Electrical Conductivity and Dielectric Studies of Various Glaserite Crystals: A Review

Glaserite (also called aphthitalite) has been considered to be either a stoichiometric compound K3Na(SO4)2 forming a solid solution with Na2SO4 or a compound NaKSO4 forming solid solutions with Na2SO4 as well as with K2SO4. Crystallization of glaserite during isothennal evaporation at 25°C of Southern Tunsian natural brines, when the density of 1.282 was reached has been reported. Aphthitalite from Kilauac(Hawaiian Islands) has also been reported and they suggested that the composition is undoubtedly variable, but has been commonly regarded as (K,Na)2SO4 with K2O:Na2O = 3:1. The glaserite structure has been originally determined by Gossner and confirmed later by Bcllanaca and Pontonnier et al. (2002). The glaserite structure and its deformed derivatives have been found or can be predicted for (A, C)2BX 4 solid solutions with cations A = Na, Ag, Mg, Ca, Cd; cations C = K, Rb, Cs, Ti, NH4, Sr, Ba, Eu and with tetrahedral complexes BXa = BcF4, SO4, SeO4, CrO4, MoO4, WO4, PO4, VO4, AsO4, SiO4, GeO4, etc. Moore. P. B (2003) considered that the formal composition of glaserite could be written as M (3) M(2) M [TO4]2. In K3Na(SO4)2, Na atoms occupy the M(j) and K atoms the M(2) and M(3) sites. K. Okada and J. Ossaka (2000) showed that K atoms first fill the M(3) sites then go to M(2) sites. The electronic stmcture of SO4' ions has been calculated by Bishop et.al.(2006). However the magnetic symmetry of the SO4" centers reported are orthorhombic and molecular symmetry is low. It is assumed that the ratio between the radii of the cations is the governing factor responsible for the formation of glaserite like structure. In glaserite, the cations and anions are arranged in two types of columns in a hexagonal arrangement one containing only cations, Na+ and K+ (type I) and the other both cations and anions, K and SO42- (type II). Since the ions in each column are tightly bound along this direction, the structure has been considered as hexagonal packing of rods. Glaserite has cation: anion ratio of 2:1. Although many of the glaserite related structures do not satisfy this condition, the discrepancy can be accounted for by imputed ionic vacancies along selected columns, thus the structures of calcium tripotassium hydrogen phosphate CaK3H(P04)2 and a - tricalcium phosphates has been reported as glaserite. The glaserite like structure are stable for compounds in which the difference between the radii of the M+ and M3+ cationsoccupying the M, X and Y positions is in the range . However, compounds that are characterized by and have glaserite like structure are also known. Thus for (Glaserite Structure type) is 0.38. After the Na3Fe(PO4)2 structure was studied, Morozov et al. (2001) found that the stability range of glaserite structure could be expanded up to. The electron irradiation induced transformation of apatite to perovoskite via glaserite structure has been reported. The schematic

Glaserites has the general formula A3C (8X4)2, where A and C = Na, K, Rb and BX4 tetrahedra = SO4, SeO4, C1O4, M0O4 and WO4. The glaserite K3Na(SO4)2 is the parent compound for many related compounds, which has been in the focus of intense work owing to their interesting crystal chemistry and importance in mineralogy. Among others K3Na(SeO4)2, K3Na(CrO4)2, K3Na(MoO4)2 and K3Na(WO4)2 are crystallizing in glaserite type structure. Glaserite crystals are in general very stable in air and having very high melting point. Many members of the glaserite family perform a phase transition from the trigonal to monoclinic form. The transition temperatures seem to be mainly depending on the size of the BX4 tetrahedron . The main structural difference between the monoclinic and trigonal structure is in the tilting of the BX4 tetrahedron and the co-ordination of the potassium ions. While in K3Na(WO4)2, the transition is finished at around 275°C, the transition temperature in the corresponding molybdatcs, K3Na(MoO4)2, with 240°C is in the same range. The transition in the selenate, K3Na(SeO4)2 is lower (61°C), while in the chromate, K3Na(CrO4)2 it is significantly lower at-34°C. In the sulphate glaserite, K3Na(SO4)2, the phase transition is found to be at -203°C. The B-X bond lengths at room temperature and phase transition temperature of some glaserite compounds is shown in table 1.

