Temperature-Graded Ferroelectric Thin Films under Two Boundary Conditions

2013 ◽  
Vol 750-752 ◽  
pp. 1910-1913
Author(s):  
Hui Chen ◽  
Xin Yue Bi ◽  
Li Jia Zhang ◽  
Yan Shen
Keyword(s):  
Boundary Condition ◽  
Temperature Gradient ◽  
Boundary Conditions ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Ferroelectric Films ◽  
Film Properties ◽  
Different Boundary Conditions ◽  
The Mean

In the framework of the mean field approximation, a transverse Ising model (TIM) was adopted to analyze the polarization properties of temperature-graded ferroelectric films under two boundary conditions, free boundary condition (FBC) and clamped boundary condition (CBC). Due to the ferroelectric distortion aroused by temperature gradient across the film, the elastic thermal stress increased. A distribution function was introduced to characterize the different boundary conditions. The results show that boundary conditions have very important influence on film properties. Polarizations under FBC are larger than that under CBC, polarization variations aroused by changed film thickness and temperature gradient under FBC are not as obvious as that under CBC, and films under different boundary conditions present obviously different physical behavior.

POLARIZATION PROPERTIES OF FERROELECTRIC THIN FILMS UNDER DIFFERENT BOUNDARY CONDITIONS

2009 ◽  
Vol 16 (04) ◽  
pp. 507-512 ◽  
Author(s):  
HUI CHEN ◽  
TAIMIN CHENG ◽  
SIQUN CHEN ◽  
TIECHEN GANG
Keyword(s):  
Thin Films ◽  
Boundary Condition ◽  
Boundary Conditions ◽  
Mean Field ◽  
Film Surface ◽  
Transverse Field ◽  
Field Approximation ◽  
Ferroelectric Thin Films ◽  
Mean Field Approximation ◽  
Structure Variation

By taking into account two types of boundary conditions (BC), free boundary condition (FBC) and zero boundary condition (ZBC), an improved transverse Ising model with the consideration of surface transition layers (STL) is used to describe the polarization properties of ferroelectric thin films in the framework of the mean field approximation. Functions representing the intra-layer and inter-layer couplings are introduced to characterize the BC and STL, which reflect the structure variation of film surface. Comparing the results obtained by employing FBC and ZBC, some effects of BC are derived in the model, which demonstrated that the BC play important roles on the properties of ferroelectric thin films. It is shown that the effect of ZBC can extend to deeper film than that of FBC. When different BC are adopted, competition between the fields (depolarization field and transverse field) and BC induces some different and interesting phenomena. Some theoretical results in this paper are found to be in reasonable accordance with experimental data and have some application importance.

scholarly journals The Combined Effect of Rotation and Magnetic Field on Finite-Amplitude Thermal Convection

1973 ◽  
Vol 26 (5) ◽  
pp. 617 ◽  
Author(s):  
R Van der Borght ◽  
JO Murphy
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Field Approximation ◽  
Finite Amplitude ◽  
Combined Effect ◽  
Mean Field Approximation ◽  
Free Boundaries ◽  
Wide Range ◽  
The Mean ◽  
Basic Equations

The combined effect of an imposed rotation and magnetic field on convective transfer in a horizontal Boussinesq layer of fluid heated from below is studied in the mean field approximation. The basic equations are derived by a variational technique and their solutions are then found over a wide range of conditions, in the case of free boundaries, by numerical and analytic techniques, in particular by asymptotic and perturbation methods. The results obtained by the different techniques are shown to be in excellent agreement. As for the linear theory, the calculations predict that the simultaneous presence' of a magnetic field and rotation may produce conflicting tendencies.

scholarly journals Locating the critical end point using the linear sigma model coupled to quarks.

2018 ◽  
Vol 172 ◽  
pp. 02003
Author(s):  
Alejandro Ayala ◽  
J. A. Flores ◽  
L. A. Hernández ◽  
S. Hernández-Ortiz
Keyword(s):  
Sigma Model ◽  
Chemical Potential ◽  
Potential Temperature ◽  
Mean Field ◽  
Field Approximation ◽  
Baryon Density ◽  
Linear Sigma Model ◽  
Mean Field Approximation ◽  
End Point ◽  
The Mean

We use the linear sigma model coupled to quarks to compute the effective potential beyond the mean field approximation, including the contribution of the ring diagrams at finite temperature and baryon density. We determine the model couplings and use them to study the phase diagram in the baryon chemical potential-temperature plane and to locate the Critical End Point.

scholarly journals UNDERSTANDING MAGNETIC INSTABILITY IN GAPLESS SUPERCONDUCTORS

2006 ◽  
Vol 21 (04) ◽  
pp. 910-913 ◽  
Author(s):  
Mei Huang
Keyword(s):  
Superconducting State ◽  
Phase Fluctuation ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Bcs Theory ◽  
Magnetic Instability ◽  
Fermi Surfaces ◽  
Strong Phase ◽  
The Mean

Magnetic instability in gapless superconductors still remains as a puzzle. In this article, we point out that the instability might be caused by using BCS theory in mean-field approximation, where the phase fluctuation has been neglected. The mean-field BCS theory describes very well the strongly coherent or rigid superconducting state. With the increase of mismatch between the Fermi surfaces of pairing fermions, the phase fluctuation plays more and more important role, and "soften" the superconductor. The strong phase fluctuation will eventually quantum disorder the superconducting state, and turn the system into a phase-decoherent pseudogap state.

Quartetting in Fermionic Matter and Alpha-Particle Condensation in Nuclear Systems

2006 ◽  
Vol 21 (31n33) ◽  
pp. 2513-2546 ◽  
Author(s):  
G. Röpke ◽  
P. Schuck
Keyword(s):  
Nuclear Matter ◽  
Cluster Formation ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Density Region ◽  
Nuclear Matter Density ◽  
Nuclear Systems ◽  
The Mean ◽  
Finite Nuclei

Quantum condensates in nuclear matter are treated beyond the mean-field approximation, with the inclusion of cluster formation. The occurrence of a separate binding pole in the four-particle propagator in nuclear matter is investigated with respect to the formation of a condensate of α-like particles (quartetting), which is dependent on temperature and density. Due to Pauli blocking, the formation of an α-like condensate is limited to the low-density region. Consequences for finite nuclei are considered. In particular, excitations of self-conjugate 2n-Z–2n-N nuclei near the n-α-breakup threshold are candidates for quartetting. We review some results and discuss their consequences. Exploratory calculations are performed for the density dependence of the α condensate fraction at zero temperature to address the suppression of the four-particle condensate below nuclear-matter density.

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