Ferroelektrik faz geçişinde iki alt örgü, Dvorak ve Levanyuk-Sannikov modelleri ile modifikasyonları

Abstract

T(K> Ps 62.5 65 67.5 70 72.5 75 (a) T(K) (b) Fig 5.Temperature dependence of Vs. a) The dots show the experimental data of HDDBACEEC crystal. The solid line is calculated from fitting of Eq(20) to the experimental data of HDDBACEEC [13] crystal, b) The dots show the experimental data of triglycine selenate [14] crystals. The solid line is calculated from fitting Eq(20) the experimental data of triglycine selenate crystal. g{P(tc)mtc)j:)=v(W'c) We then find that Tc = T0+(k + 3B2 /]6C)/ A Next define Td as the temperature at which the radical of Eq(17) vanishes Td = T0+(k + 3B2 1 AC) I A Then, the ferroelectric phase susceptibility becomes 2C X = 1 B2\\ + -[(T-Td)l(Tc-ldf^-ld)l(Tc-Td)Y where T Tc> T0 the phase transition prevents either phase from having a divergence. 5. Modification of The Levanyuk-Sannikov Model Now we consider the addition of the aP2îj2 + - if term in thermodynamic potential which is suggested by Levanyuk and Sannikov as given below: G = A(T-T0)P2 /2 + BP4 /4 + CP6 /6 + brj4 / 4-qVrj2 + a?2r/2 +-rj2 (18) Minimization of termodynamics potential Eq(18) with respect to jj and P gives that Tj2=-(2qP-2aP2-e) (19),2\.2 V b J b b p b b We fit Eq(20) to the experimental data of HDDBACEEC [13] crystal and triglycine selenate [14]. T(K> Ps 62.5 65 67.5 70 72.5 75 (a) T(K) (b) Fig 5.Temperature dependence of Vs. a) The dots show the experimental data of HDDBACEEC crystal. The solid line is calculated from fitting of Eq(20) to the experimental data of HDDBACEEC [13] crystal, b) The dots show the experimental data of triglycine selenate [14] crystals. The solid line is calculated from fitting Eq(20) the experimental data of triglycine selenate crystal. g{P(tc)mtc)j:)=v(W'c) We then find that Tc = T0+(k + 3B2 /]6C)/ A Next define Td as the temperature at which the radical of Eq(17) vanishes Td = T0+(k + 3B2 1 AC) I A Then, the ferroelectric phase susceptibility becomes 2C X = 1 B2\\ + -[(T-Td)l(Tc-ldf^-ld)l(Tc-Td)Y where T Tc> T0 the phase transition prevents either phase from having a divergence. 5. Modification of The Levanyuk-Sannikov Model Now we consider the addition of the aP2îj2 + - if term in thermodynamic potential which is suggested by Levanyuk and Sannikov as given below: G = A(T-T0)P2 /2 + BP4 /4 + CP6 /6 + brj4 / 4-qVrj2 + a?2r/2 +-rj2 (18) Minimization of termodynamics potential Eq(18) with respect to jj and P gives that Tj2=-(2qP-2aP2-e) (19),2\.2 V b J b b p b b We fit Eq(20) to the experimental data of HDDBACEEC [13] crystal and triglycine selenate [14]. T(K> Ps 62.5 65 67.5 70 72.5 75 (a) T(K) (b) Fig 5.Temperature dependence of Vs. a) The dots show the experimental data of HDDBACEEC crystal. The solid line is calculated from fitting of Eq(20) to the experimental data of HDDBACEEC [13] crystal, b) The dots show the experimental data of triglycine selenate [14] crystals. The solid line is calculated from fitting Eq(20) the experimental data of triglycine selenate crystal. g{P(tc)mtc)j:)=v(W'c) We then find that Tc = T0+(k + 3B2 /]6C)/ A Next define Td as the temperature at which the radical of Eq(17) vanishes Td = T0+(k + 3B2 1 AC) I A Then, the ferroelectric phase susceptibility becomes 2C X = 1 B2\\ + -[(T-Td)l(Tc-ldf^-ld)l(Tc-Td)Y where T Tc> T0 the phase transition prevents either phase from having a divergence. 5. Modification of The Levanyuk-Sannikov Model Now we consider the addition of the aP2îj2 + - if term in thermodynamic potential which is suggested by Levanyuk and Sannikov as given below: G = A(T-T0)P2 /2 + BP4 /4 + CP6 /6 + brj4 / 4-qVrj2 + a?2r/2 +-rj2 (18) Minimization of termodynamics potential Eq(18) with respect to jj and P gives that Tj2=-(2qP-2aP2-e) (19),2\.2 V b J b b p b b We fit Eq(20) to the experimental data of HDDBACEEC [13] crystal and triglycine selenate [14]. T(K> Ps 62.5 65 67.5 70 72.5 75 (a) T(K) (b) Fig 5.Temperature dependence of Vs. a) The dots show the experimental data of HDDBACEEC crystal. The solid line is calculated from fitting of Eq(20) to the experimental data of HDDBACEEC [13] crystal, b) The dots show the experimental data of triglycine selenate [14] crystals. The solid line is calculated from fitting Eq(20) the experimental data of triglycine selenate crystal. g{P(tc)mtc)j:)=v(W'c) We then find that Tc = T0+(k + 3B2 /]6C)/ A Next define Td as the temperature at which the radical of Eq(17) vanishes Td = T0+(k + 3B2 1 AC) I A Then, the ferroelectric phase susceptibility becomes 2C X = 1 B2\\ + -[(T-Td)l(Tc-ldf^-ld)l(Tc-Td)Y where T Tc> T0 the phase transition prevents either phase from having a divergence. 5. Modification of The Levanyuk-Sannikov Model Now we consider the addition of the aP2îj2 + - if term in thermodynamic potential which is suggested by Levanyuk and Sannikov as given below: G = A(T-T0)P2 /2 + BP4 /4 + CP6 /6 + brj4 / 4-qVrj2 + a?2r/2 +-rj2 (18) Minimization of termodynamics potential Eq(18) with respect to jj and P gives that Tj2=-(2qP-2aP2-e) (19),2\.2 V b J b b p b b We fit Eq(20) to the experimental data of HDDBACEEC [13] crystal and triglycine selenate [14]. T(K> Ps 62.5 65 67.5 70 72.5 75 (a) T(K) (b) Fig 5.Temperature dependence of Vs. a) The dots show the experimental data of HDDBACEEC crystal. The solid line is calculated from fitting of Eq(20) to the experimental data of HDDBACEEC [13] crystal, b) The dots show the experimental data of triglycine selenate [14] crystals. The solid line is calculated from fitting Eq(20) the experimental data of triglycine selenate crystal.