In recent years it has been found that the segregation energy for phosphorus atoms to grain boundaries (GB) can vary strongly with atomic position in copper. This should be contrasted to the unique value for the segregation energy that has been used for property predictions of creep strength and ductility, which are crucial properties for copper canisters for final disposal of spent nuclear fuel. In the present paper, segregation energies for P and S atoms at different atomic sites for three symmetric tilt GB types: Σ3, Σ5 and Σ11 have been computed using density functional theory (DFT). We found that the segregation energies decrease with distance from the GB plane. However, for the GBs studied, the largest energies are not found at the GB planes, but instead at the first neighboring sites relative to the GB planes. The segregation energies are typically much larger for Σ5 than for Σ3 and Σ11. Subsequently, an effective segregation energy has been defined and it is used to predict the occupancy of P and S atoms at the GBs. Based on these data, the release of free energy during cavity formation has been computed. The release of free energy is lower for copper with phosphorus (Cu-OFP) than for phosphorus free copper (Cu-OF) indicating that cavity generation occurs more readily in the latter material. The data shows with good margin that creep cavitation in Cu-OFP does not lead to brittle creep rupture and that the creep ductility is quite satisfactory.

近年来发现，磷原子向晶界（GB）的偏析能会随铜中原子位置的不同而发生很大变化。这应该与用于预测蠕变强度和延展性的偏析能量的唯一值形成对比，该值是蠕变强度和延展性的属性，这对于最终处理乏核燃料的铜罐来说是至关重要的。在本文中，使用密度泛函理论（DFT）计算了三种对称倾斜GB类型：Σ3，Σ5和Σ11在不同原子位点上P和S原子的偏析能。我们发现偏析能随与GB平面的距离而减小。但是，对于所研究的GB，最大的能量不是在GB平面上找到的，而是在相对于GB平面的第一个相邻位置上找到的。Σ5的偏析能量通常比Σ3和Σ11大得多。随后，定义了有效的偏析能，并用于预测GB处P和S原子的占有率。基于这些数据，已经计算出空腔形成过程中自由能的释放。含磷铜（Cu-OFP）的自由能释放量低于无磷铜（Cu-OF）的释放量，表明在后一种材料中更容易发生空穴产生。数据以良好的裕度表明，Cu-OFP中的蠕变空化不会导致脆性蠕变破裂，并且蠕变延展性相当令人满意。计算了腔形成过程中自由能的释放。含磷铜（Cu-OFP）的自由能释放量低于无磷铜（Cu-OF）的释放量，表明在后一种材料中更容易发生空穴产生。数据以良好的裕度表明，Cu-OFP中的蠕变空化不会导致脆性蠕变破裂，并且蠕变延展性相当令人满意。计算了腔形成过程中自由能的释放。含磷铜（Cu-OFP）的自由能释放量低于无磷铜（Cu-OF）的释放量，表明在后一种材料中更容易发生空穴产生。数据以良好的裕度表明，Cu-OFP中的蠕变空化不会导致脆性蠕变破裂，并且蠕变延展性相当令人满意。