Pseudospin Lattice Coupled Mode Model Research Articles

Phase transition investigation of ferroelectric and dielectric properties of (NH 2 CH 2 COOH)3 H2SO4 crystal using green function method and two sublattice PLCM model Hamiltonian

The Greens function technique and extended two sublattice pseudospin lattice coupled-mode (PLCM) model Hamiltonian have been applied to study the phase transition mechanism in (NH2CH2COOH)3H2SO4 compound. The two sublattice PLCM model Hamiltonian is modified by considering anharmonic phonon interactions, extra spin-lattice interactions, and an external applied electric field term. By using the double-time thermal-dependent Green function technique, the theoretical equations for the total shift, total width, normal mode frequency, transition temperature, relative permittivity, dielectric tangent loss, acoustic attenuation and spontaneous polarization are derived. By fitting the distinct model parameters in the theoretical equations, we calculated the temperature dependence of normal mode frequency, relative permittivity, tangent loss, acoustic attenuation and spontaneous polarization. The numerically obtained results are hold well and correlated with experimental data.

Phase Transition Behavior in Antiferroelectric Copper Formate Tetrahydrate Crystal

Antiferroelectric properties of copper formate tetrahydrate (CFT) crystal having phase transition temperature at were investigated theoretically. CFT have a layer-type structure in which layers of are sandwiched between the layers of copper formate in the lattice plane. By considering modified two sublattice pseudospin lattice coupled mode model Hamiltonian and double-time temperature-dependent Green function method for antiferroelectric copper formate tetrahydrate (CFT) crystal, the phase transition properties of crystal have been studied. Expressions are derived for soft mode frequency, dielectric constant and loss tangent for considered crystal. Model values are fitted in the derived expressions and the dependence of the above properties on temperature have been calculated. Theoretically obtained results are compared with experimental data and show similarities between them. Dielectric constant as a function of temperature shows a behaviour of the first-order transition with a large discontinuity at the transition point. These properties can be employed in a wide range of applications including memory devices, solar cells, biosensors and photovoltaic devices.

Dielectric properties of ferroelectric methylammonium aluminium sulphate alum (MASD) crystal

By considering two sublattice pseudospin lattice coupled mode model Hamiltonian has been modified to include the extra spin–lattice interactions, the direct spin–spin coupling interaction, an applied electric field and the phonon anharmonic interactions for MASD alum. By using double-time thermal-dependent Green function method and modified Hamiltonian formulation, the expressions for soft mode frequency, dielectric constant and dielectric tangent loss properties have been derived and evaluated. Fitting the model values of various physical parameters in theoretical obtained expressions, the thermal variations of the above quantities have been calculated. Theoretical results compare well with experimental data of others on MASD alum.

Study of structural order–disorder thermal dependence dielectric properties for PbHPO4 and PbHAsO4 crystals

By using the statistical Green function theory and extended two sublattice pseudospin lattice coupled mode model Hamiltonian for proton subsystem with mean field approximation on hydrogen bonds have been used to interpret structural phase transition thermal dependence dielectric properties in PbHPO $$_{4}$$ and PbHAsO $$_{4}$$ ferroelectric compounds. By using the retarded thermal Green function theory and Hamiltonian along with Dyson approach, the expressions for ferroelectric soft mode frequency, dielectric permittivity and dielectric tangent loss have been derived. With the putting of the model values of different physical parameters in theoretical derived expressions, the thermal dependence of ferroelectric normal mode frequency, relative permittivity and dielectric loss has been calculated for both ferroelectric compounds in two structural phases. With the help of proper fitting of model parameters, valuable theoretical results for corresponding experimental results have been calculated.

