- Email: [email protected]
Standard entropy of formation of Mo2B5 at 298 K
Journal of Alloys and Compounds 376 (2004) 111–114
Standard entropy of formation of Mo2 B5 at 298 K M. Morishita∗ , K. Koyama, S. Yagi Department of Materials Science and Chemistry, Himeji Institute of Technology, 2167 Shosha, Himeji 671-2201, Japan Received 10 November 2003; received in revised form 12 December 2003; accepted 12 December 2003
Abstract The standard entropy of formation at 298 K, f S ◦298 , of Mo2 B5 was determined from measuring the heat capacities (Cp ) from near absolute zero (2 K) to 300 K by the relaxation method. The determined f S ◦298 of Mo2 B5 was −3.543 J K−1 mol−1 . Its Debye temperature, ΘD , was found to be high (540 K), indicating that the crystal lattice is hard and the entropy of vibration is decreased. © 2004 Elsevier B.V. All rights reserved. Keywords: Standard entropy of formation; Debye temperature; Heat capacity
1. Introduction Transition metal borides have high melting points, high hardness values, excellent corrosion- and oxidationresistances. Therefore, they are expected to be constituents for new heat-, corrosion- and wear-resistant alloys. In order to design transition metal boride-dispersed alloys, their thermodynamic data are necessary. Omori et al. in our laboratory have measured the standard Gibbs energies of formation (f G◦T ) of Mo2 B and MoB of the Mo–B binary system [1], and W2 B and WB of the W–B binary system [2] by the electromotive method (EMF). The phase diagrams of the Ni–Mo–B [3] and the Ni–W–B [4] ternary systems were calculated on the basis of the data of Omori et al. [1,2]. Storms and Mueller [5] and Gilles and Pollock [6] measured the activity, a, of the Mo–B binary system by the vaporization method. Baehren and Vollath [7] measured the (f G◦T ) of Mo2 B by the gas reaction method. However, there is a large experimental error of about 10 kJ mol−1 between the data of Storms and Mueller [5] and those of others [6] measured by the vaporization method, by the gas phase reaction method [7] and by the EMF [1] method of the Mo–B binary system. Therefore, we consider that making a comparison between the data obtained by the various kinds of methods is preferable for the Mo–B binary system. ∗ Corresponding author. Tel.: +81-792-67-4915; fax: +81-792-66-8868. E-mail address: [email protected] (M. Morishita).
0925-8388/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2003.12.028
Recently relaxation [8] and semi-adiabatic calorimetric methods [9] have been developed to measure constant pressure heat capacity, Cp , from near absolute zero Kelvin to room temperature. Since the accuracy of these method is very high, the standard entropy of formation at 298 K, f S ◦298 , can be determined by them [10,11]. Also, the standard entropy of formation at any temperature, f S ◦T , can be determined by combining f S ◦298 with Cp measured from room temperature to any high temperature [11]. In the present study, therefore, we have tried to determine the f S ◦298 of Mo2 B5 from Cp values measured from near absolute zero Kelvin.
2. Experimental 2.1. Preparation of the specimen Commercial Mo (99.99%, powder, High Purity Chemical Institute Co., Osaka (HPCI)) and B (99.5%, grain, HPCI) were used as starting materials. Hydro-thermic reduction at 773 K for 10.8 ks was carried out for the Mo powder. Since oxidation loss of B occurred during melting and heat treatment, the addition of an excess of 0.8 mass% B was necessary for preparing Mo2 B5 . The amount of the addition of excess B was determined from a pre-experiment. The mixed powder (∼5 g) of the Mo and B was compressed in a steel die. Mo2 B5 was prepared by melting the powder compact in an Ar-arc furnace. After melting, the sample was subjected to a homogenizing treatment at 1623 K for
112
M. Morishita et al. / Journal of Alloys and Compounds 376 (2004) 111–114
604.8 ks. The material was shown to be a single phase by X-ray diffraction measurement and EPMA observation. 2.2. Cp measurement at 2–390 K The entropy of a material at 298 K, S ◦298 , based on the third law of thermodynamics is given by 298 Cp S ◦298 = dT (1) T 0 where T is the absolute temperature. The heat capacities of Mo2 B5 was measured in the temperature range 2–300 K by using a relaxation method [8] instrument (Quantum Design, San Diego). The samples were attached on a sample platform made from alumina with grease (ASTM standard N-grease (<300 K) and H-grease (>300 K)). A fine heater wire and a thermal relaxation wire are attached to the sample platform. Both wires were made from a gold-based alloy. The sum of the heat capacities of the sample and sample platform, Cp (sample + platform), is derived from the thermal relaxation through the wire: Cp
dT = −Kw (T − Tb ) + P(t) dT
(2)
where Kw is the thermal conductance of the wire; T and Tb the temperature of the sample and the thermal bath, respectively; and P(t) the power applied by the heater. For each measurement, initially the heat capacity of the platform coated with a grease, Cp (platform), was measured, and then the sum of the heat capacity of the sample and platform, Cp (sample + platform), was measured. The sample heat capacity, Cp (sample), was determined by subtracting Cp (platform) from Cp (sample + platform). 120
C p / k J . K − 1 -m o l −1
100
80
60
40
20
0 0
100
200
300
Temperature,T/K Fig. 1. Change in heat capacity, Cp , with temperature, T, for Mo2 B5 .
