Correlation between structure, energy, and ideal cleavage fracture for symmetrical grain boundaries in fcc metals

The misorientation phase space for symmetrical grain boundaries is explored by means of atomistic computer simulations, and the relationship between the tilt and twist boundaries in this three-parameter phase space is clucidated. The so-called random-boundary model (in which the interactions of atoms across the interface are assumed to be entirely random) is further developed to include relaxation of the interplanar spacings away from the grain boundary. This model is shown to include fully relaxed free surfaces naturally, thus permitting a direct comparison of the physical properties of grain boundaries and free surfaces, and hence the determination of ideal cleavage-fracture energies of grain boundaries. An extensive comparison with computer-simulation results for symmetrical tilt and twist boundaries shows that the random-boundary model also provides a good description of the overall structure-energy correlation for both low- and high-angle tilt and twist boundaries. Finally, the role of the interplanar spacing parallel to the grain boundary in both the grain-boundary and cleavage-fracture energies is elucidated.

[1]  A. A. Griffith.  The Phenomena of Rupture and Flow in Solids , 1921 .

[2]  J. H. Merwe.  On the Stresses and Energies associated with Inter-Crystalline Boundaries , 1950 .

[3]  W. Read,et al.  Dislocation Models of Crystal Grain Boundaries , 1950 .

[4]  J. Martin,et al.  On the Bauschinger effect in unidirectionally solidified eutectic AlAl3Ni crystals , 1974 .

[5]  C. Goux.  Structure des joints de grains: considérations cristallographiques et méthodes de calcul des structures , 1974 .

[6]  C. Rey,et al.  The elastic field of periodic dislocation networks , 1976 .

[7]  D. Turnbull,et al.  Kinetics of precipitation of Ag from Pb(Ag) alloys , 1978 .

[8]  R. Benedek.  Lattice statics calculations of the surface relaxation in metals , 1978 .

[9]  V. Vítek,et al.  A microscopic theory of brittle fracture in deformable solids: A relation between ideal work to fracture and plastic work , 1980 .

[10]  D. Wolf.  Energies of Coincidence Twist Boundaries, Stacking Faults, and Free Surfaces in Metal Oxides with NaCl Structure , 1981 .

[11]  Anthony G. Evans,et al.  Surfaces and Interfaces in Ceramic and Ceramic ― Metal Systems , 1981 .

[12]  R. Balluffi,et al.  Coincidence lattice model for the structure and energy of grain boundaries , 1981 .

[13]  R. Bonnet.  Periodic displacement and stress fields near a phase boundary in the isotropic elasticity theory , 1981 .

[14]  M. Baskes,et al.  Semiempirical, Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals , 1983 .

[15]  V. Vítek,et al.  On the structure of tilt grain boundaries in cubic metals II. Asymmetrical tilt boundaries , 1983, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[16]  M. Finnis,et al.  A simple empirical N-body potential for transition metals , 1984 .

[17]  Foiles,et al.  Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. , 1986, Physical review. B, Condensed matter.

[18]  V. Vítek,et al.  Relationships between grain boundary structure and energy , 1986 .

[19]  Smith,et al.  New approach to calculation of total energies of solids with defects: Surface-energy anisotropies. , 1987, Physical review letters.

[20]  A. Shi,et al.  Calculation of energy of low-angle grain boundaries , 1987 .

[21]  On the difference between the misorientation dependences of the energies of tilt and twist boundaries , 1987 .

[22]  S. Phillpot,et al.  Role of the densest lattice planes in the stability of crystalline interfaces: A computer simulation study☆ , 1988 .

[23]  D. Wolf.  Correlation between energy and volume expansion for grain boundaries in FCC metals , 1989 .

[24]  D. Wolf,et al.  A read-shockley model for high-angle grain boundaries , 1989 .

[25]  D. Wolf.  Structure-energy correlation for grain boundaries in F.C.C. metals—I. Boundaries on the (111) and (100) planes , 1989 .

[26]  D. Wolf.  Correlation between the energy and structure of grain boundaries in b.c.c. metals I. Symmetrical boundaries on the (110) and (100) planes , 1989 .

[27]  S. Phillpot,et al.  Structure-energy correlation for grain boundaries in silicon , 1989 .

[28]  D. Wolf.  Are symmetrical tilt boundaries “true” high-angle grain boundaries? , 1989 .

[29]  D. Wolf,et al.  On the geometrical relationship between tilt and twist grain boundaries , 1989 .

[30]  D. Wolf,et al.  Structure-energy correlation for grain boundaries in F.C.C. metals—III. Symmetrical tilt boundaries , 1990 .

[31]  D. Wolf.  Correlation between energy, surface tension and structure of free surfaces in fcc metals , 1990 .

[32]  S. Phillpot,et al.  Formalism for the calculation of local elastic constants at grain boundaries by means of atomistic simulation , 1990 .