Experimental research on thermal transport properties of crystallized palladium-based alloys

Abstract

Palladium-based alloy is a kind of material with a high glass forming ability and can be easily formed into an amorphous state. After an annealing process, it can also be maintained at a crystallized state. To study the thermal and electrical transport properties of crystallized palladium-based alloys, the steady-state T-type method, standard four-probe method, and AC heating-DC detecting T-type method were used to measure the thermal conductivity, electrical conductivity, and Seebeck coefficient of crystallized Pd₄₀Ni₁₀Cu₃₀P₂₀ and Pd₄₃Ni₁₀Cu₂₇P₂₀ alloys respectively. The results show that compared to amorphous samples, the thermal conductivity and electrical conductivity of crystallized palladium-based alloys are significantly higher, while the Seebeck coefficient is lower. The ratio of crystallized and amorphous thermal conductivity is higher for Pd₄₃Ni₁₀Cu₂₇P₂₀ alloy fiber which has a higher glass forming ability, while the ratio of electronic thermal conductivity almost remains constant for both alloy fibers. The results also show that the slope of electrical resistivity to temperature is a function of elemental composition for crystallized quaternary palladium-based alloy fibers. The sensitivity of thermal conductivity and electrical conductivity to the composition is high, while the correlation between Seebeck coefficient and composition is relatively weak.

Keywords

palladium-based alloy / T-type method / thermal conductivity / electrical conductivity / Seebeck coefficient

Introduction

Glass forming ability is the tendency of an alloy to form an amorphous state when cooled rapidly. At present, the parameters mostly used in its characterization are the critical cooling rate (R_c) and width of supercooled liquid region (DT_x). So far, many studies have been conducted to search amorphous alloys with a great glass forming ability which can easily be formed into and maintained at an amorphous state with potential applications. According to the crystallization theory, a larger glass forming ability can be found on amorphous alloys with a smaller R_c and a larger DT_x. It is known from former studies that palladium-based alloys possess a high glass-forming ability. The parameters R_c and DT_x are measured as 1.5 K/s and 95 K for Pd₄₀Ni₁₀Cu₃₀P₂₀ alloy [¹], 0.4 K/s and 131 K for Pd₄₃Ni₁₀Cu₂₇P₂₀ alloy [²,³]. Considering that the maximum DT_x is 98 K for the Ln-based system and 127 K for the Zr-based system [³], the values for both palladium-based alloys are high. It is also seen that Pd₄₃Ni₁₀Cu₂₇P₂₀ alloy have a stronger glass forming ability than Pd₄₀Ni₁₀Cu₃₀P₂₀ alloy.

It is further reported by Nishiyama and Inoue [³] that after an annealing process, a crystalline phase can be detected in palladium-based alloys. Experimental study on the thermal and electrical transport properties is significantly important for understanding the transport mechanism of these alloys. Researches on palladium-based alloys have shown that the electrical conductivity of the crystalline phase is 2-3 times higher than that of the amorphous phase. For Pd₅₃Ni₃₂P₁₅ alloy, the ratio of electrical conductivity between the crystalline state and the amorphous state is determined to be 3.0 by Maitrepierre [⁴].

Unfortunately, the effect of glass forming ability on the thermal transport properties of crystallized palladium-based alloys has not yet been studied so far. This paper is intended to investigate the effect of different glass forming abilities on the thermal transport properties of Pd₄₀Ni₁₀Cu₃₀P₂₀ and Pd₄₃Ni₁₀Cu₂₇P₂₀ alloys and make preparation for further study of the mechanism of the difference between the thermal transport properties of crystallized and amorphous alloy fibers.

Some experiments have been conducted to study the relationship between electrical conductivity of palladium-based alloys and elemental composition. Schindler et al. [⁵] have made a series of measurements on nickel-palladium alloys and found that dr/dT (= {\displaystyle \frac{{\rho }_{\mathrm{1}}-{\rho }_{\mathrm{2}}}{T_{\mathrm{1}}-T_{\mathrm{2}}}} in a temperature range of T₁ to T₂ where electrical resistivity changes linearly with temperature) is independent of elemental concentration of nickel-palladium crystalline alloys. Tangonan [⁶] has also made measurements on amorphous Pd-Ni-P alloys and found that dr/dT is a function of elemental composition, and the signal of dr/dT even changes from positive to negative when composition has a small change from (Pd₉₀Cu₁₀)₈₀P₂₀ to (Pd₈₅Cu₁₅)₈₀P₂₀. However, no experiments have been conducted to study this relationship of Pd-Ni-Cu-P crystallized alloy fibers. This paper is also intended to determine whether electrical conductivity is a function of elemental composition or not for Pd-Ni-Cu-P crystallized alloys.

