CN112487616B - Construction method of dielectric constant physical model of electric field regulation dielectric based on LGD theory - Google Patents
Construction method of dielectric constant physical model of electric field regulation dielectric based on LGD theory Download PDFInfo
- Publication number
- CN112487616B CN112487616B CN202011292563.4A CN202011292563A CN112487616B CN 112487616 B CN112487616 B CN 112487616B CN 202011292563 A CN202011292563 A CN 202011292563A CN 112487616 B CN112487616 B CN 112487616B
- Authority
- CN
- China
- Prior art keywords
- polarization
- dielectric constant
- electric field
- dielectric
- dipole
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 230000005684 electric field Effects 0.000 title claims abstract description 43
- 230000033228 biological regulation Effects 0.000 title claims abstract description 16
- 238000010276 construction Methods 0.000 title abstract description 6
- 230000010287 polarization Effects 0.000 claims abstract description 66
- 238000000034 method Methods 0.000 claims description 5
- 230000007547 defect Effects 0.000 claims description 3
- 230000001419 dependent effect Effects 0.000 claims description 3
- 238000005315 distribution function Methods 0.000 claims description 3
- 238000013178 mathematical model Methods 0.000 abstract description 5
- 239000013078 crystal Substances 0.000 abstract description 2
- 230000000694 effects Effects 0.000 description 6
- 238000013461 design Methods 0.000 description 5
- 239000003989 dielectric material Substances 0.000 description 4
- 230000001105 regulatory effect Effects 0.000 description 4
- 230000003287 optical effect Effects 0.000 description 3
- 230000007423 decrease Effects 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 239000000463 material Substances 0.000 description 2
- 238000011160 research Methods 0.000 description 2
- 229910002367 SrTiO Inorganic materials 0.000 description 1
- 230000006978 adaptation Effects 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000001276 controlling effect Effects 0.000 description 1
- 238000004146 energy storage Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
- G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
- G16C60/00—Computational materials science, i.e. ICT specially adapted for investigating the physical or chemical properties of materials or phenomena associated with their design, synthesis, processing, characterisation or utilisation
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
Abstract
The invention relates to a construction method of a physical model of dielectric constant of an electric field regulation dielectric based on an LGD theory. In the model, the dielectric constant of the dielectric medium is respectively composed of an intrinsic polarization part and a redirection polarization part, free energy is unfolded into an intrinsic polarization term and a redirection polarization term from the LGD theory, the free energy is subjected to second derivative on the intrinsic polarization from the intrinsic polarization term to obtain a mathematical model between the intrinsic part of the dielectric constant and an electric field, the influence of a local random field is considered from the redirection polarization term, the mathematical model between the redirection polarization part of the dielectric constant and the electric field is obtained based on the dual-potential well model, and the dielectric constant part contributed by the intrinsic polarization term and the dielectric constant part contributed by the redirection polarization term are added to obtain a physical model of the total dielectric constant of the crystal and the electric field.
Description
Technical Field
The invention relates to a construction method of a dielectric constant physical model of an electric field regulation dielectric based on an LGD theory, which is suitable for design research of a new dielectric constant technology of the electric field regulation dielectric.
Technical Field
The dielectric medium has very wide application, and has the functional characteristics of piezoelectric effect, electrostriction effect, electro-optic effect, pyroelectric effect and the like, so that the dielectric medium is widely manufactured into devices such as transducers, sonar, optical switching light, electro-optic modulators, electro-optic phase shifters, thermoelectric sensors, energy storages and the like, and has been widely applied to the modern social industry and daily life. The dielectric constant of the dielectric medium is regulated by an electric field to play a key role in application, and along with the gradual increase of an external electric field applied to the dielectric medium, the dielectric constant can be increased and unchanged or even reduced under different systems, however, the regulating mechanism of the electric field on the dielectric constant is not completely clear, and a general physical model capable of explaining three experimental phenomena is lacking at present.
