Ni(GB2)-S(GB0) distance (2.27 A) after all GB0 sites are occupied by S. From the S-S distance, the radius of the S atom is estimated to be 1.65 A. This radius is about 60% longer than the radius of S (1.03 A) estimated from the above Ni-S distance by subtracting the half length (1.25 A) of the nearest-neighbor Ni-Ni distance in fcc Ni. This indicates that the GB expansion in this case cannot be explained by an atomic "size effect" that is often used to explain some phenomena such as solid solubility (SOM).
From the above argument, it is evident that a short-range repulsive interaction occurs between S atoms in Ni when S atoms come sufficiently close to each other, within 3 or 4 A (SOM). We think that this force has a common origin with the well-known phenomena that Ni and S form ordered alloys, and adsorbed S atoms on Ni surfaces form ordered structures (13). These phenomena are usually explained by assuming the repulsive interaction between S atoms in Ni and on Ni surfaces. The origin of this force is based on the fact that S atoms prefer to bond with Ni atoms instead of with other S atoms. In fact, the binding energy per one S atom in an S2 molecule is 2.2 eV/S, which is appreciably smaller than those in some Ni-S ordered alloys and in the GBs and bulk unit cells as in Tables 1 and 2. In addition, the S-S distance is over 3.0 A for some Ni-S ordered alloys, except for NiS2 as in Table 2. This indicates that distances of about 2.2 to 2.5 A between neighboring sites in the GB region are too short for the repulsive S-S pair to be stable. For these reasons, the repulsive S atoms expand the GB region. Only in the NiS2 case, where S forms an S2 dimer in which the S-S distance is 2.08 A, is it close to the S-S distance in the S2 molecule, 1.91 A. However, this is an exceptional case in which S is richer than Ni.
The physical origin of this repulsive interaction (force) can be explained in the following way. The Ni-S bond has larger binding energies than the S-S bond. This indicates that the electronic levels of Ni-S bondings are formed in an energetically deeper range than those of S-S bondings (fig. S1). In this case, most electrons of S are thought to contribute to Ni-S bonds rather than S-S bonds. This results in the situation where among S atoms, the attractive interaction due to cova-lency does not work. Generally speaking, an interatomic potential is a superposition of the attractive term and a short-range repulsive term. As a result, only the short-range repulsive term remains in the S-S interatomic potential.
To measure the tensile (cohesive) strength of a GB, we performed simple tensile test calculations from first principles as in Fig. 3 (SOM). The results of these tests reveal a dramatic reduction of the maximum tensile stress (tensile strength) of the GB with the increase in S segregation. First, we see the result for the bulk unit cell that does not include the GB. As in Fig. 3A, the calculated ra CL
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