Elastic and spinodal instabilities in strained periodic states: A phase-field-crystal study.

The stability of periodic states under applied strain is investigated using the one-dimensional phase-field-crystal (PFC) model. We perform a linear stability analysis of periodic states within the one-mode approximation and identify a marginal zero-wave-number mode, corresponding to the global translational symmetry, which controls the onset of instability at long wavelengths. Two distinct instability mechanisms are found. At low mean densities, phase fluctuations in the complex amplitude dominate, leading to a phase (elastic) instability of the periodic state. At higher densities, amplitude softening and density fluctuations drives a spinodal-like melting and the onset of liquid-solid coexistence. The crossover between these two regimes occurs at a sharp threshold coinciding with the onset of coexistence, and is confirmed by direct numerical simulations of the full PFC dynamics. Our results clarify how mean density and strain control the loss of periodic order through competing elastic (phase) and amplitude-driven instabilities.