Study of Ferroelectric Properties of Hydrogen Bonded Rubidium Dihydrogen Arsenate (RdA) Crystal

A simple pseudospin lattice coupled mode model with addition of third and fourth-order phonon anharmonic interactions terms, direct spin-spin interactions terms and external electric field term has been considered for investigation of transition phenomena and dielectric properties of hydrogen bonded ferroelectric crystal Rubidium dihydrogen arsenate (RDA). A double-time thermal dependent Green’s function method has been used for derivation of response function. From response function shift, width and soft mode frequency have been derived for RDA crystal. Response function is also related to dielectric constant which has been obtained in present paper. By fitting model values of different parameters in obtained expressions, the temperature variations of normal mode frequency, dielectric constant, and loss tangent have been calculated numerically for RDA crystal. Our theoretical results are compared with experimental results. It is observed that our theoretical results agree with experimental results. Therefore, it can be concluded that the modified pseudo-spin lattice coupled mode model with the simplest approximation is quite suitable to explain the transition and dielectric properties of RDA crystal.

Phase transitions in H-bonded deuterated Rochelle salt crystal

The modified two-sublattice pseudospin lattice coupled mode model Hamiltonian is extended by adding third- and fourth-order phonon anharmonic interactions, extra spin–lattice interactions, direct spin–spin interaction and an applied electric field terms considered for the study of deuterated Rochelle salt crystal. The double-time thermal-dependent Green function, Dyson equation and symmetric decoupling scheme have been used to derive the expressions for energy shift, line width, ferroelectric soft mode frequency, dielectric constant, dielectric tangent loss and spontaneous polarization. Model values of various physical parameters are fitted in the obtained expressions; the thermal variations of ferroelectric soft mode frequency, dielectric constant, loss tangent and spontaneous polarization have been calculated for deuterated Rochelle salt crystal. Theoretical results with model values compare well with experimental data reported by others for deuterated Rochelle salt. Our expressions contain all possible interactions as compared to the earlier authors.

Temperature dependence of dielectric properties in Potassium dihydrogen arsenate crystal

Potassium Dihydrogen Arsenate (KH2AsO4, KDA) is an inorganic arsenate ferroelectric crystal which is a KDP-family member and undergoes a ferroelectric phase transition at 96 K. A simple pseudospin lattice coupled mode model (PLCM) with some higher order terms like direct spin–spin interaction, third and fourth-order phonon anharmonic interaction terms and external electric field term, with two-time temperature dependent Green’s function technique has been employed for the evaluation of expression of response function. We can obtain and calculate soft mode frequency (Ω^), Dielectric constant (ε), and loss tangent (tanδ) expressions from response function for KDA crystal. We have shown temperature dependence of soft mode frequency (Ω^), Dielectric constant (ε), and loss tangent (tanδ) in Figs. 1-3. We have compared our findings, which seemed to be in fair alignment with experimental evidence.

Phase transition thermal dependence of ferroelectric and dielectric properties in H-bonded $$\hbox {PbHPO}_{4}$$ (LHP) crystal

In this paper, the ferroelectric phase transition and dielectric properties in order-disorder type $$\hbox {PbHPO}_{4}$$ 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 $$\hbox {PbHPO}_{4}$$ 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.

Temperature dependence of ferroelectric mode frequency, dielectric constant and loss tangent in potassium dihydrogen phosphate crystal

Potassium Dihydrogen Phosphate (KH2PO4, KDP) is an inorganic phosphate which undergoes ferroelectric transition at 123 K. A simple pseudospin lattice coupled mode model with addition of third and fourth-order phonon anharmonic interaction terms, external electric field term and direct spin–spin interaction terms with double-time thermal Green’s function method has been used for derivation of response function. From response function, shift, width, and soft mode frequency have been derived for KDP crystal. Response function is also related to dielectric constant which has been calculated and compared with experimental data of literature value which shows a good agreement.

Study of ferroelectric lead monohydrogen phosphate type crystals

In this paper, the ferroelectric transition and dielectric properties of the lead monohydrogen phosphate (PbHPO4) crystal are theoretically investigated. By using Green’s function method and modified two sublattice pseudospin–lattice coupled mode model, formulae for PbHPO4 type crystals are derived. Temperature variations of ferroelectric mode frequency, dielectric constant and loss tangent are calculated for the PbHPO4 crystal. Our results agree well with the experimental data.