The Cp values of Mo2 B5 were negligibly small below 2 K. Therefore, their S ◦298 values can be approximately determined from Cp values measured from 2 K. The average of the six series was adopted as the result. Each measured Cp of Mo2 B5 was fitted by polynomial expression: Cp =
n
an T n
(3)
n=1
The polynomial was integrated to determine the S ◦298 value of Mo2 B5 . The f S ◦298 value of Mo2 B5 is given f S ◦298 (Mo2 B5 ) = S ◦298 (Mo2 B5 ) − S ◦298 (Mo) × 2 − S ◦298 (B) × 5
(4)
Table 1 Experimental molar Cp of Mo2 B5 T (K)
Cp (J K mol−1 )
T (K)
Cp (J K mol−1 )
T (K)
Cp (J K mol−1 )
1.88 2.44 2.60 3.05 3.55 4.13 4.79 5.52 7.11 9.66 12.28 14.79 17.39 19.91 22.47 25.02 27.54 30.04 32.56 35.09 37.61 40.15 42.67 45.19 47.66 50.18 52.69 55.20 57.77 60.28 62.79 65.30 67.81 70.34 72.85 75.37 77.89 80.41 82.94 85.46 87.97 90.50
0.0121 0.0159 0.0169 0.0202 0.0236 0.0279 0.0327 0.0384 0.0530 0.0781 0.1125 0.1593 0.2148 0.2919 0.3958 0.5249 0.6906 0.9207 1.225 1.627 2.140 2.592 3.214 3.904 4.688 5.524 6.447 7.366 8.302 9.355 10.43 11.58 12.74 13.80 15.02 16.17 17.40 18.55 19.61 20.73 21.97 23.11
93.01 95.53 98.06 100.58 103.10 105.62 108.14 110.66 113.18 115.70 118.22 120.71 123.23 125.76 128.28 130.80 133.32 135.84 138.35 140.87 143.39 145.90 148.41 150.92 153.43 155.92 158.41 160.93 163.44 165.96 168.48 171.00 173.52 176.05 178.57 181.09 183.61 186.12 188.65 191.17 193.69 196.20
24.26 25.47 26.61 27.82 29.03 30.23 31.41 32.58 33.79 34.99 36.17 37.36 38.58 39.75 41.01 42.05 43.23 44.50 45.68 46.92 48.07 49.21 50.56 51.65 52.61 53.90 55.17 56.22 57.41 58.47 59.72 60.85 61.98 63.15 64.18 65.27 66.32 67.53 68.68 69.73 70.91 72.11
198.72 201.23 203.74 206.25 208.76 211.26 213.78 216.30 218.82 221.32 223.83 226.35 228.86 231.38 233.89 236.41 238.93 241.45 243.96 246.47 248.99 251.49 254.01 256.52 259.04 261.55 264.06 266.58 269.09 271.61 274.12 276.61 279.15 282.97 285.39 287.93 290.49 292.97 295.45 297.88 300.42
73.07 74.14 75.19 76.26 77.30 78.27 79.32 80.45 81.51 82.72 83.48 84.42 85.35 86.20 87.28 88.04 88.98 89.85 90.84 91.71 92.49 93.52 94.24 95.02 95.78 96.74 97.57 98.53 99.35 100.1 101.0 101.8 102.4 103.0 103.9 104.1 104.9 105.1 105.5 106.1 106.2
M. Morishita et al. / Journal of Alloys and Compounds 376 (2004) 111–114
S ◦298 (Mo) and S ◦298 (B) are the third law entropies of pure Mo and B and were adopted from Refs. [12,13].
