Crystal Growth and Nonlinear Optics

Crystal Growth and Nonlinear Optics CHAPTER 1 INTRODUCTION TO CRYSTAL GROWTH AND NONLINEAR OPTICS 1.1  INTRODUCTION Crystal growth is regarded as an ancient subject, owing to the fact that the crystallization of salt and sugar were known to the ancient Indian and Chinese civilizations. The subject of crystal growth was treated as part of crystallography and never had an independent identity until the last century. It has a long history of evolution from â€Å"a substance potting art† to a science in its own right which has accelerated by the invention of transistor in 1948, and the subsequent need for high purity semiconductor single crystals. Crystals are the unacknowledged pillars of modern technology. The fundamentals of crystal growth was entirely bestowed upon the morphological studies of the naturally occurring crystals. Thus 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 materials depend on the crystal growth theory and technology. In the early twentieth century, the crystal growth evolved as a separate branch of science 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 field began after the BCF theory was formulated and also when there was a great demand for crystals during World War II. Crystal growth plays an important role 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 transition of crystals has occurred from museum to technology which stimulated crystal grower community to produce large crystals artificially. In the recent scientific era, the utility of crystals has been extended to novel devices such as nonlinear optical and piezoelectric devices. Atomic arrangement with periodicity in three dimensional pattern at equally repeated distances are called single crystals. The preparation of single crystal is more difficult than polycrystalline 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 rapid technical and scientific advancement. The application of crystals has unbounded limits because of its special optical and electrical properties over noncrystalline material. This means that the new crystals have to be grown and fabricated in order to assess their device properties. The main parameters which involve 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 not only scientific understanding, but also the driving force of applied technology which so often provides a significant influence in highlighting the lack of scientific knowledge and need for a more refined 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 possess properties such as piezoelectricity, pyroelectricity and possibly ferroelectricity. In the recent century, the development of science in many areas has been achieved through the growth of single crystals. The single crystals designed for producing second harmonic generation (SHG) received consistent attention for applications in the field of telecommunication, optical information processing, laser remote sensing and colour displays. 1.2  KINETICS OF CRYSTAL GROWTH Crystals are solid substances in general which may be obtained from solid, liquid or vapour phase. Except for solid phase, all other phases yield crystals with developed faces, which represent the crystal medium interface during the development of a crystal from the growth medium. Subsequently, the crystal faces contain information about the nature of the interfaces as well as about the phenomena taking place at the interface. In solid phase growth, some grains grow larger at the expense of others and the interface mainly concave with respect to the growing grain and lies in the interior of the bulk mass. In melt growth, the interface is forced to take the shape of the isotherm inside the crucible containing the melt. However, in both cases, a free development of the faces is rarely encountered. It is also possible to obtain valuable information about the growth processes by using suitable methods. Elementary processes involved in the development of the micromorphology of as grown surfaces of bulk single crystal and epitaxial layers, and of evaporated and etched surfaces under different experimental conditions are essentially similar irrespective of the type of a material. When a crystal nucleus attains a critical size, then it grows into crystal of macroscopic dimension with well developed faces. Several theories have been proposed to explain the mechanism of crystal growth. They are: Surface energy theory, Adsorption layer theory and Diffusion theory. The surface energy theory states that the growing crystal assumes a shape, which has a minimum surface energy. According to adsorption layer theory, a molecule arriving at a crystal surface from the bulk of the supersaturated solution or super cooled melt loses a part of its latent heat. All molecules similar to this move along the surface and join together to form a small two dimensional nucleus due to inelastic collision. Bravious proposed that the growth rate of a crystal face depends on reticular densities of a lattice point 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 difference in concentration between the point of deposition and the bulk of the solution. In diffusion theory, the molecules in contact with the crystal surface are adsorbed quickly. A concentration gradient is thus produced between the bulk of the solution and the growing crystal surface. The mass transfer from the bulk of the solution to the surface involves molecular diffusion. In general, in any crystal 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 reaction products from the growth surface 1.2.1  Solution, Solubility and Super Solubility A solution is a homogeneous mixture of a solute in a solvent. Solute is a component, which is present in a smaller quantity. For a given solute, there may be different solvents. The solvent is chosen taking into account of the following factors to grow crystals from solution: (i) Good solubility for the given solute (ii) Good temperature coefficient of solute solubility Less viscosity (iv) Less volatility (v) Less corrosion and non toxicity (vi) Low vapour pressure and (vii) Cost advantage Solubility 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 important 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 maintain 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 faster 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 data at various temperatures are essential to determine the level of supersaturation. Hence, the solubility of the solute in the ch osen solvent must be determined before starting the growth process. The relationship between the equilibrium concentrations as a function of temperature is represented by the solubility diagram in Figure 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 posi tive) and crystals can be grown only from supersaturated solutions, which contain an excess of the solute above the equilibrium value. The temperature-concentration diagram is divided into three regions, which are termed as region I, II and III 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 unstable 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 AB’C’ represents an operation carried out at constant temperature. Penetration 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 eventually fall into the solution and seed in it. In practice, a combination of cooling and evaporation as represented by the line AB†C† is also adopted. 1.2.2  Expression for Supersaturation In 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 system 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 dissolved 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 ÃŽ ±, ÃŽ ² and à Ã¢â‚¬Å" are interrelated (Khamshii 1969) 1.3  NUCLEATION In a supersaturated or super cooled system, few atoms or molecules join together and a change in energy takes place during the formation of clusters. 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 tendency 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 general A 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. 1.3.1  Types of Nucleation Nucleation may occur spontaneously or may be induced artificially. These two cases are frequently 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 nucleation Nucleation can often be induced by external processes like agitation, friction, mechanical shock, electromagnetic fields, extreme pressure, ultraviolet, X-rays, ÃŽ ³Ã¢â‚¬â€œ rays, sonic and ultrasonic radiation and so on (Mullin 2001; Laudise 1975; Gilman 1963; Stringfellow 1979; Sangwal 1987; Jancic Grootscholten 1984). 1.3.2  Energy of formation of a nucleus Any isolated droplet of a fluid 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 equilibrium with its surrounding at constant temperature and pressure would be minimum for a given volume. When a volume free energy per unit volume is considered to be constant ÃŽ £ai ÏÆ'i = minimum (1.5) whereai is area of ith face and ÏÆ'i is surface energy per unit area Thus considering the nucleus to be spherical, the energy of formation of the nucleus is determined. 1.3.3  Energy of Formation of Spherical Nucleus The 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. Therefore the total free energy change associated with the formation of homogeneous nucleation may be considered as follows. Let ΔG 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 as ΔG = ΔG S + ΔG V (1.6) where ΔGS is the surface free energy change and ΔGV is the volume free energy change. For a spherical nucleus of radius r, ΔG = Ï€r3 ΔG V + 4 Ï€r2ÃŽ ³ (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 ÃŽ ³ is the interfacial tension and ΔGv 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.