Soft mode and acoustic mode ferroelectric properties of deuterated triglycine sulphate crystal

A mathematical study about deuterated triglycine sulphate (CD2CD2COOD)3D2SO4 crystal by a theoretical model which is extended with two sublattice pseudospin lattice coupled mode model by adding third, fourth and fifth order phonon anharmonic interaction terms as well as external electric field term in the crystal Hamiltonian. Double-time temperature dependent Green’s function is used to derive soft mode frequency, dielectric permittivity, microwave absorption, quality factor, acoustic attenuation, electric conductivity, smooth function, relaxation time, ratio of figure of merits and respective applications in modern technologies. All theoretical results have a good agreement with experimental data.

Theoretical Study of Ferroelectric Triglycine Sulphate (TGS) Crystal in External Electric Fields

A modified two sub-lattice pseudospin-lattice coupled mode model of Mitsui et al [Phys. Rev., 111 (1958) 1259] by adding third, fourth order phonon anharmonic interaction and external electric field terms has been applied to ferroelectric triglycine sulphate crystal. Electric field dependence of ferroelectric, dielectric and acoustical properties has been studied. With the help of double time temperature dependent Green’s function method, expressions for shift, width, soft mode frequency, dielectric constant, loss tangent and acoustic attenuation have been derived. Numerically calculations have been made and results have been compared with experimental data reported by Bye et al [Ferroelectrics 4 (1974) 243] and Shreekumar et al [Ferroelectrics 160 (1994) 23] for TGS crystal and a good agreement has been observed.

Theoretical Study of Ferroelectric Triglycine Sulphate (TGS) Crystal in External Electric Fields

A modified two sub-lattice pseudospin-lattice coupled mode model of Mitsui et al [Phys. Rev., 111 (1958) 1259] by adding third, fourth order phonon anharmonic interaction and external electric field terms has been applied to ferroelectric triglycine sulphate crystal. Electric field dependence of ferroelectric, dielectric and acoustical properties has been studied. With the help of double time temperature dependent Green’s function method, expressions for shift, width, soft mode frequency, dielectric constant, loss tangent and acoustic attenuation have been derived. Numerically calculations have been made and results have been compared with experimental data reported by Bye et al [Ferroelectrics 4 (1974) 243] and Shreekumar et al [Ferroelectrics 160 (1994) 23] for TGS crystal and a good agreement has been observed.

Green's-function theory of ferroelectric phase transitions in hydrogen-bonded triglycine sulfate with the pseudospin-lattice coupled-mode model: A unified theory of structural phase transitions. I. Static and dynamic properties.

A pseudospin-lattice coupled-mode (PLCM) model and the statistical Green's-function theory have been used to explain the static as well as the dynamic properties of ferroelectric phase transitions in triglycine sulfate (TGS) and in its deuterated and undeuterated families. An attempt to settle the long-standing controversy over the coexistence of both order-disorder and displacive phase transitions in TGS and in many other H-bonded crystals (as observed from the studies of different static and dynamic properties) has been made by expressing the transition mechanism in these crystals as a ``mixed'' type rather than a purely order-disorder or a purely displacive type. This mixed behavior is due to the importance of the pseudospin-phonon and the higher-order anharmonic phonon-phonon interaction terms. The pseudospins are considered to be associated with the local ordering (rotation, displacements, etc.) of some ions or groups in the lattice. This makes the mechanism of structural phase transitions, in general, very complicated.As a consequence, the calculated expression for the total phonon self-energy is found to contain an extra term in addition to that which appears in the existing theoretical calculations by Cowley and others describing purely displacive phase transitions with phonon-phonon interaction only. This additional self-energy term is found, in principle, to be responsible for the observed deviations of some thermal and dielectric properties of TGS from the Landau theory, the existence of the ``double peak'' in the NMR or NQR relaxation times in TGS and in other crystals, and the appearance of both order-disorder and the displacive type of behavior in many crystals. This additional part of the self-energy is also found to be related to the ``central peak'' phenomenon. Depending on the strengths of the pseudospin-phonon interaction terms, this part of the self-energy might also be responsible for the crossover from order-disorder to displacive behavior observed in some structural transitions. This is also supported by recent EPR and other experimental observations made by M\"uller. The theoretical expressions derived for the transition temperature (${T}_{c}$), dielectric constant (\ensuremath{\epsilon}'), spontaneous polarization (${P}_{s}$), Curie-Weiss constant (C), renormalized phonon frequency, etc., have been fitted with the corresponding experimental data to find a single set of Blinc--de Gennes model parameters for the TGS family. Finally, the unified character of the PLCM model in explaining various salient features of structural phase transitions in crystals has been discussed, and supports the conclusion of our previous work.

