A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Aging Rate
Aging is a process by which a polarised ferroelectric material tries to relax to its pre-poled state. Aging of ferroelectrics is a logarithmic function with time, with the most important parameters that age with time being dielectric constant, resonant frequency and the frequency constants.
Coercive Field
The coercive field for a ferroelectric material is the electric field required to switch its polarisation from remanent [PR] to zero polarisation [P = 0]. The value of Ec for a ferroelectric crystal is dependant on many parameters including thermal & electrical history, envionmental factors, as well as type and area of switching electrodes.
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Curie Point, Tc
This is defined as the temperature at which a ferroelectric material undergoes a crystallographic phase change from an asymmetrical, non-centrosymmetric structure to a centrosymmetric crystal structure, thus losing it spontaneous polarisation. It is determined at zero applied field.
This phase change is accompanied by a peak in small signal permittivity (dielectric constant) and in the piezoelectric coefficients. It can normally be expected that the transition at TC is from the ferroelectric to the paraelectric phase.
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d-Constant [Piezoelectric Charge Coefficient]
The piezoelectric constants relating the mechanical strain produced by an applied electric field are termed the strain constants, or d cofficients. Examples include d33, d31, d15. Specifically, it is defined as the ratio of the electric charge generated per unit area to an applied force, and its units are Coulombs.Newton-1.
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Depolarisation Fields
A depolarisation field is a self-generated electric field that opposes the spontaneous polarisation.
In a crystal of finite dimensions there will be a discontinuity in the spontaneous polarisation. (Ps) at the crystal surfaces, which gives rise to a bound polarisation charge [Q = Ps.Area] of surface density Ps. This charge gives rise to an electric field called the depolarising field, which opposes the spontaneous polarisation. The magnitude of this depolarising field depends on the shape of the crystal.
In real materials the depolarisation field is neutralised by the flow of free charge throught the crystal or through the environment. Obviously, for an electrically insulating crystal in an insulating environment, this neutralisation process may be very slow.
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Dielectric Constant (Relative Permitivity): K33T
The dielectric constant is a ratio of the permittivity of the material, e, to the permittivity of free space, e0 in the unconstrained condition, well below the mechanical resonance of the sample. The "T" symbol refers to the condition - in this case constant stess (no mechanical clamping).
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Dielectric Loss Factor (Loss Tangent)
The dielectric loss factor is defined as the tangent of the loss factor - Tand, which itself represents the ratio of the resistance to the reactance of a parallel equivalent circuit for the material.
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Ferroelectric Domains
A ferroelectic domain is a region in a ferroelectric crystal exhibiting homogeneous and uniform spontanous polarisation.
It's likely that an unpoled ferroelectric polycrystal will exhibit a complex domain structure comprising of a large number of domains - each with a different polarisation orientation. The direction of the spontaneous polarisation in each unique domain is constrained, by the symmetry of the prototype, to a small number of equivalent directions.
The boundary region between two ferroelectric domains is called a domain wall.
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Ferroelectric Materials
A ferroelectic material is a material that exhibits, over some range of temperature, a spontaneous electic polarisation that can be reversed or reorientated by application of an electric field [poling].
A necessary criterion is the requirement of an everpresent spontaneous polarisation, with the requirement of reversibility or reorientation of that spontaneous polarisation being a sufficient criterion for a ferroelectric phase.
An exclusion from the definition of ferroelectrics is those materials belonging to non-polar crystal classes at all temperatures, and in which a metastable polarisation can be induced by an external electric field.
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Frequency constants
The frequency constant, N, is the product of the resonant frequency and the linear dimension governing the resonance. There are various modes of resonance including radial mode, plate length mode, cylinder length mode, thickness mode (plate, disc) and plate shear mode.
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g-coefficents [voltage constants]
These are the piezoelectric constants that relate the electric field that can be generated from an applied mechanical stress. It is defined as the ratio of the electric field produce to the mechanical stress applied. The units for these constants are Volt.meter per Newton (V.m.N-1)
High g-coefficient favour large voltage output, and are thus desirable from materials used in sensor applications.
Although g-constants are called voltage coefficients, it is perfectly feasible to refer to them as the ratio of strain developed over the applied charge density. [ units: C-1.m2]
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Mechanical Qm
Is the ratio of reactance to resistance in the series equivalent circuit that represents the piezoelectric resonator. The mechanical Q is related to the geometry and dimensions of the sample, as well as the sharpness of the resonant peak.
