Phase transition thermal dependence of ferroelectric and dielectric properties in H-bonded $$\hbox {PbHPO}_{4}$$
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Phase transition thermal dependence of ferroelectric and dielectric properties in H‑bonded PbHPO4 (LHP) crystal Muzaffar Iqbal Khan1 · Trilok Chandra Upadhyay1 Received: 24 July 2020 / Accepted: 28 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, the ferroelectric phase transition and dielectric properties in order-disorder type PbHPO4 crystal are theoretically investigated. We consider the two sublattice pseudospin lattice coupled mode (PLCM) model Hamiltonian modified by adding third and fourth-order phonon anharmonic interactions, indirect coupling interactions, direct spin–spin coupling interaction, and an applied electric field term within mean-field approximation (MFA). The model is developed as a generalization of the semi-microscopic Mitsui mode model. By using the Green’s function theory, two sublattice PLCM model Hamiltonian and Dyson’s equation, the expressions of soft mode frequency, dielectric constant and loss tangent have been derived for PbHPO4 crystal. The numerical analysis has been performed by fitting the various model parameters in the obtained expressions and the thermal variations of the soft mode frequency, dielectric constant and loss tangent have been obtained. Our theoretical results are compare good with the experimental data of Negran et al. for lead monohydrogen phosphate (LHP) crystal. Keywords Phase transition · Lead monohydrogen phosphate · Dielectric loss · Green function
1 Introduction Lead monohydrogen phosphate ( PbHPO4 , LHP) is a wellknown class of H-bonded ferroelectric crystals of KDP-type. PbHPO4 undergoes second order-phase transition at 310K [1]. Lead monohydrogen phosphate [1] is the monoclinic crystal structure in both the paraelectric phase with P2/c space group and in the ferroelectric phase with Pc space group [1, 2]. Ferroelectric phase in PbHPO4 crystal is characterized by a Pc symmetry having a spontaneous polarization ( Ps ) in the direction that makes an angle of 10◦ with the crystal a-axis [3]. The direction of the spontaneous polarization ( Ps ) is parallel to the direction of the hydrogen bond O–H–O projecting on the ac-plane [4], can be primarily attributed to the ordering of the protons which are assumed to move in a double-well potential along with their bonds [1] and the O–H–O distance [1] is 2.52Å unlike the potassium dihydrogen phosphate (KDP) crystal where Ps is perpendicular to O–H–O bond. The PO4 groups are * Muzaffar Iqbal Khan [email protected] 1
Department of Physics, Hemvati Nandan Bahuguna Garhwal University (A Central University), Srinagar (Garhwal), Uttarakhand 246174, India
bound to one another by the O–H–O bonds in the form of a one-dimensional chain by H-atoms along the c-axis of the monoclinic structure but in the KDP crystal, bonding is a three-dimensional chain. There are no H-bond crosslinks between the chains in PbHPO4 type crystal. Thus, the interchain coupling between the chains is weaker than the intrachain coupling within a chain. The H-bonds orders have been c
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