Crystal Growth and Nonlinear Optics

Crystal maturation and Nonlinear OpticsCHAPTER 1 invention TO CRYSTAL GROWTH AND NONLINEAR OPTICS1.1INTRODUCTIONCrystal appendage is regarded as an ancient affair, owing to the fact that the quartz glass of salt and sugar were known to the ancient Indian and Chinese civilizations. The subject of watch watch glasslizing ontogeny was treated as agency of watch glasslography and never had an self-reliant identity until the last century. It has a long history of evolution from a substance potting art to a attainment in its own properly which has accelerated by the invention of transistor in 1948, and the subsequent fate for high gear purity semiconductor private quartzs.Crystals argon the unacknowledged pillars of reinvigorated-fangled technology. The fundamentals of vitreous silica produce was entirely bestowed upon the morphologic studies of the naturally occurring crystals. frankincense began the scientific approach for this subject during the seventeenth century by Kepler, followed by quite a few others like Nicolous Steno, Descartes, Bartholinus, etc. This type of morphological study slowly led to the understanding of the atomistic process of crystal growth. Recent bursting research on nanostructured somatics depend on the crystal growth theory and technology. In the early twentieth century, the crystal growth evolved as a separate branch of light and several theories from Kossel, Donnay-Harker, Volmer and Burton, Cabrera and Frank (BCF) were proposed. Although science of crystal growth originated through the explanations of Nicolous Steno in 1669, the actual impetus to this battleground began after the BCF theory was formulated and also when thither was a great demand for crystals during World War II.Crystal growth plays an principal(prenominal) grapheme in material science and engineering. It is an interdisciplinary subject of physics and chemistry. initially the natural crystals were adored as gems and museum pieces. Later, a tr ansition of crystals has occurred from museum to technology which excite crystal grower community to produce large crystals artificially. In the new-fangled scientific era, the utility of crystals has been extended to novel devices such as nonlinear optical and piezoelectric devices.Atomic arrangement with periodicity in terzetto dimensional pattern at equally repeated distances be called single crystals. The preparation of single crystal is more difficult than poly crystalised material and extra effort is justified because of outstanding properties of single crystals (Laudise 1970). The single crystal growth has prominent role in the present era because of quick technical and scientific advancement. The application of crystals has unbounded limits because of its special optical and galvanic properties over non crystalline material. This means that the new crystals have to be large and fabricated in order to assess their device properties. The main parameters which remove in crystal growth are nucleation, growth rate, stability, crystalline defects, compositional inhomogeneity and thermodynamics of the source of liquid.The evolution in the crystal growth requires non intact scientific understanding, but also the driving force of applied technology which so ofttimes provides a significant influence in foreground the lack of scientific knowledge and need for a more subtile evolution of science and indeed the development of new concepts. The studies on the growth and physical properties of single crystals of amino acids and their compounds are of great interest because they stimulate properties such as piezoelectricity, pyroelectricity and possibly ferroelectricity.In the recent century, the development of science in many studys has been achieved through the growth of single crystals. The single crystals designed for producing back harmonic generation (SHG) received consistent attention for applications in the field of telecommunication, optical i n defining processing, laser remote sensing and coloration displays.1.2KINETICS OF CRYSTAL GROWTHCrystals are firm substances in general which whitethorn be obtained from solid, liquid or vapour phase. Except for solid phase, all other phases yield crystals with developed fountains, which represent the crystal specialty interface during the development of a crystal from the growth medium. Subsequently, the crystal faces tick off information or so the nature of the interfaces as well as about the phenomena taking dress at the interface.In solid phase growth, roughly grains grow larger at the expense of others and the interface mainly concavo-concave with respect to the increase grain and lies in the interior of the volume mass.In melt growth, the interface is forced to take the shape of the isotherm inside the crucible containing the melt. However, in both fictional characters, a muster out development of the faces is rarely encountered. It is also possible to obtain v aluable information about the growth processes by using suitable methods. Elementary processes involved in the development of the micromorphology of as bragging(a) scrapes of bulk single crystal and epitaxial works, and of evaporated and etched bulges under several(predicate) experimental conditions are essentially similar irrespective of the type of a material.When a crystal burden attains a critical surface, then it grows into crystal of macroscopic dimension with well developed faces. Several theories have been proposed to formulate the mechanism of crystal growth. They areSurface life force theory,adsorption stratum theory andDiffusion theory.The surface force theory states that the growing crystal assumes a shape, which has a minimum surface nil. According to adsorption layer theory, a molecule arriving at a crystal surface from the bulk of the supersaturated resolve or super cooled melt loses a part of its latent heat. All molecules similar to this move along the surface and marrow together to form a small 2 dimensional nucleus callable to inelastic collision. Bravious proposed that the growth rate of a crystal face depends on reticular densities of a lattice betoken of that face. The surface energy is the least when the face possesses the greatest reticular density. The attachment energy is due to Vander Waals force in the case of homopolar crystals and it is due to electrostatic forces in the case of ionic crystals. According to the diffusion theory matter is deposited continuously on a crystal phase at the rate proportional to the expiration in assiduousness between the point of deposition and the bulk of the ascendant.In diffusion theory, the molecules in contact with the crystal surface are adsorbed quickly. A tightfistedness gradient is thus produced between the bulk of the theme and the growing crystal surface. The mass transfer from the bulk of the solution to the surface involves molecular(a) diffusion. In general, in any c rystal growth process, the following steps are involved(i) Generation of reactants(ii) Transport of reactants to the growth surface(iii) Adsorption at the growth surface(iv) Nucleation(v) Growth and(vi) Removal of unwanted answer products from the growth surface1.2.1Solution, solvability and Super SolubilityA solution is a similar mixture of a solute in a effect. Solute is a component, which is present in a smaller metre. For a wedded solute, there may be different resultant roles. The root is chosen taking into news report of the following factors to grow crystals from solution(i) goodish solubility for the given solute(ii) Good temperature coefficient of solute solubilityLess viscosity(iv) Less volatility(v) Less wearing and non toxicity(vi) Low vapour pressure and(vii) Cost advantageSolubility of the material in a solvent decides the amount of the material, which is available for the growth and hence defines the total size limit. Solubility gradient is another impor tant parameter, which dictates the growth procedure. If the solubility gradient is very small, slow evaporation of the solvent is the best option for crystal growth in order to hold on a constant supersaturation in the solution. Growth of crystals from solution is mainly a diffusion-controlled process. The medium must be viscous enough to enable alacritous transference of the growth units from the bulk solution by diffusion. Hence, a solvent with less viscosity is preferable. Supersaturation is an important parameter for the solution growth process. The crystal grows by the access of the solute in the solution where the degree of supersaturation is maintained. The solubility information at various temperatures are essential to determine the level of supersaturation. Hence, the solubility of the solute in the chosen solvent must be determined earlier starting the growth process.The descent between the offset parsimoniousnesss as a function of temperature is represented by the solubility plot in finger 1.1 which is known as temperature-concentration diagram. Miers carried out extensive research in the relationship between supersaturation and spontaneous crystallization. The lower continuous line is the normal solubility curve for the salt concerned. Temperature and concentration at which spontaneous crystallization occurs are represented by the upper broken curve, generally referred to as the supersolubility curve. The whole concentration-temperature field is separated by the saturated solution line (solubility curve) into two regions, unsaturated and supersaturated solutions. Saturated solutions are those mixtures, which can retain their equilibrium indefinitely in contact with the solid phase with respect to which they are saturated. The solubility of most substances increase with temperature (the temperature coefficient of the solubility is positive) and crystals can be grown merely from supersaturated solutions, which contain an additional of the solute above the equilibrium value. The temperature-concentration diagram is divided into three regions, which are termed as region I, II and common chord respectively.Figure 1.1 Miers solubility curve(i)The stable (undersaturated) zone where crystallization is not possible (Region I).(ii)The region II is a metastable zone, between the solubility and supersolubility curves, where spontaneous crystallization is improbable. However, if a seed crystal is placed in metastable solution, growth would occur on it.(iii)The region III is an tender or labile (supersaturation) zone, where spontaneous crystallization is more probable.If the solution whose concentration and temperature represented by point A in the Figure. 