electrical properties of a crystalline solid is the electrical resistance R. The resistance R offered by a conductor to the flow of electric charge is found to be directly proportional to the length (1) and inversely proportional to the area of cross section (A) of the conductor. Thereforewhereis the proportionality constant called electrical resistivity. Thenis the electrical conductivityThe basic unit of conductivity is Siemens (S) (or mho). Electrical conductivity is an inherent property of most materials, and ranges from extremely conductive materials like metals to very non- conductive materials like plastics or glass. The actual cause of the resistivity must be sought as a deviation from the periodicity of the potential in which the electrons move. It is on this concept that the modern theory of conductivity is based. Deviations from the periodicity of the potential causing resistivity may be due to (a) lattice vibration (b) lattice defects such as vacancies, interstitials and dislocations (c) foreign impurity atoms and (d) boundaries. It is interesting to note that Wein in 1913, before the development of wave mechanics, put forward the hypothesis that the resistivity in pure metals was due to thermal vibrations of the atoms in the lattice. The justification of this idea had to await the development of the band theory. In metals, electrons act as moving charge carriers. The electrical conductivity of a metal is defined by where lx is the current density resulting from an applied electric fieldin the x-dircction. In the case of anisotropic solids, the conductivity depends on direction andbecomes a tensor.

Dielectrics are material with very few electrons to take part in normal electric conductivity. Dielectric materials have interesting electric properties because of the ability of an electric field to polarize the material to create electric dipoles. A dipole is an entity in which equal positive and negative charges are separated by a small distance. The electric dipole is given by where is the charge and is the distance. The simplest arrangement for measuring the components of the dielectric tensor occurs in the conventional thin parallel plate condenser. Here the electric field direction is dictated by geometry to the normal to the plates and the depolarization field is also in this direction. Hence the measurement essentially involves only a single direction. Maintaining the imposed electric field in the presence of the depolarization field, for example by fixing the potential on the capacitor requires additional charges on the

capacitance. The ratio of the capacitances of the system with either dielectric or vacuum between the plates is given by the ratio of the charge densities at constant voltage whereis the applied electric field,is the component of electric displacement vector (D) alongandis the appropriate diagonal element ofin a coordinate system one of whose axes lines up with the electric field .Obviouslyis larger than. If the direction of the field relative to crystal axes is known, µn can be expressed in terms of the components of the dielectric tensor in the crystal system by using the transformations. If the crystal axes are not known, we may choose an arbitrary system of coordinates to specify the dielectric tensor. In that case the slab directions for independent measurements could be along the x, y and z-axes and somewhere in each of the xy, the yz and the xz planes of this system. Once the schemes of the coefficients are known, it may then be examined for additional symmetry by transforming it to other frames of reference.

Dielectric materials are basically insulators having the property of storing and dissipating electrical energy when subjected to electromagnetic field. The energy storing property leads to the fabrication of most important constituents of electrical circuit known as capacitors. The dielectric phenomenon arises from the interaction of electric field with different charged particle such as electrons, ions protons and electron shells, which goes to constitute the dielectric material. All dielectric can be subdivided into two-polar and non-polar dielectrics. A dc field behaviour however provides information about the nature of charge carriers, their mobility, conduction mechanism etc. Whereas studies in ac field provide an information into the electrical nature of the molecular or atomic species, which constitutes the dielectric materials. Dielectric spectroscopy measures the dielectric permittivity as a function of frequency and temperature. It can be applied to all nonconducting materials. The frequency range extends over nearly 18 orders in magnitude: from the µHz to the THz range close to the infrared region. as well as localized charges in a material; it determines their strength, their kinetics and their interactions. Thus, dielectric spectroscopy is a powerful tool for the electrical characterisation of nonconducting or semiconducting materials. Rather than focus on details of what happens inside the dielectric materials, electrical engineers often analyze dielectrics from a macroscopic perspective. Impedance spectroscopy (IS) is one such macroscopic approach. Conducting an IS experiment on a solid electrolyte system allows a number of characteristics to be determined. The characteristics of interest will depend on the nature of the system. If the system is a single crystal the bulk electrical property will be of interest. In polycrystalline form grain boundary and defect structures will form an interesting part of the spectrum. As IS is a study of interfaces, it is not only possible to gain some insight into the structure of the material but also know how the material is behaving at the surface. The most commonly used technique for the measurement of dielectric properties is the measure of impedance in the frequency domain. For this type of experiment a single voltage is applied at varying frequencies and the resulting phase shift and amplitude of current are recorded. Phase and amplitude can be directly converted into the real and imaginary components for analysis.

