In this article we will discuss about:- 1. Introduction to Ferroelectric Materials 2. Common Ferroelectric Materials 3. Properties of Ferroelectric Materials in Static Fields 4. Spontaneous Polarisation 5. Applications of Ferroelectric Materials 6. Anti-Ferroelectric Materials 7. Permanent Electric Materials.
Introduction to Ferroelectric Materials:
If the centre of gravity of the positive and negative charges in a body do not coincide in the absence of an applied electric field, the substance has an electric dipole moment and is said to be spontaneously polarised. Such a substance is called ferroelectric. It contains small regions which are polarised in different directions even in the absence of an electric field.
When the temperature exceeds a certain value called the Curie point, the substance loses its ferroelectric properties. Above the curie point the formation of small regions — domains—is disrupted by thermal agitation and permittivity is reduced to the usual small value.
Ferroelectric materials have the following characteristics:
(i) They have a high dielectric constant which is non-linear, i.e., it depends to a considerable extent on the intensity of the electric field.
(ii) They exhibit hysteresis loops, i.e., the polarisation is not linear function of applied electric field.
Common Ferroelectric Materials:
The common ferroelectric materials known as:
1. Rochelle salt (NaKC4H4O64H2O)
2. Potassium dihydrogen phosphate (KH2PO4)
3. Potassium dideutorium phosphate (KD2PO4)
4. Potassium dihydrogen argon sulphate (KH2SO4)
5. Barium titanate (BaTiO3)
6. Strontium titanate (SrTiO3)
7. Cadmium titanate (CdTiO3)
8. Lead titanate (PbTiO3)
9. Lead zirconate (PbZrO3)
10. Mixed titanate of (5), (6), (7), (8) and (9)
11. Silicon carbide (SiC)
12. Boron nitride (NB)
13. Silicon nitride (N4Si3)
14. Aluminium nitride (NAI)
Some of the commercial ferroelectric materials are:
1. Commercial BaTiO3 ceramic
2. 0.77 BaTiO3 0.3 CaTiO3
3. 0.96 BaTiO3 0.04 PbTiO3
4. 0.90 BaTiO3 0.04 PbTiO3 0.06 CaTiO3
5. 0.84 BaTiO3 0.08 PbTiO3 0.08 CaTiO3
6. 0.80 BaTiO3 0.12 PbTiO3 0.08 CaTiO3
7. 0.45 PbTiO3 0.55 PbZrO3.
Some of the ferroelectric materials are considered below:
1. Rochelle Salt:
The average chemical composition of this ferroelectric material is NaKC4H4O64H2O. This is the first material which came in the material literature in 1930 and was called Seignatte’s salt.
Relation between electric strength (E) and permittivity (∈) of the Rochelle salt is given below:
This salt is crystalline material soluble in water and very high hygroscopic material.
This material is a salt of sodium, potassium and tarteric acid. It has two Curie points.
The relation between temperature (K) and spontaneous polarisation in Columb/m2 is given below:
2. Potassium Dihydrogen Phosphate (KD2PO4, KH2AS4):
The materials KH2PO4, KD2PO4 and KH2ASO4 were discovered in 1935.
Their ferroelectric properties are given below:
The Curie points are negative and this creates great difficulties for practical utilisation of the materials. In these materials ferroelectric properties are explained by the features of hydrogen bonds. This fact has been confirmed indirectly by sharp change of properties of these materials if hydrogen is replaced by deuterium.
The following particulars are worth noting:
3. Barium Titanate (BaTiO3) and (SrTiO3, CdTiO3, PbZrO3):
BaTiO3 (Barium titanate) or barium titanate shortly ‘tiber’ was discovered by Russian scientist B.M. Wul. In other countries as well a series of ferroelectric similar to BaTiO3 were found, these are strontium-titanate, cadmium titanate, lead titanate, lead zirconate and solid solutions of these material between them, or with BaTiO3. These materials are called ferroelectric ceramics.
Their curie temperatures are given below:
The production of BaTiO3 is done by firing equimolecular quantities of tatanium dioxide and barium oxide, practically barium oxide is introduced as barium carbonate BaCO3. The following particulars relate to Barium titanate (BaTiO3).
