The present study carries out systematic thermodynamics analysis of Grain Boundary (GB) segregation and relaxation in Nano-Grained (NG) polycrystalline alloys. GB segregation and relaxation is an internal process towards thermodynamic equilibrium, which occurs naturally in NG alloys without any applied loads, causes deformation and generates internal stresses. The analysis comprehensively investigates the multiple coupling effects among chemical concentrations and mechanical stresses in GBs and grains. A hybrid approach of eigenstress and eigenstrain is developed herein to solve the multiple coupling problem. The analysis results indicate that the GB stress and grain stress induced by GB segregation and relaxation can be extremely high in NG alloys, reaching the GPa level, which play an important role in the thermal stability of NG alloys, especially via the coupling terms between stress and concentration. The present theoretic analysis proposes a novel criterion of thermal stability for NG alloys, which is determined by the difference in molar free energy between a NG alloy and its reference single crystal with the same nominal chemical composition. If the difference at a temperature is negative or zero, the NG alloy is thermal stable at that temperature, otherwise unstable.

本研究对纳米晶（NG）多晶合金中的晶界（GB）偏析和弛豫进行了系统的热力学分析。GB的偏析和弛豫是达到热力学平衡的内部过程，该过程自然发生在NG合金中，没有施加任何载荷，会引起变形并产生内部应力。该分析全面研究了GBs和晶粒中化学浓度和机械应力之间的多重耦合效应。本文开发了本征应力和本征应变的混合方法来解决多重耦合问题。分析结果表明，NG合金中GB偏析和弛豫引起的GB应力和晶粒应力可能很高，达到了GPa水平，这对NG合金的热稳定性起着重要作用，特别是通过应力和集中力之间的耦合项。本理论分析为NG合金提出了一种新的热稳定性判据，该判据由NG合金与具有相同标称化学成分的参比单晶之间的摩尔自由能之差确定。如果温度差为负值或零，则NG合金在该温度下是热稳定的，否则不稳定。