Figure 1 (a). Crucible with the crystal at 910 °c
The analysis of commercially available piezoelectric coefficient of mono-crystalline materials such as PMN-PT (Lead Magnesium Niobate - Lead Titanate) helps to broaden the gate for silicon-integrated applications (Piezo-MEMS) becoming more compatible with micro technology batch processes. Further, advances are expected in terms of miniaturization, optimization, functionality or integration with electronics. Subsequently, operating voltage will be lower and devices response time will improve dramatically. Fabrications of the piezoelectric materials have been performed and analysis on the structure and dielectric has been carried out. This work shows how to improve the dielectric properties for synthesis material.
Piezoelectric materials are materials that are physically deformed in the presence of an electric field or, that produce an electrical charge when they are mechanically deformed. Piezoelectric converters combine most of the advantages of both inductive and electrostatic generators. Piezoelectric materials have wide applications and even can be used in our day-to-day life. But, as such every technological invention has a flip side; even our crystal (piezoelectric) has a disadvantage or limitation to be precise.
The piezoelectric materials convert the mechanical vibrations into electricity, the piezoelectric material fails if the vibrations exceed a certain limit. In general, piezoelectric crystals are very sensitive and respond to even the slightest vibrations. When these vibrations are generated, the amount of electricity depends on the crystal structure and dielectric properties. [1] - [5].
Addressing all the problems and failures discussed above, there is a solution to minimize those losses and failures. Though we cannot completely eliminate the problem of limiting to certain range of vibrations, it can surely be minimised i.e. the frequency or amplitudes can be increased under which the piezoelectric material or crystal can be operated. For this purpose, the structural properties of the piezoelectric material or the crystal needs to be increased. This can be done by varying the compositions of different materials which are being used in the fabrication. Also, utmost care must be taken while fabricating the crystal to minimise the faulty bonding and also the losses inside the crystal. By changing the compositions of the crystal, the structural properties of the crystal would change giving a higher bonding strength between the atoms, thereby increasing the strength of the piezoelectric material or the crystal.
Flux method is a method of crystal growth where the components of the desired substance are dissolved in a solvent (flux). The method is particularly suitable for crystals needing to be free from thermal strain and, it takes place in crucible made of non-reactive metal like platinum, tantalum, niobium or other non-reactive elements.
The starting materials are mixed and placed in the crucible. The crucible closed with a lid, was heated up to soak at temperature Ts at which, during 3 h, the dissolution took place. Next, the furnace was quickly cooled to temperature T1 and then slowly cooled to temperature T2 with a cooling rate from 0.7 to 2.51°C/h. At this temperature, the excess solution was removed by decanting. The crucible with the grown crystals was then cooled to room temperature. It must be pointed out that the temperature of the beginning of crystallization process was not determined. By etching in hot water solution of acetic acid, the remains of the solvent were removed as well as the crystals were softly separated from the crucible. The soak temperature and the other temperature T1 and T2 are based upon the crystal compositions that are changed. The cooling rate applied, when bringing the temperature from T1and T2 also depends upon the various percentages of the materials involved in the compositions. The values of T1 and T2 for 0.32% crystal are 1080°c and 910°c respectively with a cooling rate of 2°c /h, whereas the temperatures stand as 1070°c to 890°c for 0.21% crystal with a cooling rate of 1.7°c/h. One advantage of this method is that the crystals grown, display natural facets so that they can be used for optical experiments without the need for further polishing. A disadvantage is that most flux method syntheses produce relatively small crystals [9].
Figure 1 (a). Crucible with the crystal at 910 °c
Figure1(b). Structure of the crystal before and after finishing (1000X)
The crystal structure of a material (the arrangement of atoms within a given type of crystal) can be described in terms of its unit cell. The unit cell is a small box containing one or more atoms arranged in 3-dimensions as shown in Figure 2. The unit cells stacked in three-dimensional space describe the bulk arrangement of atoms of the crystal. The unit cell is represented in terms of its lattice parameters which are the lengths of the cell edges (a, b and c), and the angles between them (alpha, beta and gamma), while the positions of the atoms inside the unit cell are described by the set of atomic positions (xi, yi, zi) measured from a lattice point. Commonly, atomic positions are represented in terms of fractional coordinates, relative to the unit cell lengths.
