Preview

Геодинамика и тектонофизика

Расширенный поиск

ПОЧТИ АБСОЛЮТНЫЕ УРАВНЕНИЯ СОСТОЯНИЯ АЛМАЗА, Ag, Al, Au, Cu, Mo, Nb, Pt, Ta, W ДЛЯ КВАЗИГИДРОСТАТИЧЕСКИХ УСЛОВИЙ

https://doi.org/10.5800/GT-2012-3-2-0067

Полный текст:

Аннотация

По единой схеме с использованием модифицированного формализма из [Dorogokupets, Oganov, 2005, 2007] построены уравнения состояния алмаза, Ag, Al, Au, Cu, Mo, Nb, Pt, Ta, W путем одновременной оптимизации ударных данных, ультразвуковых, рентгеновских, дилатометрических и термохимических измерений в диапазоне температур от ~100 К до температуры плавления и до давлений несколько Mbar в зависимости от вещества. Комнатная изотерма была задана двумя формами: уравнением В. Хольцапфеля [Holzapfel, 2001, 2010], которое является интерполяционным между низкими давлениями (x≥1) и давлением при бесконечном сжатии (x=0), соответствующим модели Томаса-Ферми, и уравнением П. Вине [Vinet et al., 1987]. Объемная зависимость параметра Грюнейзена рассчитана по соотношениям из [Zharkov, Kalinin, 1971; Burakovsky, Preston, 2004], в которых параметры t и δ являются подгоночными. Комнатная изотерма и давление на ударной адиабате определяются тремя параметрами: K', t и δ, а параметр K0 рассчитывается из ультразвуковых измерений. В результате нам удалось с разумной точностью описать все основные термодинамические функции металлов в рамках простого уравнения состояния с минимальным набором подгоночных параметров.

Рассчитанное по комнатным изотермам давление можно сопоставить со сдвигом линии R1 люминесценции рубина, одновременные измерения которого и параметров ячейки металлов проведены в гелиевой [Dewaele et al., 2004b, 2008; Takemura, Dewaele, 2008; Takemura, Singh, 2006], водородной [Chijioke et al., 2005] и аргоновой средах [Tang et al., 2010]. Показано [Takemura, 2001], что гелиевая среда в алмазных наковальнях обеспечивает квазигидростатические условия, поэтому рубиновую шкалу, откалиброванную по десяти веществам, можно считать близкой к равновесной или почти абсолютной. Она имеет вид P(GPa)=1870⋅Δλ/λ0⋅(1+6⋅Δλ/λ0). Откорректированные по полученной рубиновой шкале комнатные изотермы других веществ также можно считать близкими к равновесным или почти абсолютным, поэтому построенные нами уравнения состояния девяти металлов и алмаза можно отнести к почти абсолютным уравнениям состояния для квазигидростатических условий. Другими словами, они являются взаимосогласованными между собой, с рубиновой шкалой давлений и близки к равновесным в термодинамическом смысле. Рассчитанные по ним P–V–T соотношения могут быть использованы в качестве взаимосогласованных шкал давления в алмазных наковальнях при изучении P–V–T свойств минералов в широкой области температур и давлений. Погрешность рекомендуемых уравнений состояния веществ и рубиновой шкалы составляет порядка 2–3 %. Расчет P–V–T соотношений и термодинамики доступен по адресу http://labpet.crust.irk.ru.

Об авторах

Петр Иванович Дорогокупец
Институт земной коры СО РАН
Россия

докт. геол.-мин. наук, зав. лабораторией петрологии, геохимии и рудогенеза,

664033, Иркутск, ул. Лермонтова, 128



Татьяна Сергеевна Соколова
Институт земной коры СО РАН
Россия

аспирант,

664033, Иркутск, ул. Лермонтова, 128



Борис Станиславович Данилов
Институт земной коры СО РАН
Россия

канд. геол.-мин. наук, н.с.,

664033, Иркутск, ул. Лермонтова, 128



Константин Дмитриевич Литасов
Институт геологии и минералогии им. В.С. Соболева СО РАН
Россия

докт. геол.-мин. наук, с.н.с.,

630090, г. Новосибирск, просп. академика Коптюга, 3



Список литературы

1. Aleksandrov I.V., Goncharov A.F., Zisman A.N., Stishov S.M., 1987. Diamond at high pressures: Raman scattering of light, equation of state, and high-pressure scale. Soviet Physics – Journal of Experimental and Theoretical Physics 66 (2), 384–390.

2. Al’tshuler L.V., Bakanova A.A., Dudoladov I.P., Dunin E.A., Trunin R.F., Chekin B.S., 1981. Shock adiabats for metals. New data, statistical analysis and general regularities. Journal of Applied Mechanics and Technical Physics 2, 3–34.

3. Al’tshuler L.V., Brusnikin S.E., Kuz’menkov E.A., 1987. Isotherms and Grüneisen functions for 25 metals. Journal of Applied Mechanics and Technical Physics 28 (1), 129–141.