3. Experimental results and discussion Fig. 1 and Table 1 show the measured Cp values of Mo2 B5 in the temperature range 2–300 K. The polynomial to fit the measured Cp was obtained as Cp (J K−1 mol−1 ) = 1.694 − 27.51 × 10−2 × T + 9.766 × 10−3 × T 2 − 60.16 × 10−6 × T 3 + 17.97 × 10−8 × T 4 − 22.62 × 10−11 × T 5 + 36.37 × 10−15 × T 6
(5)
The result of the calculation using the polynomial is shown as solid line in Fig. 1. The polynomial fitted well with the measured Cp . The S ◦298 value of Mo2 B5 was obtained from the integral of the polynomial and the result was obtained as S ◦298 (Mo2 B5 ) (J K−1 mol−1 ) = 82.837
(6)
The Cp of six nines-copper (99.9999%, Nilaco, Tokyo) was measured and its S ◦298 was calculated in order to evaluate the accuracy achieved with the applied measurement set up. Table 2 shows the measured low temperature Cp and S ◦298 of six nines-copper, compared with the reference data [14]. The measured Cp data and the calculated S ◦298 data deviate only by less than 1%. Thus the S ◦298 of Mo2 B5 was treated having also an uncertainty of 1% as given in Eq. (4). Some Cp , S ◦T and HT –H298 data calculated from the polynomials for Mo2 B5 are summarized in Table 3. Previously the Cp of the four nines-copper (99.99%, HPCI) was measured and its S ◦298 was calculated [10,11]. The present Cp of the six nines-copper was almost same as the data of the four nines-copper [10,11], and the effect of differences in purity was found to be negligibly small. The f S ◦298 of Mo2 B5 was obtained from Eq. (4): f S ◦298 (Mo2 B5 ) (J K−1 mol−1 ) = −3.543
(7)
The f S ◦298 value was found to be negative. In order to clarify the reason for such negative f S ◦298 , the Debye temperature of Mo2 B5 was calculated. The heat capacity values
Table 2 Molar heat capacity, Cp , and third law entropy, S ◦298 , of pure copper (99.9999%) S ◦298 (J K−1 mol−1 )
Cp (J K−1 mol−1 ) Temperature (K) Present study Reference [13] Deviation (%)
100 16.07 16.01 0.37
200 22.54 22.63 0.40
298 24.37 24.44 0.30
298 33.08 33.16 0.24
113
Table 3 Thermodynamic functions for Mo2 B5 T (K)
Cp (J K−1 mol−1 )
S ◦T (J K−1 mol−1 )
H ◦T –H ◦298 (kJ mol−1 )
50 100 150 200 250 298 300
5.89 27.42 51.32 73.46 93.14 105.82 106.05
2.84 13.11 28.78 46.63 65.19 82.84 83.49
−14.91 −14.11 −12.14 −9.01 −4.83 0 0.20
under constant volume, Cv , of solid substances at very low temperature can be generally given by [15]: T 3 Cv (J K−1 mol−1 ) = 1944 (8) ΘD where ΘD is Debye temperature. Since Cv and Cp differ little from one another at low temperatures [16], Cp can be approximately used instead of Cv . ΘD of Mo2 B5 was calculated by inserting the measured Cp at 9.66 K (Table 1). The obtained ΘD was 540 K. The crystal lattice of Mo2 B5 appears to be very hard based on such high ΘD . Thus the atomic bond between Mo and B appears to be very strong. It is likely that the lattice vibration frequency of Mo2 B5 is high and the entropy of vibration, f S ◦,vib , [17] is decreased. As a result, the f S ◦298 of Mo2 B5 shows a negative value. Since the equilibrium oxygen pressures of borides composed of high B content such as MoB4 and Mo2 B5 are very low, not only oxygen ions but also electrons act as carrier in solid electrolytes such as stabilized zirconia. Therefore, EMF cannot be applied for determining f G◦T of these borides. Also, errors of activity measurements when using by the vaporization method are generally known to be large due to experimental difficulties associated with high temperature. On the other hand, the f G◦T of Mo2 B5 at any temperature can be determined by combining the present f S ◦298 with the Cp values measured at high temperature and the standard enthalpy of formation at 298 K, f H ◦298 , measured by a calorimetric method such as solution calorimetry [10,11]. Consequently, the present f S ◦298 of Mo2 B5 is useful as an important basic datum.
