{'fraction_non_alphanumeric': 0.036488027366020526, 'fraction_numerical': 0.004561003420752566, 'mean_word_length': 5.097222222222222, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Temperature dependences of the electrochemical coefficients of crystals exhibiting phase transitions

The calculation of fluctuation corrections to the electromechanical coefficients of ferroelectrics is analyzed in a range of temperatures T close to the phase transition point T c . Special attention is concentrated on the striction and piezoelectric coefficients. The analysis is concerned with the «intrinsic» coefficients, i.e., those which are temperature-independent in the absence of nonlinear interactions. The corrections to the striction coefficients can have the following anomalies: g ∞ ln(T − T c ) −1/2 for a triaxial ferroelectric, g ∞ ln(T − T c ) for a uniaxial ferroelectric that does not exhibit piezoelectricity in its high-symmetry phase, and g ∞ (T − T c ) −1/2 in the presence of piezoelectricity. These anomalies occur for lower-order of nonlinearities