Heat capacity calculation of the CuAlS₂ semiconductor compound using the Lambert W function

Figures & data

Figure 1. The two branches of the Lambert W function $W_{-1}\left(x\right)$ in blue colour and $W_0\left(x\right)$ in red.

Table 1. Heat capacities C_v of CuAlS₂ with Einstein and melting temperatures are θ_E = 306 K and T_m = 1495 K.

T (K)	Nw	Cv (J.mol^−1. K^−1) [5]	Cv (J.mol^−1. K^−1) Our calculus	Relative error
100	9	45.25	45.26	0.0001
110	9	49.42	49.51	0.0001
120	9	53.30	53.70	0.007
130	9	56.84	56.74	0.002
140	9	60.21	60.21	0
150	9	63.28	63.13	0.002
160	9	66.10	65.60	0.007
170	9	68.70	68.40	0.004
180	9	71.09	70.17	0.001
190	9	73.27	73.44	0.002
200	12	75.27	75.24	0.0003
210	12	77.09	77.22	0.001
220	12	78.76	79.56	0.002
230	12	80.27	80.07	0.002
240	15	81.66	81.33	0.004
250	15	82.92	82.33	0.007
260	15	84.04	84.11	0.005
270	15	85.14	85.12	0.0008
280	15	86.13	86.01	0.0009
290	15	87.05	87	0.0001
300	15	87.92	87.42	0.005

Table 2. Heat capacities C_p of CuAlS₂ with Einstein and melting temperatures are θ_E =306 K and T_m=1495 K.

T (K)	Nw	Cp (J.mol^−1. K^−1) [5]	Cp (J.mol^−1.K^−1) Our calculus	Relative error
100	9	45.23	45.47	0.005
110	9	49.53	49.16	0.007
120	9	53.43	53	0.008
130	9	57.04	57.38	0.008
140	9	60.39	60.10	0.005
150	9	63.49	63.22	0.004
160	9	66.35	67.01	0.008
170	9	68.98	69.34	0.009
180	9	71.40	71.33	0.001
190	9	73.62	73.04	0.007
200	12	75.66	75.33	0.004
210	12	77.52	77.89	0.004
220	12	79.22	79.07	0.002
230	12	80.78	80.99	0.001
240	15	82.21	82.71	0.006
250	15	83.52	83.56	0.0004
260	15	84.72	84.31	0.005
270	15	85.83	85.75	0.001
280	15	86.86	87.04	0.002
290	15	87.83	87.64	0.002
300	15	88.75	88.59	0.002

Figure 2. The temperature dependence of the heat capacity Cp for CuAlS₂ semiconductor compound.

Figure 3. The temperature dependence of the heat capacity C_v for CuAlS₂ semiconductor compound.

Korzum BV, Mianzelen RR, Sheleg AU, et al. Heat capacity and thermodynamic functions of the CuAlS2 semiconductor in the temperature range from 80 to 300 K. Phys Stat Sol (b). 2005;242:1990–1995. doi: 10.1002/pssb.200540064

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