References [1] S. Omori, Y. Hashimoto, K. Koyama, J. Jpn. Inst. Met. 45 (1981) 1107–1111. [2] S. Omori, Y. Hashimoto, K. Koyama, Kouon-gakkaishi 7 (1981) 204–208. [3] M. Morishita, K. Koyama, S. Yagi, G. Zhang, J. Alloys Comp. 314 (2001) 212–218. [4] M. Morishita, K. Koyama, K. Maeda, G. Zhang, Mater. Trans. JIM 40 (1999) 600–605. [5] E. Storms, B. Mueller, J. Phys. Chem. 81 (1977) 318–323. [6] P.W. Gilles, B.P. Pollock, AECU-2894 (1962). [7] V.F.D. Baehren, D. Vollath, Planseeber. Pulvermetallurgie 17 (1969) 180–183.
114
M. Morishita et al. / Journal of Alloys and Compounds 376 (2004) 111–114
[8] J.S. Hwang, K.J. Lin, C. Tien, Rev. Sci. Instrum. 68 (1997) 94– 101. [9] V.K. Pecharsky, K.A. Gschneidner Jr., Phys. Rev. Lett. 23 (1997) 4494–4497. [10] M. Morishita, K. Koyama, Z. Metallkde. 94 (2003) 967–971. [11] M. Morishita, A. Navrotsky, J. Am. Ceram. Soc. 86 (2003) 1927– 1932. [12] M.W. Chase, NIST-JANAF Thermochemical Tables, 1998, p. 1578.
[13] M.W. Chase, NIST-JANAF Thermochemical Tables, 1998, p. 178. [14] M.W. Chase, NIST-JANAF Thermochemical Tables, 1998, p. 1006. [15] C. Kittel, Introduction to Solid State Physics, 7th ed., Maruzen, Tokyo, 1998, p. 138 (Translated to Japanese). [16] J.B. Ott, J. Boerio-Goates, Chemical Thermodynamics: Principles and Applications, Academic Press, San Diego, 2000, pp. 183–184. [17] R.A. Swalin, Thermodynamics of Solids, Corona, Tokyo, 1974, pp. 41–53 (Translated to Japanese).
Standard entropy of formation of Mo2 B5 at 298 K M. Morishita∗ , K. Koyama, S. Yagi Department of Materials Science and Chemistry, Himeji Institute of Technology, 2167 Shosha, Himeji 671-2201, Japan Received 10 November 2003; received in revised form 12 December 2003; accepted 12 December 2003
Abstract The standard entropy of formation at 298 K, f S ◦298 , of Mo2 B5 was determined from measuring the heat capacities (Cp ) from near absolute zero (2 K) to 300 K by the relaxation method. The determined f S ◦298 of Mo2 B5 was −3.543 J K−1 mol−1 . Its Debye temperature, ΘD , was found to be high (540 K), indicating that the crystal lattice is hard and the entropy of vibration is decreased. © 2004 Elsevier B.V. All rights reserved. Keywords: Standard entropy of formation; Debye temperature; Heat capacity
1. Introduction Transition metal borides have high melting points, high hardness values, excellent corrosion- and oxidationresistances. Therefore, they are expected to be constituents for new heat-, corrosion- and wear-resistant alloys. In order to design transition metal boride-dispersed alloys, their thermodynamic data are necessary. Omori et al. in our laboratory have measured the standard Gibbs energies of formation (f G◦T ) of Mo2 B and MoB of the Mo–B binary system [1], and W2 B and WB of the W–B binary system [2] by the electromotive method (EMF). The phase diagrams of the Ni–Mo–B [3] and the Ni–W–B [4] ternary systems were calculated on the basis of the data of Omori et al. [1,2]. Storms and Mueller [5] and Gilles and Pollock [6] measured the activity, a, of the Mo–B binary system by the vaporization method. Baehren and Vollath [7] measured the (f G◦T ) of Mo2 B by the gas reaction method. However, there is a large experimental error of about 10 kJ mol−1 between the data of Storms and Mueller [5] and those of others [6] measured by the vaporization method, by the gas phase reaction method [7] and by the EMF [1] method of the Mo–B binary system. Therefore, we consider that making a comparison between the data obtained by the various kinds of methods is preferable for the Mo–B binary system. ∗ Corresponding author. Tel.: +81-792-67-4915; fax: +81-792-66-8868. E-mail address: [email protected] (M. Morishita).
