Analytical Models For The Shear Modulus Of Alpha-Pu And Ga-Stabilized Delta-Pu Versus Temperature And Pressure From Measurements

From measurements we model some constitutive relations of pure plutonium and Ga-stabilized delta-plutonium alloy (Pu-2.3 at.%Ga), focusing on the shear modulus G versus temperature T (T is an element of [300; 750] K) and pressure P (P is an element of [0; 1] GPa). G(T) or G(P) are computed from the density-corrected elastic-waves velocities for each crystallographic phase. The models developed here in this temperature and pressure range provide useful analytical forms in contrast to the discrete values of the measurements. Because it is reasonable to expect that the bulk moduli of pure and Ga-stabilized delta-Pu also agree where they exist at the same temperatures, these models are applicable to comparisons with ab-initio calculations (which are essentially zero-temperature calculations) for pure Pu. A model for G(P, T) is also provided for use in elasto-plastic models implemented in hydrodynamic codes based on measurements of G(T) up to 750 K and G(P) up to 1 GPa. The model for G(P, T) of Pu-2.3 at.%Ga accounts for the presence of alpha' under pressure. The G(P, T) model, a continuous function from solid to liquid, uses the phase transition temperatures and the melting temperature to make it more than a simple curve fit. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3563066]