With the wide application of dielectrics in the practical industry and life, the phenomenon of regulating the dielectric constant of dielectrics by an electric field has attracted a great deal of attention from students. Chen et al, university of Alclen in 2004, was based on Landau-Ginzhurg-Devonshire @LGD) theory, based on the inherent polarization of the dielectric, the redirection of the polarized unit introduces the electric field to regulate the dielectric constant, successfully explaining the dielectric KTaO 3 And Bi-doped SrTiO 3 The experimental phenomenon that the dielectric constant is reduced along with the increase of the electric field can be only applied to a second-order phase change system, the phenomenon that the dielectric constant of a dielectric medium is reduced along with the increase of the electric field can be only explained, the experimental phenomenon that the dielectric constant of the dielectric medium is unchanged or increased along with the increase of the electric field can not be explained, and the model can not be applied to a first-order phase change system. Therefore, the research on the regulation and control mechanism of the electric field on the dielectric constant of the dielectric medium can not only deepen understanding the contribution mechanism of the microstructure on the dielectric constant and the essence of the regulation and control effect of the electric field on the dielectric constant, but also has positive significance for guiding the design of the dielectric material to realize the regulation and control effect of the electric field on the dielectric constant.
Disclosure of Invention
Aiming at the problem of accurate regulation and control dielectric constant mechanism of an electric field, a construction method of a dielectric constant physical model of the electric field regulation and control dielectric medium based on the LGD theory is provided, and a brand new approach is provided for understanding the mechanism of the electric field regulation and control dielectric constant and design materials.
The technical scheme of the invention is as follows:
a construction method of a dielectric constant physical model of an electric field regulation dielectric based on an LGD theory, wherein the dielectric constant of the physical model consists of an intrinsic polarization and a redirection polarization, the dielectric constant of the dielectric is contributed, and free energy is unfolded into an intrinsic polarization item and a redirection polarization item from the LGD theory:
wherein alpha is i ＝C(T-T 0 )＝1/ε(0)＝1/[ε 0 ε r (0)]Is a temperature dependent coefficient, C is a constant, T 0 Is Curie-Vis temperature, ε (0) is dielectric constant at zero field, ε 0 Is vacuum dielectric constant epsilon r (0) Is the relative dielectric constant at zero field, P isPolarization, β and γ are temperature independent coefficients.
G (P) first derivative of intrinsic polarization term to obtain
G (P) obtaining second derivative of inherent polarization term
In the case of a very small polarization of the dielectric, polarization P i Can be expressed as
P i ＝ε r (E)ε 0 E (18)
Equation (17) can be expressed as
Further simplified into
The reorientation polarization term is based on a dual-potential well model, assuming that the reorientation dipole elements can change between state 1 and state 2, and that the reorientation dipole elements are subjected to an external electric field E, the polarization electric field ηP generated by surrounding dipole elements 0 Eta is the generalized Lorentz factor, P, depending on the dipole lattice geometry 0 Is the polarization of the dipole unit and the random local field induced by defects, strain and the like, so the effective field received by the dipole unit is
E eff ＝E+ηP 0 -E local (21)
The dipole has a distribution function of
According to the principle of statistical mechanics, the number of dipole units in state 1 and state 2 is
Total polarization of
Due to P 0 Is small for redirection polarization and thus takes the approximate E eff ＝E-E local The above is simplified into
From the above, the dielectric constant of the redirected polarization contribution is obtained
That is to say,
the total dielectric constant of the dielectric is
ε total ＝ε i ε 0 +ε e (28)
The beneficial effects are that:
(1) The dielectric constant of the dielectric is clearly seen to be contributed by both intrinsic polarization and redirected polarization.
(2) More generic, it can be described that the dielectric constant of a dielectric increases with increasing electric field, and that the dielectric constant of a dielectric does not change or decreases with increasing electric field.
(3) By comparing the parameter differences corresponding to different rules of dielectric constant along with the change of the electric field, the key regulation and control function of the parameters can be clarified, and the design of the material can be guided according to the requirement.
Drawings
FIG. 1 is a schematic diagram of a physical model of the dielectric constant of an electric field regulation dielectric;
fig. 2 is a diagram of a local random field double potential well relaxation model.
