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Thermodynamical Cross‐Relations for Superconductors at the Critical Point
Author(s) -
Grabiec B.,
Matlak M.
Publication year - 2002
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/1521-3951(200206)231:2<299::aid-pssb299>3.0.co;2-s
Subject(s) - critical point (mathematics) , superconductivity , volume (thermodynamics) , thermodynamics , statistical physics , phase transition , critical phenomena , specific heat , physics , measure (data warehouse) , point (geometry) , theoretical physics , condensed matter physics , mathematics , mathematical analysis , computer science , database , geometry
We investigate superconducting systems using the phenomenological Landau theory of second order phase transitions, including into the considerations the critical behaviour of the chemical potential. We derive in this way a variety of new thermodynamical relations at the critical point. Twelve basic relations connect critical jumps of different thermodynamical quantities (specific heat, chemical potential derivatives with respect to temperature, pressure (volume) and number of particles, volume (pressure) derivatives with respect to temperature and pressure (volume)) with the critical temperature or its derivatives with respect to the number of particles or pressure (volume). These relations allow to find plenty of cross‐relations between different quantities at the critical point. The derived formulae can be practically used in many cases to find such thermodynamical quantities at the critical point, which are extremely difficult to measure, under the assumption that the other ones are already known. We additionally perform a test of two derived relations by using a two‐band microscopic model describing superconducting systems. We calculate the specific heat, order parameter, and chemical potential as functions of temperature to show that the tested relations are very well fulfilled.