Chemical bonding, magnetic moments, and local symmetry in transition-metal—metalloid alloys

A model is proposed that quantitatively accounts for the moment variation in transition-metal—metalloid ($T-M$) crystals and glasses. The model, formulated from valence-bond theory, assumes that each $T$ atom surrounding an $M$ atom contributes a $d$ orbital to participate in $p-d$ hybrid bonding. If each bonded $d$ orbital in Co alloys is occupied by $\frac{n_B}{5}$ nonmagnetic holes, then the moment of a Co-$M$ alloy is $\mu \left(\frac{{\mu }_B}{T\mathrm{at}.\mathrm{}}\right)=n_B-Z_M\left(\frac{n_B}{5}\right)\frac{N_M}{N_T}$. Here $n_B$ is the effective moment of pure Co in Bohr magnetons, and $Z_M$ is the number of $T$ atoms in the first shell around an $M$ atom. Hence the moment variation in Co-$M$ alloys is determined by the local symmetry of the $M$ atom and not by the valence of $M$. For Ni alloys it is found that both hybridization and the $p$ valency are responsible for the moment reduction. Symmetry arguments are used to derive the relation $\mu \left(\frac{{\mu }_B}{T\mathrm{at}.\mathrm{}}\right)=n_B-Z_M\left(\frac{n_B}{5}\right)\frac{N_M}{N_T}-\frac{\left(V_p{N}_M\right)}{N_T}$ for Ni-$M$ alloys where $V_p$ is the $p$ valency of the metalloid. The models use the hybridization concept of electron sharing rather than electron transfer so that the solid is not ionic. The decrease in magnetization comes from formation of nonpolarizable $p-d$ hybrid bonds from polarizable $3d$ transition-metal states. Therefore the model is in agreement with experiments and theories that indicate a constant number of unoccupied $3d$ levels regardless of metalloid concentration. Excellent quantitative agreement is found when the model is compared with experimental data for crystalline and amorphous Co- and Ni-metalloid alloys. It is found that amorphous alloys retain the same local environment around the metalloid atom as in the crystalline cases, and that the bonding in crystalline alloys and amorphous alloys is equivalent. The bond model predicts zero moment change for dilute bcc Fe alloys because the bonding levels in the Fe band have no uncompensated spin. Reasonable agreement with experiment is obtained for concentrations of metalloid less than 10%, but it is apparent that moment changes in many Fe alloys are caused by more...