Detailed description of the preferred embodiments
Based on LGD theory, the dielectric constant contribution of dielectrics is divided into intrinsic polarization contribution and redirected polarization, however, conventional theoretical models cannot successfully explain experimental phenomena that dielectric constants increase, do not change or even decrease with increasing electric field under different conditions, and thus it is necessary to improve the existing theoretical models to solve the difficulty. From the LGD theory, the free energy is unfolded into an intrinsic polarization term and a reorientation polarization term, and from the intrinsic polarization term, the free energy is subjected to second derivative on the intrinsic polarization to obtain a mathematical model between an intrinsic part of the dielectric constant and the electric field; starting from the redirection polarization term, considering the influence of a local random field, based on a local random field double-potential well model, obtaining a mathematical model between a redirection polarization part with a dielectric constant and an electric field, and summing the dielectric constant part contributed by the inherent polarization term and the dielectric constant part contributed by the redirection polarization term to obtain a physical model of the total dielectric constant of the crystal and the electric field. The mathematical model can be applied to devices such as optical switching, electro-optical modulators, optical deflectors and the like, and realizes high-performance device design according to a regulating and controlling mechanism of an electric field on dielectric constants. Based on this, the present invention provides a method for constructing a dielectric constant physical model of an electric field regulation dielectric based on LGD theory, please refer to fig. 1 and 2, in combination with the following implementation steps:
the dielectric constant of the dielectric consists of two parts, namely intrinsic polarization and redirection polarization, and from LGD theory, the free energy is unfolded into an intrinsic polarization term and a redirection polarization term:
wherein alpha is i ＝C(T-T 0 )＝1/ε(0)＝1/[ε 0 ε r (0)]Is a temperature dependent coefficient, C is a constant, T 0 Is Curie-Vis temperature, ε (0) is dielectric constant at zero field, ε 0 Is vacuum dielectric constant epsilon r (0) Is the relative permittivity at zero field, P is the polarization, and β and γ are temperature independent coefficients.
G (P) first derivative of intrinsic polarization term to obtain
G (P) obtaining second derivative of inherent polarization term
In the case of a very small polarization of the dielectric, polarization P i Can be expressed as
P i ＝ε r (E)ε 0 E (46)
Equation (45) can be expressed as
Further simplified into
The reorientation polarization term is based on a dual-potential well model, assuming that the reorientation dipole elements can change between state 1 and state 2, and that the reorientation dipole elements are subjected to an external electric field E, the polarization electric field ηP generated by surrounding dipole elements 0 Eta is the generalized Lorentz factor, P, depending on the dipole lattice geometry 0 Is the polarization of dipole unit and the random office induced by defect, strain, etcA field, so that the dipole element receives an effective field of
E eff ＝E+ηP 0 -E local (49)
The dipole has a distribution function of
According to the principle of statistical mechanics, the number of dipole units in state 1 and state 2 is
Total polarization of
Due to P 0 Is small for redirection polarization and thus takes the approximate E eff ＝E-E local The above is simplified into
From the above, the dielectric constant of the redirected polarization contribution is obtained
That is to say,
the total dielectric constant of the dielectric is
ε total ＝ε i ε 0 +ε e (56)
What is not described in detail in the present specification belongs to the prior art known to those skilled in the art. The foregoing is merely one embodiment of the invention, and it should be noted that modifications and adaptations to those skilled in the art may be made without departing from the principles of the present invention, which are intended to be comprehended within the scope of the present invention.
Claims (1)
1. A method for constructing a dielectric constant physical model of an electric field regulation dielectric based on LGD theory, characterized in that free energy is unfolded into an intrinsic polarization term and a reoriented polarization term from LGD theory:
wherein alpha is i ＝C(T-T 0 )＝1/ε(0)＝1/[ε 0 ε r (0)]Is a temperature-dependent coefficient, C is a constant, T is a temperature, T 0 Is Curie-Vis temperature, ε (0) is dielectric constant at zero field, ε 0 Is vacuum dielectric constant epsilon r (0) Is the relative dielectric constant under zero field, G 0 Is Gibbs free energy, P is the polarization in the dielectric, P i And P e Intrinsic and redirected polarization, respectively, beta i ，γ i And alpha e ，β e ，γ e Is a temperature independent coefficient;
g (P) is obtained by taking a first derivative of the intrinsic polarization term to obtain:
wherein E is the electric field; g (P) is obtained by taking the second derivative of the inherent polarization term, and the second derivative is obtained:
wherein ε r Is the relative dielectric constant; in the case of a very small polarization of the dielectric, polarization P i Can be expressed as
P i ＝ε r (E)ε 0 E (4)；
Equation (3) can be expressed as:
wherein ε is i Is the inherent dielectric constant epsilon i (0) Is the inherent dielectric constant, epsilon, at zero electric field i (E) Is the inherent dielectric constant under the action of an electric field, and is further simplified into:
the reorientation polarization term is based on a dual-potential well model, assuming that the reorientation dipole elements can change between state 1 and state 2, and that the reorientation dipole elements are subjected to an external electric field E, the polarization electric field ηP generated by surrounding dipole elements 0 Eta is the generalized Lorentz factor, P, depending on the dipole lattice geometry 0 Is the polarization of the dipole element, and the random local field E induced by defect and strain local The dipole element is thus subjected to an effective field E eff The method comprises the following steps:
E eff ＝E+ηP 0 -E local (7)；
the dipole's distribution function is:
wherein k is B Is Boltzmann constant, according to the principle of statistical mechanics, the number N of dipole units in state 1 and state 2 1 And N 2 The method comprises the following steps of:
the total polarization is:
where μ is the electric dipole moment, N is the total dipole element number, due to P 0 Is small for redirection polarization and thus takes the approximate E eff ＝E-E local The above is simplified as:
from the above, the dielectric constant ε of the redirected polarization contribution is obtained e ：
That is to say,
the dielectric total dielectric constant epsilon total The method comprises the following steps:
ε total ＝ε i ε 0 +ε e (17)。
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202011292563.4A CN112487616B (en) | 2020-11-18 | 2020-11-18 | Construction method of dielectric constant physical model of electric field regulation dielectric based on LGD theory |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202011292563.4A CN112487616B (en) | 2020-11-18 | 2020-11-18 | Construction method of dielectric constant physical model of electric field regulation dielectric based on LGD theory |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN112487616A CN112487616A (en) | 2021-03-12 |
| CN112487616B true CN112487616B (en) | 2024-04-09 |
Family
ID=74931496
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202011292563.4A Active CN112487616B (en) | 2020-11-18 | 2020-11-18 | Construction method of dielectric constant physical model of electric field regulation dielectric based on LGD theory |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112487616B (en) |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101696997A (en) * | 2009-10-26 | 2010-04-21 | 重庆大学 | Adaptive rapid determining method for multi-medium power frequency electric field distribution |
| CN106951603A (en) * | 2017-02-28 | 2017-07-14 | 上海电力学院 | PM2.5 arresting efficiency contribution rate curve-fitting methods based on POWER functions |
| CN106980710A (en) * | 2017-02-28 | 2017-07-25 | 上海电力学院 | ESP operating voltages contribution rate and magnetic induction intensity curve-fitting method |
| WO2017193092A1 (en) * | 2016-05-05 | 2017-11-09 | Yan Yongke | Giant piezoelectric voltage coefficient in grain oriented modified material |
| CN110908147A (en) * | 2019-11-04 | 2020-03-24 | 中国人民解放军战略支援部队航天工程大学 | Phase delay analysis method for electro-optic crystal under any incident condition |
| CN111025691A (en) * | 2019-11-04 | 2020-04-17 | 中国人民解放军战略支援部队航天工程大学 | Low-voltage large-view-field electro-optic modulator based on longitudinal electro-optic effect |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US8350444B2 (en) * | 2009-05-14 | 2013-01-08 | The Neothermal Energy Company | Method and apparatus for conversion of heat to electrical energy using polarizable materials and an internally generated poling field |
-
2020
- 2020-11-18 CN CN202011292563.4A patent/CN112487616B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101696997A (en) * | 2009-10-26 | 2010-04-21 | 重庆大学 | Adaptive rapid determining method for multi-medium power frequency electric field distribution |