4. Armstrong P.E., Dickinson J.M., Brown M.K., 1966. Temperature dependence of the elastic stiffness coefficients of niobium (columbium). Transactions of the metallurgical society of AIME 236, 1404–1408.

5. Bassett W.A., 2009. Diamond anvil cell, 50th birthday. High Pressure Research 29 (2), 163–186. http://dx.doi.org/10.1080/08957950802597239.

6. Bernstein B.T., 1962. Elastic properties of polycrystalline tungsten at elevated temperatures. Journal of Applied Physics 33 (6), 2140. http://dx.doi.org/10.1063/1.1728910.

7. Boettger J.C., Honnell K.G., Peterson J.H., Greef C., Crockett S., 2012. Tabular equation of state for gold. AIP Conference Proceedings 1426, 812–815. http://dx.doi.org/10.1063/1.3686402.

8. Bolef D.I., 1961. Elastic constants of single crystals of the bcc transition elements V, Nb, and Ta. Journal of Applied Physics 32 (1), 100–105. http://dx.doi.org/10.1063/1.1735933.

9. Bradley D.K., Eggert J.H., Smith R.F., Prisbrey S.T., Hicks D.G., Braun D.G., Biener J., Hamza A.V., Rudd R.E., Collins G.W., 2009. Diamond at 800 GPa. Physical Review Letters 102 (7), 075503. http://dx.doi.org/10.1103/PhysRevLett.102.075503.

10. Brooks C.R., Bungham R.E., 1968. The specific heat of aluminum from 330 to 890 °K and contributions from the formation of vacancies and anharmonic effects. Journal of Physics and Chemistry of Solids 29 (9), 1553–1560. http://dx.doi.org/10.1016/0022-3697(68)90097-8.

11. Burakovsky L., Preston D.L., 2004. Analytic model of the Grüneisen parameter all densities. Journal of Physics and Chemistry of Solids 65 (8–9), 1581–1587. http://dx.doi.org/10.1016/j.jpcs.2003.10.076.

12. Carroll K.J., 1965. Elastic Constants of Niobium from 4.2° to 300°K. Journal of Applied Physics 36 (11), 3689–3690. http://dx.doi.org/10.1063/1.1703072.

13. Carter W.J., Marsh S.P., Fritz J.N., McQueen R.G., 1971. The equation of state of selected materials for high-pressure references. In: Lloyd E.C. (Ed.), Accurate characterization of the high pressure environment (National Bureau of Standards, Washington, DC). National Bureau of Standards special publication, V. 326, p. 147–158.

14. Chang Y.A., Himmel L., 1966. Temperature dependence of the elastic constants of Cu, Ag, and Au above room temperature. Journal of Applied Physics 37 (9), 3567–3573. http://dx.doi.org/10.1063/1.1708903.

15. Chang Y.A., Hultgren R., 1965. The dilation contribution to the heat capacity of copper and α-brass at elevated temperatures. Journal of Physical Chemistry 69 (12), 4162–4165. http://dx.doi.org/10.1021/j100782a017.

16. Chase M.W., Jr., 1998. NIST-JANAF Thermochemical Tables. Fourth Edition. Journal of Physical and Chemical Reference Data. Monograph 9. 1963 p.

17. Chijioke D., Nellis W.J., Soldatov A., Silvera I.F., 2005. The ruby pressure standard to 150 GPa. Journal of Applied Physics 98 (11), 114905. http://dx.doi.org/10.1063/1.2135877.

18. Choudhury A., Brooks C.R., 1984. Contributions to the heat capacity of solid molybdenum in the range 300–2890 K. International Journal of Thermophysics 5 (4), 403–429. http://dx.doi.org/10.1007/BF00500869.

19. Collard S.M., McLellan R.B., 1991. High-temperature elastic constants of gold single-crystals. Acta Metallurgica Materialia 39 (12), 3143–3151. http://dx.doi.org/10.1016/0956-7151(91)90048-6.

20. Collard S.M., McLellan R.B., 1992. High-temperature elastic constants of platinum single crystals. Acta Metallurgica Materialia 40 (4), 699–702. http://dx.doi.org/10.1016/0956-7151(92)90011-3.

21. Dewaele A., Loubeyre P., Mezouar M., 2004a. Refinement of the equation of state of tantalum. Physical Review B 69 (9), 092106. http://dx.doi.org/10.1103/PhysRevB.69.092106.

22. Dewaele A., Loubeyre P., Mezouar M., 2004b. Equations of state of six metals above 94 GPa. Physical Review B 70 (9), 094112. http://dx.doi.org/10.1103/PhysRevB.70.094112.

23. Dewaele A., Loubeyre P., Occelli F., Mezouar M., Dorogokupets P.I., Torrent M., 2006. Hydrostatic equation of state of iron up to 205 GPa. Implications for the Earth’s core. Physical Review Letters 97 (21), 215504. http://dx.doi.org/10.1103/PhysRevLett.97.215504.

