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Ferroelectricity is a characteristic of certain materials that have a spontaneous
electric polarization In classical electromagnetism, polarization density (or electric polarization, or simply polarization) is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. When a dielectric is ...
that can be reversed by the application of an external electric field. All ferroelectrics are also
piezoelectric Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied Stress (mechanics), mechanical s ...
and
pyroelectric Pyroelectricity (from the two Greek words ''pyr'' meaning fire, and electricity) is a property of certain crystals which are naturally electrically polarized and as a result contain large electric fields. Pyroelectricity can be described as the a ...
, with the additional property that their natural electrical polarization is reversible. The term is used in analogy to
ferromagnetism Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials ...
, in which a material exhibits a permanent
magnetic moment In electromagnetism, the magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include loops of electric current (such as electromagnets ...
. Ferromagnetism was already known when ferroelectricity was discovered in 1920 in
Rochelle salt Potassium sodium tartrate tetrahydrate, also known as Rochelle salt, is a double salt of tartaric acid first prepared (in about 1675) by an apothecary, Pierre Seignette, of La Rochelle, France. Potassium sodium tartrate and monopotassium phospha ...
by
Joseph Valasek Joseph Valasek (27 April 1897-4 October 1993) was an American physicist and professor emeritus of physics at the University of Minnesota. He specialized in geometrical and physical optics, experimental optics and spectroscopy, and x-rays. He is cr ...
.See and Thus, the prefix ''ferro'', meaning iron, was used to describe the property despite the fact that most ferroelectric materials do not contain iron. Materials that are both ferroelectric ''and'' ferromagnetic are known as
multiferroics Multiferroics are defined as materials that exhibit more than one of the primary ferroic properties in the same phase: * ferromagnetism – a magnetisation that is switchable by an applied magnetic field * ferroelectricity – an electric polarisa ...
.


Polarization

When most materials are electrically polarized, the polarization induced, ''P'', is almost exactly proportional to the applied external electric field ''E''; so the polarization is a linear function. This is called linear dielectric polarization (see figure). Some materials, known as paraelectric materials, show a more enhanced nonlinear polarization (see figure). The electric
permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' (epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...
, corresponding to the slope of the polarization curve, is not constant as in linear dielectrics but is a function of the external electric field. In addition to being nonlinear, ferroelectric materials demonstrate a spontaneous nonzero polarization (after
entrainment Entrainment may refer to: * Air entrainment, the intentional creation of tiny air bubbles in concrete * Brainwave entrainment, the practice of entraining one's brainwaves to a desired frequency * Entrainment (biomusicology), the synchronization o ...
, see figure) even when the applied field ''E'' is zero. The distinguishing feature of ferroelectrics is that the spontaneous polarization can be ''reversed'' 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 hysteresis loop. They are called ferroelectrics by analogy to
ferromagnetic Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials ...
materials, which have spontaneous
magnetization In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or Di ...
and exhibit similar hysteresis loops. Typically, materials demonstrate ferroelectricity only below a certain phase transition temperature, called the
Curie temperature In physics and materials science, the Curie temperature (''T''C), or Curie point, is the temperature above which certain materials lose their permanent magnetic properties, which can (in most cases) be replaced by induced magnetism. The Cur ...
(''T''C) 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 ''T''C completely, because their paraelectric phase has a centrosymmetric crystal structure.


Applications

The nonlinear nature of ferroelectric materials can be used to make capacitors with adjustable capacitance. Typically, a
ferroelectric capacitor Ferroelectric capacitor is a capacitor based on a ferroelectric material. In contrast, traditional capacitors are based on dielectric materials. Ferroelectric devices are used in digital electronics as part of ferroelectric RAM, or in analog electro ...
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 compared to dielectric (non-tunable) capacitors of similar capacitance. The spontaneous polarization of ferroelectric materials implies a hysteresis effect which can be used as a memory function, and ferroelectric capacitors are indeed used to make
ferroelectric RAM Ferroelectric RAM (FeRAM, F-RAM or FRAM) is a random-access memory similar in construction to DRAM but using a ferroelectric layer instead of a dielectric layer to achieve non-volatility. FeRAM is one of a growing number of alternative non-vo ...
for computers and
RFID Radio-frequency identification (RFID) uses electromagnetic fields to automatically identify and track tags attached to objects. An RFID system consists of a tiny radio transponder, a radio receiver and transmitter. When triggered by an electromag ...
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 sample quality for devices to work reliably. Ferroelectric materials are required by symmetry considerations to be also piezoelectric and pyroelectric. The combined properties of memory,
piezoelectricity Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied mechanical stress. The word ''p ...
, and
pyroelectricity Pyroelectricity (from the two Greek words ''pyr'' meaning fire, and electricity) is a property of certain crystals which are naturally electrically polarized and as a result contain large electric fields. Pyroelectricity can be described as the a ...
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 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. Another idea of recent interest is the ''ferroelectric tunnel junction'' (''FTJ'') 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. Yet another burgeoning application is
multiferroics Multiferroics are defined as materials that exhibit more than one of the primary ferroic properties in the same phase: * ferromagnetism – a magnetisation that is switchable by an applied magnetic field * ferroelectricity – an electric polarisa ...
, 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.,
Catalytic Catalysis () is the process of increasing the rate of a chemical reaction by adding a substance known as a catalyst (). Catalysts are not consumed in the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recyc ...
properties of ferroelectrics have been studied since 1952 when Parravano observed anomalies in CO oxidation rates over ferroelectric sodium and potassium niobates near the
Curie temperature In physics and materials science, the Curie temperature (''T''C), or Curie point, is the temperature above which certain materials lose their permanent magnetic properties, which can (in most cases) be replaced by induced magnetism. The Cur ...
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
Sabatier principle The Sabatier principle is a qualitative concept in chemical heterogeneous catalysis named after the French chemist Paul Sabatier. It states that the interactions between the catalyst and the substrate should be "just right"; that is, neither too st ...
. 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
adsorption Adsorption is the adhesion of atoms, ions or molecules from a gas, liquid or dissolved solid to a surface. This process creates a film of the ''adsorbate'' on the surface of the ''adsorbent''. This process differs from absorption, in which ...
to strong
desorption Desorption is the physical process where a previously adsorbed substance is released from a surface. This happens when a molecule gains enough energy to overcome the activation barrier of the bounding energy that keeps it in the surface. There ...
, thus a compromise between desorption and adsorption is no longer needed. Ferroelectric polarization can also act as an energy harvester. Polarization can help the separation of photo-generated electron-hole pairs, leading to enhanced photocatalysis. Also, due to
pyroelectric Pyroelectricity (from the two Greek words ''pyr'' meaning fire, and electricity) is a property of certain crystals which are naturally electrically polarized and as a result contain large electric fields. Pyroelectricity can be described as the a ...
and
piezoelectric Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied Stress (mechanics), mechanical s ...
effects under varying temperature (heating/cooling cycles) or varying strain (vibrations) conditions extra charges can appear on the surface and drive various (electro)chemical reactions forward.