0925-8388/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2003.12.028
Recently relaxation [8] and semi-adiabatic calorimetric methods [9] have been developed to measure constant pressure heat capacity, Cp , from near absolute zero Kelvin to room temperature. Since the accuracy of these method is very high, the standard entropy of formation at 298 K, f S ◦298 , can be determined by them [10,11]. Also, the standard entropy of formation at any temperature, f S ◦T , can be determined by combining f S ◦298 with Cp measured from room temperature to any high temperature [11]. In the present study, therefore, we have tried to determine the f S ◦298 of Mo2 B5 from Cp values measured from near absolute zero Kelvin.
2. Experimental 2.1. Preparation of the specimen Commercial Mo (99.99%, powder, High Purity Chemical Institute Co., Osaka (HPCI)) and B (99.5%, grain, HPCI) were used as starting materials. Hydro-thermic reduction at 773 K for 10.8 ks was carried out for the Mo powder. Since oxidation loss of B occurred during melting and heat treatment, the addition of an excess of 0.8 mass% B was necessary for preparing Mo2 B5 . The amount of the addition of excess B was determined from a pre-experiment. The mixed powder (∼5 g) of the Mo and B was compressed in a steel die. Mo2 B5 was prepared by melting the powder compact in an Ar-arc furnace. After melting, the sample was subjected to a homogenizing treatment at 1623 K for
112
M. Morishita et al. / Journal of Alloys and Compounds 376 (2004) 111–114
604.8 ks. The material was shown to be a single phase by X-ray diffraction measurement and EPMA observation. 2.2. Cp measurement at 2–390 K The entropy of a material at 298 K, S ◦298 , based on the third law of thermodynamics is given by 298 Cp S ◦298 = dT (1) T 0 where T is the absolute temperature. The heat capacities of Mo2 B5 was measured in the temperature range 2–300 K by using a relaxation method [8] instrument (Quantum Design, San Diego). The samples were attached on a sample platform made from alumina with grease (ASTM standard N-grease (<300 K) and H-grease (>300 K)). A fine heater wire and a thermal relaxation wire are attached to the sample platform. Both wires were made from a gold-based alloy. The sum of the heat capacities of the sample and sample platform, Cp (sample + platform), is derived from the thermal relaxation through the wire: Cp
dT = −Kw (T − Tb ) + P(t) dT
(2)
where Kw is the thermal conductance of the wire; T and Tb the temperature of the sample and the thermal bath, respectively; and P(t) the power applied by the heater. For each measurement, initially the heat capacity of the platform coated with a grease, Cp (platform), was measured, and then the sum of the heat capacity of the sample and platform, Cp (sample + platform), was measured. The sample heat capacity, Cp (sample), was determined by subtracting Cp (platform) from Cp (sample + platform). 120
C p / k J . K − 1 -m o l −1
100
80
60
40
20
0 0
100
200
300
Temperature,T/K Fig. 1. Change in heat capacity, Cp , with temperature, T, for Mo2 B5 .