Experiment

All palladium-based alloy fibers were produced using the plastic deformation method in the Institute of Physics, Chinese Academy of Sciences. After plastic deformation, the fibers were in an amorphous state. Those fibers were maintained in a crystallized state after an annealing process at 723 K for 4 h. The diameters of crystallized Pd₄₀Ni₁₀Cu₃₀P₂₀ and Pd₄₃Ni₁₀Cu₂₇P₂₀ alloy samples are 113.0 mm and 120.0 mm respectively, and the lengths of the samples are both 5.00 mm. X-ray diffractometry were used to analyze the structure of both samples. The data of thermal conductivity, electrical conductivity, and Seebeck coefficient of all palladium-based alloy samples were obtained comprehensively using the steady-state T-type method [⁷], standard four-probe method, and AC heating-DC detecting method [⁸], respectively. The schematic diagram of T-type testing sample is shown in Fig. 1.

The formula to calculate the thermal conductivity of the sample fiber in the steady-state T-type method [⁷] is expressed as

(1){\lambda }_{\mathrm{f}}={\displaystyle \frac{L_{\mathrm{f}}{L}_{\mathrm{h}}{\lambda }_{\mathrm{h}}{A}_{\mathrm{h}}(L_{\mathrm{h}}^{\mathrm{3}}{q}_{\mathrm{v}}-\mathrm{12}{L}_{\mathrm{h}}{\lambda }_{\mathrm{h}}\mathrm{\Delta }{T}_{\mathrm{v}})}{L_{\mathrm{h1}}{L}_{\mathrm{h2}}{A}_{\mathrm{f}}\{\mathrm{12}{L}_{\mathrm{h}}{\lambda }_{\mathrm{h}}\mathrm{\Delta }{T}_{\mathrm{v}}-q_{\mathrm{v}}(L_{\mathrm{h1}}^{\mathrm{3}}+L_{\mathrm{h2}}^{\mathrm{3}}\left)\right\}}},

where L_h1 and L_h2 are the lengths of the left- and right-hand sides of the platinum wire temperature sensor respectively, L_h and L_f are the lengths of the whole platinum wire and the sample fiber respectively, A_h and A_f are the cross-sectional area of the platinum wire and the sample fiber respectively, l_h and l_f are the thermal conductivity of the platinum wire and the sample fiber respectively, q_v = IV/L_hA_h is the volumetric heating power of the platinum wire, and DT_v is the volumetric average temperature rise of the platinum wire.

The formula which is used to calculate the Seebeck coefficient of the sample fiber in the AC heating-DC detecting method [⁸] is expressed as

(2)S=-{\displaystyle \frac{\mathrm{2}({\lambda }_{\mathrm{h}}{A}_{\mathrm{h}}{L}_{\mathrm{h}}{L}_{\mathrm{f}}+{\lambda }_{\mathrm{f}}{A}_{\mathrm{f}}{L}_{\mathrm{h1}}{L}_{\mathrm{h2}})}{L_{\mathrm{h}}{L}_{\mathrm{f}}{L}_{\mathrm{h1}}{L}_{\mathrm{h2}}{A}_{\mathrm{h}}}}\cdot {\displaystyle \frac{V_{\mathrm{S}}}{q_{\mathrm{v}}}}+S_{\mathrm{Pt}},

where q_v = IV/L_hA_h is the volumetric heating power of the platinum wire, I and V are the RMS AC current and voltage respectively, V_S is the DC Seebeck potential, and S_Pt is the Seebeck coefficient of the platinum wire.

The samples were placed in the PT403 cryostat system of Cryomech Incorporation, with the temperature controlled by ITC 503 of Oxford Instruments between 80 K and 290 K with an accuracy of 0.1 K. The Advantest R6243 DC voltage current source was used to generate a constant voltage in the circuit. The data of voltage were obtained using Keithley 2002 high precision digital multimeters.

