Thermodynamic Stability of Nano-grained Alloys Against Grain Coarsening and Precipitation of Macroscopic Phases
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INTRODUCTION
NANO-MATERIALS play an increasing scientific and social role.[1–19] In the past, nano-materials were simplified to single nano-particles. However, it has been clear for some decades that the real use of nanomaterials is expected if they form macroscopic articles with nano-structure inside. One class of such materials is the poly-crystalline nano-grained (NG) alloys. It should be admitted that producing such NG alloys is easier than to ensure their long-term stability, especially at high-temperatures when diffusion is fast enough to drive GEORGE KAPTAY is with the Department of Nanotechnology, University of Miskolc, Miskolc, Egyetemvaros, 3515 Hungary, and also with the MTA-ME Materials Science Research Group, Miskolc, Egyetemvaros, 3515 Hungary, and also with the BAY-ENG Division, Bay Zoltan Applied Research Ltd, Miskolc, 2 Igloi, 3519, Hungary. Contact e-mail: [email protected] Manuscript submitted March 31, 2019.
METALLURGICAL AND MATERIALS TRANSACTIONS A
materials towards their equilibrium state within reasonable times.[20–28] That is why the purpose of this paper is to develop a model for thermodynamic stability of such NG alloys. Although there is plenty of previous literature on both the synthesis[29–47] and on modeling the stabilization of NG alloys[48–88]) (see also reviews[89–93]), the present paper is novel as it puts this question into a wider framework of the nano-Calphad method,[94,95] i.e., into the thermodynamic framework originally developed by Gibbs.[96] All previous models on GB stability apply the simplest Langmuir–McLean model[97,98] (see also Reference 99) for modeling grain boundary (GB) energy. Since the pioneering works of Weismuller[48,49] it is known that for the stabilization of PC-NG alloys strong repulsion between the components is needed in the bulk alloy. Thus, there is an inner contradiction in the previous sentences, as the original Langmuir model[97] treated the surface layer as an ideal solution, and so this modeling framework is not suited to describe strongly interacting systems. The novelty of the present paper is
that here the extended Butler equation is applied to describe the GB energy.[100] As the Butler equation[101] was originally designed for strongly interacting systems, it provides a more natural framework to describe the stability of strongly interacting NG alloys. The interplay between thermodynamic and kinetic reasons of the stability of NG alloys has been also discussed[102–106] (see also References 107 through 111). However, in the present paper only thermodynamic aspects will be discussed in a novel way.
II.
An average grain for modelling Fig. 1—Crystalline grains of polyhedral shapes are surrounded by amorphous grain boundaries marked by thick lines around the grains.
ON THERMODYNAMIC INSTABILITY OF ONE-COMPONENT NG METALS
Following the original ideas of Gibbs,[96] the total absolute Gibbs energy of a one-component (A) NG metal (GA , J) can be written as: where GA;b (J) is the bulk term of GA without grain boundaries, the latter being, the
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