REPRESENTATIONS OF THE LOCAL ATOMIC DENSITY

We describe two measures of the local atomic density in a monatomic cr ystal. A new measure (rho(f)) has,the form of a function of the sum of inverse powers of the neighbour distance, and it is accurate to 2% fo r six simple crystalline reference structures ranging from diamond to face-centred cubic. For any periodic structure, rho(f) reproduces the global average density exactly for any uniform dilation or compression in the limit of an infinite cut-off, and to high accuracy with a smoo th cut-off. We compare it with a Gaussian measure (rho(g)) of local de nsity for large constant-volume strains of the six reference structure s. The changes in rho(f) are an order of magnitude less than the shear strains for bond-length changes of <10%. However, rho(g) is even less sensitive to constant-volume strains, rho(g) is also transferable bet ween structures, provided that a constant self-term tan on-site term) is included in the density. The measure of local density is primarily intended for atomistic simulations of inhomogeneous systems in which t he atom-atom interactions or other terms describing the energy depend on the local volume.