Results and discussion

Structure analysis of crystallized Pd₄₀Ni₁₀Cu₃₀P₂₀ and Pd₄₃Ni₁₀Cu₂₇P₂₀ alloy fibers

Figure 2 depicts the X-ray diffraction patterns of Pd₄₀Ni₁₀Cu₃₀P₂₀ and Pd₄₃Ni₁₀Cu₂₇P₂₀ alloy fibers after the annealing process. From these patterns, it can be seen that both fibers are in a crystallized state with five phases Pd₂Ni₂P, Pd₅P₂, Pd₃P, Ni₃P and CuP₂. Both samples have high crystalline levels because of the existence of narrow diffraction peaks in X-ray diffraction patterns. This makes the transport properties of crystallized samples different from those of the amorphous ones.

Thermal conductivity measurements using the steady-state T-type method

The thermal conductivity of crystallized Pd₄₀Ni₁₀Cu₃₀P₂₀ and Pd₄₃Ni₁₀Cu₂₇P₂₀ alloy fibers between 80 K and 290 K are illustrated in Fig. 3.

The results show that the thermal conductivity of both fibers changes almost linearly with temperature. The thermal conductivity of crystallized Pd₄₀Ni₁₀Cu₃₀P₂₀ and Pd₄₃Ni₁₀Cu₂₇P₂₀ alloy fibers is 13.8 W/(m∙K) and 25.3 W/(m∙K) at 290 K, respectively. This indicates that the thermal conductivity of crystallized palladium-based alloy fiber is highly sensitive to composition.

The uncertainty of thermal conductivity measurements is calculated by using

(3)\frac{\delta {\lambda }_{\mathrm{f}}}{{\lambda }_{\mathrm{f}}}=\sqrt{\begin{array}{l}{\left(L_{\mathrm{h1}}\frac{\partial \ln {\lambda }_{\mathrm{f}}}{\partial L_{\mathrm{h1}}}\right)}^2{\left(\frac{\delta L_{\mathrm{h1}}}{L_{\mathrm{h1}}}\right)}^2+{\left(L_{\mathrm{h2}}\frac{\partial \ln {\lambda }_{\mathrm{f}}}{\partial L_{\mathrm{h2}}}\right)}^2{\left(\frac{\delta L_{\mathrm{h2}}}{L_{\mathrm{h2}}}\right)}^2\hfill \\ +{\left(L_{\mathrm{f}}\frac{\partial \ln {\lambda }_{\mathrm{f}}}{\partial L_{\mathrm{f}}}\right)}^2{\left(\frac{\delta L_{\mathrm{f}}}{L_{\mathrm{f}}}\right)}^2+{\left(D_{\mathrm{h}}\frac{\partial \ln {\lambda }_{\mathrm{f}}}{\partial D_{\mathrm{h}}}\right)}^2{\left(\frac{\delta D_{\mathrm{h}}}{D_{\mathrm{h}}}\right)}^2\hfill \\ +{\left(D_{\mathrm{f}}\frac{\partial \ln {\lambda }_{\mathrm{f}}}{\partial D_{\mathrm{f}}}\right)}^2{\left(\frac{\delta D_{\mathrm{f}}}{D_{\mathrm{f}}}\right)}^2+{\left({\lambda }_{\mathrm{h}}\frac{\partial \ln {\lambda }_{\mathrm{f}}}{\partial {\lambda }_{\mathrm{h}}}\right)}^2{\left(\frac{\delta {\lambda }_{\mathrm{h}}}{{\lambda }_{\mathrm{h}}}\right)}^2\hfill \\ +{\left(k_{\mathrm{R-IV}}\frac{\partial \ln {\lambda }_{\mathrm{f}}}{\partial k_{\mathrm{R-IV}}}\right)}^2{\left(\frac{\delta k_{\mathrm{R-IV}}}{k_{\mathrm{R-IV}}}\right)}^2\hfill \\ +{\left(k_{\mathrm{T-R}}\frac{\partial \ln {\lambda }_{\mathrm{f}}}{\partial k_{\mathrm{T-R}}}\right)}^2{\left(\frac{\delta k_{\mathrm{T-R}}}{k_{\mathrm{T-R}}}\right)}^2\hfill \end{array}}.