Relation between Temperature and Permittivity when the Frequency of Electric Field (Weak) is 1.5 mc/s:
Relation between Frequency and Permittivity:
Relation between Temperature and tan δ:
4. Boron Nitride (NB), (N4Si3, Nal) and SiC:
These are called oxide free ceramics and are of great importance. They are various nitrides, sulphides, carbides, that is combination of various chemical elements with nitrogen, sulphur and carbon respectively. Some of them are semiconductor materials. Silicon carbide is one of them while others are ceramics used as dielectric materials.
Nitrides are used for extremely heat resistant dielectrics.
NB, N4Si3 and NAI are used for extremely heat resistant dielectrics.
The characteristics of NB are given below:
(i) Heat conductivity … 0.12 to 0.24 W/cm heat 1000°C
(ii) Melting point … 3000°C
(iii) Insulating properties … good.
Properties of Ferroelectric Materials in Static Fields:
Fig. 7.39 shows the polarisation versus electric field curve of a ferroelectric material. The hysteresis loop obtained is similar to the hysteresis loop of a ferromagnetic material.
Consider a virgin specimen of a ferroelectric material, i.e., a specimen with no initial polarisation.
On application of a progressively increasing electric field E, the polarisation increases along the curve OLM in Fig. 7.39.
Next let the field be reduced so that polarisation reduces from its initial value at M along the curve MNPQ. It may be seen that when E = 0, there exists a certain residual polarisation or remanent polarisation Pr. Stated otherwise, the material is spontaneously polarised.
On further reducing the electric field E in the negative direction, the polarisation ultimately reduces to zero at E = – Ec at point P on the curve. This electric field Ec is referred to as the coercive field.
If the electric field is made further negative, the polarisation also becomes negative and finally reaches a value equal to – E1. Point Q in Fig. 7.39 represents this condition.
Next on increasing E from – E1 to + E1, the polarisation moves along the curve QSM. The closed curve MNPQSM constitutes the so-called hysteresis curve.
Any further reversal of E between the limits E1 and – E1 results in retracing of the hysteresis curve. The curve OLM traced during the initial polarisation of the material is called the initial polarisation curve.
The qualitative explanation of hysteresis loop is as under:
A macroscopic specimen of ferroelectric material may be considered to be formed of several domains, each of which is spontaneously polarised but in different directions. In initial or virgin condition, in this macroscopic specimen, the polarisation vectors of individual domains cancel out resulting in net zero polarisation.
Next when an electric field is applied, the domains with polarisation along the direction of applied field grow at the cost of other domains.
As the applied electric field is increased progressively, polarisation increases as indicated by the curve OLM. However, stage is soon reached when almost all the spontaneous polarisation gets oriented along the field. Under this condition, the entire specimen may be considered to behave as a single domain. No further increase in spontaneous polarisation then results inspite of increase of applied electric field E. Only a slight increase in polarisation P results with increasing field E clue to normal polarisation.
The temperature dependence of the permittivity of ferroelectric materials is very important. The temperature at which the permittivity has a sharply defined peak is called the curie point.
The ferroelectric materials below curie point have the special properties.
Above the curie temperature the materials have no ferroelectric properties and become ordinary insulating materials, the curie point in particular can be greatly shifted at higher range above or below the curie temperature.
Let, E = Field intensity applied to the specimen,
Ei = Induced internal field,
P = Polarisation,
γ = Internal field constant,
∈0 = Permittivity of vacuum,
α = Polarisability, and
N = Number of small cube units in the material.
Let us now study the temperature dependence of dielectric constant ∈r, making use of eqn. (7.33). For simplicity, let us assume α and γ to be temperature independent and let N alone be a function of temperature. Let λve represents the coefficient of volume expansion of the dielectric material.
Then we, have-
The negative sign signifies that with the increase of temperature T, the volume increases and hence N decreases. For normal dielectric with ∈r now exceeding a few tens, the expansion of the material with increase of temperature causes very small change in ∈r, provided α and γ are independent of temperature T. However, if we reduce the temperature sufficiently, quantity N α γ /∈0 increase and approaches unity.