24. Dewaele A., Torrent M., Loubeyre P., Mezouar M., 2008. Compression curves of transition metals in the Mbar range: Experiments and projector augmented-wave calculations. Physical Review B 78 (10), 104102. http://dx.doi.org/10.1103/PhysRevB.78.104102.

25. Dorogokupets P.I., 2002. Critical analysis of equations of state for NaCl. Geochemistry International 40. Supplement 1, S132–S144.

26. Dorogokupets P.I., 2007. Equation of state of magnesite for the conditions of the Earth’s lower mantle. Geochemistry International 45 (6), 561–568. http://dx.doi.org/10.1134/S0016702907060043.

27. Dorogokupets P.I., 2010. P–V–T equations of state of MgO and thermodynamics. Physics and Chemistry of Minerals 37 (9), 677–684. http://dx.doi.org/10.1007/s00269-010-0367-2.

28. Dorogokupets P.I., Dewaele A., 2007. Equations of state of MgO, Au, Pt, NaCl-B1, and NaCl-B2: Internally consistent hightemperature pressure scales. High Pressure Research 27 (4), 431–446. http://dx.doi.org/10.1080/08957950701659700.

29. Dorogokupets P.I., Oganov A.R., 2003. Equations of State of Cu and Ag and Revised Ruby Pressure Scale. Doklady Earth Sciences 391A (6), 854–857.

30. Dorogokupets P.I., Oganov A.R., 2004. Intrinsic anharmonicity in equations of state of solids and minerals. Doklady Earth Sciences 395 (2), 238–241.

31. Dorogokupets P.I., Oganov A.R., 2005. Ruby pressure scale: revision and alternatives. In: Proceedings Joint 20th AIRAPT and 43th EHPRG International Conference on High Pressure Science and Technology, June 27 to July 1, 2005, Karlsruhe, Germany. http://deposit.ddb.de/ep/netpub/10/83/76/978768310/_data_stat/Posters/P133.pdf.

32. Dorogokupets P.I., Oganov A.R. 2006. Equations of state of Al, Au, Cu, Pt, Ta, and W and revised ruby pressure scale. Doklady Earth Sciences 410 (1), 1091–1095. http://dx.doi.org/10.1134/S1028334X06070208.

33. Dorogokupets P.I., Oganov A.R., 2007. Ruby, metals, and MgO as alternative pressure scales: A semiempirical description of shockwave, ultrasonic, X-ray, and thermochemical data at high temperatures and pressures. Physical Review B 75 (2), 024115. http://dx.doi.org/10.1103/PhysRevB.75.024115.

34. Dorogokupets P.I., Sokolova T.S., 2011. Almost absolute equations of state of metals. Fazovyye perekhody, uporyadochennyye sostoyaniya i novyye materialy 5 (in Russian) [Дорогокупец П.И., Соколова Т.С. Почти абсолютные уравнения состояния металлов // Фазовые переходы, упорядоченные состояния и новые материалы. 2011. № 5]. http://ptosnm.ru/catalog/i/667.

35. Dubrovinsky L.S., Saxena S.K., 1997. Thermal expansion of periclase (MgO) and tungsten (W) to melting temperatures. Physics and Chemistry of Minerals 24 (8), 547–550. http://dx.doi.org/10.1007/s002690050070.

36. Dubrovinsky L.S., Saxena S.K., Tutti F., Rekhi S., 2000. In situ X-Ray study of thermal expansion and phase transition of iron at multimegabar pressure. Physical Review Letters 84 (8), 1720–1723. http://dx.doi.org/10.1103/PhysRevLett.84.1720.

37. Featherston F.H., Neighbours J.R., 1963. Elastic constants of tantalum, tungsten, and molybdenum. Physical Review 130 (4), 1324–1333. http://dx.doi.org/10.1103/PhysRev.130.1324.

38. Fei Y., Ricolleau A., Frank M., Mibe K., Shen G., Prakapenka V., 2007. Toward an internally consistent pressure scale. Proceedings of the National Academy of Sciences 104 (22), 9182–9186. http://dx.doi.org/10.1073/pnas.0609013104.

39. Fortov V.E., Lomonosov I.V. 2010. Shock waves and equations of state of matter. Shock Waves 20 (1), 53–71. http://dx.doi.org/10.1007/s00193-009-0224-8.

40. Gerlich D., Fisher E.S., 1969. The high temperature elastic moduli of aluminum. Journal of Physics and Chemistry of Solids 30 (5), 1197–1205. http://dx.doi.org/10.1016/0022-3697(69)90377-1.

41. Giauque W.F., Meads P.F., 1941. The heat capacities and entropies of aluminum and copper from 15 to 300 K. Journal of the American Chemical Society 63 (7), 1897–1901. http://dx.doi.org/10.1021/ja01852a027.

