The modified van der Waals equation of state: Part IV: Crystalline materials

PVT data of crystallizable materials (CM), minerals, alkali, alkali halides, metals, mineral oxides and hydroxides, rare gas, water, organic compounds and polymers, published in the literature are reanalyzed. It is shown that all these materials under pressure verify the modified van der Waals equation of state (mVW-EOS), discussed recently [J. Rault, Eur. Phys. J. E 40 , 82 (2017)]. The characteristic parameters P * V * of this EOS depend only on the nature of the material and not on its state (liquid, glassy, solid of different structure) and whatever are its conductivity and magnetic properties (insulator, conductor, superconductor, paramagnetic, ferromagnetic). This EOS explains the following properties: (a) the fan structure of the isobars V ( T ), and of the tangents to the isotherms V ( P ); (b) the superposition principle of the isotherms V ( P ); (c) the αB rule: the constancy of the thermal pressure coefficient ( dP / dT ) V = αB , product of the thermal expansion coefficient α and the bulk modulus B ; (d) its relation with the Slater conjecture: ( dP / dT ) V ~ dP / dT m in crystallized materials, T m being the melting temperature. The characteristic pressure P * ( T and V independent) is compared with the various pressures: (i) P coh = E coh / V , the cohesive energy density; (ii) P L m = L m / ΔV m , L m and ΔV m being the enthalpy and volume jumps at the melting, respectively; (iii) P D = ΔH a /D V a , ratio of the activation parameters of the autodiffusion coefficient; (iv) P X = X ∕ X ′, X being the bulk modulus B , shear modulus G , elastic constants C ij , and the yield stress σ y of the CM, X ′ their pressure derivative (at ambient conditions). All the elastic constants B , G , C ij and the yield stress σ y are linear functions of P at low pressure ( P < P * ) and extrapolate to zero at the same negative pressure − P X = − P * . (e) P Bγ = B ∕ γ * ratio of the bulk modulus B and Grüneisen parameter γ * at zero pressure. (f) PΔV m is the pressure deduced from the linear relation between the volume jump ΔV m ( P ) at the transition (melting or crystalline transition) and the pressure. The universal relation P * = P coh = P L m = P D = P B = P G = P Cij = P σy = P Δ V m is observed and discussed. In molecular compounds such as H 2 O, H 2 , and polymers with different intra- and intermolecular interactions, the compression involves two different processes, at low and high pressures, verifying the mVW-EOS with characteristic pressures P 1 * a