The Cp values of Mo2 B5 were negligibly small below 2 K. Therefore, their S ◦298 values can be approximately determined from Cp values measured from 2 K. The average of the six series was adopted as the result. Each measured Cp of Mo2 B5 was fitted by polynomial expression: Cp =
n
an T n
(3)
n=1
The polynomial was integrated to determine the S ◦298 value of Mo2 B5 . The f S ◦298 value of Mo2 B5 is given f S ◦298 (Mo2 B5 ) = S ◦298 (Mo2 B5 ) − S ◦298 (Mo) × 2 − S ◦298 (B) × 5
(4)
Table 1 Experimental molar Cp of Mo2 B5 T (K)
Cp (J K mol−1 )
T (K)
Cp (J K mol−1 )
T (K)
Cp (J K mol−1 )
1.88 2.44 2.60 3.05 3.55 4.13 4.79 5.52 7.11 9.66 12.28 14.79 17.39 19.91 22.47 25.02 27.54 30.04 32.56 35.09 37.61 40.15 42.67 45.19 47.66 50.18 52.69 55.20 57.77 60.28 62.79 65.30 67.81 70.34 72.85 75.37 77.89 80.41 82.94 85.46 87.97 90.50
0.0121 0.0159 0.0169 0.0202 0.0236 0.0279 0.0327 0.0384 0.0530 0.0781 0.1125 0.1593 0.2148 0.2919 0.3958 0.5249 0.6906 0.9207 1.225 1.627 2.140 2.592 3.214 3.904 4.688 5.524 6.447 7.366 8.302 9.355 10.43 11.58 12.74 13.80 15.02 16.17 17.40 18.55 19.61 20.73 21.97 23.11
93.01 95.53 98.06 100.58 103.10 105.62 108.14 110.66 113.18 115.70 118.22 120.71 123.23 125.76 128.28 130.80 133.32 135.84 138.35 140.87 143.39 145.90 148.41 150.92 153.43 155.92 158.41 160.93 163.44 165.96 168.48 171.00 173.52 176.05 178.57 181.09 183.61 186.12 188.65 191.17 193.69 196.20
24.26 25.47 26.61 27.82 29.03 30.23 31.41 32.58 33.79 34.99 36.17 37.36 38.58 39.75 41.01 42.05 43.23 44.50 45.68 46.92 48.07 49.21 50.56 51.65 52.61 53.90 55.17 56.22 57.41 58.47 59.72 60.85 61.98 63.15 64.18 65.27 66.32 67.53 68.68 69.73 70.91 72.11
198.72 201.23 203.74 206.25 208.76 211.26 213.78 216.30 218.82 221.32 223.83 226.35 228.86 231.38 233.89 236.41 238.93 241.45 243.96 246.47 248.99 251.49 254.01 256.52 259.04 261.55 264.06 266.58 269.09 271.61 274.12 276.61 279.15 282.97 285.39 287.93 290.49 292.97 295.45 297.88 300.42
73.07 74.14 75.19 76.26 77.30 78.27 79.32 80.45 81.51 82.72 83.48 84.42 85.35 86.20 87.28 88.04 88.98 89.85 90.84 91.71 92.49 93.52 94.24 95.02 95.78 96.74 97.57 98.53 99.35 100.1 101.0 101.8 102.4 103.0 103.9 104.1 104.9 105.1 105.5 106.1 106.2
M. Morishita et al. / Journal of Alloys and Compounds 376 (2004) 111–114
S ◦298 (Mo) and S ◦298 (B) are the third law entropies of pure Mo and B and were adopted from Refs. [12,13].
3. Experimental results and discussion Fig. 1 and Table 1 show the measured Cp values of Mo2 B5 in the temperature range 2–300 K. The polynomial to fit the measured Cp was obtained as Cp (J K−1 mol−1 ) = 1.694 − 27.51 × 10−2 × T + 9.766 × 10−3 × T 2 − 60.16 × 10−6 × T 3 + 17.97 × 10−8 × T 4 − 22.62 × 10−11 × T 5 + 36.37 × 10−15 × T 6
(5)
The result of the calculation using the polynomial is shown as solid line in Fig. 1. The polynomial fitted well with the measured Cp . The S ◦298 value of Mo2 B5 was obtained from the integral of the polynomial and the result was obtained as S ◦298 (Mo2 B5 ) (J K−1 mol−1 ) = 82.837
(6)
The Cp of six nines-copper (99.9999%, Nilaco, Tokyo) was measured and its S ◦298 was calculated in order to evaluate the accuracy achieved with the applied measurement set up. Table 2 shows the measured low temperature Cp and S ◦298 of six nines-copper, compared with the reference data [14]. The measured Cp data and the calculated S ◦298 data deviate only by less than 1%. Thus the S ◦298 of Mo2 B5 was treated having also an uncertainty of 1% as given in Eq. (4). Some Cp , S ◦T and HT –H298 data calculated from the polynomials for Mo2 B5 are summarized in Table 3. Previously the Cp of the four nines-copper (99.99%, HPCI) was measured and its S ◦298 was calculated [10,11]. The present Cp of the six nines-copper was almost same as the data of the four nines-copper [10,11], and the effect of differences in purity was found to be negligibly small. The f S ◦298 of Mo2 B5 was obtained from Eq. (4): f S ◦298 (Mo2 B5 ) (J K−1 mol−1 ) = −3.543
