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Abstract The paper shows that symmetry forms a basis for relations between different properties of material. In this way, the key quantities for specification of an atomistic model are identified. Material symmetry distinguishes representative processes of small strains. It is proved that the errors in the densities of the energies stored in these processes determine the range of inaccuracies with which an atomistic model recreates processes of small deformations. The errors are equal to the inaccuracies in the eigenvalues of the elasticity tensor, that is in the Kelvin moduli. For cubic crystals, the elementary processes indicated by the symmetry initiate the key paths of large deformations: Bain and trigonal ones. Therefore, the substantial errors in the Kelvin moduli lead to incorrect reconstructing the metastable phases: bcc, sc and bct. The elastic constants commonly used in the literature do not provide such information as the Kelvin moduli. Using the eigenvalues of the elasticity tensor as well as other key properties indicated by the symmetry, the EAM model proposed by A.F. Voter for copper is specified. The obtained potential more accurately reproduces small and large deformations and additionally, correctly describes defect formation as well as Cu dimer properties
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