Technical Comments

Comment on "Grain Boundary Decohesion by Impurity Segregation in a Nickel-Sulfur System"

Science  09 Sep 2005:
Vol. 309, Issue 5741, pp. 1677
DOI: 10.1126/science.1112072

Yamaguchi et al. (1) examined the embrittlement of nickel (Ni) by progressively adding sulfur (S) atoms to a grain boundary (GB). From first-principles calculations, they concluded that S atoms tend to aggregate at the GB and that the repulsive S-S interactions induce boundary expansion, thus weakening Ni-Ni binding across the boundary. The agreement between their calculated critical S concentration and the measured data (2) suggests that the GB embrittlement of Ni is due to the aggregation of S segregants. Although we believe that the first-order calculations of Yamaguchi et al. (1) are reliable, we question the interpretations of the calculated binding energies and argue that the distribution of S near the GB remains uncertain.

According to the Yamaguchi et al. calculations, the average binding energy for a S atom on site GB0/GB2 (Fig. 1) with a 100% occupation is –4.75/–4.66 eV, and the binding energy drops to –4.23 eV when both GB0 and GB2 sites are fully occupied. With the calculated segregation energy ΔEseg, which is defined as the energy lowering when an impurity moves from inner bulk (binding energy = –2.96 eV/S) to the GB region, Yamaguchi et al. estimated the occupation number using McLean's equation of equilibrium segregation (3), CGB = [Cbulkexp(ΔEseg/RT)] / [1 + Cbulkexp(ΔEseg/RT)], with the impurity concentration in the bulk and the temperature as parameters. They noted that a binding energy of –4.23 eV is large enough for S atoms to segregate fully to the GB0 and GB2 sites, and went on to discuss the volume expansion effect of such GB0-GB2 S combinations.

Fig. 1.

Schematic model of a NiΣ5 (012) tilt GB. The gray and yellow circles represent Ni and S atoms, respectively. The site numbering follows Yamaguchi et al. [see figure 1 in (1)]. Embedded Image; b = <100>; c = <012>.

This conclusion is only valid if the segregation process starts and terminates instantly, and we know that segregation can take hours or days (2). As shown in (1), when GB0 (GB2) sites are occupied by S, the binding energy of GB2 (GB0) sites reduces greatly as a result of the repelling interaction between S atoms. For instance, if an S monolayer is formed at GB0 sites first, then the binding energy for a 1/4 monolayer of S at GB2 sites decreases from –4.67 to –3.45 eV. The occupation probability is only on the order of 1% under the experimental conditions in (2) (T = 918 K and Cbulk = 25 atomic parts per million), according to McLean's equation. This means that a high concentration of GB0-GB2 pairs is unlikely to appear at the Ni GB.

To conduct a more comprehensive search for S-S pairs at the NiΣ5 (012) tilt GB, we calculated the binding energy of S in the form of both GB0-GBn (n = 1, 3, 4, 5, 6) and GB2-GBm (m = 1, 3, 4, 5, 6, –2, –3, –4, –5, –6) pairs at one monolayer concentration using the same code [Vienna Ab initio Simulation Package (4)] and parameters reported in (1). Our calculations demonstrate that although the GBn (n = 3, 4, 5, 6) site is still less stable than the GB0 site, the binding energy difference is greatly reduced when GB0 is occupied by S. For example, a GB0-GB3 pair is 0.05 eV less stable than a GB0-GB2 pair; in an isolated 1/4 monolayer, S at the GB3 site is 1.16 eV less stable than at the GB2 site (1). Interestingly, we find that although the binding energy of the GB1 site in an isolated monolayer is only 3.25 eV, it increases considerably to 4.29 eV when all GB2 sites are occupied by S. The binding energy of other sites, on the other hand, increases to lesser extents, and the occupation probability under the experimental conditions remains low. Moreover, we calculated the binding energy of a 1/4 monolayer GB1 progressively added, to a GB2 4/4 monolayer. The binding energies are 4.15, 4.23, 4.26, and 4.55 in sequence. Our first-principles calculations thus suggest the formation of GB2-GB1 S combinations at a high concentration.

Using the same technique as in (1), we evaluated the tensile strength of six cases of S segregation, namely, (i) clean GB; (ii) GB2 4/4; (iii) GB2 4/4, GB1 1/4; (iv) GB2 4/4, GB1 2/4; (v) GB2 4/4, GB1 3/4; and (vi) GB2 4/4, GB1 4/4. The tensile strengths are 26, 16, 14, 11, 7.2, and 3.9 GPa, respectively. The calculated tensile strength for the clean GB (26 Gpa) is the same as that reported by Yamaguchi et al. The decrease in tensile strength is proportional to the increase of the GB2-GB1 S-S pair concentration, and in the range of S occupations from (GB2 4/4, GB1 2/4) to (GB2 4/4, GB1 4/4), strong GB decohesion occurs. The GB displacement (with respect to the clean GB) caused by (GB2 4/4, GB1 4/4) is about 0.6Å, much smaller than that caused by (GB2 4/4, GB0 4/4) (1.2Å), which has been shown here to be unstable. Further detailed analysis will clarify whether GB expansion or directional change of chemical bonding is the key to the strong decohesion caused by S aggregation.


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