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Orientation States
This term refers to the various possible stable orientations of the spontaneous polarisation for a given ferroelectric phase. A ferroelectric crystal has two or more such orientation states in the absence of an electric field, and can be switched from one to another of these states by an applied electric field. Any two of these orientation states are cystalographically identical (enantiomorphous), but different in their spontanous polarisation orientation at zero electric field.
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Piezoelectricity
Piezoelectricity is the generation of electricity as a result of a mechanical pressure, or more precisely... "electrical polarisation produced by mechanical strain in crystals belonging to certain classes, the polarisation being proportional to the strain and changing sign with it."
Refer to Electroceramics Tutorial for further Information
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Piezoelectric Coupling Coefficient
k33, k31, kp and k15 are electromechanical coupling coefficients that describe the efficiency with which energy is interconverted between mechanical and electrical forms in the material.
The ratio of the stored converted energy to the input energy is defined as the square of the coupling coefficient.
Note that, due to these coefficients being energy ratios, they are dimensionless.
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Permittivity (small signal, ferroelectric material)
Defined as the incremental change in electric displacement per unit electric field when the magnitude of the meausring field is very small compared to the coercive electric field.
The small signal relative permittivity, k, is equal to the ratio of the absolute permittivity e to the permittivity of free space e0, that is k = e / e0.
This value for small signal permittivity may depend on the remanent polarisation, electric field, mechanical stress, sample history, or frequency of the measuring field.
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Polarisation
Polarisation is the electric dipole moment per unit volume, and is related to electric displacement, D though the linear expression:
Di= Pi+ e0Ei
where e0 (usually called the permittivity of free space) equals 8.854e10-12 coulomb/volt-meter.
Note that in ferroelectric materials both D and P are non-linear functions of E and can depend on the previous history of the material. When the term e0E in the above expression is negligible compared to P [as is the case for most ferroelectric materials], D is nearly equal to P. Thus, the D versus E and P versus E plots of the hysteresis loop become equivalent.
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Poling
Poling is the electrical process by which the myriad of randomly orientated crystallites, each containing many domains (only a few allowed orientations), in a polycrystalline ferroelectric ceramic are aligned to produce a useful electroactive material. Without this orientation the material is unlikely to exhibit any net macroscopic polarisation.
An external dc electric field, exceeding the coercive field, orientates the domains within a grain, producing a net remanent polarisation and a ceramic material that acts in a very similar way to a single crystal possessing both ferroelectric and piezoelectric properties. This electrical process of aligning is known as "poling", and is identified as key to turning an inert ceramic into an electromechanically active material, with all it possible uses.
The technique of poling a ferroelectric crystal consists of applying an electric field along one of the alternative polar axes. Due to the coercive field generally being minimum near Tcit is common practive to cool through Tc with the field applied.
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Pyroelectricity
Pyroelectric materials characteristically develop an electric polarisation if their temperature is changed. All pyroelectric crystals are necessarily piezoelectric, with some also being ferroelectric .
Refer to Electroceramics Tutorial for further Information
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Remanent Polarisation (ferroelectric material)
Remanent polarisation Pr is defined as the value of the polarisation that remains after an applied electric field is removed. It can be measured by integrating the compensating surface charge released on heating a poled ferroelectric to a temperature above its Curie Point
See Saturation Remanent Polarisation
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Saturation Remanent Polarisation
When the magnitude of the applied electric field is sufficient to saturate the polarisation - usually at a value of three times the coercive field - the polarisation remaining after the field is removed is termed saturation remanent polarisation Pr. In a single domain ferroelectric material, the saturation remenant polarisation is equal to the spontaneous polarisation.
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Spontanous Polarisation
Is defined as the magnitude of the polarisation within a single ferroelectic domain in the absence of an external electric field.
A spontaneous polarisation is a fundamental property of all pyroelectric crystals, although it's reversible and reorientable only in ferroelectrics .. Most ferroelectric phases originate form a non-polar prototypic phase and all of the polarisation is reorientable. However, if the prototypic phase is polar, only a proportion of the total spontaneous polarisation may be reorientated. The reorientable or reversible portion is commonly called the spontaneous polarisation.
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Switching (ferroelectic materials)
Switching is the process by which the remanent polarisation is reorientated into a new position of Pr (generally equal and opposite). It is possible to induce switching both by an electric field and mechanical stress.
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