Elastic Moduli of Refractory Spinels

Abstract

Elastic moduli of spinel phases in the system Mg(Al, Cr, Fe) 2 O 1 were determined from sonic analyses of porous, polycrystalline specimens prepared by hot‐pressing. A special iterative least‐squares technique (ILS) and standard curve‐fitting techniques were used to obtain moduli at zero porosity by extrapolation. A minimal standard error of estimate was achieved in all cases by using an exponential form for the porosity dependence and the ILS technique. Moduli were checked for self‐consistency. Extrapolated moduli for MgAl 2 O 1 agreed well with respective moduli calculated from single‐crystal elastic constants and Birch's law. Longitudinal and shear sound velocities decreased with increasing phase density in the solid‐solution systems and systematics indicate that elastic moduli of arbitrary solid solutions can be estimated to lt; ± 10% from the phase density.