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We present an \emph{ab initio} study of the effect of macroscopic deformationon energetics of twelve alloying elements in bcc Fe under three speciallydesigned strain modes. We find that there exists a universal linear relation ofdescribing the volume dependence of substitutional energy of alloying elementsvia introducing two factors --- the system shape factor ($f_{\scriptsize{ss}}$)and the size factor of alloying element $M$ ($\Omega^{M}_{\scriptsize{sf}}$):$E_{\scriptsize{sub}} \sim f_{\scriptsize{ss}}\Omega^{M}_{\scriptsize{sf}}V$.$\Omega^{M}_{\scriptsize{sf}}$ well describes the effect of intrinsicalloying-atom size and the influence of chemical interaction with matrix atom,and $f_{\scriptsize{ss}}$ characterizes the degree of system lattice distortionunder deformation. This relation is further validated using the published dataof stained-modulated doping in GaP

Role of Alloying-Atom Size Factor and System Shape Factor in Energetics of bcc Fe under Macroscopic Deformation