A comprehensive collection of spin-echo NMR spectra from nuclei of both host and transition-metal impurities ($T$) in pseudobinary ${\mathrm{Fe}}_{3\ensuremath{-}x}{T}_{x}\mathrm{Si}$ alloys taken at about 1.3 K are presented and analyzed. We summarize some new data on $3d$ elements and also review briefly some results already reported. Previously unpublished results for $4d$ and $5d$ elements are reported. ${\mathrm{Fe}}_{3}$Si has two inequivalent Fe sites and one Si site. From the analysis of the solute spectra we show that the $3d$, $4d$, and $5d$ elements under Fe or to the right of Fe in the periodic table (Ni, Co, Ru, Pd, Os, and Ir) enter the Fe site with four Fe and four Si first neighbors. The $3d$ elements to the left of Fe (Mn, V, Cr, and Ti) enter the Fe site which has eight Fe first neighbors. In addition, we report that in Fe-rich nonstoichiometric alloys Ni, Ru, Rh, and Pd prefer $A$, $C$ sites with the smallest number of Fe first neighbors. The roles of electronic structure, electronegativity, and atomic size in producing the observed selectivity are analyzed. Finally a comparison between impurity hyperfine fields in ${\mathrm{Fe}}_{3}$Si and Fe, Ni, and Co hosts is made. The dependence of impurity hyperfine fields on both the moment of the host and the position of the impurity in the periodic table, found for Fe, Ni, and Co hosts, are also shown to exist in the case of ${\mathrm{Fe}}_{3}$Si alloys. Using these dependences, we make tentative predictions of the fields at some nuclei for which spectra were not observed.
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