Kinetics behaviour of metastable equiatomic Cu–Fe solid solution as function of the number of collisions induced by mechanical alloying A. Contini a,⇑ , F. Delogu b , S. Garroni a , G. Mulas a , S. Enzo a a Dipartimento di Chimica e Farmacia, Università degli Studi di Sassari, via Vienna 2, 07100 Sassari, Italy b Dipartimento di Ingegneria Meccanica, Chimica, e dei Materiali, Università degli Studi di Cagliari, via Marengo 2, 09123 Cagliari, Italy article info Article history: Available online 8 December 2013 Keywords: Mechanochemistry Solid state reactions Critical loading conditions Kinetics analysis Rietveld method abstract We have addressed a new study by mechanical alloying on the nominally immiscible Cu 50 Fe 50 system with the aim of relating the solid state transformation process, with formation of a disordered unstable solid solution having the face centered cubic habit, to parameters reflecting the impulsive, discontinuous nature of the process. The milling set-up, tools and powder were adjusted in order to ensure completely anelastic hits. Phase analysis, structure and microstructure parameters of such powder system have been followed accurately in the course of the kinetics by X-ray Diffraction using the Rietveld method. The experimental kinetics data points of the amount of transformed solid solution show a typical sigmoidal behavior. It was assumed that dissolution only occurs in the volumes of material that have undergone the necessary critical loading conditions, which is accounted by a discrete series expansion. The mass fraction effectively processed at each collision can be regarded as an apparent rate constant for the microstruc- tural refinement and phase transformation processes. Analysis of model curves fitting the experimental data suggests that it takes up an average of 6 impacts of coupled powder particles to drive the system to the new unstable nano-crystalline state. Ó 2013 Elsevier B.V. All rights reserved. 1. Introduction The mechanical processing of powder mixtures by ball milling provides a valuable route to synthesize materials hardly obtainable by conventional thermal methods [1–5]. One of the most striking examples is the formation of homogeneous solid solutions of immiscible elements, which points out the capability of mechanical processing to successfully tackle the thermodynamic tendency to demixing when the metal microstructure is suitably refined [6–14]. The mutual dissolution of atomic species was initially ascribed to the occurrence of local melting processes, and to the enhancement of thermal diffusion rates due to the unusually high content of defects generated by mechanical deformation [1–3,15]. However, theoretical studies have increasingly pointed out the crucial role played by the rearrangement of local structures mediated by the nucleation and propagation of dislocations, and by the turbulent dynamics of atomic displacements at sheared interfaces [16–28]. Accordingly, the mechanical alloying (MA) behavior must be expected to be significantly affected by mechanical properties, even if their influence has not yet been clearly understood. In this respect, it has been suggested that the deformation-induced enhancement of atomic mixing could be inversely proportional to a small power of hardness [29]. A deeper insight on this point has been recently obtained by a molecular dynamics study of the deformation behavior of heterogeneous composites formed by a Cu matrix containing a nanometer-sized particle of a metal immiscible with Cu [30]. When the metals have similar mechanical properties, the dislocations can transfer from the Cu matrix to the metal particle, and the metals dissolve into each other due the repeated shearing of the metal particle [30]. Instead, for two metals with significantly different mechanical properties, the deformation mostly localizes in the softer phase, and the atomic mixing is driven by diffusive-like atomic displacements [30]. Moving within such conceptual framework [31], the present study aims at providing a quantitative evaluation of the kinetics of the MA of Cu 50 Fe 50 powder mixtures, which is the first necessary step towards a correlation of transformation rates and mechanical properties. 2. Experimental and modeling approach The equiatomic powder mixtures were prepared by submitting commercial Cu and Fe powders with a 99.99% purity level to mechanical processing. The powders were handled inside a glove box under Ar atmosphere with impurities below 10 ppm. In each milling run, a powder charge m p of 8 g was sealed in a hardened steel reactor with a single stainless steel ball of 8 g. The reactor was fixed on a Spex Mixer/Mill 8000, and the mill operated at a frequency of about 14.6 Hz. The mass m p of powder employed induces an inelastic collision regime, resulting in average collision frequency and velocity of 29.2 Hz and 4.1 m s 1 [32,33]. Because of inelas- tic collisions which are minimizing the wear debris from the tools, the effects of contaminants are supposed to be unimportant. 0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.11.232 ⇑ Corresponding author. Address: Department of Chemistry and Pharmacy, Via Vienna 2, 07100, University of Sassari, Sassari, Italy. Tel.: +39 3467634770. E-mail address: alessandro.contini@hotmail.com (A. Contini). Journal of Alloys and Compounds 615 (2014) S551–S554 Contents lists available at ScienceDirect Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom