1290:
554:
90:
441:, another key ferroelectric material, although the structure is rather similar to barium titanate the driving force for ferroelectricity is more complex with interactions between the lead and oxygen ions also playing an important role. In an order-disorder ferroelectric, there is a dipole moment in each unit cell, but at high temperatures they are pointing in random directions. Upon lowering the temperature and going through the phase transition, the dipoles order, all pointing in the same direction within a domain.
82:
239:. Sabatier principle states that the surface-adsorbates interaction has to be an optimal amount: not too weak to be inert toward the reactants and not too strong to poison the surface and avoid desorption of the products: a compromise situation. This set of optimum interactions is usually referred to as "top of the volcano" in activity volcano plots. On the other hand, ferroelectric polarization-dependent chemistry can offer the possibility of switching the surface—adsorbates interaction from strong
1285:{\displaystyle {\begin{array}{ll}\Delta E=&{\frac {1}{2}}\alpha _{0}\left(T-T_{0}\right)\left(P_{x}^{2}+P_{y}^{2}+P_{z}^{2}\right)+{\frac {1}{4}}\alpha _{11}\left(P_{x}^{4}+P_{y}^{4}+P_{z}^{4}\right)\\&+{\frac {1}{2}}\alpha _{12}\left(P_{x}^{2}P_{y}^{2}+P_{y}^{2}P_{z}^{2}+P_{z}^{2}P_{x}^{2}\right)\\&+{\frac {1}{6}}\alpha _{111}\left(P_{x}^{6}+P_{y}^{6}+P_{z}^{6}\right)\\&+{\frac {1}{2}}\alpha _{112}\left\\&+{\frac {1}{2}}\alpha _{123}P_{x}^{2}P_{y}^{2}P_{z}^{2}\end{array}}}
74:
483:, and the prediction could immediately be verified by several observations of behavior connected to ferroelectricity in smectic liquid-crystal phases that are chiral and tilted. The technology allows the building of flat-screen monitors. Mass production between 1994 and 1999 was carried out by Canon. Ferroelectric liquid crystals are used in production of reflective
282:
surface charge. This can cause current flow in the case of a ferroelectric capacitor even without the presence of an external voltage across the capacitor. Two stimuli that will change the lattice dimensions of a material are force and temperature. The generation of a surface charge in response to the application of an external stress to a material is called
217:) in which a contact is made up by nanometer-thick ferroelectric film placed between metal electrodes. The thickness of the ferroelectric layer is small enough to allow tunneling of electrons. The piezoelectric and interface effects as well as the depolarization field may lead to a giant electroresistance (GER) switching effect.
2933:
452:
lead zirconate. Different compositions are used for different applications; for memory applications, PZT closer in composition to lead titanate is preferred, whereas piezoelectric applications make use of the diverging piezoelectric coefficients associated with the morphotropic phase boundary that is
281:
The internal electric dipoles of a ferroelectric material are coupled to the material lattice so anything that changes the lattice will change the strength of the dipoles (in other words, a change in the spontaneous polarization). The change in the spontaneous polarization results in a change in the
205:
make ferroelectric capacitors very useful, e.g. for sensor applications. Ferroelectric capacitors are used in medical ultrasound machines (the capacitors generate and then listen for the ultrasound ping used to image the internal organs of a body), high quality infrared cameras (the infrared image is
177:
simply consists of a pair of electrodes sandwiching a layer of ferroelectric material. The permittivity of ferroelectrics is not only adjustable but commonly also very high, especially when close to the phase transition temperature. Because of this, ferroelectric capacitors are small in physical size
193:
cards. In these applications thin films of ferroelectric materials are typically used, as this allows the field required to switch the polarization to be achieved with a moderate voltage. However, when using thin films a great deal of attention needs to be paid to the interfaces, electrodes and
1723:
3125:
1948:
4544:
Wanlin Zhu, John Hayden, Fan He, Jung-In Yang, Pannawit
Tipsawat, Mohammad D. Hossain, Jon-Paul Maria, and Susan Trolier-McKinstry, "Strongly temperature dependent ferroelectric switching in AlN, Al1-xScxN, and Al1-xBxN thin films", Appl. Phys. Lett. 119, 062901 (2021)
234:
of these materials. Surface-perpendicular component of the ferroelectric polarization can dope polarization-dependent charges on surfaces of ferroelectric materials, changing their chemistry. This opens the possibility of performing catalysis beyond the limits of the
4594:
4681:
Cao, Yanwei; Wang, Zhen; Park, Se Young; Yuan, Yakun; Liu, Xiaoran; Nikitin, Sergey M.; Akamatsu, Hirofumi; Kareev, M.; Middey, S.; Meyers, D.; Thompson, P.; Ryan, P. J.; Shafer, Padraic; N’Diaye, A.; Arenholz, E.; Gopalan, Venkatraman; Zhu, Yimei;
3260:
4392:
Benke, Annegret; Mehner, Erik; Rosenkranz, Marco; Dmitrieva, Evgenia; Leisegang, Tilmann; Stöcker, Hartmut; Pompe, Wolfgang; Meyer, Dirk C. (30 July 2015). "Pyroelectrically Driven •OH Generation by Barium
Titanate and Palladium Nanoparticles".
437:. This leads to an asymmetrical shift in the equilibrium ion positions and hence to a permanent dipole moment. The ionic displacement in barium titanate concerns the relative position of the titanium ion within the oxygen octahedral cage. In
206:
projected onto a two dimensional array of ferroelectric capacitors capable of detecting temperature differences as small as millionths of a degree
Celsius), fire sensors, sonar, vibration sensors, and even fuel injectors on diesel engines.
2259:
2752:
2714:
3356:). Elimination of this region, and connection of the top and bottom portions of the 'S' curve by vertical lines at the discontinuities gives the hysteresis loop of internal polarization due to an external electric field.
1565:
2959:
158:) and are paraelectric above this temperature: the spontaneous polarization vanishes, and the ferroelectric crystal transforms into the paraelectric state. Many ferroelectrics lose their pyroelectric properties above
3354:
2119:
2583:
1801:
429:, a typical ferroelectric of the displacive type, the transition can be understood in terms of a polarization catastrophe, in which, if an ion is displaced from equilibrium slightly, the force from the local
2420:
1388:
132:
by a suitably strong applied electric field in the opposite direction; the polarization is therefore dependent not only on the current electric field but also on its history, yielding a
3364:
Sliding ferroelectricity is widely found but only in two-dimensional (2D) van der Waals stacked layers. The vertical electric polarization is switched by in-plane interlayer sliding.
524:
It should be possible to produce materials which combine both ferroelectric and metallic properties simultaneously, at room temperature. According to research published in 2018 in
1477:
1543:
1510:
1444:
3133:
2619:
224:, where researchers are looking for ways to couple magnetic and ferroelectric ordering within a material or heterostructure; there are several recent reviews on this topic.
1394:. Typically, this involves adding a gradient term, an electrostatic term and an elastic term to the free energy. The equations are then discretized onto a grid using the
230:
properties of ferroelectrics have been studied since 1952 when
Parravano observed anomalies in CO oxidation rates over ferroelectric sodium and potassium niobates near the
1766:
1390:
must be consistent with the crystal symmetry. To investigate domain formation and other phenomena in ferroelectrics, these equations are often used in the context of a
2149:
1793:
528:, scientists were able to produce a two-dimensional sheet of material which was both ferroelectric (had a polar crystal structure) and which conducted electricity.
2928:{\displaystyle \Delta E={\frac {1}{2}}\alpha _{0}\left(T-T_{0}\right)P_{x}^{2}+{\frac {1}{4}}\alpha _{11}P_{x}^{4}+{\frac {1}{6}}\alpha _{111}P_{x}^{6}-E_{x}P_{x}}
4103:
Kolpak, Alexie M.; Grinberg, Ilya; Rappe, Andrew M. (2007-04-16). "Polarization
Effects on the Surface Chemistry of $ {\mathrm{PbTiO}}_{3}$ -Supported Pt Films".
502:" properties, and may have wide-ranging applications in device and nano-technology and also influence the electrical nature of dust in the interstellar medium.
57:, meaning iron, was used to describe the property despite the fact that most ferroelectric materials do not contain iron. Materials that are both ferroelectric
4217:
Laursen, Anders B.; Man, Isabela
Costinela; Trinhammer, Ole L.; Rossmeisl, Jan; Dahl, Søren (December 2011). "The Sabatier Principle Illustrated by Catalytic H
2627:
263:
effects under varying temperature (heating/cooling cycles) or varying strain (vibrations) conditions extra charges can appear on the surface and drive various
1718:{\displaystyle \Delta E={\frac {1}{2}}\alpha _{0}\left(T-T_{0}\right)P_{x}^{2}+{\frac {1}{4}}\alpha _{11}P_{x}^{4}+{\frac {1}{6}}\alpha _{111}P_{x}^{6}}
4986:
4981:
3120:{\displaystyle {\frac {\partial \Delta E}{\partial P_{x}}}=\alpha _{0}\left(T-T_{0}\right)P_{x}+\alpha _{11}P_{x}^{3}+\alpha _{111}P_{x}^{5}-E_{x}=0}
117:, corresponding to the slope of the polarization curve, is not constant as in linear dielectrics but is a function of the external electric field.
5007:
3294:
1956:
197:
Ferroelectric materials are required by symmetry considerations to be also piezoelectric and pyroelectric. The combined properties of memory,
4941:
1943:{\displaystyle {\frac {\partial \Delta E}{\partial P_{x}}}=\alpha _{0}\left(T-T_{0}\right)P_{x}+\alpha _{11}P_{x}^{3}+\alpha _{111}P_{x}^{5}}
1479:. These coefficients may be obtained experimentally or from ab-initio simulations. For ferroelectrics with a first order phase transition,
1559:
of a ferroelectric for a cubic to tetragonal phase transition may be obtained by considering the 1D expression of the free energy which is:
4641:
2431:
2425:
and eliminating solutions which take the square root of a negative number (for either the first or second order phase transitions) gives:
273:
is a technique to record optical information on pieces of ferroelectric material. The images are nonvolatile and selectively erasable.
148:
109:; so the polarization is a linear function. This is called linear dielectric polarization (see figure). Some materials, known as
3810:
M.Ye. Zhuravlev; R.F. Sabirianov; S.S. Jaswal; E.Y. Tsymbal (2005). "Giant
Electroresistance in Ferroelectric Tunnel Junctions".
2270:
4260:
Seh, Zhi Wei; Kibsgaard, Jakob; Dickens, Colin F.; Chorkendorff, Ib; Nørskov, Jens K.; Jaramillo, Thomas F. (13 January 2017).
4894:
4875:
4853:
4524:
4420:
Kakekhani, Arvin; Ismail-Beigi, Sohrab (2016). "Ferroelectric oxide surface chemistry: water splitting via pyroelectricity".
3737:
3582:
3557:
1768:, the spontaneous polarization. We find the derivative of the free energy, and set it equal to zero in order to solve for
1331:
305:. Among the piezoelectric classes, 10 have a spontaneous electric polarization which varies with temperature; thus they are
4667:
540:, the free energy of a ferroelectric material, in the absence of an electric field and applied stress may be written as a
247:, thus a compromise between desorption and adsorption is no longer needed. Ferroelectric polarization can also act as an
173:
The nonlinear nature of ferroelectric materials can be used to make capacitors with adjustable capacitance. Typically, a
4261:
37:, with the additional property that their natural electrical polarization is reversible. The term is used in analogy to
3712:
4558:
Clark, Noel A.; Lagerwall, Sven T. (June 1980). "Submicrosecond bistable electro‐optic switching in liquid crystals".
4934:
4368:
309:. Ferroelectricity is a subset of pyroelectricity, which brings spontaneous electronic polarization to the material.
5012:
4645:
4612:
3545:
3378:
4138:
Yun, Yang; Altman, Eric I. (December 2007). "Using
Ferroelectric Poling to Change Adsorption on Oxide Surfaces".
548:. If a sixth order expansion is used (i.e. 8th order and higher terms truncated), the free energy is given by:
147:
Typically, materials demonstrate ferroelectricity only below a certain phase transition temperature, called the
3404:
120:
In addition to being nonlinear, ferroelectric materials demonstrate a spontaneous nonzero polarization (after
5017:
3517:
4927:
491:
316:
286:. A change in the spontaneous polarization of a material in response to a change in temperature is called
1449:
3410:
3255:{\displaystyle E_{x}=\alpha _{0}\left(T-T_{0}\right)P_{e}+\alpha _{11}P_{e}^{3}+\alpha _{111}P_{e}^{5}}
1515:
1482:
537:
409:
270:
1416:
5022:
2591:
185:
effect which can be used as a memory function, and ferroelectric capacitors are indeed used to make
3466:
1395:
29:
that can be reversed by the application of an external electric field. All ferroelectrics are also
4776:"Sliding ferroelectricity in 2D van der Waals materials: Related physics and future opportunities"
4613:"Pyroelectric Materials for Uncooled Infrared Detectors: Processing, Properties, and Applications"
498:
or propane exhibited ferroelectric properties. This new class of ferroelectric materials exhibit "
128:
is zero. The distinguishing feature of ferroelectrics is that the spontaneous polarization can be
4914:
3383:
1731:
510:
445:
367:
174:
4611:
Aggarwal, M.D.; A.K. Batra; P. Guggilla; M.E. Edwards; B.G. Penn; J.R. Currie Jr. (March 2010).
3288:
461:
298:
2254:{\displaystyle \alpha _{0}\left(T-T_{0}\right)+\alpha _{11}P_{s}^{2}+\alpha _{111}P_{s}^{4}=0}
3902:
W. Eerenstein; N.D. Mathur; J.F. Scott (2006). "Multiferroic and magnetoelectric materials".
3398:
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3700:
3681:
3644:
3612:
3502:
3446:
3428: – Electrically insulating substance able to be polarised by an applied electric field
1771:
417:
Ferroelectric phase transitions are often characterized as either displacive (such as BaTiO
98:
26:
448:(PZT), which is part of the solid solution formed between ferroelectric lead titanate and
8:
2709:{\displaystyle P_{s}=\pm {\sqrt{\frac {\alpha _{0}\left(T_{0}-T\right)}{\alpha _{111}}}}}
1728:
This free energy has the shape of a double well potential with two free energy minima at
252:
23:
4791:
4713:
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4193:
4079:
4040:
3997:
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3833:
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3616:
301:
can be found in crystals. There are 21 non-centrosymmetric classes, within which 20 are
4823:
4810:
4775:
4754:
4730:
4699:
4687:
4374:
4292:
4027:
Parravano, G. (February 1952). "Ferroelectric
Transitions and Heterogenous Catalysis".
4009:
3974:
3935:
3845:
3819:
3792:
3766:
3511:
1391:
506:
449:
236:
4310:
Zhang, Yan; Xie, Mengying; Adamaki, Vana; Khanbareh, Hamideh; Bowen, Chris R. (2017).
165:
completely, because their paraelectric phase has a centrosymmetric crystal structure.
4890:
4887:
Effective Field
Approach to Phase Transitions and Some Applications to Ferroelectrics
4871:
4849:
4827:
4815:
4735:
4520:
4470:
4378:
4364:
4333:
4312:"Control of electro-chemical processes using energy harvesting materials and devices"
4296:
4284:
4262:"Combining theory and experiment in electrocatalysis: Insights into materials design"
4155:
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4013:
4005:
3978:
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3733:
3708:
3578:
3553:
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1407:
514:
388:
264:
248:
231:
186:
3849:
3487: – materials that exhibit more than one of the primary ferroic order parameters
4805:
4795:
4725:
4717:
4595:"Novel ferroelectric behaviour of N2O films: spontaneous potentials of up to 40 V."
4575:
4512:
4460:
4429:
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4197:
4147:
4112:
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473:
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198:
45:. Ferromagnetism was already known when ferroelectricity was discovered in 1920 in
30:
4116:
3841:
425:), though often phase transitions will demonstrate elements of both behaviors. In
113:
materials, show a more enhanced nonlinear polarization (see figure). The electric
4966:
4516:
4449:"Piezopotential-Driven Redox Reactions at the Surface of Piezoelectric Materials"
3451:
3440:
3425:
480:
434:
426:
374:
348:
306:
287:
256:
202:
110:
42:
34:
4351:
Fang, Liang; You, Lu; Liu, Jun-Ming (2018). "Ferroelectrics in Photocatalysis".
89:
4721:
4504:
4088:
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1403:
499:
469:
430:
327:
81:
50:
38:
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541:
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62:
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3437: – Electric charge generated in certain solids due to mechanical stress
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4448:
4337:
4288:
4159:
4124:
3970:
3931:
3896:
3656:
3624:
433:
due to the ions in the crystal increases faster than the elastic-restoring
114:
4753:
P. Chandra; P.B. Littlewood (2006). "A Landau Primer for Ferroelectrics".
73:
4950:
4759:
4610:
4064:"Ferroelectrics: A pathway to switchable surface chemistry and catalysis"
3949:; Fiebig, M. (2005). "The renaissance of magnetoelectric multiferroics".
3824:
3771:
3472:
294:
3923:
3665:
3349:{\displaystyle {\frac {\partial ^{2}\Delta E}{\partial P_{x}^{2}}}<0}
2114:{\displaystyle 0={\frac {\partial \Delta E}{\partial P_{x}}}=P_{s}\left}
517:. A single atom thick ferroelectric monolayer can be created using pure
178:
compared to dielectric (non-tunable) capacitors of similar capacitance.
105:, is almost exactly proportional to the applied external electric field
4961:
4433:
4328:
4311:
4062:
Kakekhani, Arvin; Ismail-Beigi, Sohrab; Altman, Eric I. (August 2016).
3481: – An inorganic, nonmetallic solid prepared by the action of heats
3454: – phenomenon in which a material may exhibit a spontaneous strain
3401: – Group of crystalline polar polymers that are also ferroelectric
3279:(but on the Y axis) gives an S-shaped curve which is multi-valued in P
2727:) may be obtained from the free energy expansion by including the term
398:
394:
244:
240:
182:
133:
4919:
4246:
4151:
4048:
3888:
227:
4579:
4546:
3632:
3600:
3548:. In Frederick Seitz; T. P. Das; David Turnbull; E. L. Hahn (eds.).
2578:{\displaystyle P_{s}=\pm {\sqrt {{\frac {1}{2\alpha _{111}}}\left}}}
479:
In 1974 R.B. Meyer used symmetry arguments to predict ferroelectric
4704:
3575:
Principles and applications of ferroelectrics and related materials
457:
3901:
3757:; J.F. Scott (2005). "Physics of thin-film ferroelectric oxides".
181:
The spontaneous polarization of ferroelectric materials implies a
4505:"Piezoelectric and Pyroelectric Materials and Their Applications"
3478:
2949:, again by setting the derivative of the energy with respect to P
518:
4668:"Rutgers Physicists Create New Class of 2D Artificial Materials"
3697:
Piezoelectric and acoustic materials for transducer applications
4259:
3867:(2007). "Multiferroics: Progress and prospects in thin films".
2738:
corresponding to the energy due to an external electric field E
405:
4391:
2132:
solution of this equation rather corresponds to a free energy
4503:
Whatmore, R. W. (1991), Miller, L. S.; Mullin, J. B. (eds.),
4216:
4178:"Ferroelectric-Based Catalysis: Switchable Surface Chemistry"
536:
An introduction to Landau theory can be found here. Based on
476:
in some ferroelectric crystals is still not well understood.
4688:"Artificial two-dimensional polar metal at room temperature"
3752:
3287:. The central part of the 'S' corresponds to a free energy
2621:, the solution for the spontaneous polarization reduces to:
4619:
4447:
Starr, Matthew B.; Shi, Jian; Wang, Xudong (11 June 2012).
4061:
3984:
M. Fiebig (2005). "Revival of the magnetoelectric effect".
484:
190:
4642:"Discovery of ferroelectricity in an elementary substance"
4490:
McGraw-Hill Concise Encyclopedia of Science and Technology
2415:{\displaystyle P_{s}^{2}={\frac {1}{2\alpha _{111}}}\left}
251:. Polarization can help the separation of photo-generated
4752:
4598:
Poster Session Presented at ECAMP 2010, Salamanca, Spain.
4846:
Domain Structure in Ferroelectrics and Related Materials
4309:
3407: – Microscopy technique for piezoelectric materials
444:
An important ferroelectric material for applications is
4176:
Kakekhani, Arvin; Ismail-Beigi, Sohrab (29 June 2015).
3507:
Pages displaying short descriptions of redirect targets
3430:
Pages displaying short descriptions of redirect targets
3413: – Imaging technique using ferroelectric materials
3633:"Piezo-Electric and Allied Phenomena in Rochelle Salt"
3475: – Solid-state electronics based on electron spin
2136:
in the ferroelectric phase, the desired solutions for
1383:{\displaystyle \alpha _{i},\alpha _{ij},\alpha _{ijk}}
4419:
4175:
3699:. Springer Science & Business Media. p. 21.
3601:"Piezoelectric and allied phenomena in Rochelle salt"
3297:
3136:
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2630:
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1959:
1804:
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1734:
1568:
1518:
1485:
1452:
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are the components of the polarization vector in the
557:
22:
is a characteristic of certain materials that have a
3489:
Pages displaying wikidata descriptions as a fallback
3456:
Pages displaying wikidata descriptions as a fallback
3388:
Pages displaying wikidata descriptions as a fallback
2143:
correspond to setting the remaining factor to zero:
346:
333:
136:
loop. They are called ferroelectrics by analogy to
4102:
3386: – capacitor based on a ferroelectric material
255:, leading to enhanced photocatalysis. Also, due to
4488:Land, Cecil (2004). "Photoferroelectric imaging".
3505: – Phenomena involving electrical occurrences
3348:
3254:
3119:
2927:
2708:
2613:
2577:
2414:
2253:
2113:
1942:
1787:
1760:
1717:
1537:
1504:
1471:
1438:
1382:
1284:
4999:
4884:
3572:
3514: – Overview of and topical guide to physics
3443: – Voltage created when a crystal is heated
4868:Physics of Ferroelectrics: A modern perspective
4780:Proceedings of the National Academy of Sciences
4680:
4353:Ferroelectric Materials for Energy Applications
1328:directions respectively, and the coefficients,
16:Characteristic of certain crystalline materials
4843:
4557:
4509:Electronic Materials: From Silicon to Organics
494:found that prosaic films of chemicals such as
4935:
4511:, Boston, MA: Springer US, pp. 283–290,
3945:
3862:
3543:
3463: – Polarization due to a strain gradient
194:sample quality for devices to work reliably.
4866:; Jean-Marc Triscone; Charles H Ahn (2007).
4446:
3359:
2938:We find the stable polarization values of P
505:Other ferroelectric materials used include
41:, in which a material exhibits a permanent
4942:
4928:
4746:
4350:
3727:
3630:
3598:
3552:. Vol. 4. Academic Press. p. 5.
2567:
2406:
124:, see figure) even when the applied field
4809:
4799:
4758:
4729:
4703:
4464:
4327:
4201:
4137:
4087:
4026:
3983:
3823:
3770:
3664:
2943:under the influence of the external field
1402:and solved subject to the constraints of
4774:Wu, Menghao; Li, Ju (14 December 2021).
4604:
4502:
4140:Journal of the American Chemical Society
357:
352:
341:
339:
88:
80:
72:
4949:
4453:Angewandte Chemie International Edition
3856:
3546:"Ferroelectrics and Antiferroelectrics"
209:Another idea of recent interest is the
5008:Electric and magnetic fields in matter
5000:
4592:
3694:
3679:Chiang, Y. et al.: Physical Ceramics,
3591:
453:found close to the 50/50 composition.
220:Yet another burgeoning application is
144:and exhibit similar hysteresis loops.
4923:
4551:
4171:
4169:
3986:Journal of Physics D: Applied Physics
3746:
3395: – Novel type of computer memory
1545:for a second order phase transition.
4773:
4492:(5 ed.). New York: McGraw-Hill.
4487:
4481:
3721:
3566:
3537:
3372:
4395:The Journal of Physical Chemistry C
2742:interacting with the polarization P
13:
4837:
4686:; Chakhalian, J. (18 April 2018).
4225:Decomposition on Metal Surfaces".
4166:
3803:
3319:
3311:
3302:
2977:
2969:
2966:
2756:
1980:
1972:
1969:
1819:
1811:
1808:
1569:
1472:{\displaystyle \alpha _{111}>0}
562:
140:materials, which have spontaneous
14:
5034:
4904:
4547:https://doi.org/10.1063/5.0057869
3272:(on the X axis) as a function of
1538:{\displaystyle \alpha _{11}>0}
1505:{\displaystyle \alpha _{11}<0}
544:in terms of the order parameter,
421:) or order-disorder (such as NaNO
4646:National University of Singapore
4422:Journal of Materials Chemistry A
3379:Category:Ferroelectric materials
1439:{\displaystyle \alpha _{0}>0}
4767:
4674:
4660:
4634:
4586:
4538:
4496:
4440:
4413:
4385:
4344:
4303:
4253:
4210:
4131:
4096:
4055:
4029:The Journal of Chemical Physics
4020:
168:
68:
4848:. Cambridge University Press.
4600:– via Aarhus University.
3688:
3673:
3405:Piezoresponse force microscopy
2614:{\displaystyle \alpha _{11}=0}
77:Linear dielectric polarization
1:
4227:Journal of Chemical Education
4117:10.1103/PhysRevLett.98.166101
3842:10.1103/PhysRevLett.94.246802
3531:
3518:Index of electronics articles
1413:In all known ferroelectrics,
211:ferroelectric tunnel junction
4517:10.1007/978-1-4615-3818-9_19
472:crystals. The nature of the
360:
311:
276:
101:, the polarization induced,
7:
3577:. Clarendon Press, Oxford.
3573:M. Lines; A. Glass (1979).
3367:
1761:{\displaystyle P_{x}=P_{s}}
466:domain structure hysteresis
265:(electro)chemical reactions
61:ferromagnetic are known as
10:
5039:
4722:10.1038/s41467-018-03964-9
4089:10.1016/j.susc.2015.10.055
4006:10.1088/0022-3727/38/8/R01
3789:10.1103/RevModPhys.77.1083
3411:Photoferroelectric imaging
271:Photoferroelectric imaging
93:Ferroelectric polarization
4957:
4885:Julio A. Gonzalo (2006).
4361:10.1002/9783527807505.ch9
3759:Reviews of Modern Physics
3469: – Branch of physics
531:
322:
314:
293:Generally, there are 230
85:Paraelectric polarization
4407:10.1021/acs.jpcc.5b04589
4316:Chemical Society Reviews
4203:10.1021/acscatal.5b00507
3467:Condensed matter physics
3360:Sliding ferroelectricity
1550:spontaneous polarization
1396:finite difference method
97:When most materials are
5013:Ferroelectric materials
4915:University of Cambridge
4911:Ferroelectric Materials
4844:A. S. Sidorkin (2006).
4801:10.1073/pnas.2115703118
4593:Plekan, Oksana (2010).
4560:Applied Physics Letters
4281:10.1126/science.aad4998
4105:Physical Review Letters
3963:10.1126/science.1113357
3812:Physical Review Letters
3384:Ferroelectric capacitor
511:polyvinylidene fluoride
462:transition temperatures
446:lead zirconate titanate
175:ferroelectric capacitor
4466:10.1002/anie.201201424
3730:Ferroelectric Memories
3695:Safari, Ahmad (2008).
3657:10.1103/PhysRev.17.475
3625:10.1103/PhysRev.15.505
3544:Werner Känzig (1957).
3350:
3256:
3121:
2929:
2719:The hysteresis loop (P
2710:
2615:
2579:
2416:
2255:
2115:
1944:
1789:
1762:
1719:
1539:
1506:
1473:
1440:
1384:
1286:
538:Ginzburg–Landau theory
323:21 noncentrosymmetric
99:electrically polarized
94:
86:
78:
4692:Nature Communications
3682:John Wiley & Sons
3399:Ferroelectric polymer
3351:
3257:
3122:
2930:
2711:
2616:
2580:
2417:
2256:
2116:
1945:
1790:
1788:{\displaystyle P_{s}}
1763:
1720:
1540:
1507:
1474:
1441:
1400:finite element method
1385:
1287:
526:Nature Communications
92:
84:
76:
27:electric polarization
5018:Electrical phenomena
4977:antiferroelectricity
4889:. World Scientific.
4355:. pp. 265–309.
3503:Electrical phenomena
3447:Antiferroelectricity
3295:
3283:for some values of E
3134:
2960:
2753:
2628:
2592:
2432:
2271:
2150:
1957:
1802:
1772:
1732:
1566:
1516:
1483:
1450:
1417:
1332:
555:
4951:Polarization states
4792:2021PNAS..11815703W
4786:(50): e2115703118.
4714:2018NatCo...9.1547C
4572:1980ApPhL..36..899C
4401:(32): 18278–18286.
4239:2011JChEd..88.1711L
4194:2015APS..MARY26011K
4146:(50): 15684–15689.
4080:2016SurSc.650..302K
4041:1952JChPh..20..342P
3998:2005JPhD...38R.123F
3924:10.1038/nature05023
3916:2006Natur.442..759E
3881:2007NatMa...6...21R
3834:2005PhRvL..94x6802Z
3781:2005RvMP...77.1083D
3728:J.F. Scott (2000).
3705:2008pamt.book.....S
3649:1921PhRv...17..475V
3631:J. Valasek (1921).
3617:1920PhRv...15..505.
3599:J. Valasek (1920).
3550:Solid State Physics
3336:
3251:
3223:
3097:
3069:
2901:
2863:
2825:
2512:
2351:
2288:
2264:whose solution is:
2244:
2216:
2105:
2077:
1939:
1911:
1714:
1676:
1638:
1277:
1262:
1247:
1194:
1176:
1156:
1133:
1115:
1095:
1072:
1054:
1034:
981:
963:
945:
892:
877:
859:
844:
826:
811:
758:
740:
722:
674:
656:
638:
460:often show several
317:Crystalline classes
299:crystalline classes
253:electron-hole pairs
53:. Thus, the prefix
4434:10.1039/C6TA00513F
4329:10.1039/c7cs00387k
4275:(6321): eaad4998.
3512:Outline of physics
3346:
3322:
3252:
3237:
3209:
3117:
3083:
3055:
2945:, now denoted as P
2925:
2887:
2849:
2811:
2706:
2611:
2575:
2498:
2412:
2337:
2274:
2251:
2230:
2202:
2111:
2091:
2063:
1940:
1925:
1897:
1785:
1758:
1715:
1700:
1662:
1624:
1535:
1502:
1469:
1436:
1380:
1282:
1280:
1263:
1248:
1233:
1180:
1162:
1142:
1119:
1101:
1081:
1058:
1040:
1020:
967:
949:
931:
878:
863:
845:
830:
812:
797:
744:
726:
708:
660:
642:
624:
507:triglycine sulfate
450:anti-ferroelectric
361:non ferroelectric
342:non piezoelectric
237:Sabatier principle
189:for computers and
95:
87:
79:
4995:
4994:
4896:978-981-256-875-5
4877:978-3-540-34591-6
4855:978-1-904602-14-9
4526:978-1-4615-3818-9
4459:(24): 5962–5966.
4428:(14): 5235–5246.
4322:(24): 7757–7786.
4247:10.1021/ed101010x
4233:(12): 1711–1715.
4152:10.1021/ja0762644
4049:10.1063/1.1700412
3739:978-3-540-66387-4
3584:978-0-19-851286-8
3559:978-0-12-607704-9
3528:
3527:
3393:Ferroelectric RAM
3338:
2991:
2875:
2837:
2773:
2704:
2698:
2573:
2565:
2473:
2404:
2312:
1994:
1833:
1688:
1650:
1586:
1408:Linear elasticity
1392:phase field model
1221:
1003:
914:
780:
691:
581:
515:lithium tantalate
415:
414:
353:non pyroelectric
232:Curie temperature
187:ferroelectric RAM
149:Curie temperature
5030:
5023:Phases of matter
4987:ferrielectricity
4972:ferroelectricity
4944:
4937:
4930:
4921:
4920:
4900:
4881:
4859:
4832:
4831:
4813:
4803:
4771:
4765:
4764:
4762:
4760:cond-mat/0609347
4750:
4744:
4743:
4733:
4707:
4678:
4672:
4671:
4664:
4658:
4657:
4655:
4653:
4638:
4632:
4631:
4629:
4627:
4617:
4608:
4602:
4601:
4590:
4584:
4583:
4555:
4549:
4542:
4536:
4535:
4534:
4533:
4500:
4494:
4493:
4485:
4479:
4478:
4468:
4444:
4438:
4437:
4417:
4411:
4410:
4389:
4383:
4382:
4348:
4342:
4341:
4331:
4307:
4301:
4300:
4266:
4257:
4251:
4250:
4214:
4208:
4207:
4205:
4188:(8): 4537–4545.
4173:
4164:
4163:
4135:
4129:
4128:
4100:
4094:
4093:
4091:
4059:
4053:
4052:
4024:
4018:
4017:
3982:
3943:
3910:(7104): 759–65.
3900:
3889:10.1038/nmat1805
3869:Nature Materials
3860:
3854:
3853:
3827:
3825:cond-mat/0502109
3818:(24): 246802–4.
3807:
3801:
3800:
3774:
3772:cond-mat/0503372
3750:
3744:
3743:
3725:
3719:
3718:
3692:
3686:
3677:
3671:
3670:
3668:
3628:
3595:
3589:
3588:
3570:
3564:
3563:
3541:
3508:
3490:
3461:Flexoelectricity
3457:
3435:Piezoelectricity
3431:
3389:
3373:
3355:
3353:
3352:
3347:
3339:
3337:
3335:
3330:
3317:
3310:
3309:
3299:
3261:
3259:
3258:
3253:
3250:
3245:
3236:
3235:
3222:
3217:
3208:
3207:
3195:
3194:
3185:
3181:
3180:
3179:
3159:
3158:
3146:
3145:
3126:
3124:
3123:
3118:
3110:
3109:
3096:
3091:
3082:
3081:
3068:
3063:
3054:
3053:
3041:
3040:
3031:
3027:
3026:
3025:
3005:
3004:
2992:
2990:
2989:
2988:
2975:
2964:
2934:
2932:
2931:
2926:
2924:
2923:
2914:
2913:
2900:
2895:
2886:
2885:
2876:
2868:
2862:
2857:
2848:
2847:
2838:
2830:
2824:
2819:
2810:
2806:
2805:
2804:
2784:
2783:
2774:
2766:
2715:
2713:
2712:
2707:
2705:
2703:
2697:
2696:
2687:
2686:
2682:
2675:
2674:
2660:
2659:
2649:
2648:
2640:
2639:
2620:
2618:
2617:
2612:
2604:
2603:
2584:
2582:
2581:
2576:
2574:
2572:
2568:
2566:
2564:
2560:
2553:
2552:
2538:
2537:
2528:
2527:
2511:
2506:
2497:
2492:
2491:
2474:
2472:
2471:
2470:
2454:
2452:
2444:
2443:
2421:
2419:
2418:
2413:
2411:
2407:
2405:
2403:
2399:
2392:
2391:
2377:
2376:
2367:
2366:
2350:
2345:
2336:
2331:
2330:
2313:
2311:
2310:
2309:
2293:
2287:
2282:
2260:
2258:
2257:
2252:
2243:
2238:
2229:
2228:
2215:
2210:
2201:
2200:
2188:
2184:
2183:
2182:
2162:
2161:
2120:
2118:
2117:
2112:
2110:
2106:
2104:
2099:
2090:
2089:
2076:
2071:
2062:
2061:
2049:
2045:
2044:
2043:
2023:
2022:
2008:
2007:
1995:
1993:
1992:
1991:
1978:
1967:
1949:
1947:
1946:
1941:
1938:
1933:
1924:
1923:
1910:
1905:
1896:
1895:
1883:
1882:
1873:
1869:
1868:
1867:
1847:
1846:
1834:
1832:
1831:
1830:
1817:
1806:
1794:
1792:
1791:
1786:
1784:
1783:
1767:
1765:
1764:
1759:
1757:
1756:
1744:
1743:
1724:
1722:
1721:
1716:
1713:
1708:
1699:
1698:
1689:
1681:
1675:
1670:
1661:
1660:
1651:
1643:
1637:
1632:
1623:
1619:
1618:
1617:
1597:
1596:
1587:
1579:
1544:
1542:
1541:
1536:
1528:
1527:
1511:
1509:
1508:
1503:
1495:
1494:
1478:
1476:
1475:
1470:
1462:
1461:
1445:
1443:
1442:
1437:
1429:
1428:
1389:
1387:
1386:
1381:
1379:
1378:
1360:
1359:
1344:
1343:
1291:
1289:
1288:
1283:
1281:
1276:
1271:
1261:
1256:
1246:
1241:
1232:
1231:
1222:
1214:
1208:
1204:
1200:
1199:
1195:
1193:
1188:
1175:
1170:
1155:
1150:
1138:
1134:
1132:
1127:
1114:
1109:
1094:
1089:
1077:
1073:
1071:
1066:
1053:
1048:
1033:
1028:
1014:
1013:
1004:
996:
990:
986:
982:
980:
975:
962:
957:
944:
939:
925:
924:
915:
907:
901:
897:
893:
891:
886:
876:
871:
858:
853:
843:
838:
825:
820:
810:
805:
791:
790:
781:
773:
767:
763:
759:
757:
752:
739:
734:
721:
716:
702:
701:
692:
684:
679:
675:
673:
668:
655:
650:
637:
632:
618:
614:
613:
612:
592:
591:
582:
574:
542:Taylor expansion
474:phase transition
312:
284:piezoelectricity
249:energy harvester
199:piezoelectricity
20:Ferroelectricity
5038:
5037:
5033:
5032:
5031:
5029:
5028:
5027:
4998:
4997:
4996:
4991:
4982:helielectricity
4967:paraelectricity
4953:
4948:
4907:
4897:
4878:
4856:
4840:
4838:Further reading
4835:
4772:
4768:
4751:
4747:
4679:
4675:
4666:
4665:
4661:
4651:
4649:
4640:
4639:
4635:
4625:
4623:
4615:
4609:
4605:
4591:
4587:
4580:10.1063/1.91359
4566:(11): 899–901.
4556:
4552:
4543:
4539:
4531:
4529:
4527:
4501:
4497:
4486:
4482:
4445:
4441:
4418:
4414:
4390:
4386:
4371:
4349:
4345:
4308:
4304:
4264:
4258:
4254:
4224:
4220:
4215:
4211:
4174:
4167:
4136:
4132:
4101:
4097:
4068:Surface Science
4060:
4056:
4025:
4021:
3957:(5733): 391–2.
3861:
3857:
3808:
3804:
3751:
3747:
3740:
3726:
3722:
3715:
3693:
3689:
3678:
3674:
3637:Physical Review
3605:Physical Review
3596:
3592:
3585:
3571:
3567:
3560:
3542:
3538:
3534:
3529:
3506:
3488:
3455:
3452:Ferroelasticity
3441:Pyroelectricity
3429:
3426:Paraelectricity
3387:
3370:
3362:
3331:
3326:
3318:
3305:
3301:
3300:
3298:
3296:
3293:
3292:
3286:
3282:
3277:
3270:
3246:
3241:
3231:
3227:
3218:
3213:
3203:
3199:
3190:
3186:
3175:
3171:
3164:
3160:
3154:
3150:
3141:
3137:
3135:
3132:
3131:
3105:
3101:
3092:
3087:
3077:
3073:
3064:
3059:
3049:
3045:
3036:
3032:
3021:
3017:
3010:
3006:
3000:
2996:
2984:
2980:
2976:
2965:
2963:
2961:
2958:
2957:
2952:
2948:
2941:
2919:
2915:
2909:
2905:
2896:
2891:
2881:
2877:
2867:
2858:
2853:
2843:
2839:
2829:
2820:
2815:
2800:
2796:
2789:
2785:
2779:
2775:
2765:
2754:
2751:
2750:
2745:
2741:
2736:
2732:
2726:
2722:
2699:
2692:
2688:
2670:
2666:
2665:
2661:
2655:
2651:
2650:
2647:
2635:
2631:
2629:
2626:
2625:
2599:
2595:
2593:
2590:
2589:
2548:
2544:
2543:
2539:
2533:
2529:
2523:
2519:
2507:
2502:
2496:
2487:
2483:
2479:
2475:
2466:
2462:
2458:
2453:
2451:
2439:
2435:
2433:
2430:
2429:
2387:
2383:
2382:
2378:
2372:
2368:
2362:
2358:
2346:
2341:
2335:
2326:
2322:
2318:
2314:
2305:
2301:
2297:
2292:
2283:
2278:
2272:
2269:
2268:
2239:
2234:
2224:
2220:
2211:
2206:
2196:
2192:
2178:
2174:
2167:
2163:
2157:
2153:
2151:
2148:
2147:
2141:
2129:
2100:
2095:
2085:
2081:
2072:
2067:
2057:
2053:
2039:
2035:
2028:
2024:
2018:
2014:
2013:
2009:
2003:
1999:
1987:
1983:
1979:
1968:
1966:
1958:
1955:
1954:
1934:
1929:
1919:
1915:
1906:
1901:
1891:
1887:
1878:
1874:
1863:
1859:
1852:
1848:
1842:
1838:
1826:
1822:
1818:
1807:
1805:
1803:
1800:
1799:
1779:
1775:
1773:
1770:
1769:
1752:
1748:
1739:
1735:
1733:
1730:
1729:
1709:
1704:
1694:
1690:
1680:
1671:
1666:
1656:
1652:
1642:
1633:
1628:
1613:
1609:
1602:
1598:
1592:
1588:
1578:
1567:
1564:
1563:
1557:
1523:
1519:
1517:
1514:
1513:
1490:
1486:
1484:
1481:
1480:
1457:
1453:
1451:
1448:
1447:
1424:
1420:
1418:
1415:
1414:
1368:
1364:
1352:
1348:
1339:
1335:
1333:
1330:
1329:
1314:
1307:
1300:
1279:
1278:
1272:
1267:
1257:
1252:
1242:
1237:
1227:
1223:
1213:
1206:
1205:
1189:
1184:
1171:
1166:
1161:
1157:
1151:
1146:
1128:
1123:
1110:
1105:
1100:
1096:
1090:
1085:
1067:
1062:
1049:
1044:
1039:
1035:
1029:
1024:
1019:
1015:
1009:
1005:
995:
988:
987:
976:
971:
958:
953:
940:
935:
930:
926:
920:
916:
906:
899:
898:
887:
882:
872:
867:
854:
849:
839:
834:
821:
816:
806:
801:
796:
792:
786:
782:
772:
765:
764:
753:
748:
735:
730:
717:
712:
707:
703:
697:
693:
683:
669:
664:
651:
646:
633:
628:
623:
619:
608:
604:
597:
593:
587:
583:
573:
571:
558:
556:
553:
552:
534:
481:liquid crystals
431:electric fields
427:barium titanate
424:
420:
386:
379:
371:
328:centrosymmetric
297:among which 32
288:pyroelectricity
279:
203:pyroelectricity
171:
164:
157:
71:
43:magnetic moment
17:
12:
11:
5:
5036:
5026:
5025:
5020:
5015:
5010:
4993:
4992:
4990:
4989:
4984:
4979:
4974:
4969:
4964:
4958:
4955:
4954:
4947:
4946:
4939:
4932:
4924:
4918:
4917:
4906:
4905:External links
4903:
4902:
4901:
4895:
4882:
4876:
4860:
4854:
4839:
4836:
4834:
4833:
4766:
4745:
4684:Rabe, Karin M.
4673:
4659:
4633:
4603:
4585:
4550:
4537:
4525:
4495:
4480:
4439:
4412:
4384:
4369:
4343:
4302:
4252:
4222:
4218:
4209:
4165:
4130:
4111:(16): 166101.
4095:
4054:
4035:(2): 342–343.
4019:
3855:
3802:
3745:
3738:
3720:
3714:978-0387765402
3713:
3687:
3685:1997, New York
3672:
3590:
3583:
3565:
3558:
3535:
3533:
3530:
3526:
3525:
3521:
3520:
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3509:
3493:
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3491:
3482:
3476:
3470:
3464:
3458:
3449:
3444:
3438:
3432:
3416:
3415:
3414:
3408:
3402:
3396:
3390:
3381:
3371:
3369:
3366:
3361:
3358:
3345:
3342:
3334:
3329:
3325:
3321:
3316:
3313:
3308:
3304:
3284:
3280:
3275:
3268:
3263:
3262:
3249:
3244:
3240:
3234:
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3212:
3206:
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3108:
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3100:
3095:
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3076:
3072:
3067:
3062:
3058:
3052:
3048:
3044:
3039:
3035:
3030:
3024:
3020:
3016:
3013:
3009:
3003:
2999:
2995:
2987:
2983:
2979:
2974:
2971:
2968:
2950:
2946:
2939:
2936:
2935:
2922:
2918:
2912:
2908:
2904:
2899:
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2880:
2874:
2871:
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2861:
2856:
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2823:
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2809:
2803:
2799:
2795:
2792:
2788:
2782:
2778:
2772:
2769:
2764:
2761:
2758:
2746:, as follows:
2743:
2739:
2734:
2730:
2724:
2720:
2717:
2716:
2702:
2695:
2691:
2685:
2681:
2678:
2673:
2669:
2664:
2658:
2654:
2646:
2643:
2638:
2634:
2610:
2607:
2602:
2598:
2586:
2585:
2571:
2563:
2559:
2556:
2551:
2547:
2542:
2536:
2532:
2526:
2522:
2518:
2515:
2510:
2505:
2501:
2495:
2490:
2486:
2482:
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2469:
2465:
2461:
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2423:
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2398:
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2386:
2381:
2375:
2371:
2365:
2361:
2357:
2354:
2349:
2344:
2340:
2334:
2329:
2325:
2321:
2317:
2308:
2304:
2300:
2296:
2291:
2286:
2281:
2277:
2262:
2261:
2250:
2247:
2242:
2237:
2233:
2227:
2223:
2219:
2214:
2209:
2205:
2199:
2195:
2191:
2187:
2181:
2177:
2173:
2170:
2166:
2160:
2156:
2139:
2127:
2122:
2121:
2109:
2103:
2098:
2094:
2088:
2084:
2080:
2075:
2070:
2066:
2060:
2056:
2052:
2048:
2042:
2038:
2034:
2031:
2027:
2021:
2017:
2012:
2006:
2002:
1998:
1990:
1986:
1982:
1977:
1974:
1971:
1965:
1962:
1951:
1950:
1937:
1932:
1928:
1922:
1918:
1914:
1909:
1904:
1900:
1894:
1890:
1886:
1881:
1877:
1872:
1866:
1862:
1858:
1855:
1851:
1845:
1841:
1837:
1829:
1825:
1821:
1816:
1813:
1810:
1782:
1778:
1755:
1751:
1747:
1742:
1738:
1726:
1725:
1712:
1707:
1703:
1697:
1693:
1687:
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1679:
1674:
1669:
1665:
1659:
1655:
1649:
1646:
1641:
1636:
1631:
1627:
1622:
1616:
1612:
1608:
1605:
1601:
1595:
1591:
1585:
1582:
1577:
1574:
1571:
1555:
1534:
1531:
1526:
1522:
1501:
1498:
1493:
1489:
1468:
1465:
1460:
1456:
1435:
1432:
1427:
1423:
1377:
1374:
1371:
1367:
1363:
1358:
1355:
1351:
1347:
1342:
1338:
1312:
1305:
1298:
1293:
1292:
1275:
1270:
1266:
1260:
1255:
1251:
1245:
1240:
1236:
1230:
1226:
1220:
1217:
1212:
1209:
1207:
1203:
1198:
1192:
1187:
1183:
1179:
1174:
1169:
1165:
1160:
1154:
1149:
1145:
1141:
1137:
1131:
1126:
1122:
1118:
1113:
1108:
1104:
1099:
1093:
1088:
1084:
1080:
1076:
1070:
1065:
1061:
1057:
1052:
1047:
1043:
1038:
1032:
1027:
1023:
1018:
1012:
1008:
1002:
999:
994:
991:
989:
985:
979:
974:
970:
966:
961:
956:
952:
948:
943:
938:
934:
929:
923:
919:
913:
910:
905:
902:
900:
896:
890:
885:
881:
875:
870:
866:
862:
857:
852:
848:
842:
837:
833:
829:
824:
819:
815:
809:
804:
800:
795:
789:
785:
779:
776:
771:
768:
766:
762:
756:
751:
747:
743:
738:
733:
729:
725:
720:
715:
711:
706:
700:
696:
690:
687:
682:
678:
672:
667:
663:
659:
654:
649:
645:
641:
636:
631:
627:
622:
617:
611:
607:
603:
600:
596:
590:
586:
580:
577:
572:
570:
567:
564:
561:
560:
533:
530:
456:Ferroelectric
422:
418:
413:
412:
402:
391:
384:
377:
369:
363:
362:
359:
358:ferroelectric
355:
354:
351:
344:
343:
340:
338:
331:
330:
324:
320:
319:
278:
275:
170:
167:
162:
155:
70:
67:
51:Joseph Valasek
39:ferromagnetism
15:
9:
6:
4:
3:
2:
5035:
5024:
5021:
5019:
5016:
5014:
5011:
5009:
5006:
5005:
5003:
4988:
4985:
4983:
4980:
4978:
4975:
4973:
4970:
4968:
4965:
4963:
4960:
4959:
4956:
4952:
4945:
4940:
4938:
4933:
4931:
4926:
4925:
4922:
4916:
4912:
4909:
4908:
4898:
4892:
4888:
4883:
4879:
4873:
4869:
4865:
4861:
4857:
4851:
4847:
4842:
4841:
4829:
4825:
4821:
4817:
4812:
4807:
4802:
4797:
4793:
4789:
4785:
4781:
4777:
4770:
4761:
4756:
4749:
4741:
4737:
4732:
4727:
4723:
4719:
4715:
4711:
4706:
4701:
4697:
4693:
4689:
4685:
4677:
4669:
4663:
4647:
4643:
4637:
4621:
4614:
4607:
4599:
4596:
4589:
4581:
4577:
4573:
4569:
4565:
4561:
4554:
4548:
4541:
4528:
4522:
4518:
4514:
4510:
4506:
4499:
4491:
4484:
4476:
4472:
4467:
4462:
4458:
4454:
4450:
4443:
4435:
4431:
4427:
4423:
4416:
4408:
4404:
4400:
4396:
4388:
4380:
4376:
4372:
4370:9783527807505
4366:
4362:
4358:
4354:
4347:
4339:
4335:
4330:
4325:
4321:
4317:
4313:
4306:
4298:
4294:
4290:
4286:
4282:
4278:
4274:
4270:
4263:
4256:
4248:
4244:
4240:
4236:
4232:
4228:
4213:
4204:
4199:
4195:
4191:
4187:
4183:
4182:ACS Catalysis
4179:
4172:
4170:
4161:
4157:
4153:
4149:
4145:
4141:
4134:
4126:
4122:
4118:
4114:
4110:
4106:
4099:
4090:
4085:
4081:
4077:
4073:
4069:
4065:
4058:
4050:
4046:
4042:
4038:
4034:
4030:
4023:
4015:
4011:
4007:
4003:
3999:
3995:
3991:
3987:
3980:
3976:
3972:
3968:
3964:
3960:
3956:
3952:
3948:
3947:Spaldin, N.A.
3941:
3937:
3933:
3929:
3925:
3921:
3917:
3913:
3909:
3905:
3898:
3894:
3890:
3886:
3882:
3878:
3874:
3870:
3866:
3859:
3851:
3847:
3843:
3839:
3835:
3831:
3826:
3821:
3817:
3813:
3806:
3798:
3794:
3790:
3786:
3782:
3778:
3773:
3768:
3764:
3760:
3756:
3749:
3741:
3735:
3731:
3724:
3716:
3710:
3706:
3702:
3698:
3691:
3684:
3683:
3676:
3667:
3662:
3658:
3654:
3650:
3646:
3642:
3638:
3634:
3626:
3622:
3618:
3614:
3610:
3606:
3602:
3594:
3586:
3580:
3576:
3569:
3561:
3555:
3551:
3547:
3540:
3536:
3524:
3519:
3516:
3513:
3510:
3504:
3501:
3500:
3499:
3498:
3494:
3486:
3485:Multiferroics
3483:
3480:
3477:
3474:
3471:
3468:
3465:
3462:
3459:
3453:
3450:
3448:
3445:
3442:
3439:
3436:
3433:
3427:
3424:
3423:
3422:
3421:
3417:
3412:
3409:
3406:
3403:
3400:
3397:
3394:
3391:
3385:
3382:
3380:
3377:
3376:
3375:
3374:
3365:
3357:
3343:
3340:
3332:
3327:
3323:
3314:
3306:
3290:
3289:local maximum
3278:
3271:
3247:
3242:
3238:
3232:
3228:
3224:
3219:
3214:
3210:
3204:
3200:
3196:
3191:
3187:
3182:
3176:
3172:
3168:
3165:
3161:
3155:
3151:
3147:
3142:
3138:
3130:
3129:
3114:
3111:
3106:
3102:
3098:
3093:
3088:
3084:
3078:
3074:
3070:
3065:
3060:
3056:
3050:
3046:
3042:
3037:
3033:
3028:
3022:
3018:
3014:
3011:
3007:
3001:
2997:
2993:
2985:
2981:
2972:
2956:
2955:
2954:
2944:
2920:
2916:
2910:
2906:
2902:
2897:
2892:
2888:
2882:
2878:
2872:
2869:
2864:
2859:
2854:
2850:
2844:
2840:
2834:
2831:
2826:
2821:
2816:
2812:
2807:
2801:
2797:
2793:
2790:
2786:
2780:
2776:
2770:
2767:
2762:
2759:
2749:
2748:
2747:
2737:
2700:
2693:
2689:
2683:
2679:
2676:
2671:
2667:
2662:
2656:
2652:
2644:
2641:
2636:
2632:
2624:
2623:
2622:
2608:
2605:
2600:
2596:
2569:
2561:
2557:
2554:
2549:
2545:
2540:
2534:
2530:
2524:
2520:
2516:
2513:
2508:
2503:
2499:
2493:
2488:
2484:
2480:
2476:
2467:
2463:
2459:
2455:
2448:
2445:
2440:
2436:
2428:
2427:
2426:
2408:
2400:
2396:
2393:
2388:
2384:
2379:
2373:
2369:
2363:
2359:
2355:
2352:
2347:
2342:
2338:
2332:
2327:
2323:
2319:
2315:
2306:
2302:
2298:
2294:
2289:
2284:
2279:
2275:
2267:
2266:
2265:
2248:
2245:
2240:
2235:
2231:
2225:
2221:
2217:
2212:
2207:
2203:
2197:
2193:
2189:
2185:
2179:
2175:
2171:
2168:
2164:
2158:
2154:
2146:
2145:
2144:
2142:
2135:
2131:
2107:
2101:
2096:
2092:
2086:
2082:
2078:
2073:
2068:
2064:
2058:
2054:
2050:
2046:
2040:
2036:
2032:
2029:
2025:
2019:
2015:
2010:
2004:
2000:
1996:
1988:
1984:
1975:
1963:
1960:
1953:
1952:
1935:
1930:
1926:
1920:
1916:
1912:
1907:
1902:
1898:
1892:
1888:
1884:
1879:
1875:
1870:
1864:
1860:
1856:
1853:
1849:
1843:
1839:
1835:
1827:
1823:
1814:
1798:
1797:
1796:
1780:
1776:
1753:
1749:
1745:
1740:
1736:
1710:
1705:
1701:
1695:
1691:
1685:
1682:
1677:
1672:
1667:
1663:
1657:
1653:
1647:
1644:
1639:
1634:
1629:
1625:
1620:
1614:
1610:
1606:
1603:
1599:
1593:
1589:
1583:
1580:
1575:
1572:
1562:
1561:
1560:
1558:
1551:
1546:
1532:
1529:
1524:
1520:
1499:
1496:
1491:
1487:
1466:
1463:
1458:
1454:
1433:
1430:
1425:
1421:
1411:
1409:
1405:
1401:
1397:
1393:
1375:
1372:
1369:
1365:
1361:
1356:
1353:
1349:
1345:
1340:
1336:
1327:
1323:
1319:
1315:
1308:
1301:
1273:
1268:
1264:
1258:
1253:
1249:
1243:
1238:
1234:
1228:
1224:
1218:
1215:
1210:
1201:
1196:
1190:
1185:
1181:
1177:
1172:
1167:
1163:
1158:
1152:
1147:
1143:
1139:
1135:
1129:
1124:
1120:
1116:
1111:
1106:
1102:
1097:
1091:
1086:
1082:
1078:
1074:
1068:
1063:
1059:
1055:
1050:
1045:
1041:
1036:
1030:
1025:
1021:
1016:
1010:
1006:
1000:
997:
992:
983:
977:
972:
968:
964:
959:
954:
950:
946:
941:
936:
932:
927:
921:
917:
911:
908:
903:
894:
888:
883:
879:
873:
868:
864:
860:
855:
850:
846:
840:
835:
831:
827:
822:
817:
813:
807:
802:
798:
793:
787:
783:
777:
774:
769:
760:
754:
749:
745:
741:
736:
731:
727:
723:
718:
713:
709:
704:
698:
694:
688:
685:
680:
676:
670:
665:
661:
657:
652:
647:
643:
639:
634:
629:
625:
620:
615:
609:
605:
601:
598:
594:
588:
584:
578:
575:
568:
565:
551:
550:
549:
547:
543:
539:
529:
527:
522:
520:
516:
512:
508:
503:
501:
500:spontelectric
497:
496:nitrous oxide
493:
488:
486:
482:
477:
475:
471:
470:ferromagnetic
468:, much as do
467:
463:
459:
454:
451:
447:
442:
440:
439:lead titanate
436:
432:
428:
411:
407:
403:
400:
396:
392:
390:
383:
376:
372:
365:
364:
356:
350:
345:
337:
336:piezoelectric
332:
329:
325:
321:
318:
313:
310:
308:
304:
303:piezoelectric
300:
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261:piezoelectric
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222:multiferroics
218:
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142:magnetization
139:
138:ferromagnetic
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100:
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66:
64:
63:multiferroics
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349:pyroelectric
307:pyroelectric
295:space groups
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257:pyroelectric
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172:
169:Applications
159:
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115:permittivity
111:paraelectric
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3473:Spintronics
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1404:Gauss's law
513:(PVDF) and
492:David Field
347:10 classes
334:20 classes
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4962:dielectric
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4532:2022-09-22
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2124:Since the
395:Tourmaline
245:desorption
243:to strong
241:adsorption
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