42. Gulseren O., Cohen R.E., 2002. High-pressure thermoelasticity of body-centered-cubic tantalum. Physical Review B 65 (6), 064103. http://dx.doi.org/10.1103/PhysRevB.65.064103.

43. Gurvich L.V., Veiz I.V., Medvedev V.V. et al., 1979. Thermodynamic properties of individual substances. Vol. 2, Book 2. Nauka, Moscow, 344 p. (in Russian) [Гурвич Л.В., Вейц И.В., Медведев В.А. и др. Термодинамические свойства индивидуальных веществ. М.: Наука, 1979. Т. 2. Кн. 2. 344 с.].

44. Gurvich L.V., Veiz I.V., Medvedev V.V. et al., 1981. Thermodynamic properties of individual substances. Vol. 3, Book 2. Nauka, Moscow, 400 p. (in Russian) [Гурвич Л.В., Вейц И.В., Медведев В.А. и др. Термодинамические свойства индивидуальных веществ. М.: Наука, 1981. Т. 3. Кн. 2. 400 с.].

45. Gurvich L.V., Veiz I.V., Medvedev V.V. et al., 1982. Thermodynamic properties of individual substances. Vol. 4, Book 2. Nauka, Moscow, 560 p. (in Russian) [Гурвич Л.В., Вейц И.В., Медведев В.А. и др. Термодинамические свойства индивидуальных веществ. М.: Наука, 1982. Т. 4. Кн. 2. 560 с.].

46. Hemley R.J., Percy W., 2010. Bridgman's second century. High Pressure Research 30 (4), 581–619. http://dx.doi.org/10.1080/08957959.2010.538974.

47. Hirao N., Akahama Y., Ohishi Y., Kawamura H., 2009. In situ X-ray study at multimegabar pressures and the diamond anvil Raman gauge. In: P-V-T equations of state of materials, G-COE International Summer School, 3-5 August, 2009, Geodynamic Research Center, Ehime University, Ehime, Japan.

48. Hirose K., Sata N., Komabayashi Y., Ohishi Y., 2008. Simultaneous volume measurements of Au and MgO to 140 GPa and thermal equation of state of Au based on the MgO pressure scale. Physics of the Earth and Planetary Interiors 167 (3–4), 149–154. http://dx.doi.org/10.1016/j.pepi.2008.03.002.

49. Hixson R.S., Fritz J.N., 1992. Shock compression of tungsten and molybdenum. Journal of Applied Physics 71 (4), 1721–1728. http://dx.doi.org/10.1063/1.351203.

50. Ho P.S., Ruoff A.L., 1969. Pressure Dependence of the Elastic Constants for Aluminum from 77° to 300°K. Journal of Applied Physics 40 (8), 3151–3156. http://dx.doi.org/10.1063/1.1658157.

51. Holland T.J.B., Powell R., 1998. An internally-consistent thermodynamic dataset for phases of petrological interest. Journal of Metamorphic Geology 16 (3), 309–343. http://dx.doi.org/10.1111/j.1525-1314.1998.00140.x.

52. Holland T.J.B., Powell R., 2011. An improved and extended internally consistent thermodynamic dataset for phases of petrological interest, involving a new equation of state for solids. Journal of Metamorphic Geology 29 (3), 333–383. http://dx.doi.org/10.1111/j.1525-1314.2010.00923.x.

53. Holmes N., Moriarty J., Gather G., Nellis W., 1989. The equation of state of platinum to 660 GPa (6.6 Mbar). Journal of Applied Physics 66 (7), 2962–2967. http://dx.doi.org/10.1063/1.344177.

54. Holzapfel W.B., 2001. Equations of state for solids under strong compression. Zeitschrift für Kristallographie 216 (9), 473–488. http://dx.doi.org/10.1524/zkri.216.9.473.20346.

55. Holzapfel W.B., 2003. Refinement of ruby luminescence pressure scale. Journal of Applied Physics 93 (3), 1813–1818. http://dx.doi.org/10.1063/1.1525856.

56. Holzapfel W.B., 2005. Progress in the realization of a practical pressure scale for the range 1–300 GPa. High Pressure Research 25 (2), 87–96. http://dx.doi.org/10.1080/09511920500147501.

57. Holzapfel W.B., 2010. Equations of state for Cu, Ag, and Au and problems with shock wave reduced isotherms. High Pressure Research 30 (3), 372–394. http://dx.doi.org/10.1080/08957959.2010.494845.

58. Holzapfel W.B., Hartwig M., Sievers W., 2001. Equations of state for Cu, Ag, and Au for wide ranges in temperature and pressure up to 500 GPa and above. Journal of Physical and Chemical Reference Data 30 (2), 515–529. http://dx.doi.org/10.1063/1.1370170.

