacities of diamond-like phases at the region of temperature 0-300K
Tables at a glance
Figures at a glance