The role of defects on thermophysical properties: Thermal expansion of V, Nb, Ta, Mo and W

Materials Science and Engineering R: Reports

Volumn 23, Issue 3, 1998, Pages 101-137

  Wang, Kai ^a   Reeber, Robert R ^a  

^a North Carolina State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTALS; DEFECTS; DIFFUSION; ELECTRON SCATTERING; EQUATIONS OF STATE; MATHEMATICAL MODELS; POLYNOMIALS; SPECIFIC HEAT; THERMAL EXPANSION; THERMAL VARIABLES MEASUREMENT; THERMODYNAMIC PROPERTIES;

HIGH TEMPERATURE ANHARMONICITY; HIGH TEMPERATURE THERMAL DEFECT; MOLAR VOLUME; THERMAL EXPANSION COEFFICIENT; THERMOPHYSICAL PROPERTY; VIBRATION MODEL;

REFRACTORY METALS;

EID: 0032120509     PISSN: 0927796X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0927-796X(98)00011-4     Document Type: Article

References (170)

1. A. Seeger, H. Mehrer, in: A. Seeger, D. Schumacher, W. Schillling, J. Diehl (Eds.), Vacancies and Interstitials in Metals, North-Holland, Amsterdam, 1970, p. 1.
2. K. Maier, M. Peo, B. Saile, H.E. Schaefer, A. Seeger, Philos. Mag. 40 (1979) 701.
3. Ya.A. Kraftmakher, Philos. Mag. 74 (1996) 811.
4. Th. Hehenkamp, in: A. Seeger, D. Schumacher, W. Schillling, J. Diehl (Eds.), Vacancies and Interstitials in Metals, North-Holland, Amsterdam, 1970, p. 91.
5. Th. Hehenkamp, J. Phys. Chem. (Solids) 55 (1994) 907.
6. W.E. Schoknecht, R.O. Simmons, in: M.G. Graham, H.E. Hagy (Eds.), Thermal Expansion - 1971, American Institute of Physics, New York, 1972, p. 169.
7. A. Einstein, Ann. Phys. 35 (1911) 679.
8. M. Born, K. Huang, Dynamical Theory of Crystal Lattices, Oxford Univ. Press, New York, 1954.
9. M. Blackman, Hdb. Phys. 7 (1955) 325.
10. A.A. Maradudin, E.W. Montroll, G.H. Weiss, Theory of Lattice Dynamics in the Harmonic Approximation, Academic Press, New York, London, 1963.
11. W. Ludwig, Recent developments in lattice theory, in: G. Höhler (Ed.), Springer Tracts in Modern Physics, 43, Springer-Verlag, New York, 1967.
12. H. Bilz, W. Kress, Phonon Dispersion Relations in Insulators, Springer-Verlag, New York, 1979.
13. H.R. Glyde, M.L. Klein, Crit. Rev. Solid State Sci. 2 (1971) 181.
14. B.J. Parsons, Proc. R. Soc. London Ser. A 352 (1977) 397.
15. P. Gillet, F. Guyot, Y. Wang, Geophys. Res. Lett. 23 (1996) 3043.
16. J.F. Nye, Physical Properties of Crystals, Oxford Univ. Press, London, 1960.
17. L.W. Finger, Y. Ohashi, Am. Mineral. 61 (1976) 303.
18. S.M. Jessen, H. Küppers, J. Appl. Cryst. 24 (1991) 239.
19. J.G. Collins, G.K. White, Prog. Low Temp. Phys. 4 (1964) 450.
20. B. Yates, Thermal Expansion, Plenum, New York, 1973.
21. T.H.K. Barron, J.G. Collins, G.K. White, Adv. Phys. 29 (1980) 609.
