While mechanical alloying is a commercial entity for oxide-dispersion-strengthened superalloys, its application to other systems has run into a number of scientific and commercial barriers. In part, this is due to the inadequate scientific underpinning. This article reviews the status of the modeling of the mechanical alloying processes and suggests an approach to improving current knowledge of the process. INTRODUCTIONMechanical alloying (MA) presents a unique means for producing a wide variety of far-from-equilibrium structures and phases possessing unusual mechanical and physical properties. The attributes ofMA include the production of a fine dispersion of second-phase particles, the extension of solubility limits, the refinement of the matrix microstructure down to the nanometer range, the synthesis of novel crystalline phases, the development of amorphous phases, and the possibility of alloying difficult-toalloy elements.The demand for further progress in MA necessitates the development of mathematical models of transformations in particles undergoing repetitive plastic deformation/cold welding. A brief overview of existing models is presented here, and the difficulties arising from the far-from-equilibrium attributes of the MA process are outlined. Further development of the macrokinetic description of solid-state diffusion and phase transformations under the conditions of continuous-defect generation due to plastic strain will bring together the mechanistic and atomistic approaches and permit modeling of metastable phase formation phenomena observed in MA (e.g., solid-solubility extension, nanograins, amorphous phases, etc.). STATUS OF MA MODELINGSince the first experimental results were reported, 1 and especially after the discovery of metastable phase formation in the course of ball milling,2-4 MA has attracted considerable attention from materials scientists, not only due to the unique properties of the products and promising commercial applications but also because of the unusual physical phenomena involved. An increasing demand for the adjustment of the properties of novel materials produced by 36 MA to particular applications and the improvement of the MA regimes and apparatus designs for commercial scaling necessitates the development of mathematical models of MA. Modeling and computer simulation are based on theoretical concepts and a formal mathematical description of the process. However, theoretical works in this area are not as abundant as experimental research (see reviews by Johnson,s Weeber and Bakker,6 Koch/ Ma and Atzmon 8 and others).Three typical mechanisms of metastable phase formation during MA have been observed: 6 • The gradual disordering of crystal lattice and eventual amorphization. A similar mechanism (but without the crystal-to-amorphous transition) can occur in immiscible systems (e.g., Fe-Cu), resulting in the formation of supersaturated solid solutions during MA.8 • A coexistence of crystalline and amorphous phases and the gradual growth of the latter. This implies the exist...

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