Relating structural, magnetization, and hyperfine field studies to a local environment model in ${\mathrm{Fe}}_{3-x}{\mathrm{V}}_x\mathrm{Si}$ and ${\mathrm{Fe}}_{3-x}{\mathrm{Mn}}_x\mathrm{Si}$

X-ray, magnetization, and spin-echo NMR techniques have been used to measure the changes in the atomic ordering along with the effect of these changes on the local moment and the internal field distributions in ${\mathrm{Fe}}_{3-x}{\mathrm{V}}_x\mathrm{Si}$ alloys for $0\le x\le 1.00$. We have shown that V continues to enter predominantly the $B$ sites in the ${\mathrm{Fe}}_3$Si matrix up to $x\approx 1.0$, which is the limit of V solubility. The ${\mathrm{Fe}}_{3-x}{\mathrm{V}}_x\mathrm{Si}$ alloys are ferromagnetic up to $x\approx 0.9$ with the saturation magnetization decreasing linearly with $x$. V substitution into the $B$ sites reduces the moments of the first-near-neighbor (1nn) $\mathrm{Fe}(A,C)$ atoms linearly from their initial value of $1.35{\mu }_B$ while the moments of $\mathrm{Fe}\mathrm{}\left(B\right)\mathrm{}$ atoms remain constant at $2.20{\mu }_B$. A model giving a detailed mechanism for the origin of the satellite structure observed in the NMR spectra is proposed for ${\mathrm{Fe}}_{3-x}{\mathrm{V}}_x\mathrm{Si}$ as well as for ${\mathrm{Fe}}_{3-x}{\mathrm{Mn}}_x\mathrm{Si}$, a previously measured system. According to this model, the changes in the transition-metal internal fields at $B$ sites are produced as a result of changes in the $4s$ spin polarization induced by the perturbations of the 1nn $\mathrm{Fe}(A,C)$ moments. The values calculated from this model for the on-site hyperfine fields of $\mathrm{Fe}\mathrm{}\left(B\right)\mathrm{}$ and $\mathrm{Mn}\mathrm{}\left(B\right)\mathrm{}$ are -205 and -192 kOe, respectively. The on-site contribution to the V hyperfine field is estimated to be about 3 kOe with this model, in reasonable agreement with the very low moment value found for V. This detailed work suggests that the $\mathrm{Fe}\mathrm{}(A,C)\mathrm{}$ 1nn shell screens the $B$ sites from any direct interaction with a more distant neighbor either magnetically or chemically. Using all of the NMR and magnetization data together with the model, a canting of the Mn moments in ${\mathrm{Fe}}_{3-x}{\mathrm{M}}_x\mathrm{Si}$ for $0.75<x<\mathrm{}1.6\mathrm{}$ has been predicted. In addition, the disorder contributions to the NMR spectra have been identified.