59. Jacobsen S.D., Holl C.M., Adams K.A., Fischer R.A., Martin E.S., Bina C.R., Lin J.F., Prakapenka V.B., Kubo A., Dera P., 2008. Compression of single-crystal magnesium oxide to 118 GPa and a ruby pressure gauge for helium pressure media. American Mineralogist 93 (11–12), 1823–1828. http://dx.doi.org/10.2138/am.2008.2988.

60. Jamieson J.C., Fritz J.N., Manghnani M.H., 1982. Pressure measurement at high temperature in X-ray diffractions studies: Gold as a primary standard. In: Akimoto S., Manghani M.H. (Eds.), High-Pressure Research in Geophysics. Center for Academic Publications, Tokyo, p. 27–48.

61. Jin K., Wu Q., Geng H., Li X., Cai L., Zhou X., 2011. Pressure–volume–temperature equations of state of Au and Pt up to 300 GPa and 3000 K: internally consistent pressure scales. High Pressure Research 31 (4), 560–580. http://dx.doi.org/10.1080/08957959.2011.611469.

62. Jin K., Wu Q., Jing F., Li X., 2009. Simple method for reducing shock wave equation of state to zero Kelvin isotherm for metals. Journal of Applied Physics 105 (4), 043510. http://dx.doi.org/10.1063/1.3078804.

63. Jones A.H., Isbell W.H., Maiden C.J., 1966. Measurements of the very high-pressure properties of materials using a light-gas gun. Journal of Applied Physics 37 (9), 3493–3499. http://dx.doi.org/10.1063/1.1708887.

64. Kamm G.N., Alers G.A., 1964. Low-temperature elastic moduli of aluminum. Journal of Applied Physics 35 (2), 327–330. http://dx.doi.org/10.1063/1.1713309.

65. Kirby K.K., 1991. Platinum – A thermal expansion reference material. International Journal of Thermophysics 12 (4), 679–685. http://dx.doi.org/10.1007/BF00534223.

66. Klotz S., Chervin J.-C., Munsch P., Le Marchand G., 2009. Hydrostatic limits of 11 pressure transmitting media. Journal of Physics D: Applied Physics 42 (7), 075413. http://dx.doi.org/10.1088/0022-3727/42/7/075413.

67. Knopoff I., 1965. Approximate compressibility of elements and compounds. Physical Review 138 (5A), A1445–A1447. http://dx.doi.org/10.1103/PhysRev.138.A1445.

68. Knudson M.D., Lemke R.W., Hayes D.B., Hall C.A., Deeney C., Asay J.R., 2003. Near-absolute Hugoniot measurements in aluminum to 500 GPa using a magnetically accelerated flyer plate technique. Journal of Applied Physics 94 (7), 4420–4431. http://dx.doi.org/10.1063/1.1604967.

69. Kono Y., Irifune T., Higo Y., Inoue T., Barnhoorn A., 2010. P–V–T relation of MgO derived by simultaneous elastic wave velocity and in situ X-ray measurements: A new pressure scale for the mantle transition region. Physics of the Earth and Planetary Interiors 183 (1–2), 196–211. http://dx.doi.org/10.1016/j.pepi.2010.03.010.

70. Leisure R.G., Hsu D.K., Seiber B.A., 1973. Elastic properties of tantalum over the temperature range 4-300 K. Journal of Applied Physics 44 (8), 3394–3397. http://dx.doi.org/10.1063/1.1662772.

71. Levashov P.R., Khishchenko K.V., Lomonosov I.V., Fortov V.E., 2004. Database on shock-wave experiments and equations of state available via Internet. AIP Conference Proceedings 706, 87–90. http://dx.doi.org/10.1063/1.1780190. (Available from http://teos.ficp.ac.ru/rusbank/, http://www.ihed.ras.ru/rusbank/).

72. Li B.S., Woody K., Kung J., 2006. Elasticity of MgO to 11 GPa with an independent absolute pressure scale: Implications for pressure calibration. Journal of Geophysical Research 111 (B11), B11206. http://dx.doi.org/10.1029/2005JB004251.

73. Liebermann R.C., 2011. Multi-anvil, high pressure apparatus: a half-century of development and progress. High Pressure Research 31 (4), 493–532. http://dx.doi.org/10.1080/08957959.2011.618698.

74. Lowrie R., Gonas A.M., 1965. Dynamic elastic properties of polycrystalline tungsten, 24–1800 °C. Journal of Applied Physics 36 (7), 2189–2192. http://dx.doi.org/10.1063/1.1714447.

75. Maglic K.D., 2003. Recommended specific heat capacity functions of group VA elements. International Journal of Thermophysics 24 (2), 489–500. http://dx.doi.org/10.1023/A:1022976122789.

76. Mao H.K., Bell P.M., Shaner J.W., Steinberg D.J., 1978. Specific volume measurements of Cu, Mo, Pd, and Ag and calibration of the ruby R1 fluorescence pressure gauge from 0.06 to 1 Mbar. Journal of Applied Physics 49 (6), 3276–3283. http://dx.doi.org/10.1063/1.325277.

