22 1 Deformation and Fracture of Perfect Crystals on the energy-strain curve.However,the IS is determined by the stress as- sociated with the first point of inflection on the original energy-strain curve which corresponds to the maximal energy gradient.Note that atomic con- figurations related to energy minima behind the first point of inflection may mimic stable or metastable atomic arrangements that could be encountered when investigating thin films or extended defects such as interfaces or disloca- tions.Similar configurations can also be reached during the strain-controlled deformation path of a crystal (the constant strain ensembles),provided that they are not preceded by any instabilities of the second kind. The instabilities of the second kind (so-called shear instabilities)can be derived by considering a requirement that the free energy (and at T=0 also the total internal energy)be minimum in subsequent constant stress ensembles in accordance with the second law of thermodynamics 66,78-80, 87,92-94.The main point of such an analysis was the assumption that the crystal is subjected both to the applied load and to an infinite variety of small perturbing forces.Any of the forces can make the crystal fail in a different mode than that related to the main loading force.The proposed stability assessment requires information about an elastic response of the system to small deviations from the current state (let us call it the reference state). Therefore,in the case of a quasi-static loading,the stability assessment is in a sense independent of the deformation path which led the system to this state,because the same atomic arrangement can be obtained via many various transformations of an arbitrary original state.For that reason,the further deformations used to investigate the stability have nothing to do with the original deformation path.If the solid is strained infinitesimally from the reference state associated with the stress oij (in the standard notation)by a strain tensor sij,the related Cauchy(true)stress Tij can be written as T=0十Bk1ekl, where 1 BL=CL+2(6k01+dk01+6M0jk+d10ik-20k0) (1.10) is the elastic stiffness matrix (i,j,k,l=1,2,3)introduced by Wallace [95] that is generally asymmetric with respect to the interchange of indices.Con- struction of this matrix is crucial for the stability assessment.As was shown in [92,94,96],the system becomes unstable once its symmetrized counterpart A=专B+B) attains a zero determinant,i.e., Al=0 (1.11)22 1 Deformation and Fracture of Perfect Crystals on the energy–strain curve. However, the IS is determined by the stress as￾sociated with the first point of inflection on the original energy–strain curve which corresponds to the maximal energy gradient. Note that atomic con- figurations related to energy minima behind the first point of inflection may mimic stable or metastable atomic arrangements that could be encountered when investigating thin films or extended defects such as interfaces or disloca￾tions. Similar configurations can also be reached during the strain-controlled deformation path of a crystal (the constant strain ensembles), provided that they are not preceded by any instabilities of the second kind. The instabilities of the second kind (so-called shear instabilities) can be derived by considering a requirement that the free energy (and at T = 0 also the total internal energy) be minimum in subsequent constant stress ensembles in accordance with the second law of thermodynamics [66, 78–80, 87, 92–94]. The main point of such an analysis was the assumption that the crystal is subjected both to the applied load and to an infinite variety of small perturbing forces. Any of the forces can make the crystal fail in a different mode than that related to the main loading force. The proposed stability assessment requires information about an elastic response of the system to small deviations from the current state (let us call it the reference state). Therefore, in the case of a quasi-static loading, the stability assessment is in a sense independent of the deformation path which led the system to this state, because the same atomic arrangement can be obtained via many various transformations of an arbitrary original state. For that reason, the further deformations used to investigate the stability have nothing to do with the original deformation path. If the solid is strained infinitesimally from the reference state associated with the stress σij (in the standard notation) by a strain tensor εij , the related Cauchy (true) stress τij can be written as τij = σij + Bijklεkl, where Bijkl = Cijkl + 1 2 (δikσjl + δjkσil + δilσjk + δjlσik − 2δklσij ) (1.10) is the elastic stiffness matrix (i, j, k, l = 1, 2, 3) introduced by Wallace [95] that is generally asymmetric with respect to the interchange of indices. Con￾struction of this matrix is crucial for the stability assessment. As was shown in [92,94,96], the system becomes unstable once its symmetrized counterpart A = 1 2  BT + B attains a zero determinant, i.e., |A| = 0 (1.11)