22. H.D. Merchant, K.K. Shukla, H.D. Pandey, Crit. Rev. Solid State Sci. 3 (1973) 451.
23. Y.S. Touloukian, R.K. Kirby, R.E. Taylor, P.D. Desai (Eds.), Thermophysical Properties of Matter, Vol. 12, IFI/ Plenum, New York, 1975.
24. Y.S. Touloukian, R.K. Kirby, R.E. Taylor, T.Y.R. Lee (Eds.), Thermophysical Properties of Matter, Vol. 13, IFI/ Plenum, New York, 1977.
25. R.S. Krishnan, R. Srinivasan, S. Devanarayanan, Thermal Expansion of Crystals, Pergamon, NY, 1979.
26. K. Becker, Z. Phys. 40 (1927) 37.
27. M. Hart, J. Cryst. Growth 55 (1981) 409.
28. R.R. Reeber, K. Wang, Mater. Chem. Phys. 46 (1996) 259.
29. A.D. Krawitz, D.G. Reichel, R. Hitterman, J. Am. Ceram. Soc. 72 (1989) 515.
30. R.R. Reeber, Low Temperature Thermal Expansion of Wurtzite-Phases of IIB-VIB Compounds, PhD thesis, Ohio State University, 1969.
31. M.H. Fizeau, Comp. Rend. 58 (1864) 923.
32. G.R. Clusener, in: M.G. Graham, H.E. Hagy (Eds.), Thermal Expansion-1971, American Institute of Physics, New York, 1972, p. 51.
33. G.K. White, Cryogenics 1 (1961) 1.
34. R.H. Carr, C.A. Swenson, Cryogenics 47 (1964) 6.
35. J.M. Shapiro, D.R. Taylor, G.M. Graham, Can. J. Phys. 42 (1964) 835.
36. K. Andres, Cryogenics 2 (1961) 93.
37. R.V. Jones, J. Sci. Instr. 1 (1968) 958.
38. A.P. Miiller, A. Cezairliyan, Int. J. Thermophys. 3 (1982) 259.
39. A. Cezairliyan, J.L. McClure, J. Res. Natl. Bur. Stand. 75A (1971) 283.
40. A.P. Miiller, A. Cezairliyan, Int. J. Thermophys. 12 (1991) 643.
41. T.A. Hahn, R.K. Kirby, in: M.G. Graham, H.E. Hagy (Eds.), Thermal Expansion-1971, American Institute of Physics, New York, 1972, p. 13.
42. S.K. Saxena, G. Shen, J. Geophys. Res. 97 (1992) 19813.
43. K. Wang, R.R. Reeber, in: A. Pechenik, R.K. Kalia, P. Vashishta (Eds.), Computer-Aided Design of High Temperature Materials, Oxford Univ. Press, New York, 1998 (in press).
44. L.S. Dubrovinsky, S.K. Saxena, Phys. Chem. Miner. 24 (1997) 547.
45. R.R. Reeber, K. Goessel, K. Wang, Eur. J. Mineral. 7 (1995) 1039.
46. S.P. Srivastava, J. Phys. Chem. (Solids) 39 (1978) 1143.
47. R.A. MacDonald, W.M. MacDonald, Phys. Rev. B 24 (1981) 1715.
48. R.A. MacDonald, Thermal Expansion 8 (1984) 11.
49. R.A. MacDonald, R.C. Shukla, D.K. Kahaner, Phys. Rev. B 29 (1984) 6489.
50. A.M. Sherry, M. Kumar, J. Phys. Chem. (Solids) 52 (1991) 1145.
51. M. Kumar, S.P. Upadhyay, J. Phys. Chem. (Solids) 54 (1993) 773.
52. M. Kumar, Solid State Commun. 92 (1994) 463.
53. L.L. Boyer, Phys. Rev. Lett. 42 (1979) 584.
54. L.L. Boyer, Phys. Rev. B 27 (1980) 1271.
55. L.L. Boyer, Thermal Expansion 7 (1982) 131.
56. L.L. Boyer, Thermal Expansion 8 (1984) 21-30.