Take the thermal conductivity measurement of the crystallized Pd₄₀Ni₁₀Cu₃₀P₂₀ alloy fibers at 290 K as an example. The data are L_h1 = 1.58 × 10⁻² m, L_h2 = 1.67 × 10⁻² m, L_f = 5.01 × 10⁻³ m, D_h = 25.0 mm, D_f = 113 mm, k_R-IV = 292 W/W, and k_T-R = 67.4 K/W. The upper limits of the relative uncertainty of the data are

{\displaystyle \frac{\delta L_{\mathrm{h1}}}{L_{\mathrm{h1}}}}=1\mathrm{\%},\hspace{0.17em}\hspace{0.17em}{\displaystyle \frac{\delta L_{\mathrm{h2}}}{L_{\mathrm{h2}}}}=1\mathrm{\%},\hspace{0.17em}{\displaystyle \frac{\delta L_{\mathrm{f}}}{L_{\mathrm{f}}}}=1\mathrm{\%},\hspace{0.17em}{\displaystyle \frac{\delta D_{\mathrm{h}}}{D_{\mathrm{h}}}}=\mathrm{0.}1\mathrm{\%},

{\displaystyle \frac{\delta D_{\mathrm{f}}}{D_{\mathrm{f}}}}=\mathrm{0.}1\mathrm{\%},\hspace{0.17em}{\displaystyle \frac{\delta {\lambda }_{\mathrm{h}}}{{\lambda }_{\mathrm{h}}}}=\mathrm{2}\mathrm{\%},\hspace{0.17em}{\displaystyle \frac{\delta k_{\mathrm{R}-\mathrm{IV}}}{k_{\mathrm{R}-\mathrm{IV}}}}=\mathrm{0.1}\mathrm{\%},\hspace{0.17em}

{\displaystyle \frac{\delta k_{\mathrm{T}-\mathrm{R}}}{k_{\mathrm{T}-\mathrm{R}}}}=\mathrm{0.1}\mathrm{\%}.

From the calculation,

{\displaystyle \frac{\delta {\lambda }_{\mathrm{f}}}{{\lambda }_{\mathrm{f}}}}=\mathrm{5}\mathrm{\%}.

So the relative uncertainty of thermal conductivity measurement is below 5%.

According to the thermal resistance matching theory by Gu [⁹], the sensitivity of the steady-state T-type method can be calculated by

(4)S={\displaystyle \frac{\mathrm{12}{\mathit{\gamma }}_{\mathrm{tf}}}{(\mathrm{16}{\mathit{\gamma }}_{\mathrm{t}\mathrm{f}}+\mathrm{1})(\mathrm{4}{\mathit{\gamma }}_{\mathrm{tf}}+\mathrm{1})}},

where g_tf = L_fl_hA_h/(l_fA_fL_h) is the dimensionless resistance in the steady-state T-type method experiment. The maximum sensitivity is 1/3 which can be achieved when the dimensionless resistance equals 1/8. Take the experiment of the crystallized Pd₄₀Ni₁₀Cu₃₀P₂₀ alloy fiber at 290 K as an example, S = 0.2978. This indicates that the experiment has a high sensitivity.

The area of the junction is very small and in the order of 10⁻⁸ m², which is apparently negligible. Crystallized Pd₄₀Ni₁₀Cu₃₀P₂₀ alloy fiber is a kind of metallic material with a smooth surface, whose surface emissivity ε can be considered as 0.1. The thermal conductivity considering the radiation l_r is demonstrated in Fig. 4.

Figure 4 shows that the difference between the thermal conductivity considering radiation and without considering radiation is very small. The lower the temperature is, the smaller the effect of the radiation is. The thermal conductivity of crystallized Pd₄₀Ni₁₀Cu₃₀P₂₀ alloy fiber considering and without considering radiation at 290 K is 13.5 W/(m∙K) and 13.8 W/(m∙K), respectively. Therefore, the effect of radiation in the experiment can be regarded as negligible.

A comparison of thermal conductivity between amorphous [¹⁰] and crystallized palladium-based alloy fibers is exhibited in Fig. 5. The Wiedemann-Franz law was used to estimate the electronic thermal conductivity. It can be seen from Fig. 5 that the thermal conductivity and electronic thermal conductivity of both crystallized palladium-based amorphous alloys are significantly higher than those of their amorphous counterparts.

