Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from their atomic-scale properties. Thus, solid-state physics forms a theoretical basis of materials science, it has direct applications, for example in the technology of transistors and semiconductors. Solid materials are formed from densely packed atoms; these interactions produce the mechanical, electrical and optical properties of solids. Depending on the material involved and the conditions in which it was formed, the atoms may be arranged in a regular, geometric pattern or irregularly; the bulk of solid-state physics, as a general theory, is focused on crystals. This is because the periodicity of atoms in a crystal — its defining characteristic — facilitates mathematical modeling. Crystalline materials have electrical, optical, or mechanical properties that can be exploited for engineering purposes.
The forces between the atoms in a crystal can take a variety of forms. For example, in a crystal of sodium chloride, the crystal is made up of ionic sodium and chlorine, held together with ionic bonds. In others, the atoms share form covalent bonds. In metals, electrons are shared amongst the whole crystal in metallic bonding; the noble gases do not undergo any of these types of bonding. In solid form, the noble gases are held together with van der Waals forces resulting from the polarisation of the electronic charge cloud on each atom; the differences between the types of solid result from the differences between their bonding. The physical properties of solids have been common subjects of scientific inquiry for centuries, but a separate field going by the name of solid-state physics did not emerge until the 1940s, in particular with the establishment of the Division of Solid State Physics within the American Physical Society; the DSSP catered to industrial physicists, solid-state physics became associated with the technological applications made possible by research on solids.
By the early 1960s, the DSSP was the largest division of the American Physical Society. Large communities of solid state physicists emerged in Europe after World War II, in particular in England and the Soviet Union. In the United States and Europe, solid state became a prominent field through its investigations into semiconductors, superconductivity, nuclear magnetic resonance, diverse other phenomena. During the early Cold War, research in solid state physics was not restricted to solids, which led some physicists in the 1970s and 1980s to found the field of condensed matter physics, which organized around common techniques used to investigate solids, liquids and other complex matter. Today, solid-state physics is broadly considered to be the subfield of condensed matter physics that focuses on the properties of solids with regular crystal lattices. Many properties of materials are affected by their crystal structure; this structure can be investigated using a range of crystallographic techniques, including X-ray crystallography, neutron diffraction and electron diffraction.
The sizes of the individual crystals in a crystalline solid material vary depending on the material involved and the conditions when it was formed. Most crystalline materials encountered in everyday life are polycrystalline, with the individual crystals being microscopic in scale, but macroscopic single crystals can be produced either or artificially. Real crystals feature defects or irregularities in the ideal arrangements, it is these defects that critically determine many of the electrical and mechanical properties of real materials. Properties of materials such as electrical conduction and heat capacity are investigated by solid state physics. An early model of electrical conduction was the Drude model, which applied kinetic theory to the electrons in a solid. By assuming that the material contains immobile positive ions and an "electron gas" of classical, non-interacting electrons, the Drude model was able to explain electrical and thermal conductivity and the Hall effect in metals, although it overestimated the electronic heat capacity.
Arnold Sommerfeld combined the classical Drude model with quantum mechanics in the free electron model. Here, the electrons are modelled as a Fermi gas, a gas of particles which obey the quantum mechanical Fermi–Dirac statistics; the free electron model gave improved predictions for the heat capacity of metals, however, it was unable to explain the existence of insulators. The nearly free electron model is a modification of the free electron model which includes a weak periodic perturbation meant to model the interaction between the conduction electrons and the ions in a crystalline solid. By introducing the idea of electronic bands, the theory explains the existence of conductors and insulators; the nearly free electron model rewrites the Schrödinger equation for the case of a periodic potential. The solutions in this case are known as Bloch states. Since Bloch's theorem applies only to periodic potentials, since unceasing random movements of atoms in a crystal disrupt periodicity, this use of Bloch's theorem is only an approximation, but it has proven to be a tremendously valuable approximation, without which most solid-state physics analysis would be intractable.
Deviations from periodici
The scientific method is an empirical method of acquiring knowledge that has characterized the development of science since at least the 17th century. It involves careful observation, applying rigorous skepticism about what is observed, given that cognitive assumptions can distort how one interprets the observation, it involves formulating hypotheses, via induction, based on such observations. These are principles of the scientific method, as distinguished from a definitive series of steps applicable to all scientific enterprises. Though diverse models for the scientific method are available, there is in general a continuous process that includes observations about the natural world. People are inquisitive, so they come up with questions about things they see or hear, they develop ideas or hypotheses about why things are the way they are; the best hypotheses lead to predictions. The most conclusive testing of hypotheses comes from reasoning based on controlled experimental data. Depending on how well additional tests match the predictions, the original hypothesis may require refinement, expansion or rejection.
If a particular hypothesis becomes well supported, a general theory may be developed. Although procedures vary from one field of inquiry to another, they are the same from one to another; the process of the scientific method involves making conjectures, deriving predictions from them as logical consequences, carrying out experiments or empirical observations based on those predictions. A hypothesis is a conjecture, based on knowledge obtained while seeking answers to the question; the hypothesis might be specific, or it might be broad. Scientists test hypotheses by conducting experiments or studies. A scientific hypothesis must be falsifiable, implying that it is possible to identify a possible outcome of an experiment or observation that conflicts with predictions deduced from the hypothesis; the purpose of an experiment is to determine whether observations agree with or conflict with the predictions derived from a hypothesis. Experiments can take place anywhere from a garage to CERN's Large Hadron Collider.
There are difficulties in a formulaic statement of method, however. Though the scientific method is presented as a fixed sequence of steps, it represents rather a set of general principles. Not all steps take place in every scientific inquiry, they are not always in the same order; some philosophers and scientists have argued. Robert Nola and Howard Sankey remark that "For some, the whole idea of a theory of scientific method is yester-year's debate, the continuation of which can be summed up as yet more of the proverbial deceased equine castigation. We beg to differ." Important debates in the history of science concern rationalism as advocated by René Descartes. The term "scientific method" emerged in the 19th century, when a significant institutional development of science was taking place and terminologies establishing clear boundaries between science and non-science, such as "scientist" and "pseudoscience", appeared. Throughout the 1830s and 1850s, by which time Baconianism was popular, naturalists like William Whewell, John Herschel, John Stuart Mill engaged in debates over "induction" and "facts" and were focused on how to generate knowledge.
In the late 19th and early 20th centuries, a debate over realism vs. antirealism was conducted as powerful scientific theories extended beyond the realm of the observable. The term "scientific method" came into popular use in the twentieth century, popping up in dictionaries and science textbooks, although there was little scientific consensus over its meaning. Although there was a growth through the middle of the twentieth century, by the end of that century numerous influential philosophers of science like Thomas Kuhn and Paul Feyerabend had questioned the universality of the "scientific method" and in doing so replaced the notion of science as a homogeneous and universal method with that of it being a heterogeneous and local practice. In particular, Paul Feyerabend argued against there being any universal rules of science. Historian of science Daniel Thurs maintains that the scientific method is a myth or, at best, an idealization; the scientific method is the process. As in other areas of inquiry, science can build on previous knowledge and develop a more sophisticated understanding of its topics of study over time.
This model can be seen to underlie the scientific revolution. The ubiquitous element in the model of the scientific method is empiricism, or more epistemologic sensualism; this is in opposition to stringent forms of rationalism: the scientific method embodies that reason alone cannot solve a particular scientific problem. A strong formulation of the scientific method is not always aligned with a form of empiricism in which the empirical data is put forward in the form of experience or other abstracted forms of knowledge; the scientific method is of necessity als
In philosophy, systems theory and art, emergence occurs when an entity is observed to have properties its parts do not have on their own. These properties or behaviors emerge only. For example, smooth forward motion emerges when a bicycle and its rider interoperate, but neither part can produce the behavior on their own. Emergence plays a central role of complex systems. For instance, the phenomenon of life as studied in biology is an emergent property of chemistry, psychological phenomena emerge from the neurobiological phenomena of living things. In philosophy, theories that emphasize emergent properties have been called emergentism. All accounts of emergentism include a form of epistemic or ontological irreducibility to the lower levels. Philosophers understand emergence as a claim about the etiology of a system's properties. An emergent property of a system, in this context, is one, not a property of any component of that system, but is still a feature of the system as a whole. Nicolai Hartmann, one of the first modern philosophers to write on emergence, termed this a categorial novum.
This idea of emergence has been around since at least the time of Aristotle. The many scientists and philosophers who have written on the concept include John Stuart Mill and Julian Huxley; the philosopher G. H. Lewes coined the term "emergent", writing in 1875: Every resultant is either a sum or a difference of the co-operant forces. Further, every resultant is traceable in its components, because these are homogeneous and commensurable, it is otherwise with emergents, instead of adding measurable motion to measurable motion, or things of one kind to other individuals of their kind, there is a co-operation of things of unlike kinds. The emergent is unlike its components insofar as these are incommensurable, it cannot be reduced to their sum or their difference. In 1999 economist Jeffrey Goldstein provided a current definition of emergence in the journal Emergence. Goldstein defined emergence as: "the arising of novel and coherent structures and properties during the process of self-organization in complex systems".
