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We develop a novel technique for simulation of the mechanics of micron-scale solid systems: Coarse Grained Molecular Dynamics (CGMD). It captures the important atomistic e ects without the computational cost of conventional molecular dynamics (MD). The CGMD equations of motion are derived directly from nite temperature MD through a statistical coarse graining procedure, so they agree with MD as the mesh size is reduced to the atomic scale. This allows a seamless coupling of length scales. The use of e cient CGMD in peripheral regions extends atomistic simulation to much larger systems than amenable to MD alone.

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We present the first direct calculation by simulation of the excess surface free energy of a crystal–liquid interface. We perform these calculations on the (111), (100), and (110) interfaces of a truncated Lennard-Jones face-centered-cubic crystal–liquid system at the triple point by the molecular dynamics technique. Bulk crystal and liquid systems are first cleaved and then combined with one another reversibly. The work required to do this is integrated and equals the excess surface Helmholtz (and Gibbs) free energy. The free energies are found to be 0.35±0.02, 0.34±0.02, and 0.36±0.02 (dimensionless units) for the (111), (100), and (110) faces, respectively. The three faces are therefore energetically isotropic within our error bars and the equilibrium form of the crystal is approximately spherical.

We have coupled the continuum, the atomistic, and the quantum descriptions of matter for a unified treatment of the dynamic fracture of silicon. We have devised schemes for handshaking between the finite-element, molecular dynamics and semi-empirical tight-binding representations. We illustrate and validate the methodology for brittle crack propagation in silicon.