57. S. Biernacki, M. Scheffler, Phys. Rev. Lett. 63 (1989) 290.
58. Z. Gong, G.K. Horton, E.R. Cowley, Phys. Rev. B 38 (1988) 10820.
59. Z. Gong, G.K. Horton, E.R. Cowley, Phys. Rev. B 40 (1989) 3294.
60. D.G. Isaak, R.E. Cohen, M.J. Mehl, J. Geophys. Res. 95 (1990) 7055.
61. A. Agnon, M.S.T. Bukowinski, Phys. Rev. B 41 (1990) 7755.
62. C.H. Xu, C.Z. Wang, C.T. Chan, K.M. Ho, Phys. Rev. B 43 (1991) 5024.
63. P. Pavone, K. Karch, O. Schütt, W. Windl, D. Strauch, Phys. Rev. B. 48 (1993) 3156.
64. I. Inbar, R.E. Cohen, Geophys. Res. Lett. 22 (1995) 1533.
65. J.B. Wachtman Jr., T.G. Scuderi, G.W. Cleek, J. Am. Ceram. Soc. 45 (1962) 319.
66. R.R. Reeber, Phys. Status Solidi A 32 (1975) 321.
67. I. Suzuki, J. Phys. Earth 23 (1975) 145.
68. I. Suzuki, S. Okajima, LK. Seya, J. Phys. Earth 27 (1979) 63.
69. K. Wang, R.R. Reeber, J. Mater. Res. 11 (1996) 1800.
70. Grüneisen, E., Handbuch der Physik, 10 (1926) 1, Engl. transl. NASA RE 2-18-59W, 1959.
71. Grüneisen, E., Handbuch der Physik, 10 (1926) 1, Engl. transl. NASA RE 2-18-59W, 1959.
72. T.H.K. Barron, Philos. Mag. 46 (1955) 720.
73. O.L. Anderson, Equation of State of Solids and Ceramic Science, Oxford Univ. Press, New York, 1995.
74. O.L. Anderson, D.L. Isaak, H. Oda, Rev. Geophys. 30 (1992) 57.
75. H. Ibach, Phys. Status Solidi 31 (1969) 625.
76. D. Lu, L. Wang, J. Infrared Millm. Waves 13 (1994) 174 (in Chinese).
77. M. Blackman, Proc. Phys. Soc. London 70B (1957) 827.
78. R.R. Reeber, J.L. Haas Jr., Thermal Expansion 8 (1984) 31.
79. R.R. Reeber, K. Wang, J. Electron. Mater. 25 (1996) 63.
80. K. Wang, R.R. Reeber, J. Phys. Chem. (Solids) 56 (1995) 895.
81. P.A. Varotsos, K.D. Alexopoulos, Thermodynamics of Point Defects and their Relation with Bulk Properties, North-Holland, Amsterdam, 1986.
82. K. Wang, R.R. Reeber, Phys. Chem. Miner. 23 (1996) 354.
83. K. Wang, R.R. Reeber, Phys. Status Solidi A 146 (1994) 621.
84. K. Wang, R.R. Reeber, J. Appl. Cryst. 28 (1995) 306.
85. K. Wang, R.R. Reeber, Geophys. Res. Lett. 22 (1995) 1297.
86. F. Birch, J. Geophys. Res. 73 (1968) 817.
87. K. Wang, R.R. Reeber, High Temp. Mater. Sci. 35 (1996) 181.
88. K. Wang, R.R. Reeber, High Temp. Mater. Sci. 36 (1996) 185.
89. P. Varotsos, K. Alexopoulos, Phys. Rev. B 22 (1980) 3130.
90. K. Alexopoulos, P. Varotsos, Phys. Rev. B 24 (1981) 3606.
91. C. Falter, W. Zierau, J. Appl. Phys. 51 (1980) 2070.
92. P. Varotsos, W. Ludwig, K. Alexopoulos, Phys. Rev. B 18 (1978) 2683.
93. G.A. Slack, S.F. Bartram, J. Appl. Phys. 46 (1975) 89.
94. G.K. White, R.D. Roberts, High Temp.-High Pressures 15 (1983) 321.
95. P. Gustafson, Int. J. Thermophys. 6 (1985) 395.