77. Mao H.K., Wu Y., Chen L.C., Shu J.F., Jephcoat A.P., 1990. Static compression of iron to 300 GPa and Fe0.8Ni0.2 alloy to 260 GPa: Implications for composition of the core. Journal of Geophysical Research 95 (B13), 21737–21742. http://dx.doi.org/10.1029/JB095iB13p21737.

78. Mao H.K., Xu J., Bell P.M., 1986. Calibration of the ruby pressure gauge to 800 kbar under quasi-hydrostatic conditions. Journal of Geophysical Research 91 (B5), 4673–4676. http://dx.doi.org/10.1029/JB091iB05p04673.

79. Marsh S.P. (Ed.), 1980. LASL Shock Hugoniot Data. University of California Press, Berkeley, 658 p. (Available from http://teos.ficp.ac.ru/rusbank).

80. Matsui M., Ito E., Katsura T., Yamazaki D., Yoshino T., Yokoyama A., Funakoshi K., 2009. The temperature-pressure-volume equation of state of platinum. Journal of Applied Physics 105 (1), 013505. http://dx.doi.org/10.1063/1.3054331.

81. McLellan R.B., Ishikawan T., 1987. The elastic properties of aluminum at high temperatures. Journal of Physics and Chemistry of Solids 48 (7), 603–606. http://dx.doi.org/10.1016/0022-3697(87)90147-8.

82. McQueen R.G., Fritz J.N., Marsh S.P., 1963. On the equation of state of stishovite. Journal of Geophysical Research 68 (8), 2319–2322. http://dx.doi.org/10.1029/JZ068i008p02319.

83. McQueen R.G., Fritz J.N., Marsh S.P., 1965. On the equation of state of stishovite. In: Zharkov V.N. (Ed.), Dynamical research of solids at high pressures. Mir, Moscow, p. 194–203. (in Russian) [Мак-Куин Р., Фритц Дж., Марш С. Об уравнении состояния стишовита // Динамические исследования твердых тел при высоких давлениях / Под ред. В.Н. Жаркова. М.: Мир, 1965. С. 194–203].

84. McSkimin H.J., Andreatch P., 1972. Elastic moduli of diamond as a function of pressure and temperature. Journal of Applied Physics 43 (7), 2944–2948. http://dx.doi.org/10.1063/1.1661636.

85. McSkimin H.J., Bond W.L., 1957. Elastic moduli of diamond. Physical Review 105 (1), 116–121. http://dx.doi.org/10.1103/PhysRev.105.116.

86. Mitchell A.C., Nellis W.J., 1981. Shock compression of aluminum, copper and tantalum. Journal of Applied Physics 52 (5), 3363–3374. http://dx.doi.org/10.1063/1.329160.

87. Mitchell A.C., Nellis W.J., Moriarty J.A., Heinle R.A., Holmes N.C., Tipton R.E., Repp G.W., 1991. Equation of state of Al, Cu, Mo, and Pb at shock pressures up to 2.4 TPa (24 Mbar). Journal of Applied Physics 69 (5), 2981–2986. http://dx.doi.org/10.1063/1.348611.

88. Morgan J.A., 1974. The equation of state of platinum to 680 GPa. High Temperatures – High Pressures 6 (2), 195–202.

89. Neighbours J.R., Alers G.A., 1958. Elastic Constants of Silver and Gold. Physical Review 111 (3), 707–712. http://dx.doi.org/10.1103/PhysRev.111.707.

90. Nellis W.J., Moriarty J.A., Mitchell A.C., Ross M., Dandrea R.G., Ashcroft N.W., Holmes N.C., Gathers G.R., 1988. Metals physics at ultrahigh pressure: Aluminum, Copper and Lead as Prototypes. Physical Review Letters 60 (14), 1414–1417. http://dx.doi.org/10.1103/PhysRevLett. 60.1414.

91. Novikova S.I., 1974. Thermal expansion of solids. Nauka, Moscow, 291 p. (in Russian) [Новикова С.И. Тепловое расширение твердых тел. М.: Наука, 1974. 291 с.].

92. Occelli F., Loubeyre P., Letoullec R., 2003. Properties of diamond under hydrostatic pressures up to 140 GPa. Nature Materials 2 (3), 151–154. http://dx.doi.org/10.1038/nmat831.

93. Ono S., Brodholt J.P., Price G.D., 2011. Elastic, thermal and structural properties of platinum. Journal of Physics and Chemistry of Solids 72 (3), 169–175. http://dx.doi.org/10.1016/j.jpcs.2010.12.004.

94. Overton W.C., Gaffney J., 1955. Temperature variation of the elastic constants of cubic elements. I. Copper. Physical Review 98 (4), 969–977. http://dx.doi.org/10.1103/PhysRev.98.969.

