A robust three-parameter reference curve for condensed phase materials

Abstract

Many isothermal equations of state lead to numerical problems under tension conditions due to negative bulk modulus. We summarize the properties of four existing models and devise a continuous non-piecewise reference curve to address this issue. The final functional form contains three fitting parameters that are directly related to the bulk modulus and its pressure derivative at the reference state and at infinite pressures. We also include bounds that guarantee the monotonicity of its pressure derivative in all volume space. To demonstrate the qualitative features of each isotherm, we conduct calibrations against experimental data for cyclotetramethylene tetranitramine, magnesium oxide, gold, and platinum. Pressure residuals and root mean square deviations show that the proposed functional form is capable of adequately fitting the data compared to other three-parameter models.

Equation of State for Single Crystal 3,3′-Diamino-4,4′-azoxyfurazan

“…The EoS are derived from the standard decomposition of the Helmholtz free energy of a crystal, F ( V , T ) = F c ( V ) + F i o n ( V , T ) into a static lattice energy, or cold curve, F c ( V ), that depends only on specific volume, and the thermal ionic contribution, F ion ( V , T ), that depends on the set of vibrational normal modes of the crystal . Whereas the Rose–Vinet function was used to represent the cold curve in our earlier EoS for RDX, HMX, and PETN, − in this study we have used the MACAW reference curve of Lozano and Aslam. , One motivation for the development of the MACAW reference curve was to eliminate regions with negative bulk moduli when the material is put into tension, V > V 0 , where V 0 is the equilibrium volume of the crystal. While real materials cannot support large tensile stresses, the presence of regions of negative bulk modulus in expansion, which may occur in the popular Burch–Murnaghan or Rose–Vinet forms, leads to severe numerical instabilities in hydrocodes and finite element simulations that are circumvented by the use of the MACAW form .…”

An equation of state based on the scaling properties of vibrational spectra at high pressure

“…Finally, a pertinent issue in the evaluation of any proposed EOS is the value of ¢ ¥ B [7,[20][21][22][23]-the infinite pressure limit of the compressibility. Some researchers believe (based on the Thomas-Fermi theory) that its Figure 6.…”

“…Equations of state are useful for the prediction of thermodynamical properties [1][2][3][4][5][6][7] and for gaining an insight into the nature of the inter-atomic interactions in various classes of solids-such as covalent, ionic, metallic, and rare gases [8]. The application of pressure makes the inter-atomic distances shorter and most materials transform into solids under high enough pressure [9,10].…”

Properties of Erythritol Tetranitrate from Molecular Dynamics Simulation

“…The isothermal compression curves can be represented accurately by the MACAW reference curve that was proposed recently by Lozano and Aslam. , The MACAW reference curve is particularly useful for hydrocode simulations because unlike other empirical equations of state, it does not lead to negative bulk moduli when the material is put into tension, and it can be inverted analytically. The MACAW reference curve takes the form P = A true( V V 0 true) − ( B + 1 ) exp ( 2 3 C true( 1 − true( V V 0 true) 3 / 2 true) ) ( C ( V V 0 ) 3 / 2 + B ) − A ( B + C ) where P is the pressure, V the specific volume, V 0 the specific volume where P = 0, and A , B , and C are adjustable parameters.…”

“…The isothermal compression curves can be represented accurately by the MACAW reference curve that was proposed recently by Lozano and Aslam. 31,32 The MACAW reference curve is particularly useful for hydrocode simulations because unlike other empirical equations of state, it does not lead to negative bulk moduli when the material is put into tension, and it can be inverted analytically. The MACAW reference curve takes the form…”