VOLUME 58, NUMBER 1 PHYSICAL REVIEW LETTERS 5 JANUARY 1987 Localized Grain-Boundary Electronic States and Intergranular Fracture M. E. Eberhart ' and D. D. Vvedensky Materials Science and Technology Division, Los Alarnos National Laboratory, Los Alamos, New Mexico 87501 The appearance of localized grain-boundary electronic states is shown to provide a reliable indication of intergranular fracture in polycrystalline materials. Representative densities of states are presented for some L12 intermetallic compounds by use of polyhedral models of grain-boundary structure. The role of certain segregated impurities as inhibitors of intergranular brittleness is briefly discussed and suggestions are made for direct experimental verification of our model. PACS numbers: 73.90.+f, 61.70.Ng, 62.20. Mk, 81.40. Np One of the ultimate objectives for electronic structure theory of solids is the first-principles design of materials. Already parameter-free calculations yield quantitatively accurate descriptions of a number of structural, electron- ic, and magnetic properties of single crystals. However, only recently has there been an attempt to correlate the results of electronic structure calculations with mechani- cal response. ' Despite the complex origins of mechani- cal behavior and the relatively poor characterization of the pertinent microscopic structures, general trends in certain mechanical properties may be correlated with specific features of electronic structure. A particularly pertinent illustration is the control of mechanical proper- ties of semiconductors by doping with electrically active impurities. In this Letter we examine the influence of grain- boundary-induced electronic structure on the tendency toward intergranular fracture of polycrystalline materi- als. Our calculations were motivated by the observation that the extent to which the grain boundary disrupts the mechanical properties of the parent crystal depends upon the ease with which s hybridization can be enhanced to accommodate the oblique bonding geometries at grain boundaries. For intergranularly brittle materials, where enhanced s character resulting from bond misorientation is inhibited from hybridizing with bulk states, we identi- fy the appearance of localized grain-boundary electronic states near the Fermi energy as being indicative of a marked decrease in the mechanical stability of the inter- face relative to the parent crystal, because the energy barriers to bond movement and charge redistribution have been lowered. ' Thus, broadly speaking, the grain boundary is more responsive to an external stimulus and can accommodate greater strain than the parent crystal, which leads to localization of strain and subsequently to intergranular fracture. To apply these general considerations to specific ma- terials, we use the multiple-scattering La cluster meth- od to calculate the density of states (DOS) of a poly- hedral model of grain-boundary structure' and compare this with the DOS of the corresponding single crystal to identify the states appearing as a direct result of grain- boundary geometry. Since the pertinent changes in local electronic structure arise quite generally from the lower symmetry and concomitant decrease in coordination numbers at the grain boundary, we do not expect our findings to result from any particular choice of pol- yhedral model. " Our calculations reveal that the grain-boundary elec- tronic structures of materials prone to intergranular fracture consistently show (1) a decidedly more uniform charge distribution than the parent crystal, and (2) the appearance of diffuse states near the Fermi energy that are absent from the DOS of the parent crystal ~ Further- more, extensive calculations'' have sho~n that our mod- el is capable of discriminating between materials known to fail intergranularly (Ni and Fe containing S, P, or H segregants, Ni3A1, Ni3Si, and Ir) and those exhibiting significant plastic deformation prior to failure (Ni, Fe, Al, Cu, Cu3Pd, and Ni3A1 with segregated B at grain boundaries, and Ir with segregated Th at grain boun- daries). We present below representative calculations for ductile and intergranularly brittle materials from the family of L12 intermetallic compounds (Cu3Au struc- ture). Our approach differs fundamentally from previous electronic models' ' of intergranular fracture in two ways. (1) We initially investigate the intrinsic mechani- cal response of grain boundaries rather than considering the effects of segregants. One complicating feature of segregated impurities is that a single impurity can induce a qualitatively different charge distribution locally than that from interacting impurities. ' Thus, while the metallicity or covalency of impurity-induced bonds may prove useful in studying intergranular brittleness, the question of interactions between impurities must first be systematically addressed. (2) The interface states that we identify as being indicative of intergranular brittle- ness are experimentally measurable, either directly with photoemission techniques, or indirectly with the various thermal, magnetic, or electrical transport measurements used so successfully in studying Friedel-Anderson states in dilute alloys. The development of growth techniques for bicrystals' will prove invaluable in facilitating con- trolled grain-boundary experiments. The nickel aluminides are members of a class of in- 1986 The American Physical Society 61