(7)
The f S ◦298 value was found to be negative. In order to clarify the reason for such negative f S ◦298 , the Debye temperature of Mo2 B5 was calculated. The heat capacity values
Table 2 Molar heat capacity, Cp , and third law entropy, S ◦298 , of pure copper (99.9999%) S ◦298 (J K−1 mol−1 )
Cp (J K−1 mol−1 ) Temperature (K) Present study Reference [13] Deviation (%)
100 16.07 16.01 0.37
200 22.54 22.63 0.40
298 24.37 24.44 0.30
298 33.08 33.16 0.24
113
Table 3 Thermodynamic functions for Mo2 B5 T (K)
Cp (J K−1 mol−1 )
S ◦T (J K−1 mol−1 )
H ◦T –H ◦298 (kJ mol−1 )
50 100 150 200 250 298 300
5.89 27.42 51.32 73.46 93.14 105.82 106.05
2.84 13.11 28.78 46.63 65.19 82.84 83.49
−14.91 −14.11 −12.14 −9.01 −4.83 0 0.20
under constant volume, Cv , of solid substances at very low temperature can be generally given by [15]: T 3 Cv (J K−1 mol−1 ) = 1944 (8) ΘD where ΘD is Debye temperature. Since Cv and Cp differ little from one another at low temperatures [16], Cp can be approximately used instead of Cv . ΘD of Mo2 B5 was calculated by inserting the measured Cp at 9.66 K (Table 1). The obtained ΘD was 540 K. The crystal lattice of Mo2 B5 appears to be very hard based on such high ΘD . Thus the atomic bond between Mo and B appears to be very strong. It is likely that the lattice vibration frequency of Mo2 B5 is high and the entropy of vibration, f S ◦,vib , [17] is decreased. As a result, the f S ◦298 of Mo2 B5 shows a negative value. Since the equilibrium oxygen pressures of borides composed of high B content such as MoB4 and Mo2 B5 are very low, not only oxygen ions but also electrons act as carrier in solid electrolytes such as stabilized zirconia. Therefore, EMF cannot be applied for determining f G◦T of these borides. Also, errors of activity measurements when using by the vaporization method are generally known to be large due to experimental difficulties associated with high temperature. On the other hand, the f G◦T of Mo2 B5 at any temperature can be determined by combining the present f S ◦298 with the Cp values measured at high temperature and the standard enthalpy of formation at 298 K, f H ◦298 , measured by a calorimetric method such as solution calorimetry [10,11]. Consequently, the present f S ◦298 of Mo2 B5 is useful as an important basic datum.
References [1] S. Omori, Y. Hashimoto, K. Koyama, J. Jpn. Inst. Met. 45 (1981) 1107–1111. [2] S. Omori, Y. Hashimoto, K. Koyama, Kouon-gakkaishi 7 (1981) 204–208. [3] M. Morishita, K. Koyama, S. Yagi, G. Zhang, J. Alloys Comp. 314 (2001) 212–218. [4] M. Morishita, K. Koyama, K. Maeda, G. Zhang, Mater. Trans. JIM 40 (1999) 600–605. [5] E. Storms, B. Mueller, J. Phys. Chem. 81 (1977) 318–323. [6] P.W. Gilles, B.P. Pollock, AECU-2894 (1962). [7] V.F.D. Baehren, D. Vollath, Planseeber. Pulvermetallurgie 17 (1969) 180–183.
114
M. Morishita et al. / Journal of Alloys and Compounds 376 (2004) 111–114
[8] J.S. Hwang, K.J. Lin, C. Tien, Rev. Sci. Instrum. 68 (1997) 94– 101. [9] V.K. Pecharsky, K.A. Gschneidner Jr., Phys. Rev. Lett. 23 (1997) 4494–4497. [10] M. Morishita, K. Koyama, Z. Metallkde. 94 (2003) 967–971. [11] M. Morishita, A. Navrotsky, J. Am. Ceram. Soc. 86 (2003) 1927– 1932. [12] M.W. Chase, NIST-JANAF Thermochemical Tables, 1998, p. 1578.
[13] M.W. Chase, NIST-JANAF Thermochemical Tables, 1998, p. 178. [14] M.W. Chase, NIST-JANAF Thermochemical Tables, 1998, p. 1006. [15] C. Kittel, Introduction to Solid State Physics, 7th ed., Maruzen, Tokyo, 1998, p. 138 (Translated to Japanese). [16] J.B. Ott, J. Boerio-Goates, Chemical Thermodynamics: Principles and Applications, Academic Press, San Diego, 2000, pp. 183–184. [17] R.A. Swalin, Thermodynamics of Solids, Corona, Tokyo, 1974, pp. 41–53 (Translated to Japanese).