95. Pavlovskii M.N., 1971. Shock compression of diamond. Soviet Physics – Solid State 13 (3), 741–742.

96. Reeber R.R., Wang K., 1996. Thermal expansion, molar volume and specific heat of diamond from 0 to 3000 K. Journal of Electronic Materials 25 (1), 63–67. http://dx.doi.org/10.1007/BF02666175.

97. Robie R.A., Hemingway B.S., Fisher J.R., 1978. Thermodynamic properties of minerals and related substances at 298.15 K and 1 bar (105 Pascals) pressure and at high temperatures. United States Geological Survey Bulletin 1452. 456 p.

98. Ruoff A.L., 1967. Linear shock-velocity-particle-velocity relationship. Journal of Applied Physics 38 (13), 4976–4980. http://dx.doi.org/10.1063/1.1709263.

99. Ruoff A.L., Xia H., Xia Q., 1992. The effect of a tapered aperture on X-ray diffraction from a sample with a pressure gradient: Studies on three samples with a maximum pressure of 560 GPa. Review of Scientific Instruments 63 (10), 4342–4348. http://dx.doi.org/10.1063/1.1143734.

100. Sabbah R., An X.W., Chickos J.S., Leitao M.L.P., Roux M.V., Torres L.A., 1999. Reference materials for calorimetry and differential thermal analysis. Thermochimica Acta 331 (2), 93–204. http://dx.doi.org/10.1016/S0040-6031(99)00009-X.

101. Shim S.H., Duffy T.S., Kenichi T., 2002. Equation of state of gold and its application to the phase boundaries near 660 km depth in Earth's mantle. Earth and Planetary Science Letters 203 (2), 729–739. http://dx.doi.org/10.1016/S0012-821X(02)00917-2.

102. Silvera I.F., Chijioke A.D., Nellis W.J., Soldatov A., Tempere J., 2007. Calibration of the ruby pressure scale to 150 GPa. Physica Status Solidi 244 (1), 460–467. http://dx.doi.org/10.1002/pssb.200672587.

103. Soga N., 1966. Comparison of measured and predicted bulk moduli of tantalum and tungsten at high temperatures. Journal of Applied Physics 37 (9), 3416–3420. http://dx.doi.org/10.1063/1.1708873.

104. Sokolova T.S., Dorogokupets P.I., 2011. EoS for gold. Fazovyye perekhody, poryadochennyye sostoyaniya i novyye materialy 5 (in Russian) [Соколова Т.С., Дорогокупец П.И. Уравнение состояния золота // Фазовые переходы, упорядоченные состояния и новые материалы. 2011. № 5]. http://ptosnm.ru/catalog/i/671.

105. Speziale S., Zha C-S., Duffy T., Hemley R., Mao H., 2001. Quasi-hydrostatic compression of magnesium oxide to 52 GPa: Implications for the pressure-volume-temperature equation of state. Journal of Geophysical Research 106 (B1), 512–528. http://dx.doi.org/10.1029/2000JB900318.

106. Sun T., Umemoto K., Wu Z., Zheng J.-C., Wentzcovitch R.M., 2008. Lattice dynamics and thermal equation of state of platinum. Physical Review B 78 (2), 024304. http://dx.doi.org/10.1103/PhysRevB.78.024304.

107. Syassen K., 2008. Ruby under pressure. High Pressure Research 28 (2), 75–126. http://dx.doi.org/10.1080/08957950802235640.

108. Takemura K., 2001. Evaluation of the hydrostaticity of a helium-pressure medium with powder X-ray diffraction techniques. Journal of Applied Physics 89 (1), 662–668. http://dx.doi.org/10.1063/1.1328410.

109. Takemura K., Dewaele A., 2008. Isothermal equation of state for gold with a He-pressure medium. Physical Review B 78 (10), 104119. http://dx.doi.org/10.1103/PhysRevB.78.104119.

110. Takemura K., Singh A.K., 2006. High-pressure equation of state for Nb with a helium-pressure medium: Powder x-ray diffraction experiments. Physical Review B 73 (22), 224119. http://dx.doi.org/10.1103/PhysRevB.73.224119.

111. Tallon J.L., Wolfenden A., 1979. Temperature dependence of the elastic constants of aluminum. Journal of Physics and Chemistry of Solids 40 (11), 831–837. http://dx.doi.org/10.1016/0022-3697(79)90037-4.

112. Talmor Y., Walker E., 1977. Elastic constants of niobium up to the melting point. Solid State Communications 23 (9), 649–651. http://dx.doi.org/10.1016/0038-1098(77)90541-5.

113. Tang L.-Y., Liu L., Liu J., XiaoW., Li Y.-C., Li X.-D., Bi Y., 2010. Equation of state of tantalum up to 133 GPa. Chinese Physics Letters 27 (1), 016402. http://dx.doi.org/10.1088/0256-307X/27/1/016402.

