The energetics of triple lines are often negligible in polycrystalline systems, but may play a significant role in the finest nanocrystals, and in fact lower the excess defect energies of those polycrystals. This paper develops a methodology to assess polycrystalline average grain boundary and triple junction excess energies for pure fcc metals Ni, Cu, Al, Pd, Pt, Ag and Au using embedded atom method potentials. It is found that there are correlations between the triple line energy and physical quantities such as grain boundary and dislocation line energy, but with a negative sign indicating that triple junctions reduce intergranular excess energy per area on average. The relationship with grain boundary energy is of order ∼−4.5 × 10 m, and the triple junction energy is about −1/12 of the dislocation line energy. Despite their low energy, triple junctions can significantly affect total system energy due to their high density in the finest nanocrystals; for example, 6-nm Pd nanocrystals have an effective intergranular energy of ∼0.83 J/m (compared with the large grain size limit of 0.93 J/m), translating to a measurable bulk excess enthalpy of ∼6 kJ/mol. Such excess enthalpy is experimentally assessable, and the present framework can be used to measure triple junction energies. For instance, re-analyzing data of Lu and Sun (Phil. Mag., 1997) we obtain grain boundary and triple junction energies of 0.33 J/m and −3.0 × 10 J/m respectively for Selenium nanocrystals, which can be compared with modeled values of 0.76 J/m and −1.02 × 10 J/m by using our method with a published bond-order potential for Se.

中文翻译：

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多晶金属中的三结过剩能量


三重线的能量在多晶系统中通常可以忽略不计，但可能在最精细的纳米晶体中发挥重要作用，并且实际上降低了这些多晶的过量缺陷能量。本文开发了一种使用嵌入原子法电势评估纯面心立方金属 Ni、Cu、Al、Pd、Pt、Ag 和 Au 的多晶平均晶界和三结过剩能量的方法。研究发现，三重线能与晶界、位错线能等物理量之间存在相关性，但负号表明三重结平均减少了单位面积的晶间过剩能量。与晶界能的关系约为~−4.5 × 10 m，三结能约为位错线能的-1/12。尽管能量较低，但三结可以显着影响总系统能量，因为它们在最细的纳米晶体中具有高密度。例如，6 nm Pd 纳米晶体的有效晶间能约为 0.83 J/m（与 0.93 J/m 的大晶粒尺寸限制相比），转化为可测量的体积过剩焓约为 6 kJ/mol。这种过量的焓可以通过实验评估，并且本框架可用于测量三联结能量。例如，重新分析 Lu 和 Sun 的数据（Phil. Mag., 1997），我们得到硒纳米晶体的晶界和三结能量分别为 0.33 J/m 和 -3.0 × 10 J/m，这可以与通过使用我们的方法和已发布的 Se 的键序势，模拟了 0.76 J/m 和 -1.02 × 10 J/m 的值。