The microscopic behavior of a dielectric material under an electric filed can be attributed to the polarization phenomena of the charged particles, which constitutes the dielectrics. This may an extra nuclear electron, and positively charged nuclei, anion, and cations etc. The oppositively charged species with a reasonable bond between them will form a dipole which will behave as one unit. These dipoles under an electric field may undergo special translational or rotational displacement, which will be reflected in macroscopic behavior of dielectric. The polarization effect will also be dependent on the nature of the dipole and frequency of the applied field under an ac field but the polarization of the dielectric may not follow the field variation. This displacement due to polarization may persist even when the field is stopped. This gives rise to a decay time to attain the equilibrium and the phenomenon is known as relaxation. The decay time is known as relaxation time.

The Debye model is frequently used to explain the dielectric behaviour of materials. A good description of the experimental results is often obtained by using a distribution of relaxation times. The dielectric Measurements are made in a very wide range of frequencies and temperatures and for many types of materials. Jonscher made a very comprehensive review on the subject, and presented a model, the many-body model, for the dielectric spectroscopy. This model introduces the idea of correlated states in the material, arising from interactions between individual dipoles in an interactive system, which form a narrow half-filled band. The preferred orientations of the system can be represented by two potential wells, where their relative occupancy determines the total polarisation, and the application of the external field will excite these states making transitions between the two wells.

Frequency dependent measurements of the ac conductivity have been recognised as an important tool for the study of ionic transport properties of the solids. For this, the conductivity data of solid electrolytes are generally analysed in terms of equivalent circuits composed of frequency independent resistances and capacitances. In most of the cases, the ac response cannot be simulated correctly by simple R-C circuits, e.g. the cases of depressed semicircles in the impedance formalism. To explain such deviation from the ideal behaviour various empirical functions have been formulated which are helpful to fit the experimental data. Most dielectric samples used for impedance measurements have some form of evaporated or otherwise applied metallic electrodes which may be relatively thin, say, of the order of 1µm or less. With samples of conductance and capacitance this may lead to effects which are not negligible and which may affect the shape of the characteristics, giving a false impression of the properties of the material in question. In recent years Jonscher's universal law of dielectric response has been used to model the observed properties of the solid electrolytes. This approach considers theories of cooperative migration and when applied for simulation, needs frequency dependent elements in the equivalent circuits. A R Kulkarni and H S Maiti studied the electrolyte/electrode interface using various electrodes namely silver, graphite and lithium.

Methods of measuring dc and ac electrical conductivity of single crystal are detailed and presented in this chapter. DC electrical conductivity can be measured using electrometer and ac conductivity & dielectric properties of the crystal can be measured using an impedance analyzer. A kiethley programmable electrometer (model 617) is used with internal source for dc measurements and Hioki impedance analyzer discussed in detail. Method of growing a single crystal is also discussed. For the growth of the crystal, a constant temperature bath with digitally programmable temperature controller is used. Since conductivity and dielectrics are anisotropic properties that should be measured in all possible directions, large single crystals should be grown. Growing large single crystal with optical quality is a tedious process. Another objective is the identification of the crystallographic planes. The crystallographic planes can be identified using a well-known method named ―stereographic projection‖. In this study a detailed description is given, how the crystallographic planes are identified using Stereographic projection. This can be cross-checked by a computer program ―Shape‖.

Conductivity measurement has widespread use in industrial applications that involve the measurement of conductivity on materials such as metals, crystals, amorphous materials etc. The unit of conductivity is Siemens/cm (S/cm), which is identical to the older unit of mhos/cm. In this section, methods for obtaining conductivity data on crystals are described. The use of conductivity measurements in research work is very important, and many excellent accounts of various measurement techniques are already available. Various methods have been used to measure conductivity properties. In this study the electrical properties of some Glaserite crystals are studied.