114. Tange Y., Nishihara Y., Tsuchiya T., 2009. Unified analyses for P-V-T equation of state of MgO: A solution for pressurescale problems in high P-T experiments. Journal of Geophysical Research 114 (B3), B03208. http://dx.doi.org/10.1029/2008JB005813.

115. Touloukian Y.S., Buico E.H., 1970. Specific heat: metallic elements and alloys. Thermophysical Properties of Matter, vol. 4. IFI/Plenum Press, New York.

116. Touloukian Y.S., Kirby R.K., Taylor R.E., Desai P.D., 1975. Thermal expansion: metallic elements and alloys. Thermophysical properties of matter, vol. 12. IFI/Plenum Press, New York, 1348 p.

117. Touloukian Y.S., Kirby R.K., Taylor R.E., Desai P.D., 1977. Thermal expansion: nonmetallic solids. Thermophysical Properties of Matter, vol. 13. IFI/Plenum Press, New York, 1486 p.

118. Victor A.C., 1962. Heat capacity of diamond at high temperatures. Journal of Chemical Physics 36 (7), 1903–1911. http://dx.doi.org/10.1063/1.1701288.

119. Vinet P., Ferrante J., Rose J.H., Smith J.R., 1987. Compressibility of solids. Journal of Geophysical Research 92 (B9), 9319–9325. http://dx.doi.org/ 10.1029/JB092iB09p09319.

120. Wang K., Reeber R.R., 1998. The role of defects on thermophysical properties: thermal expansion of V, Nb, Ta, Mo and W. Materials Science and Engineering 23 (3), 101–137. http://dx.doi.org/10.1016/S0927-796X(98)00011-4.

121. Wang K., Reeber R.R., 2000. The perfect crystal, thermal vacancies and the thermal expansion coefficient of aluminum. Philosophical Magazine A 80 (7), 1629–1643. http://dx.doi.org/10.1080/01418610008212140.

122. White G.K, Collocott S.J., 1984. Heat capacities of reference materials: Cu and W. Journal of Physical and Chemical Reference Data 13 (4), 1251–1257. http://dx.doi.org/10.1063/1.555728.

123. Wilthan B., Cagran C., Brunner C., Pottlacher G., 2004. Thermophysical properties of solid and liquid platinum. Thermochimica Acta 415 (1–2), 47–54. http://dx.doi.org/10.1016/j.tca.2003.06.003.

124. Yokoo M., Kawai N., Nakamura K.G., Kondo K., 2008. Hugoniot measurement of gold at high pressures of up to 580 GPa. Applied Physics Letters 92 (5), 051901. http://dx.doi.org/10.1063/1.2840189.

125. Yokoo M., Kawai N., Nakamura K.G., Kondo K., Tange Y., Tsuchiya T., 2009. Ultrahigh-pressure scales for gold and platinum at pressures up to 550 GPa. Physical Review B 80 (10), 104114. http://dx.doi.org/10.1103/PhysRevB.80.104114.

126. Zha C.-S., Mao H.K., Hemley R.J., 2000. Elasticity of MgO and a primary pressure scale to 55 GPa. Proceedings of the National Academy of Sciences 97 (25), 13494–13499. http://dx.doi.org/10.1073/pnas.240466697.

127. Zharkov V.N., Kalinin V.A., 1971. Equations of state for solids at high pressures and temperatures. Consultants Bureau, New York, 257 p.

128. Zouboulis E.S., Grimsditch M., Ramdas A.K., Rodriges S., 1998. Temperature dependence of the elastic moduli of diamond: A Brillouin-scattering study. Physical Review B 57 (5), 2889–2896. http://dx.doi.org/10.1103/PhysRevB.57.2889.


Для цитирования:


Дорогокупец П.И., Соколова Т.С., Данилов Б.С., Литасов К.Д. ПОЧТИ АБСОЛЮТНЫЕ УРАВНЕНИЯ СОСТОЯНИЯ АЛМАЗА, Ag, Al, Au, Cu, Mo, Nb, Pt, Ta, W ДЛЯ КВАЗИГИДРОСТАТИЧЕСКИХ УСЛОВИЙ. Геодинамика и тектонофизика. 2012;3(2):129-166. https://doi.org/10.5800/GT-2012-3-2-0067

For citation:


Dorogokupets P.I., Sokolova T.S., Danilov B.S., Litasov K.D. NEAR-ABSOLUTE EQUATIONS OF STATE OF DIAMOND, Ag, Al, Au, Cu, Mo, Nb, Pt, Ta, AND W FOR QUASI-HYDROSTATIC CONDITIONS. Geodynamics & Tectonophysics. 2012;3(2):129-166. (In Russ.) https://doi.org/10.5800/GT-2012-3-2-0067

Просмотров: 799


Creative Commons License
Контент доступен под лицензией Creative Commons Attribution 4.0 License.


ISSN 2078-502X (Online)