96. L.R. Fokin, V.Ya Chekhovskoi, High Temp. 29 (1991) 94.
97. W.L. James, M.E. Straumanis, Z. Phys. Chem. 29 (1961) 134.
98. M.E. Straumanis, S. Zyszczynski, J. Appl. Cryst. 3 (1970) 1.
99. M.H. Mueller, Scripta Met. 11 (1977) 693.
100. M.E. Straumanis, R.P. Shodhan, Trans. Metall. Soc. AIME 242 (1968) 1185.
101. W. Parrish, Acta Cryst. 13 (1960) 838.
102. H.D. Erfling, Ann. Phys. 41 (1942) 467.
103. A.P. Nasekovskii, Sov. Phys. J. 12 (1969) 45.
104. M. Linkoaho, E. Rantavuori, Phys. Status Solidi 37 (1970) K89.
105. M.I. Lesnaya, G.G. Volokitin, V.A. Kashchuk, High Temp. 14 (1975) 1072.
106. E.M. Savitskii, I.V. Burov, N.A. Tomilin, Sov. Phys. Dokl. 28 (1983) 676.
107. Y. Iwasaki, M. Kaneko, K. Hayashi, Y. Ochiai, M. Hayakawa, K. Aso, J. Phys. E 22 (1989) 498.
108. S.V. Stankus, High Temp. 31 (1993) 514.
109. Yu.M. Smirnov, V.A. Finkel', Sov. Phys. JETP 22 (1966) 750.
110. G.K. White, Cryogenics 2 (1962) 292.
111. G.A. Mochalov, O.S. Ivanov, Ind. Lab. 35 (1969) 139.
112. F.L. Yaggee, E.R. Gilbert, J.W. Styles, J. Less Common Met. 19 (1969) 39.
113. D.G. Westlake, S.T. Ockers, J. Less Common Met. 22 (1970) 2257
114. B.R. Brodskiy, B.E. Neymark, Russ. Met. 6 (1971) 156.
115. R. Roberge, J. Less Common Met. 40 (1975) 161.
116. V.A. Petukhov, V. Ya, V.Ya Chekhovskoi, V.G. Andrianova, A.G. Mozgovoi, High Temp. 15 (1977) 561.
117. V.A. Petukhov, V.Ya. Chekhovskoi, A.G. Mozgovoi, High Temp. 16 (1978) 353.
118. V.P. Popov, V.A. Pervakov, Phys. Met. Metallogr. 53 (1982) 193.
119. F. Righini, R.B. Roberts, A. Rosso, High Temp.-High Pressures 18 (1986) 573.
120. P.C. de Camargo, F.R. Brotzen, S. Steinemann, J. Phys. F 17 (1987) 1065.
121. A.P. A.P. Miiller, A. Cezairliyan, Int. J. Thermophys. 9 (1988) 195.
122. P. Hidnert, H.S. Krider, J. Res. Natl. Bur. Stand. 11 (1933) 279.
123. C.R. Tottle, J. Inst. Met. 85 (1957) 375.
124. T.J. Heal, Proc. U.N. Int. Conf. Peaceful Uses At. Energy, 2nd Geneva, 5 (1958) 208.
125. P.M. Johnson, R.L. Lincon, E.R. McClure, U.S. Bureau of Mines Rep. BMRI-7142, 1968, 13 pp.
126. V.P. Lebedev, A.A. Mamalui, V.A. Pervakov, N.S. Petrenko, V.P. Popov, V.I. Khotkevich, Ukr. Fiz. Zh. 14 (1969) 746.
127. Yu.A. Lisovskii, Sov. Phys.-Solid State 14 (1973) 2015.
128. A.N. Amatumi, T.I. Malyutina, V.Ya. Chekhovskoi, V.A. Petukhov, High Temp.-High Pressures 8 (1976) 565.
129. I. Suh, H. Ohta, Y. Waseda, J. Mater. Sci. 23 (1988) 757.
130. R. Chanchani, P.M. Hall, IEEE Trans. Comp. Hybrids Manuf. Technol. 13 (1990) 743.
131. L.W. Schad, P. Hidnert, Natl. Bur. Stand. Tech. News Bull. 15 (1919) 31.
132. P. Hidnert, W.B. Gero, Natl. Bur. Stand. Tech. News Bull. 19 (1924) 429.
