The segregation of P and S to grain boundaries (GBs) in fcc Cu has implications in diverse physical-chemical properties of the material and this can be of particular high relevance when the material is employed in high performance applications. Here, we studied the segregation of P and S to the symmetric tilt Σ9 ($2\overline{2}\overline{1}$) [110], 38.9° GB of fcc Cu. This GB is characterized by a variety of segregation sites within and near the GB plane, with considerable differences in both atomic site volume and coordination number and geometry. We found that the segregation energies of P and S vary considerably both with distance from the GB plane and sites within the GB plane. The segregation energy is significantly large at the GB plane but drops to almost zero at a distance of only ≈3.5 Å from this. Additionally, for each impurity there are considerable variations in energy (up to 0.6 eV) between segregation sites in the GB plane. These variations have origins both in differences in coordination number and atomic site volume with the effect of coordination number dominating. For sites with the same coordination number, up to a certain atomic site volume, a larger atomic site volume leads to a stronger segregation. After that limit in volume has been reached, a larger volume leads to weaker segregation. The fact that the segregation energy varies with such magnitude within the Σ9 GB plane may have implications in the accumulation of these impurities at these GBs in the material. Because of this, atomic-scale variations of concentration of P and S are expected to occur at the Σ9 GB center and in other GBs with similar features.

中文翻译：

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铜中P和S杂质向Σ9晶界的偏析

Fcc Cu中P和S到晶界（GBs）的偏析对材料的多种物理化学性质都有影响，当在高性能应用中使用该材料时，这可能具有特别高的相关性。在这里，我们研究了P和S向对称倾斜Σ9（$2\overline{2}\overline{\mathrm{1个}}$）[110]，38.9°GB的fcc Cu。该GB的特征在于GB平面内和附近的各种偏析位点，原子位点的体积，配位数和几何形状均存在相当大的差异。我们发现，P和S的离析能随距GB平面的距离和GB平面内的位点的变化而变化很大。在GB平面上，分离能非常大，但在距此仅≈3.5Å的距离处下降到几乎为零。另外，对于每种杂质，GB平面中的偏析位点之间的能量都有很大的变化（最高0.6 eV）。这些变化的根源在于配位数和原子位点体积的差异，而配位数主导。对于具有相同协调编号的站点，直到特定的原子站点数量，较大的原子位点体积导致更强的偏析。达到该体积限制后，较大的体积将导致偏析变弱。偏析能在Σ9GB平面内以这样的幅度变化的事实可能会影响这些杂质在材料中这些GB处的积累。因此，预计在Σ9GB中心和其他具有类似特征的GB中会发生P和S浓度原子级变化。