Materials

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 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
piezoelectricity Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied mechanical stress. The word ''p ...
. A change in the spontaneous polarization of a material in response to a change in temperature is called
pyroelectricity Pyroelectricity (from the two Greek words ''pyr'' meaning fire, and electricity) is a property of certain crystals which are naturally electrically polarized and as a result contain large electric fields. Pyroelectricity can be described as the a ...
. Generally, there are 230
space group In mathematics, physics and chemistry, a space group is the symmetry group of an object in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of an object that leave it uncha ...
s among which 32 crystalline classes can be found in crystals. There are 21 non-centrosymmetric classes, within which 20 are
piezoelectric Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied Stress (mechanics), mechanical s ...
. Among the piezoelectric classes, 10 have a spontaneous electric polarization, that varies with the temperature, therefore they are
pyroelectric Pyroelectricity (from the two Greek words ''pyr'' meaning fire, and electricity) is a property of certain crystals which are naturally electrically polarized and as a result contain large electric fields. Pyroelectricity can be described as the a ...
. Ferroelectricity is a subset of pyroelectricity, which brings spontaneous electronic polarization to the material. Ferroelectric phase transitions are often characterized as either displacive (such as BaTiO3) or order-disorder (such as NaNO2), though often phase transitions will demonstrate elements of both behaviors. In
barium titanate Barium titanate (BTO) is an inorganic compound with chemical formula BaTiO3. Barium titanate appears white as a powder and is transparent when prepared as large crystals. It is a Ferroelectricity, ferroelectric, Pyroelectricity, pyroelectric, and ...
, 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
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
s due to the ions in the crystal increases faster than the elastic-restoring
force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...
s. 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
lead titanate Lead(II) titanate is an inorganic compound with the chemical formula PbTiO3. It is the lead salt of titanic acid. Lead(II) titanate is a yellow powder that is insoluble in water. At high temperatures, lead titanate adopts a cubic perovskite ...
, 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. An important ferroelectric material for applications is
lead zirconate titanate Lead zirconate titanate is an inorganic compound with the chemical formula (0≤''x''≤1), commonly abbreviated as PZT. Also called lead zirconium titanate, it is a ceramic perovskite material that shows a marked piezoelectric effect, meaning ...
(PZT), which is part of the solid solution formed between ferroelectric lead titanate and anti-ferroelectric 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 found close to the 50/50 composition. Ferroelectric
crystals A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macrosc ...
often show several
transition temperature Transition temperature is the temperature at which a material changes from one crystal state (allotrope) to another. More formally, it is the temperature at which two crystalline forms of a substance can co-exist in equilibrium. For example, when ...
s and domain structure hysteresis, much as do
ferromagnetic Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials ...
crystals. The nature of the
phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...
in some ferroelectric crystals is still not well understood. In 1974 R.B. Meyer used symmetry arguments to predict ferroelectric
liquid crystals Liquid crystal (LC) is a state of matter whose properties are between those of conventional liquids and those of solid crystals. For example, a liquid crystal may flow like a liquid, but its molecules may be oriented in a crystal-like way. Th ...
, 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
LCoS Liquid crystal on silicon (LCoS or LCOS) is a miniaturized reflective active-matrix liquid-crystal display or "microdisplay" using a liquid crystal layer on top of a silicon backplane. It is also referred to as a spatial light modulator. LCoS was ...
. In 2010 David Field found that prosaic films of chemicals such as nitrous oxide or propane exhibited ferroelectric properties. This new class of ferroelectric materials exhibit " spontelectric" properties, and may have wide-ranging applications in device and nano-technology and also influence the electrical nature of dust in the interstellar medium. Other ferroelectric materials used include
triglycine sulfate Triglycine sulfate (TGS) is a chemical compound with a formula (NH2CH2COOH)3·H2SO4. The empirical formula of TGS does not represent the molecular structure, which contains protonated glycine moieties and sulfate ions. TGS with protons replaced by ...
,
polyvinylidene fluoride Polyvinylidene fluoride or polyvinylidene difluoride (PVDF) is a highly non-reactive thermoplastic fluoropolymer produced by the polymerization of vinylidene difluoride. PVDF is a specialty plastic used in applications requiring the highest pur ...
(PVDF) and
lithium tantalate Lithium tantalate ( Li Ta O3) is a perovskite which possesses unique optical, piezoelectric and pyroelectric properties which make it valuable for nonlinear optics, passive infrared sensors such as motion detectors, terahertz generation and de ...
. 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 ''Nature Communications'', scientists were able to produce a "two-dimensional" sheet of material which was both "ferroelectric" (had a polar crystal structure) and which conducted electricity.


Theory

An introduction to Landau theory can be found here. Based on
Ginzburg–Landau theory In physics, Ginzburg–Landau theory, often called Landau–Ginzburg theory, named after Vitaly Ginzburg and Lev Landau, is a mathematical physical theory used to describe superconductivity. In its initial form, it was postulated as a phenomenol ...
, the free energy of a ferroelectric material, in the absence of an electric field and applied stress may be written as a
Taylor expansion In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor seri ...
in terms of the order parameter, ''P''. If a sixth order expansion is used (i.e. 8th order and higher terms truncated), the free energy is given by: : \begin \Delta E= & \frac\alpha_0\left(T-T_0\right)\left(P_x^2+P_y^2+P_z^2\right)+ \frac\alpha_\left(P_x^4+P_y^4+P_z^4\right)\\ & +\frac\alpha_\left(P_x^2 P_y^2+P_y^2 P_z^2+P_z^2P_x^2\right)\\ & +\frac\alpha_\left(P_x^6+P_y^6+P_z^6\right)\\ & +\frac\alpha_\left _x^4\left(P_y^2+P_z^2\right) +P_y^4\left(P_x^2+P_z^2\right)+P_z^4\left(P_x^2+P_y^2\right)\right\ & +\frac\alpha_P_x^2P_y^2P_z^2 \end where ''Px'', ''Py'', and ''Pz'' are the components of the polarization vector in the ''x'', ''y'', and ''z'' directions respectively, and the coefficients, \alpha_i, \alpha_, \alpha_ 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 phase field model. 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
finite difference method In numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time interval (if applicable) are ...
or
finite element method The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat ...
and solved subject to the constraints of
Gauss's law In physics and electromagnetism, Gauss's law, also known as Gauss's flux theorem, (or sometimes simply called Gauss's theorem) is a law relating the distribution of electric charge to the resulting electric field. In its integral form, it sta ...
and
Linear elasticity Linear elasticity is a mathematical model of how solid objects deform and become internally stressed due to prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mec ...
. In all known ferroelectrics, \alpha_0 > 0 and \alpha_ > 0. These coefficients may be obtained experimentally or from ab-initio simulations. For ferroelectrics with a first order phase transition, \alpha_ < 0, whereas \alpha_ > 0 for a second order phase transition. The ''spontaneous polarization'', ''Ps'' of a ferroelectric for a cubic to tetragonal phase transition may be obtained by considering the 1D expression of the free energy which is: : \Delta E=\frac\alpha_0\left(T-T_0\right)P_x^2+\frac\alpha_P_x^4+\frac\alpha_P_x^6 This free energy has the shape of a double well potential with two free energy minima at P_x = P_s, the spontaneous polarization. We find the derivative of the free energy, and set it equal to zero in order to solve for P_s: : \frac=\alpha_0\left(T-T_0\right)P_x+\alpha_P_x^3+\alpha_P_x^5 : 0=\frac=P_s \left \alpha_0\left(T-T_0\right)+\alpha_P_s^2+\alpha_P_s^4\right Since the ''Ps = 0'' solution of this equation rather corresponds to a free energy ''maxima'' in the ferroelectric phase, the desired solutions for ''Ps'' correspond to setting the remaining factor to zero: : \alpha_0\left(T-T_0\right)+\alpha_P_s^2+\alpha_P_s^4=0 whose solution is: :P_s^2=\frac\left \alpha_\pm\sqrt \;\right/math> and eliminating solutions which take the square root of a negative number (for either the first or second order phase transitions) gives: :P_s= \pm \sqrt If \alpha_=0, the solution for the spontaneous polarization reduces to: :P_s= \pm\sqrt /math> The hysteresis loop (Px versus Ex) may be obtained from the free energy expansion by including the term ''-Ex Px'' corresponding to the energy due to an external electric field Ex interacting with the polarization Px, as follows: : \Delta E=\frac\alpha_0\left(T-T_0\right)P_x^2+\frac\alpha_P_x^4+\frac\alpha_P_x^6 - E_x P_x We find the stable polarization values of Px ''under the influence of the external field'', now denoted as Pe, again by setting the derivative of the energy with respect to Px to zero: : \frac=\alpha_0\left(T-T_0\right)P_x+\alpha_P_x^3+\alpha_P_x^5 - E_x = 0 : E_x=\alpha_0\left(T-T_0\right)P_e+\alpha_P_e^3+\alpha_P_e^5 Plotting ''Ex'' (on the X axis) as a function of ''Pe'' (but on the Y axis) gives an 'S' shaped curve which is multi-valued in Pe for some values of Ex. The central part of the 'S' corresponds to a free energy
local maximum In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given ra ...
(since \frac<0 ). 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.


Sliding ferroelectricity

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.


See also

* :Ferroelectric materials * * * * Physics * * * * * * * * *s * Lists * * *


References


Further reading

* * *


External links


Ferroelectric Materials
at
University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...
{{Authority control Ferroelectric materials Electric and magnetic fields in matter Electrical phenomena Phases of matter