1.1, is cooled without loss of solvent (Line ABC) spontaneous crystallization cannot occur until conditions represented by point C are reached. At this point, crystallization is spontaneous. Further cooling to some point D will produce spurious nucleation. The evaporation of solvent from the solution results in supersaturation. The line ABC represents an operation carried out at constant temperature. Pe earningsration beyond the supersolubility curve into the labile zone rarely happens, as the surface from which evaporation takes place is usually supersaturated to a greater degree than the bulk of solution. Crystals, which appear on this surface lastly fall into the solution and seed in it. In practice, a conspiracy of cooling and evaporation as represented by the line ABC is also adopted.1.2.2Expression for SupersaturationIn order to grow crystals, the solution must be supersaturated. Supersaturation is the driving force, which governs the rate of crystal growth. The supersaturation of a dodge may be expressed in number of ways. The basic units of concentration as well as temperature must be specified.The degree of supersaturation of a solution is defined using the concept of absolute supersaturation (1.1)where C is the concentration of the dissolve d substance at a given moment and Co is its solubility limit. The degree of supersaturation can also be defined as the relative supersaturation, which is given by (1.2)or as the coefficient of supersaturation. (1.3)The quantities , and are interconnected (Khamshii 1969)1.3NUCLEATIONIn a supersaturated or super cooled system, few atoms or molecules join together and a change in energy takes place during the formation of bunch togethers. The cluster of atoms or molecules is called embryo. An embryo may grow or disintegrate and disappear completely. If the embryo grows to a particular size, critical size known as critical nucleus, then there is a purpose for the nucleus to grow. Thus, nucleation is an important phenomenon in crystal growth and is the precursor of crystal growth and of the overall crystallization process. The formation of stable nucleus occurs only by the addition of a number of molecules (A1) until a critical cluster is formed. In generalA n-1 + A 1 A n (Critical) (1.4)Any further addition to the critical nucleus results in nucleation followed by growth. Once these nucleus grow beyond a certain size, they become stable under the average condition of supersaturation of the solution. Further, the creation of a new phase in the homogeneous solution demands for the expenditure of certain quantity of energy. Once embryos achieve this critical size there is a high probability that they will grow, relatively unhindered, to macroscopic size.1.3.1Types of NucleationNucleation may occur impromptu or may be induced artificially. These two cases are often referred to as homogeneous and heterogeneous nucleation respectively. The term primary will be reserved for both the cases of nucleation in the systems that do not contain crystalline matter. On the other hand, the nucleus is often generated in the vicinity of crystals presented in the supersaturated system. This phenomenon is referred to as secondary nucleation. Figure 1.2 shows the classification of nucleation.The spontaneous formation of crystalline nucleus in the interior of the parent phase is called homogeneous nucleation. If the nucleus forms heterogeneously around ions, impurity molecules or on dust particles, on surfaces or at structural irrgularities such as dislocations or other imperfections is called heterogeneous nucleation.Figure 1.2 Schematic diagram indicating the classification of nucleationNucleation can often be induced by external processes like agitation, friction, mechanical shock, electromagnetic fields, extreme pressure, ultraviolet, X-rays, rays, sonic and ultrasonic radiation and so on (Mullin 2001 Laudise 1975 Gilman 1963 Stringfellow 1979 Sangwal 1987 Jancic Grootscholten 1984).1.3.2 zip of formation of a nucleusAny isolated droplet of a quiet is most stable when its free energy is maximum and thus its area is minimum. The growth of an embryo or a crystal could be considered as an example of this principle. The total energy of the crystal in equ ilibrium with its skirt at constant temperature and pressure would be minimum for a given volume. When a volume free energy per unit volume is considered to be constantai i = minimum (1.5)whereai is area of ith face andi is surface energy per unit areaThus considering the nucleus to be spherical, the energy of formation of the nucleus is determined.1.3.3Energy of Formation of Spherical sumThe formation of a droplet nucleus due to supersaturation of vapour demands the expenditure of a certain quantity of energy in the creation of new phase. then the total free energy change associated with the formation of homogeneous nucleation may be considered as follows. Let G be the overall excess free energy of the embryo between the two phases. Since the volume and surface free energies, the total free energy associated with the process can be written asG = G S + G V (1.6)where GS is the surface free energy change and GV is the volume free energy change. For a spherical nucleus of radius r ,G = r3 G V + 4 r2 (1.7)The first term expresses the formation of the new surface and the second term expresses the difference in the chemical potential between the crystalline phase and the surrounding mother liquid. Where is the interfacial tension and Gv is the free energy change per unit volume, which is a negative quantity, r the radius of the nucleus. Since the surface free energy increases with r2 and volume free energy decreases with r3, the total net free energy change increases with increase in size and attains a critical value after which it decreases. The size corresponding to the maximum free energy change is called critical nucleus.