Figure 2. 3-Dimensional arrangement of atoms in a Unit Cell
The atom positions within the unit cell can be calculated through application of symmetry operations to the asymmetric unit. The asymmetric unit refers to the smallest possible occupation of space within the unit cell. This does not however, imply that the entirety of the asymmetric unit must lie within the boundaries of the unit cell. Symmetric transformations of atom positions are calculated from the space group of the crystal structure, and this is usually a black box operation performed by computer programs. However, manual calculation of the atomic positions within the unit cell can be performed from the asymmetric unit, through the application of the symmetry operators described within the 'International Tables for Crystallography [10].
It is a tool used for determining the atomic and molecular structure of a crystal, in which the crystalline atoms cause a beam of incident X-rays to diffract into many specific directions. By measuring the angles and intensities of these diffracted beams, a crystallographer can produce a three dimensional picture of the density of electrons within the crystal. From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical bonds, their disorder and various other information.
These scattering methods generally use monochromatic X-rays, which are restricted to a single wavelength with minor deviations. A broad spectrum of X-rays (that is, a blend of X-rays with different wavelengths) can also be used to carry out X-ray diffraction, a technique known as the Laue method. This is the method used in the original discovery of X-ray diffraction. Laue scattering provides much structural information with only a short exposure to the X-ray beam, and is therefore used in the structural studies of very rapid events (Time resolved crystallography). However, it is not as well-suited as monochromatic scattering for determining the full atomic structure of a crystal and therefore, works better with crystals with relatively simple atomic arrangements. The Laue back reflection mode records X-rays scattered backwards from a broad spectrum source. This is useful if the sample is too thick for X-rays to transmit through it. The diffracting planes in the crystal are determined by knowing that the normal to the diffracting plane bisects the angle between the incident beam and the diffracted beam. A Greninger chart can be used to interpret the back reflection Laue photograph.
The structural analysis are done under X-ray Diffraction unit for the crystal. The results were as follows:
Figure 3 depicts the fragments of x-ray diffraction patterns for (X=0.32) PMN-PT.
Figure 3. Fragments of X-ray diffraction patterns for(X=0.32) PMN-PT
The theoretical dielectric strength of a material is an intrinsic property of the bulk material and is dependent on the configuration of the material or the electrodes with which the field is applied. The "intrinsic dielectric strength" is measured using pure materials under ideal laboratory conditions. At breakdown, the electric field frees bound electrons. If the applied electric field is sufficiently high, free electrons from background radiation may become accelerated to velocities that can liberate additional electrons during collisions with neutral atoms or molecules in a process called avalanche breakdown. Breakdown occurs quite abruptly (typically in nanoseconds), resulting in the formation of an electrically conductive path and a disruptive discharge through the material. For solid materials, a breakdown event severely degrades, or even destroys, its insulating capability
Factors affecting the apparent dielectric strength are,
The relative permittivity of a material under given conditions reflects the extent to which it concentrates electrostatic lines of flux. In technical terms, it is the ratio of the amount of electrical energy stored in a material by an applied voltage, relative to that stored in a vacuum. Likewise, it is also the ratio of the capacitance of a capacitor using that material as a dielectric, compared to a similar capacitor that has vacuum as its dielectric.
The dielectric constant measurement, also known as relative permittivity, is one of the most popular methods of evaluating insulators such as rubber, plastics, and powders. It is used to determine the ability of an insulator to store electrical energy. The complex dielectric constant consists of a real part (k'), which represents the storage capability and an imaginary part (D), which represents the loss.
Dielectric constant measurements can be performed easier and faster than chemical or physical analysis techniques making them an excellent material analysis tool. The dielectric constant is defined as the ratio of the capacitance of the material to the capacitance of air, or it is given as,
where, Cx = capacitance with a dielectric material and C0 = capacitance without material, or vacuum.