Has Globalisation Destroyed the Power of the Modern State? Essay

There is not doubt that globalisation is one of the buzzwords of the twenty first century, radically transforming international relations around the world, and directly or indirectly altering the way we view global politics, but how much has it affected nation states and their power? Globalisation is a complex and abstract term which has been given many definitions and meanings. For the purpose of this essay, I shall use a single definition which is closest to what I think globalisation is, and when referred to in the essay, this is what is meant. Heywood (2011) states that â€Å"Globalization is the emergence of a complex web of interconnectedness that means that our lives are increasingly shaped by events that occur, and decisions that are made, at a great distance from us.† The causes of this interconnectedness can be broken down into three engines of globalisation; Cultural, Political and Economic. Cultural globalisation is facilitated by technological advances in communic ations and especially the internet. This enables a large amount of the developed worlds population instant access to vast amounts of information unaffected by physical borders (except when censorship is in place), which in turn is making the world more culturally homogeneous. The rise of multinational actors like transnational corporations (TNC’s (for example Sony, Nestlà © and Nike)), non governmental organisations (NGO’s (for example Greenpeace, Oxfam and Amnesty International)) and other international organisations (eg; UN, EU and NATO) means that there are more authoritative actors on the world stage, as opposed to historically, states being the only predominant actor. Globalisation means that the economic market is now truly global, as money can be shifted worldwide in an instant. This has facilitated businesses to operate in different countries to their home country to take advantage of cheaper labour costs, local resources and other factors, which mean goods are now manufactured on a global scale. All these factors mean that geographical distance and territorial borders are becoming â€Å"less significant† (Heywood 2011). Since the creation of the modern idea of statehood after the Peace of Westphalia (1648), the nation state has been vastly the most predominant actor on the world stage. Sovereignty allowed states to have sole power over what happened within their own borders, and disputes between states usually brought about war. The classic definition of a state as outlined in the Montevideo Convention has four features: 1) A defined territory. 2) A permanent population. 3) An effective government. 4) The capacity to enter into relations with other states.