| WO2017193092A1 (en) * | 2016-05-05 | 2017-11-09 | Yan Yongke | Giant piezoelectric voltage coefficient in grain oriented modified material |
| CN106951603A (en) * | 2017-02-28 | 2017-07-14 | 上海电力学院 | PM2.5 arresting efficiency contribution rate curve-fitting methods based on POWER functions |
| CN106980710A (en) * | 2017-02-28 | 2017-07-25 | 上海电力学院 | ESP operating voltages contribution rate and magnetic induction intensity curve-fitting method |
| CN110908147A (en) * | 2019-11-04 | 2020-03-24 | 中国人民解放军战略支援部队航天工程大学 | Phase delay analysis method for electro-optic crystal under any incident condition |
| CN111025691A (en) * | 2019-11-04 | 2020-04-17 | 中国人民解放军战略支援部队航天工程大学 | Low-voltage large-view-field electro-optic modulator based on longitudinal electro-optic effect |
Non-Patent Citations (8)
| Title |
|---|
| AR Damodaran and etc,..Three State Ferroelastic Switching and Large Electromechanical Responses in PbTiO3 Thin Films.Advanced Materials.2017,全文. * |
| dc electric-field dependence of the dielectric constant in polar dielectrics： Multipolarization mechanism model;Chen Ang and Zhi Yu;PHYSICAL REVIEW;全文 * |
| Nonlinear Dielectric Properties of PMN Relaxor Crystals within Landau-Ginzburg-Devonshire Approximation;J. Dec , S. Miga , W. Kleemann & B. Dkhil;Ferroelectrics;全文 * |
| Relaxor ferroelectric complex perovskites：structure，properties and phase transitions;ZG Ye;Key Engineering Materials;全文 * |
| Yi-De Liou and etc,..Deterministic optical control of room temperature multiferroicity in BiFeO3 thin films.natural materials.2019,全文. * |
| 二维铁电材料的理论研究进展;万文辉;刘畅;管闪;姚裕贵;;湘潭大学学报(自然科学版)(05);全文 * |
| 基于表面等离子体激元的新型金属光栅波导的研究;张建伟;蔡祥宝;连艳杰;;南京邮电大学学报(自然科学版)(05);全文 * |
| 掺杂BaFe12-xMxO19(M=Zr/Ti/Nb) 陶瓷的制备、电磁性能及低电场介电可调性研究;王敏;中国优秀硕士学位论文全文库;全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN112487616A (en) | 2021-03-12 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Rauls et al. | The effect of temperature on the large field electromechanical response of relaxor ferroelectric 8/65/35 PLZT | |
| Ruan et al. | Large Electro‐Optic Effect in La‐Doped 0.75 Pb (Mg1/3Nb2/3) O3–0.25 PbTiO3 Transparent Ceramic by Two‐Stage Sintering | |
| Chang et al. | Kovacs effect enhanced broadband large field of view electro-optic modulators in nanodisordered KTN crystals | |
| Liu et al. | Gate-tunable coherent perfect absorption of terahertz radiation in graphene | |
| Ray | Analysis of smart nanobeams integrated with a flexoelectric nano actuator layer | |
| CN112487616B (en) | Construction method of dielectric constant physical model of electric field regulation dielectric based on LGD theory | |
| Sun et al. | A phenomenological model on phase transitions in nanocrystalline barium titanate ceramic | |
| Hong et al. | Role of point defects in the formation of relaxor ferroelectrics | |
| Irzaman et al. | Optical and structural properties of lanthanum doped lithium niobate thin films | |
| Huang et al. | Improving strain in single crystal by composition-gradients design | |
| CN112350071A (en) | Reflective terahertz polarization converter | |
| John et al. | Tunable optical anisotropy in epitaxial phase-change VO2 thin films | |
| Thakur et al. | Effect of irradiation on pyroelectric and electrocaloric parameters in lead-free relaxor ferroelectric ceramic | |
| Chew et al. | Primary and secondary pyroelectric effects of ferroelectric 0-3 composites | |
| Shen et al. | Ultralow‐Power Piezo‐Optomechanically Tuning on CMOS‐Compatible Integrated Silicon‐Hafnium‐Oxide Platform | |
| Hoshyarmanesh et al. | Piezoelectric transducers on curved dispersive bending wave and poke-charged touch screens | |
| Wan et al. | Growth and optical properties of 0.62 Pb (Mg1/3Nb2/3) O3-0.38 PbTiO3 single crystals by a modified Bridgman technique | |
| Koruza | Transparent crystals with ultrahigh piezoelectricity | |
| Wu et al. | Zinc oxide (ZnO) hybrid metasurfaces exhibiting broadly tunable topological properties | |
| Lappalainen et al. | Characterization of optical properties of nanocrystalline doped PZT thin films | |
| Shim et al. | Controlling the infrared optical properties of rf-sputtered NiO films for applications of infrared window | |
| Wu et al. | Active KTaO3 hybrid terahertz metamaterial | |
| Mabuchi et al. | Transient thermal response of functionally graded piezoelectric laminates with an infinite row of parallel cracks normal to the bimaterial interface | |
| Gnawali et al. | Optical properties of titanium dioxide—vanadium dioxide multilayer thin-film structures | |
| US10788728B2 (en) | Light beam steering using electro-optical and conductive materials |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |