Microscopic Derivation of Free Energy Under Electric Field in Ferroelectric and Ferroelectric Heterostructures Containing Free Carriers

2006 ◽  
Vol 333 (1) ◽  
pp. 57-67 ◽  
Author(s):  
Yukio Watanabe
Author(s):  
Claudio Giorgi ◽  
Angelo Morro

AbstractThe purpose of the paper is to establish vector-valued rate-type models for the hysteretic properties in deformable ferroelectrics within the framework of continuum thermodynamics. Unlike electroelasticity and piezoelectricity, in ferroelectricity both the polarization and the electric field are simultaneously independent variables so that the constitutive functions depend on both. This viewpoint is naturally related to the fact that an hysteresis loop is a closed curve in the polarization–electric field plane. For the sake of generality, the deformation of the material and the dependence on the temperature are allowed to occur. The constitutive functions are required to be consistent with the principle of objectivity and the second law of thermodynamics. Objectivity implies that the constitutive equations are form invariant within the set of Euclidean frames. Among other results, the second law requires a general property on the relation between the polarization and the electric field via a differential equation. This equation shows a dependence fully characterized by two quantities: the free energy and a function which is related to the dissipative character of the hysteresis. As a consequence, different hysteresis models may have the same free energy. Models compatible with thermodynamics are then determined by appropriate selections of the free energy and of the dissipative part. Correspondingly, major and minor hysteretic loops are plotted.


Rare Metals ◽  
2007 ◽  
Vol 26 (5) ◽  
pp. 508-514
Author(s):  
J ZHANG ◽  
Z CHEN ◽  
Y WANG ◽  
B LIU ◽  
Y LI

Author(s):  
Setia Budi Sumandra ◽  
Bhisma Mahendra ◽  
Fahrudin Nugroho ◽  
Yusril Yusuf

Carbon nanotubes (CNTs) have benefits in various fields, they are disadvantageous due to their tendency to form aggregates and poorly controlled alignment of the CNT molecules (characterized by order parameters). These deficiencies can be overcome by dispersing the CNTs in nematic liquid crystal (LC) and placing the mixture under the influence of an electric field. In this study, Doi and Landau–de Gennes free energy density equations are used to analytically confirm that an electric field increases the order parameters of CNTs and LCs in a dispersion mixture. The anchoring strength of the nematic LC is also found to affect the order parameters of the CNTs and LC. Further, increasing the length-to-diameter ratio of the CNTs increases their alignment without affecting the LC alignment. These findings indicate that CNT molecular alignment can be controlled by adjusting the CNT length-to-diameter ratio, anchoring the LCs, and adjusting the electric field strength.


2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Jun-Yong Lee ◽  
Jeong-Seon Yu ◽  
Jong-Hyun Kim

Abstract Colloidal particles dispersed in nematic liquid crystals are aligned along the orientation that minimizes the elastic free energy. Through applying an electric field to a nematic colloidal system, the orientation of the director can change. Consequently, colloidal particles realign to minimize the total free energy, which is the sum of the elastic and electric free energies. Herein, we demonstrate that if the preferred rotation directions given by the electric and elastic free energies are different during realignment, the rotation direction of the particle can be controlled by how we apply the electric field. When the strength of the electric field gradually increases, the particles rotate in the same direction as the rotation of the director. However, when a sufficiently high electric field is suddenly applied, the particles rotate in the opposite direction. In this study, we analyzed the effect of free energy on the bidirectional rotation behavior of the particles using a theoretical model. This study provides an effective approach to control the rotational behavior of colloidal particles over a wide-angle range between two orientational local minima.


2007 ◽  
Vol 280-283 ◽  
pp. 1647-1650
Author(s):  
Guoliang Wang ◽  
Kai Ming Liang ◽  
Wei Liu ◽  
An Min Hu ◽  
Feng Zhou ◽  
...  

By means of SEM, the micro-morphology of silver particles separated from borosilicate glass by the heat-treatment with an electric field is investigated. The distribution of the silver particles appears clusters. This result is explained by an energy viewpoint. Based on hermodynamics theory of phase separation, the calculation of the free energy change during the heat-treatment in an electric field is performed by means of the Ansoft Maxwell software. The results of this calculation analysis are found to be very close to the experimental data.


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