Getting the Best Essay Topics on Domestic Violence

Getting the Best Essay Topics on Domestic Violence Domestic violence is thought to be a widespread problem but it's also among the most under-reported crimes, which makes it troublesome to provide a realistic estimate of the amount of incidents. It is a type of abuse. It is among the serious social problems that should not be ignored. It is most commonly referred to as Spousal Abuse. Female immigrants or refugees face lots of the exact challenges as other abused ladies. Building prisons and increasing incarceration isn't the only remedy to the issue of violence. A Socio-Economic Crisis Domestic violence against women isn't a person or family issue. Ideas, Formulas and Shortcuts for Essay Topics on Domestic Violence Still, every one of them would show up in the overall list. Typically, it takes as many as 2 hours of time to comb through dozens of sites until you discover something exciting to write about. Our site features custom writing help and editing help. There are an infinite number of websites that have sample papers on a wide selection of topic. If you already know the guidelines you'll have to follow, try and stay with it. Standard policy formation has ever centered on the women since they've been historically exposed to the matter of domestic violence. The policy is going to be implemented by the USA department of health and human services. I n the standard context, the policies are confined to the women. Others, however, appear to be relatively immune' to detrimental short-term consequences. Distinct kinds of physicians take part in intervening for the victims. Providing superior MH and wellness services to children who witness domestic violence, in actuality, is among the best approaches to reducing the upcoming prevalence of violence. The communities are predicted to support the policy since it's developed for the mutual advantage of all of the members. The Nuiances of Essay Topics on Domestic Violence When you compose an excellent essay, you need to pay exclusive attention to its structure. If you would like to base your doctoral project on the topic of domestic violence, you should choose a great topic for your work. The format and structure of the essay will also vary based on the kind of paper you're likely to write. As soon as you have mastered the format of 3 paragraphs it's possible to move to the five paragraphs. It's great because the subject of your graduate paper ought to be appealing for you in the very first location. You must be proficient in the topic, have an overall idea about the chosen issue and can get the best arguments to show your thesis. For example, your thesis might handle a specific kind of injury. Failing to have a really awesome thesis only means you are not going to have an excellent domestic violence paper. A Startling Fact about Essay Topics on Domestic Violence Uncovered It is very important that you create an outstanding perspective on your topic you may support and defend. The development of one approach to the problem is called for to be able to curb the hidden matter. You need to be able to receive enough info to research your dissertation idea. Scholarship essay examples are supplied for insight on the best way to write a scholarship essay. You must also provide your landlord a copy of a security program, which you'll be able to create with the assista nce of your community domestic violence or sexual assault agency. Ally you need to do is to correctly submit your order instructions and create the payment. The camping educates the women about how to manage a number of the sexual assault incidences that could possibly be classified as rapes like date rape and statutory rape. New Questions About Essay Topics on Domestic Violence Decide whether it's reasonable, to provide the offender yet another chance. The abuser would control the sort of people that you hang around with, even to the extent they won't want to have the individual hanging or even talking to your own friends and family members. Sexual abuse is very hard to detect due to its intimate nature. For ladies, escaping an abusive relationship is quite hard. How the society or a specific community enables the practice doesn't make it right. The suppression of the real details of how their partners are abusing them is a little price which they have to pay to keep the social perspective that the remainder of the community has about them. However good a policy is, the real benefits will be contingent on how the policy educators communicate it. The use of the media in making everybody aware of the issue. Where to Find Essay Topics on Domestic Violence It is normal for the victim for less money as the abuse remains. Physical abuse may also include behaviors like denying the casualty of health care when needed, depriving the victim of sleep or other functions essential to live. Abuse as a young child, was a casualty of abuse for a kid, abused former partners and unemployed or underemployed. Psychological abuse, or behavior that is directed at intimidating and persecuting an individual, is also regarded to be a type of domestic violence the moment it takes place in the family. To safeguard your own well being you would need to leave. Research hypothesis The significant objective of the research is to establish the source of gun violence in American schools and also discover the point to which tighter gun control measures can help to manage the problem. It's quite simple to use together with self explanatory. The best alternative for folks who suffer from any sort of domestic violence is to break the relationship.

The Effects Of Obesity On The Health Organization - 905 Words

Being out of the healthy weight range is called obesity or overweight, which according to The World Health Organization, WHO, (2010 ) is measured by body mass index (BMI), which is the weight of the body over the height squared. People who have a BMI over 25 kg/m^(-2) are considered overweight, while people who have a BMI over 30 kg/m^(-2) are considered obese. Obesity can be the main cause of many cardiovascular diseases. This severe issue can be caused by many factors, and even though there are some unpreventable causes like genetics, this essay is going to focus on some of preventable causes only. In the following paragraphs, a brief information of obesity effects are to be presented, and three causes are going to presented along with solutions for each cause. The three causes of obesity are some biological enhanced food, lack of physical activity, and regular consumption of fast food. Lastly, recommendations will be given in order to reduce obesity or maintain a healthy BMI . Obesity is considered a deadly disease if not cured as it can cause some other terminal diseases like cancer, diabetes, and cardiovascular diseases as more than 200,000 deaths in the UK annually were caused due to obesity surpassing cancer deaths, which is only around 150,000 deaths, S. Allender and M. Rayner (2007). In addition, obesity is guilty of 8% to 15% loss of disability adjusted life years (DALYs) in Europe and North America. Firstly, some biological enhanced food is a one cause ofShow MoreRelatedChildhood Obesity Analysis1473 Words   |  6 PagesParents Child Caretakers Obesity in America is literally a growing problem, affecting every age group. Children are the most venerable group because they have no control over where they have dinner or how often they have fast food. Parents and guardians make decisions about food and are responsible for the health of children. Childhood obesity has more than doubled in the last twenty years. 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