The k' value of dry air is 1.00053, which for most measurement applications is usually close enough to the value of vacuum, which is 1.0000. Thus if a material is to be used for insulating purposes only, it would be better to have a lower dielectric constant, or as close to air as possible. To the contrary, if a material is to be used in electrical applications for storage of electrical charge, the higher the dielectric constant the better. More charge is stored when a dielectric is present than, if no dielectric (air) is present. The dielectric material increases the storage capacity of the plate capacitor; hence the dielectric constant of any solid or liquid would be greater than 1. This is illustrated in Figures 4 and 5.
Figure 4. Specimen
Figure 5: Air
When making these measurements, connection of the material to the measuring instrument (an LCR Meter) is one of the major challenges faced, special fixtures are generally required depending on the material type. With copier toner, PVC compounds, and other powders, the material can be compressed into a test slab or disk at a given thickness so, that it can be measured in a dielectric cell. In simplest terms, a dielectric cell is more than a test fixture with two adjustable plates into which the sample is installed for evaluation of its electrical properties. The most common piece of test equipment for holding a variety of solid materials is the LD-3, a liquid tight, three terminal connection cells with electrode spacing adjustable by a precision micrometer. When connected to an automatic LCR meter, the capacitance (C) and, loss (D) measurements can be readout directly yielding fast, reasonable results [7], [11] and [12].
In the simpler versions of this instrument, the true values of these quantities are not measured; rather, the impedance is measured internally and converted for display to the corresponding capacitance or inductance value. Readings will be reasonably accurate if the capacitor or inductor device under test does not have a significant resistive component of impedance. More advanced designs measure true inductance or capacitance, and also the equivalent series resistance of capacitors and the Q factor of inductive components. Usually, the device under test (DUT) is subjected to an AC voltage source.
The meter measures the voltage across and the current through the DUT. From the ratio of these, the meter can determine the magnitude of the impedance. The phase angle between the voltage and current is also measured in more advanced instruments; in combination with the impedance, the equivalent capacitance or inductance, and resistance, of the DUT can be calculated and displayed. The meter must assume either a parallel or a series model for these two elements. The most useful assumption, and the one usually adopted, is that LR measurements have the elements in series (as would be encountered in an inductor coil) and, that CR measurements have the elements in parallel (as would be encountered in measuring a capacitor with a leaky dielectric). An LCR meter can also be used to judge the inductance variation with respect to the rotor position in permanent magnet machines (however, care must be taken as some LCR meters can be damaged by the generated EMF produced by turning the rotor of a permanent-magnet motor). Figure 6 shows the LCR meter.
Hand held LCR meters typically have selectable test frequencies of 100 Hz, 120 Hz, 1kHz, 10kHz, and 100kHz for top end meters. The display resolution and measurement range capability will typically change with test frequency.
Bench top LCR meters typically have selectable test frequencies of more than 100 kHz. They often include possibilities to superimpose a DC voltage or current on the AC measuring signal. Lower end meters offer the possibility to externally supply these DC voltages or currents while higher end devices can supply them internally. In addition, bench top meters allow the usage of special fixtures to measure SMD components, air-core coils or transformers.
Figure 6. QuadTech 7600 Precision LCR Meter shown with Dielectric Products LD-3 Cell
The analysis was carried out on three crystals with varying compositions as shown in Table 2.
Table 1. Lattice Parameters
Table 2. Dielectric Strength for Different Compositions
After a thorough study of these results from the structural analysis, and the dielectric analysis, it has been concluded that the PMN-PT crystal having a composition of 0.32% of x has the best properties for wide applications, where it can be used as sensing elements or as a voltage generator with 10% increase in the TITANIUM concentration.
It can be used where we require high sensing element applications. Disadvantage of this flux method is that it produces relatively small crystals, but high sensing property. If large crystals need to be fabricated, Bridgeman procedure can be used. But we will not get that much dielectric property. The reasons were the structure was Monoclinic which shows that it has a single mirror plane thereby which the voltage generation can be maximum. The dielectric constant was way higher than those other crystals, which show its high capacitive and electrical characteristics. The results have been compared to those which are presently existing and have been evaluated. Thus by increasing the Titanium composition in the present existing materials, it can be derived that the crystals strength are increased widely to sustain beyond the present limits.