Intergranular fracture of tungsten containing phosphorus impurities: A first principles investigation

Abstract

In the present work we have studied the influence of phosphorus impurities on the grain boundary strength of tungsten by means of quantum mechanical calculations based on density functional theory. As model grain boundary we consider the Σ5(310)[001] high angle configuration. The results show that by the introduction of a clean (i.e. impurity free) grain boundary in the bulk, the strength and peak stress of the cohesive zone are reduced and they are further reduced by the introduction of impurities. This effect can be attributed to the formation of polar bonds between W and P, which leads to a weakening of the interface. Based on a thermodynamic analysis of the cohesive zone during the straining we find that diffusion of impurities may occur to retain thermodynamic equilibrium for constant chemical potential. This contributes to the gradual reduction of the peak stress related to fracture, which can contribute to diffusion driven delayed cracking, even when subjected to static loads.

Atomistic investigation of the impact of phosphorus impurities on the tungsten grain boundary decohesion

“…The fact that the fractured surfaces are typically decorated with P atoms is an indication that the P atom sites are bond weakening sites in the GB proximity, at which decohesion originates. This is in line with our previous DFT investigation, which revealed charge transfer from W to P in the GB proximity [22]. Such behaviour causes the formation of negatively charged ions, which in agreement with predictions of the unified theory of Cottrell [86] promotes screening across the interface.…”

“…5(g, h). This is in contrast to our previous findings [22], where significant reductions in the peak stress and work of separation were found. This discrepancy is likely due to the fact that atomic relaxations were allowed in [22], while they were prevented for the validation herein -both for the DFT and classical modelling.…”

“…This is in contrast to our previous findings [22], where significant reductions in the peak stress and work of separation were found. This discrepancy is likely due to the fact that atomic relaxations were allowed in [22], while they were prevented for the validation herein -both for the DFT and classical modelling. In fact, for iron and nickel GBs it has been found that rigid and relaxed GB separation modelling can give contradictory results and that atomic relaxation is necessary to quantitatively capture the impact of impurities on the GB strength [52,78].…”

“…Below the concentration of 20-40 wppm it has been reported that P does not impact the fracture behaviour notably [2]. To gain further insight on the role of impurities on the GB strength of W, ab initio modelling based on density functional theory (DFT) has been employed to elucidate the impact on work of separation [18][19][20][21][22][23][24][25][26]. It has been reported that while P has an embritteling effect on 𝛴3(111) [ 110], 𝛴3(112) [ 110] and 𝛴5(013) [100] GBs [18][19][20][21][22], for the 𝛴27(552) [ 110] GB it promotes improved cohesion [18].…”

“…To gain further insight on the role of impurities on the GB strength of W, ab initio modelling based on density functional theory (DFT) has been employed to elucidate the impact on work of separation [18][19][20][21][22][23][24][25][26]. It has been reported that while P has an embritteling effect on 𝛴3(111) [ 110], 𝛴3(112) [ 110] and 𝛴5(013) [100] GBs [18][19][20][21][22], for the 𝛴27(552) [ 110] GB it promotes improved cohesion [18]. These findings suggest that the intrinsic properties of the GB govern whether P enhances or reduces the cohesion, which merits further investigation.…”