By Julio a Gonzalo
This booklet starts off through introducing the potent box process, the best method of section transitions. It offers an intuitive approximation to the physics of such diversified phenomena as liquid-vapor transitions, ferromagnetism, superconductivity, order-disorder in alloys, ferroelectricity, superfluidity and ferroelasticity. the relationship among the powerful box strategy and Landau's thought is under pressure. the most assurance is dedicated to precise purposes of the potent box suggestion to ferroelectric structures, either hydrogen bonded ferroelectrics, like these within the TGS relations, and oxide ferroelectrics, like natural and combined perovskites.
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Additional resources for Effective field approach to phase transitions and some applications to ferroelectrics
The use of the term "ferroelectrics," instead of the original term "seignetteelectrics" became widespread for these materials, and their number has kept growing. At present, the number of known ferroelectrics is in several hundreds and new ferroelectrics are often added to the list. In part, the initial drive to find new ferroelectrics was prompted by the excellent piezoelectric properties of these materials, which make them useful in "sonar" devices for submarine detection. 45 46 Effective Field Approach to Phase Transitions A ferroelectric crystal can be defined as a piezoelectric possessing a spontaneous electric polarization that is reversible under the action of an external electric field.
C. calorimetry. From experimental data for the transition temperature Tc = (3N[i2 /ks, the Curie constant, C = AnNfi2/k&, and the saturation (low T) spontaneous polarization, PSQ = N/J,, one can get the basic ferroelectric parameters H= 4TT TC/C, (15) H = kBC/4irPs0, (16) N = 4irP*0/kBC, (17) for a number of representative ferroelectric cystals and then make comparisons with independently observable experimental quantities whenever possible. 1. T c (K) Basic parameters for selected ferroelectric crystals.
And a spin s, s', successively absorbing and emitting phonons with energy huq and momentum q. Then, assuming that only pairs of electrons with opposite momenta (k = —k') 31 32 Effective Field Approach to Phase Transitions and opposite spin (s' = — s) give non-zero contributions in the interaction energy term, one gets the Bardeen-Cooper-Schrieffer (BCS) hamiltonian, HBCS = HT + HV = Y^£kctsCks - 2 H V kk'Ck's'C-k'sC~ks'Cks, (1) where HT is the kinetic energy term, mks = <4-scks is the operator giving the number of individual electrons in terms of creation and annihilation operators of electrons with momentum A;(energy ek) and spin s, Hy is the potential energy of the paired electrons (k, s and k', s'), Vkk' includes the (attractive) electron-phonon interaction energy and the (repulsive) screened Coulomb electron-electron interaction, and c^,5,,clfc,s,c_fcs/,Cfcs is the operator giving the pair density of electrons in terms of the c + and c operators.