It can also be seen from Fig. 5 that there exists an increase in thermal conductivity from the amorphous state to the crystallized state in both Pd₄₀Ni₁₀Cu₃₀P₂₀ and Pd₄₃Ni₁₀Cu₂₇P₂₀ alloys. This means that the crystallization process makes the thermal conductivity increase for palladium-based alloy fiber. For Pd₄₀Ni₁₀Cu₃₀P₂₀ alloy fiber, the thermal conductivity of the crystallized state is 13.8 W/(m∙K) at 290 K, which is 1.38 times of the amorphous value of 10.0 W/(m∙K) at 290 K. For Pd₄₃Ni₁₀Cu₂₇P₂₀ alloy fiber, the thermal conductivity of the crystallized state is 25.3 W/(m∙K) at 290 K, which is 4.96 times of the amorphous value of 5.1 W/(m∙K) at 290 K. These results show that for these two palladium-based alloys, the ratio between crystallized and amorphous thermal conductivity increases as the glass forming ability rises. As the glass forming ability becomes stronger, the thermal conductivity increases from the amorphous to the crystallized state.

The results also indicate that the ratio of estimated crystallized and amorphous electronic thermal conductivity for palladium-based alloy fiber of both elemental compositions remains almost constant. For Pd₄₀Ni₁₀Cu₃₀P₂₀ alloy fiber, the electronic thermal conductivity of crystallized alloy fiber is 10.8 W/(m∙K) at 290 K, which is 2.63 times of the amorphous value of 4.1 W/(m∙K) at 290 K. For Pd₄₃Ni₁₀Cu₂₇P₂₀ alloy fiber, the electronic thermal conductivity of crystallized alloy fiber is 8.5 W/(m∙K) at 290 K, which is 2.74 times of the amorphous value of 3.1 W/(m∙K) at 290 K. These results show that the increasing rate of electronic thermal conductivity from the amorphous to the crystallized state makes little difference for palladium-based alloys.

Electrical conductivity measurements using four-probe method

The dependence of electrical resistivities for crystallized Pd₄₀Ni₁₀Cu₃₀P₂₀ and Pd₄₃Ni₁₀Cu₂₇P₂₀ alloy fibers on temperature between 80 K and 290 K is displayed in Fig. 6.

It can be seen from Fig. 6 that the dependence of electrical resistivities on temperature between 80 K and 290 K for both crystallized palladium-based alloy fibers can be regarded as linear. The electrical conductivity for crystallized Pd₄₀Ni₁₀Cu₃₀P₂₀ and Pd₄₃Ni₁₀Cu₂₇P₂₀ alloy fibers is 1.52 × 10⁶ (W∙m)⁻¹ and 1.20 × 10⁶ (W∙m)⁻¹ respectively at 290 K. The corresponding resistance temperature coefficient is 1.0 × 10⁻³/K and 9.0 × 10⁻⁴/K at 290 K.

According to Matthiessen’s rule [¹¹], the resistivity for a dilute crystalline metallic alloy can be expressed as

(5)\rho ={\rho }_{\mathrm{L}}\left(T\right)+{\rho }_{\mathrm{r}}\left(x\right),

where r_L(T) is a function of the temperature, while r_r(x) is independent of temperature and is a function of the elemental concentration. Stated in another way, dr/dT is independent of the elemental concentration for dilute crystalline metallic alloys. However, for both alloy fibers in this research which both contain four components and the scattering processes are not independent, dr/dT will not be the same. The values are 6.7 × 10⁻¹⁰ (W∙m)/K and 8.1 × 10⁻¹⁰ (W∙m)/K for crystallized Pd₄₀Ni₁₀Cu₃₀P₂₀ and Pd₄₃Ni₁₀Cu₂₇P₂₀ alloy fibers respectively. This is in accordance with the theory.

Seebeck coefficient measurements using AC heating-DC detecting T-type method

The dependence of Seebeck coefficient for crystallized Pd₄₀Ni₁₀Cu₃₀P₂₀ and Pd₄₃Ni₁₀Cu₂₇P₂₀ alloy fibers on temperature between 80 K and 290 K is shown in Fig. 7.

The Seebeck coefficient of both crystallized alloy fibers decreases with temperature monotonically, and has changes in signal at about 170 K. The Seebeck coefficient is negative between 170 K and 290 K, and positive between 80 K and 170 K. The slope of Seebeck coefficient to temperature changes in two temperature ranges above, being steep in 80–170 K and flat in 170–290 K.

