Reexploring the cation ordering and magnetic cation substitution effects on the elastic anisotropy of aluminum spinels

We study the effects of cation inversion x (Mg <--> Al, with x representing the fraction of Mg and Al exchanged), and magnetic substitution (Mn --> Mg) on the elastic properties of the MgAl2O4 spinel system using density functional theory and Brillouin scattering techniques. Our computations show that cation inversion decreases the molar volume of spinel, and produces a stiffening of C11 and a softening of C12. Simulations and experiments agree within 2%. Density functional theory also captures the qualitative effect of Mg <--> Al on C44, that is an initial softening for inversion degree x < 0.125 and stiffening at x = 1, with a disagreement of < 4%. The Zener anisotropy factor A decreases with increasing degree of inversion. All these trends are preserved at high pressures. The substitution of Mn for Mg produces and increases the molar volume of spinel, and it is accompanied by the softening of both C11 and C44, and the stiffening of C12, in good agreement with experimental results at ambient conditions. All these effects, which are qualitatively opposite to those of cation inversion, are enhanced at high pressures. The effect of Mn --> Mg on the elastic anisotropy of spinel is, however, qualitatively similar to that of cation inversion, i.e., it causes a decrease in the Zener factor A.