The conductivity of a material is measured in terms of its resistivity. Resistance is most often measured with a digital multimeter. Resistance in the gigaohm and higher ranges must be measured accurately. These measurements are made by using an electrometer, which can measure both very low current and high impedance voltage. Two methods are used to measure high resistance, the constant voltage method and the constant current method. In the constant voltage method a known voltage is applied and electrometer ammeter is used to measure the resulting current. In the constant current method, a constant current is forced through the crystal and the voltage drop across the crystal is measured.

Alternating current measurements are widely used to overcome certain difficulties in dc measurements. Among these are polarization effects in ionic conductors and electrolytes, barriers at internal surfaces and contact resistance. Assuming that the sample is represented by a parallel combination of capacitance and resistance, the values of series

unknown directly. DC Conductivity Measurements- The dc conductivity of the sample was measured using a Keithely (model 617) programmable electrometer with an internal source. In this setup the sample is considered as a resistance. Across the sample a voltage is applied and corresponding current was noted. Using Ohm‘s law the resistance R was calculated. From the resistance the resistivitywas found out using the relationwhere A is the area of the sample and 1 is the thickness. The conductivity is the reciprocal of resistivity.

The sample preparation techniques and the details of the instrument used for the crystal growth are described. The samples prepared were Tripotassium sodium disulphate (K3Na (SO4)2 (or K.NS), Tripotassium sodium dichromate (K3Na (CrO4)2 (or KNCr) and Tripotassium sodium diselinate (K3Na (SeO4) 2 (or KNSe). These are water-soluble crystals and hence they are grown from their aqueous solutions.

This study deals with the topic of measuring dc and ac electrical conductivities and dielectric properties of three selected glaserite crystals namely Tripotassium sodium disulphate (K3Na (SO4) 2 or KNS), Tripotassium sodium dichromate (K3Na (CrO4)2 or KNCr) and Tripotassium sodium diselinate (K3Na (SeO4)2or KNSe). These are purely ferroelastic crystals. The scope of this work involves calculation of bulk properties, knowing the nature and mechanism of conductivity, variations of dc conductivity with temperature, variations of ac conductivity with temperature and frequency, dielectric behavior at different temperatures and frequencies, detection of any phase transition present and determination of power law parameters and activation energies of the crystals under investigation which are reported for the first time. Large single crystals are necessary for the electrical conductivity and dielectric measurements, since these properties are measured in all possible directions. These crystals are not readily available and hence they are grown in the laboratory by slow evaporation technique at constant temperature as a part of the present work. A. K. Radzhabov, E.V. Charnaya, B. Morz, C. Tien, Z. Tylczynski, C.S. Wur (2004). Physics of the Solid State, Vol 46, No.4, pp. 775 – 779. D. M. Bishop, M.Randic and J.R.Morton (2006). J. Chem.Phys. 45, p. 1880. Ferry (1997). Effects of Dynamic Spatial Disorder on Ionic Transport Properties in Polymer Electrolytes based on Poly (Propylene Glycol) (4000), Journal of Chemical Physics, 107, pp. 9168-9175. Gilberto T. Niitsu, Hirotoshi Nagata, Ana C.M. Rodrigues (2004). Journal of Applied Physics, Volume 95, Number 6. J.P. Runt, J.J. Fitzgerald (1997). Dielectric Spectroscopy of Polymeric Materials, American Chemical Society, Washington, DC. K. Jonscher (2001). A new understanding of the dielectric relaxation of solids. J. Mat. Science, 16, p. 2037. K. Okada and J. Ossaka (2000). Structures of Potassium Sodium Sulphate and Tripotassium Sodium Disulphate, Acta Cryst. B 36, pp. 919 – 921. N.F. Mott (2001). E.A. Davis: Electronic Process in Non-Crystalline materials. Clarendon Press, Oxford. P. B. Moore (2003). Am. Mineral, 58, pp. 32-42. Pontonnier, L. M. Caillet and S. Aleonard (2002). Mat. Res. Bull, 7, pp. 799-812. V. A. Morozov, B. I. Lazoryak, A. P. Malakho, K. V. Pokholok, S. N. Polyakov, T. P. Terekhina (2001). The Glaserite like structure of Double Sodium and iron phosphate Na3Fe (PO4)2, J. Solid State Chem. 160, p. 377.

Research Scholar, Satya Sai University, Shehore