133. F.C. Nix, D. MacNair, Phys. Rev. 61 (1942) 74.
134. K. Andres, Phys. Kondens. Mater. 2 (1964) 294.
135. E.E. Totskii, High Temp. 2 (1964) 181.
136. S.I. Novikova, Thermal Expansion of Solids [in Russian], Nauka, Moscow, 1974 (referenced by Amitin et al.).
137. V.A. Petukhov, V.Ya. Chekhovskoi, V.M. Zaichenko, High Temp. 14 (1976) 645.
138. G.K. White, T.F. Smith, R.H. Carr, Cryogenics 18 (1978) 301.
139. A.P. Miiller, A. Cezairliyan, Int. J. Thermophys. 6 (1985) 695.
140. J. Disch, Z. Phys. 5 (1921) 173.
141. A.G. Worthing, Phys. Rev. 28 (1926) 190.
142. Y. Waseda, K. Hirata, M. Ohtani, High Temp.-High Pressures 7 (1975) 221.
143. V.A. Petukhov, V.Ya. Chekhovskoi, A.G. Mozgovoi, High Temp. 15 (1977) 449.
144. A.P. Miiller, A. Cezairliyan, Int. J. Thermophys. 3 (1982) 259.
145. P. P. Hidnert, J. Res. Natl. Bur. Stand. 2 (1929) 887.
146. J.W. Edwards, R. Speiser, H.L. Johnson, J. Appl. Phys. 22 (1951) 424.
147. C.G. Fink, Trans. Am. Electrochem. Soc. 17 (1910) 229.
148. I. Langmuir, Phys. Rev. 7 (1916) 302.
149. J. Demarquay, C. R. 220 (1945) 81.
150. R.G. Ross, W. Hume-Rothery, J. Less Common Met. 5 (1963) 258.
151. Ya.A. Kraftmakher, I.M. Cheremisina, J. Appl. Mech. Tech. Phys. 2 (1965) 107.
152. H.W. King, C.M. Preece, Adv. X-Ray Anal. 10 (1966) 354.
153. E. Fitzer, S. Weisenburger, High Temp.-High Pressures 4 (1972) 559.
154. E.G. Shevchenko, T.I. Malyutina, V.K. Borina, L.M. Kafel, Measurement Tech. 29 (1986) 866.
155. A. Lahav, K.A. Grim, J. Appl. Phys. 67 (1990) 734.
156. A.P. Miiller, A. Cezairliyan, Int. J. Thermophys. 11 (1990) 619.
157. V.T. Deshpande, R. Pawar, Curr. Sci. 31 (1962) 497.
158. R.K. Kirby, High Temp.-High Pressures 4 (1972) 459.
159. V.A. Petukhov, V.Ya. Chekhovskoi, High Temp.-High Pressures 4 (1972) 671.
160. R.B. Roberts, J. Phys. E. 8 (1975) 600.
161. G.K. White, T.F. Smith, R.H. Carr, Cryogenics 18 (1978) 301.
162. C.A.V. Rodrigues, J. Plusquellec, P. Azou, Thermal Expansion 8 (1981) 105.
163. R.R. Reeber, K. Wang, in: Proceedings of the 20th Army Science Conference, Norfolk, VA, June, 1996.
164. R. R. Wanner, Can. J. Phys. 48 (1970) 1270.
165. D.R. Lide (Ed.), CRC Handbook of Chemistry and Physics, 73, CRC Press, Ann Arbor, 1992.
166. Ya. A. Kraftmakher, P.G. Strelkov, in: A. Seeger, D. Schumacher, W. Schillling, J. Diehl (Eds.), Vacancies and Interstitials in Metals, North-Holland, Amsterdam, 1970, p. 59.
167. G.K. White, Phys. B 149 (1988) 255.
168. J.E. Kluin, Th. Hehenkamp, Phys. Rev. B 44 (1991) 11597.
169. R.O. Simmons, R.W. Balluffi, Phys. Rev. 129 (1963) 1533.
170. P. Varotsos, Phys. Rev. B 37 (1988) 6511.