Let the quantity N α γ / ∈0 equal unity at temperature Tf, then at this temperature Tf spontaneous polarization sets in. simultaneously the quantity (∈r – 1) becomes extremely large in the vicinity of this Curie temperature Tf.
Fig. 7.40 shows the variation of (∈r – 1) as a function of N α γ / ∈0 as given by eqn. (7.33).
Thus it is evident that temperature for which N α γ / ∈0 = 1, gives the Curie temperature for the material while N α γ / ∈0 < 1 corresponds to temperature above the ferroelectric Curie temperature Tf. Thus we may state that a Curie temperature arises in a material of high ∈r simply as a result of contraction of the material on cooling.
Ferroelectric materials are the dielectrics analogous to ferromagnetic materials.
Their uses are parallel to those of ferromagnetic materials in such applications as high permeability materials:
1. Magnetostrictive transducers.
2. Magnetic amplifiers.
3. Magnetic information storage devices.
An advantage of ferroelectric material is its large dielectric constant, which permits the use of physically small capacitors.
Several other characteristics that should be taken into consideration are:
(i) The materials coefficient.
(ii) Voltage or bias sensitivity.
(iii) Breakdown characteristics.
The temperature variance of the dielectric constant of several typical types of high- dielectric-constant dielectrics is shown in Fig. 7.41.
The voltage or bias sensitivity shown in Fig. 7.42 indicates that the higher-dielectric- constant materials are more sensitive to increasing bias fields. The Kβ/K0 ratio is the incremental change in dielectric constant, where Kβ is the value of dielectric constant with D.C. bias voltage and K0 is without the D.C. bias voltage.
In ferroelectrcis a high electric field applied to a device can cause voltage breakdown. The general rule is that, the higher the dielectric constant, the lower the dielectric strength. A figure of 2.5 kV/mm at room temperature for high-dielectric-constant materials (4,000 to 6,000) is nominally accepted value, and this can be increased to 15 kV/mm for low dielectric constant (~ 30) dielectrics. These values would have to be derated for elevated temperatures.
Capacitors with very high dielectric constants, in the order of 100,000 and higher, have been developed by treating BaTiO3 in a reducing atmosphere. These capacitors are semiconductor in nature and rather lossy and are therefore, limited to very-low voltage applications such as those in transistor circuits. Other ferroelectrics and the properties are shown in the Table 7.14.
Applications in Transducers:
Ceramics can be made from barium titanate and other additants by sintering together crystalline powders of these materials with certain binders to hold them together as they are being sintered. Such ceramics have many of the properties of single crystals.
Large value and more constant values over temperature ranges can be obtained by the use of lead stannate (PbSnO3) with BaTiO3. The Curie temperature is lowered and spread out over a wide temperature range. The tan δ is in between 1 to 2%. Unfortunately the permittivity decreases with time somewhat faster than do those for lower initial permittivity.
The major use of ferroelectrics is in electro-mechanical transducers. This fact arises from the fact that the single crystal increases in dimensions in the direction of spontaneous polarisation. All the dimensions increases equally so that the ceramic appears unpolarised.
When field E is applied normal to the thickness direction, the thickness is increased. In addition to the increase in thickness, a decrease occurs in the radial direction. This mode can be used to drive a radial resonance in a disc of the material or a length vibration of the slab as shown in Fig. 7.43.
Anti-ferroelectric materials are the materials of ionic crystals having lines of ions spontaneously polarised; with neighbouring lines polarised in antiparallel direction. They are very similar to the anti-ferromagnetic materials. The similar law is followed by the anti- ferroelectric materials.
Tungsten trioxide (WO3) was discovered first to show such anti-ferroelectric properties.
A thorough study of PbZrO3 was done to show the anti-ferroelectric properties. The anti- ferroelectric properties of lead zirconate were shown on room temperature by many workers.
Permanent Electric Materials:
The materials having permanent electric moment are called ‘electrets’.
The electrets are made by the solidification of mixtures of certain organic waxes in a strong electric field. Some of the wax molecules carry permanent dipole moments, they are oriented by the electric field and are frozen in their oriented state with solidification. The electric moment so produced in such materials may persist for several years.
These materials are very similar to the permanent magnet materials.