Temperature dependence of the elastic moduli of diamond: A Brillouin-scattering study

Abstract

Using the modified formalism of [Dorogokupets, Oganov, 2005, 2007, equations of state are developed for diamond, Ag, Al, Au, Cu, Mo, Nb, Pt, Ta, and W by simultaneous optimization of shock-wave data, ultrasonic, X-ray, dilatometric and thermochemical measurements in the temperature range from ~100 K to the melting temperature and pressures up to several Mbar, depending on the substance. The room-temperature isotherm is given in two forms: (1) the equation from [Holzapfel, 2001[Holzapfel, , 2010 which is the interpolation between the low pressure (x≥1) and the pressure at infinite compression (x=0); it corresponds to the Thomas-Fermi model, and (2) the equation from [Vinet et al., 1987]. The volume dependence of the Grüneisen parameter is calculated according to equations from [Zharkov, Kalinin, 1971;Burakovsky, Preston, 2004] with adjustable parameters, t and δ. The room-temperature isotherm and the pressure on the Hugoniot adiabat are determined by three parameters, K', t and δ, and K 0 is calculated from ultrasonic measurements. In our study, reasonably accurate descriptions of all of the basic thermodynamic functions of metals are derived from a simple equation of state with a minimal set of adjustable parameters.The pressure calculated from room-temperature isotherms can be correlated with a shift of the ruby R1 line. Simultaneous measurements of the shift and unit cell parameters of metals are conducted in mediums containing helium [Dewaele et al., 2004b;2008;Takemura, Dewaele, 2008;Takemura, Singh, 2006], hydrogen [Chijioke et al., 2005] and argon [Tang et al., 2010]. According to [Takemura, 2001], the helium medium in diamond anvil cells provides for quasi-hydrostatic conditions; therefore, the ruby pressure scale, that is calibrated for the ten substances, can be considered close to equilibrium or almost absolute. The ruby pressure scale is given as P(GPa)=1870⋅Δλ/λ 0 ⋅(1+6⋅Δλ/λ 0 ). The room-temperature isotherms corrected with regard to the ruby scale can also be considered close to equilibrium or almost absolute. Therefore, the equations of state of the nine metals and diamond, which are developed in our study, can be viewed as almost absolute equations of state for the quasi-hydrostatic conditions. In other words, these equations agree with each other, with the ruby pressure scale, and they are close to equilibrium in terms of thermodynamics. The PVT relations derived from these equations can be used as mutually agreed pressure scales for diamond anvil cells in studies of PVT properties of minerals in a wide range of temperatures and pressures. The error of the recommended equations of the state of substances and the ruby pressure scale is about 2 or 3 per cent. Calculated PVT relations and thermodynamics data are available at http://labpet.crust.irk.ru.

Density Functional Study of the Carbon Dependence of the Structural, Mechanic, Thermodynamic, and Dynamic Properties of SiC Alloys

“…Our calculated bulk modulus agrees well with the experimental values [17,18] for Si and C, respectively, and as a function of the carbon concentration, it is determined by the following equation: B = 97.406 − 109.616x + 917.418x 2 − 1792.981x 3 + 1345.715x 4 (3)…”

Temperature dependence of elastic moduli of polycrystalline β plutonium

“…5 95,96 are plotted for comparison. 97 The values and temperature dependence of the Poisson's ratios for β-Pu and γ-Pu are similar to that of many metals while α-Pu has small values and almost no (slightly negative) temperature dependence which is more characteristic of covalent bonding.…”

“…% Ga is also plotted. The Poisson's ratios of aluminum 91,92 , austenitic steel 93 , α-Fe 94 and diamond 95,96 are plotted for comparison. 97 α-Pu, β-Pu and γ-Pu (and δ-Pu 2.36 at.…”

Равновесные Структуры Из Углеродных Алмазоподобных Кластеров И Их Упругие Свойства

“…1 и 4, в табл. 5 приводятся экспериментальные данные для кубического алмаза из работ [59][60][61][62]. Из сравне-ния можно видеть, что объемный модуль кубического алмаза (∼ 440 GPa) превосходит объемные модули всех рассмотренных алмазоподобных фаз.…”