Abstract
Statistical thermodynamics allows us to estimate atomistic interactions in interstitial non-stoichiometric compounds MXx through analysis of experimentally determined pressure-temperature-composition (PTC) relationships for MXx being in equilibrium with X2 in gaseous state (X=H,N,P or S) or for non-stoichiometric carbide MCx being in equilibrium with excess C. In case of analysis for MCx, chemical activity a(C) of C in place of partial pressure p(X2) of X2 gas must be known. On statistical modelling of crystal lattice structure for MXx, an a priori assumption of constant nearest-neighbour X-X interaction energy E(X-X) within a homogeneity composition range at arbitrary temperature T was accepted to determine number θ of available interstitial sites for occupation by X atoms per M atom. Values of interaction parame-ters estimated as such appear rational and realistic noting consistency of the values for M’s in the same group in the Periodic Table of the Elements and compatibility with enthalpy values evaluated by conventional thermodynamic approach. Engineering insights gained for MXx through analysis of atomistic interaction parameter values evaluated by the statistical thermodynamics are reviewed comprehensively in this paper. M might be substitutional alloy A1-yBy composed of constituents, A and B, or MZz containing another interstitial constituent Z besides X. Insights acquired from this line of statistical thermodynamic analysis appear to be of pragmatic use for advanced alloy design as shall be demonstrated hereafter.
Highlights
Statistical thermodynamic analysis procedures were comprehensively summarized by Fowler and Guggenheim in a classical monograph published in 1949 [1]
Statistical thermodynamic parameters evaluated for extensive range of interstitial non-stoichiometric compounds including hydride, carbide, nitride, phosphide and sulfide were compiled in a monograph published by the author [2] that included calculation results reported by 2012 [3]-[46]
As might be understood from expressions for fundamental equations reviewed in 2.1., reference state of energy in the statistical thermodynamic analysis is each constituent atom in infinite separation in vacuum whereas the reference state of constituent in conventional thermodynamic analysis is the pure substance in standard state
Summary
Statistical thermodynamic analysis procedures were comprehensively summarized by Fowler and Guggenheim in a classical monograph published in 1949 [1]. Statistical thermodynamic parameters evaluated for extensive range of interstitial non-stoichiometric compounds including hydride, carbide, nitride, phosphide and sulfide were compiled in a monograph published by the author [2] that included calculation results reported by 2012 [3]-[46]. All these analyses [2]-[48] were made accepting an a priori assumption of constant interaction energy E ( X − X ) between nearest-neighbour interstitial atoms X within a homogeneity composition range of MXx lattice at arbitrary T. If such variation of E ( X − X ) takes place in MXx, it is more natural to accept phase change to occur rather than to hold the same crystal lattice structure [2]
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