Deriving linear isotherms for solids

Internal Pressures of Lithium and Cesium Fluids at Different Temperatures

“…In the present work, we begin with the exact thermodynamic relation (∂E/∂V) T ) T(∂p/∂T) Fp (10) in which T(∂p/∂T) F is usually called the thermal pressure and (∂E/∂V) T is called the internal pressure. 20,21 In the present work, we assume that any kinetic energy contribution to the internal energy E will vanish on taking the derivative, since the temperature is held constant.…”

“…X-ray diffraction and small-angle X-ray scattering of cesium fluids have been measured by reducing electron density down to the range where the compressibility of the interacting electron gas has been theoretically predicted to become negative. It suggests that an attractive interaction among like charges, ions in this case, is enhanced. − Despite the fact that the description of the metallic fluids at the molecular level is very complicated, they obey some relatively simple rules . Among these we refer to a general regularity which has been reported for pure dense fluids, according to which ( Z − 1) V 2 is linear with respect to ρ 2 , and each isotherm can be taken as, false( Z − 1 false) V 2 = A + B ρ 2 where Z ≡ p V / R T is the compression factor, ρ = 1/ V is the molar density, and A and B are the temperature-dependent parameters as follows: A = A′′ − A′ R T B = B′ R T Here A ′ and B ′ are related to intermolecular attractive and repulsive forces, respectively, while A ′′ is related to the nonideal thermal pressure and R T has its usual meaning. , The regularity was originally suggested on the basis of a simple lattice-type model applied to a Lennard−Jones (12-6) fluid.…”

“…[6][7][8][9] Despite the fact that the description of the metallic fluids at the molecular level is very complicated, they obey some relatively simple rules. 10 Among these we refer to a general regularity which has been reported for pure dense fluids, according to which (Z -1)V 2 is linear with respect to F 2 , and each isotherm can be taken as, (Z -1)V 2 ) A + BF 2 (1)…”

An Accurate Equation of State for Fluids and Solids

“…Nevertheless, at present, there exist several equations of state that are reasonably accurate for a variety of dense materials. [2][3][4][5][6][7][8][9][10][11][12] Despite their complexity at the molecular level, dense systems exhibit a number of simple regularities, 13,14 some of which have been known experimentally for a long time. The existence of these regularities suggests that it might be possible to write a general effective potential that embodies the common features that appear in the equations of state of many different materials.…”

“…On the basis of this reasoning, several effective, near-neighbor pair potentials have been introduced in the literature, and associated equations of state have been derived. 7,[9][10][11][12] This work has provided simple analytical forms for equations of state that can accurately "fit" experimental data for a varied selection of materials and over significant ranges of state parameters.…”