Green's-function theory of ferroelectric phase transitions in hydrogen-bonded triglycine sulfate with the pseudospin-lattice coupled-mode model: A unified theory of structural phase transitions. II. Nonlinear properties.

Green's-function theory of ferroelectric phase transitions in hydrogen-bonded triglycine sulfate with the pseudospin-lattice coupled-mode model: A unified theory of structural phase transitions. II. Nonlinear properties.

Phenomenological explanation of the anomalous dielectric behavior of alums with pseudo-spin-lattice coupled-mode model

With the use of the pseudo-spin-lattice coupled-mode (PLCM) model and the statistical Green's-function technique a phenomenological explanation of the hitherto unexplained ferroelectric phase transitions in (C${\mathrm{H}}_{3}$N${\mathrm{H}}_{3}$)Al${(\mathrm{S}{\mathrm{O}}_{4})}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}12${\mathrm{H}}_{2}$O (MASD) and (N${\mathrm{H}}_{4}$)Fe${(\mathrm{S}{\mathrm{O}}_{4})}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}12${\mathrm{H}}_{2}$O (AFeSD) alums has been given. The pseudospins assumed to be associated with the protons of the monovalent methylammonium group and the ammonium groups, respectively, in MASD and AFeSD alums undergo ordering at low temperatures. From our calculations the expression for the electrical susceptibility ($\ensuremath{\chi}$) comes out to be of the form $\ensuremath{\chi}={A}_{0}^{\ensuremath{'}}+{B}_{0}^{\ensuremath{'}}+{C}_{0}^{\ensuremath{'}}+\ensuremath{\cdots}$, where ${A}_{0}^{\ensuremath{'}}$ is a temperature-independent term and ${B}_{0}^{\ensuremath{'}}$ is a measure of the contribution from phonon-phonon interaction. The third term ${C}_{0}^{\ensuremath{'}}$ arises from the rotation of the monovalent ions. For ferroelectric alums ${C}_{0}^{\ensuremath{'}}$ is found to be highly temperature dependent, and for other nonferroelectric alums both ${B}_{0}^{\ensuremath{'}}$ and ${C}_{0}^{\ensuremath{'}}$ show negligibly small dependences on temperature. A single set of model parameters (Blinc---de Gennes parameters) has been calculated for AFeSD from fitting the experimental data of dielectric constant ($\ensuremath{\epsilon}$), Curie-Weiss constant ($C$) and transition temperature (${T}_{C}$) with the corresponding theoretical expressions. However, in the case of MASD alum, we must vary the renormalized phonon frequency ${\overline{\ensuremath{\omega}}}_{0}[={\ensuremath{\omega}}_{0}+{\overline{A}}^{\ensuremath{'}}(0, T)]$ with temperature to fit the entire $\ensuremath{\epsilon}\ensuremath{-}T$ curve with a single set of model parameters. This is due to the presence of strong phonon-phonon interaction in MASD alum, causing the strongly temperature-dependent anharmonicity parameter ${\overline{A}}^{\ensuremath{'}}(0, T)$. The present success of the PLCM model for explaining the phase transitions in alums definitely indicates the unified character of this model, which may also be applied to many other crystals.