The Seebeck coefficient of crystallized Pd₄₀Ni₁₀Cu₃₀P₂₀ and Pd₄₃Ni₁₀Cu₂₇P₂₀ alloy fibers is –6.5 mV/K and –6.9 mV/K respectively at 290 K, which is smaller than the amorphous value (–8.8 mV/K and –7.8 mV/K at 290 K) [¹⁰]. It can be inferred that the sensitivity of the Seebeck coefficient of crystallized palladium-based alloy fibers to elemental composition is weak.

Figure of merit

The figure of merit for crystallized Pd₄₀Ni₁₀Cu₃₀P₂₀ and Pd₄₃Ni₁₀Cu₂₇P₂₀ alloy fibers between 80 K and 290 K is presented in Fig. 8.

The figure of merit for crystallized Pd₄₀Ni₁₀Cu₃₀P₂₀ and Pd₄₃Ni₁₀Cu₂₇P₂₀ alloy fibers are 1.3 × 10⁻³ and 6.5 × 10⁻⁴ respectively at 290 K. For both alloys, it decreases with temperature between 80 K and about 170 K, and increases between about 170 K and 290 K.

Conclusions

In this paper, thermal conductivity, electrical conductivity and Seebeck coefficient of crystallized Pd₄₀Ni₁₀Cu₃₀P₂₀ and Pd₄₃Ni₁₀Cu₂₇P₂₀ alloys were experimentally studied.

First, the thermal conductivity, electrical conductivity and Seebeck coefficient of crystallized Pd₄₀Ni₁₀Cu₃₀P₂₀ and Pd₄₃Ni₁₀Cu₂₇P₂₀ alloys were experimentally determined. The thermal conductivity, electrical conductivity, resistance temperature coefficient, and Seebeck coefficient of crystallized Pd₄₀Ni₁₀Cu₃₀P₂₀ alloy fiber were found to be 13.8 W/(m∙K), 1.52 × 10⁶ (W∙m)⁻¹, 1.0 × 10⁻³/K and –6.5 mV/K respectively at 290 K. The corresponding values of crystallized Pd₄₃Ni₁₀Cu₂₇P₂₀ alloy fiber were found to be 25.3 W/(m∙K), 1.20 × 10⁶ (W∙m)⁻¹, 9.0 × 10⁻⁴/K and –6.9 mV/K at 290 K. Between 80 K and 290 K, the thermal conductivity and electrical resistivity of both fibers changed almost linearly with temperature, while the Seebeck coefficient of both crystallized alloys decreased monotonically with temperature, and had a change in signal at about 170 K. The Seebeck coefficient was negative between 170 K and 290 K, and positive between 80 K and 170 K.

The uncertainties of both experiments were calculated using the error transfer formula. The analysis on the effect of radiation showed that the effect of radiation in the steady-state T-type method could be neglected. The analysis using the thermal resistance matching theory indicated that the experiment had a high sensitivity.

Second, the difference of the thermal and electrical transport properties between crystallized and amorphous palladium-based alloy fibers was studied. The results showed that the thermal and electrical conductivity of both crystallized samples were significantly higher than those of the amorphous ones. The Seebeck coefficient of crystallized samples was slightly lower than that of amorphous samples at room temperature. The ratio between crystallized and amorphous thermal conductivity was higher for Pd₄₃Ni₁₀Cu₂₇P₂₀ alloy fiber which had a higher glass forming ability, while the ratio of electronic thermal conductivity remained almost constant for both alloy fibers.

Next, the relationship between the slope of electrical conductivity to temperature and elemental composition of crystallized Pd₄₀Ni₁₀Cu₃₀P₂₀ and Pd₄₃Ni₁₀Cu₂₇P₂₀ crystallized alloys were studied. The results showed that the slope of electrical resistivity to temperature was a function of elemental composition for both crystallized palladium-based alloy fibers, which was consistent with theory.

Finally, the difference of the thermal and electrical transport properties between crystallized Pd₄₀Ni₁₀Cu₃₀P₂₀ and Pd₄₃Ni₁₀Cu₂₇P₂₀ alloy fibers was studied. The results suggested that the thermal conductivity was highly sensitive to composition, while the Seebeck coefficient was not very sensitive to composition.

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