The spinels CoB$_2$O$_4$ with magnetic Co$^{2+}$ ions on the diamond lattice A site can be frustrated because of competing near-neighbor ($J_1$) and next-near neighbor ($J_2$) interactions. Here we describe attempts to tune the relative strengths of
these interactions by substitution on the non-magnetic B-site. The system we employ is CoAl$_{2-x}$Ga$_x$O$_4$, where Al is systematically replaced by the larger Ga, ostensibly on the B site. As expected, Ga substitution expands the lattice, resulting in Co atoms on the A-site being pushed further from one other and thereby weakening magnetic interactions. In addition, Ga distributes between the B and the A site in a concentration dependent manner displacing an increasing amount of Co from the A site with increasing $x$. This increased inversion, which is confirmed by neutron diffraction studies carried out at room temperature, affects magnetic ordering very significantly, and changes the nature of the ground state. Modeling of the magnetic coupling illustrates the complexity that arises from the cation site disorder.
Near or less than 10% Nb substitution on the Ti site in perovskite SrTiO$_3$ results in metallic behavior, in contrast to what is seen in BaTiO$_3$. Given the nearly identical structure and electron counts of the two materials, the distinct ground st
ates for low substitution have been a long-standing puzzle. Here we find from neutron studies of average and local structure, the subtle yet critical difference that we believe underpins the distinct electronic properties in these fascinating materials. While SrTi$_{0.875}$Nb_${0.125}$O$_3$ possesses a distorted non-cubic structure at 15 K, the BO$_6$ octahedra in the structure are regular. BaTi$_{0.875}$Nb$_{0.125}$O$_3$ on the other hand shows evidence for local cation off-centering whilst retaining a cubic structure.
The local structures of Zn$_{1-x}$Mg$_x$O alloys have been studied by Raman spectroscopy and by synchrotron x-ray pair distribution function (PDF) analysis. Within the solid solution range ($0leq{x}leq{0.15}$) of Zn$_{1-x}$Mg$_x$O, the wurtzite frame
work is maintained with Mg homogeneously distributed throughout the wurtzite lattice. The $E_2^mathrm{high}$ Raman line of Zn$_{1-x}$Mg$_x$O displays systematic changes in response to the evolution of the crystal lattice upon the Mg-substitution. The red-shift and broadening of the $E_2^mathrm{high}$ mode are explained by the expansion of hexagonal $ab$-dimensions, and compositional disorder of Zn/Mg, respectively. Synchrotron x-ray PDF analyses of Zn$_{1-x}$Mg$_x$O reveal that the Mg atoms have a slightly reduced wurtzite parameter $u$ and more regular tetrahedral bond distances than the Zn atoms. For both Zn and Mg, the internal tetrahedral geometries are independent of the alloy composition.