In 2002 systems scientist Peter Corning described the qualities of Goldstein's definition in more detail: The common characteristics are: radical novelty. Corning suggests a narrower definition, requiring that the components be unlike in kind, that they involve division of labor between these components, he says that living systems, while emergent, cannot be reduced to underlying laws of emergence: Rules, or laws, have no causal efficacy. They serve to describe regularities and consistent relationships in nature; these patterns may be illuminating and important, but the underlying causal agencies must be separately specified. But that aside, the game of chess illustrates... why any laws or rules of emergence and evolution are insufficient. In a chess game, you cannot use the rules to predict'history' – i.e. the course of any given game. Indeed, you cannot reliably predict the next move in a chess game. Why? Because the'system' involves more than the rules of the game, it includes the players and their unfolding, moment-by-moment decisions among a large number of available options at each choice point.
The game of chess is inescapably historical though it is constrained and shaped by a set of rules, not to mention the laws of physics. Moreover, this is a key point, the game of chess is shaped by teleonomic, feedback-driven influences, it is not a self-ordered process. Usage of the notion "emergence" may be subdivided into two perspectives, that of "weak emergence" and "strong emergence". In terms of physical systems, weak emergence is a type of emergence in which the emergent property is amenable to computer simulation. Crucial in these simulations is. If not, a new entity is formed with new, emergent properties: this is called strong emergence, which cannot be simulated by a computer; some common points between the two notions are that emergence concerns new properties produced as the system grows, to say ones which are not shared with its components or prior states. It is assumed that the properties are supervenient rather than metaphysically primitive. Weak emergence describes new properties arising in systems as a result of the interactions at an elemental level.
However, it is stipulated that the properties can be determined only by observing or simulating the system, not by any process of a reductionist analysis. As a consequence the emerging properties are scale dependent: they are only observable if the system is large enough to exhibit the phenomenon. Chaotic, unpredictable behaviour can be seen as an emergent phenomenon, while at a microscopic scale the behaviour of the constituent parts can be deterministic. B
In philosophy, empiricism is a theory that states that knowledge comes only or from sensory experience. It is one of several views of epistemology, the study of human knowledge, along with rationalism and skepticism. Empiricism emphasises the role of empirical evidence in the formation of ideas, rather than innate ideas or traditions. However, empiricists may argue. Empiricism in the philosophy of science emphasises evidence as discovered in experiments, it is a fundamental part of the scientific method that all hypotheses and theories must be tested against observations of the natural world rather than resting on a priori reasoning, intuition, or revelation. Empiricism used by natural scientists, says that "knowledge is based on experience" and that "knowledge is tentative and probabilistic, subject to continued revision and falsification". Empirical research, including experiments and validated measurement tools, guides the scientific method; the English term empirical derives from the Ancient Greek word ἐμπειρία, cognate with and translates to the Latin experientia, from which the words experience and experiment are derived.
A central concept in science and the scientific method is that it must be empirically based on the evidence of the senses. Both natural and social sciences use working hypotheses that are testable by observation and experiment; the term semi-empirical is sometimes used to describe theoretical methods that make use of basic axioms, established scientific laws, previous experimental results in order to engage in reasoned model building and theoretical inquiry. Philosophical empiricists hold no knowledge to be properly inferred or deduced unless it is derived from one's sense-based experience; this view is contrasted with rationalism, which states that knowledge may be derived from reason independently of the senses. For example, John Locke held that some knowledge could be arrived at through intuition and reasoning alone. Robert Boyle, a prominent advocate of the experimental method, held that we have innate ideas; the main continental rationalists were advocates of the empirical "scientific method".
Vaisheshika darsana, founded by the ancient Indian philosopher Kanada, accepted perception and inference as the only two reliable sources of knowledge. This is enumerated in his work Vaiśeṣika Sūtra; the earliest Western proto-empiricists were the Empiric school of ancient Greek medical practitioners, who rejected the three doctrines of the Dogmatic school, preferring to rely on the observation of phantasiai. The Empiric school was allied with Pyrrhonist school of philosophy, which made the philosophical case for their proto-empiricism; the notion of tabula rasa connotes a view of mind as an blank or empty recorder on which experience leaves marks. This denies; the image dates back to Aristotle: What the mind thinks must be in it in the same sense as letters are on a tablet which bears no actual writing. Aristotle's explanation of how this was possible was not empiricist in a modern sense, but rather based on his theory of potentiality and actuality, experience of sense perceptions still requires the help of the active nous.
These notions contrasted with Platonic notions of the human mind as an entity that pre-existed somewhere in the heavens, before being sent down to join a body on Earth. Aristotle was considered to give a more important position to sense perception than Plato, commentators in the Middle Ages summarized one of his positions as "nihil in intellectu nisi prius fuerit in sensu"; this idea was developed in ancient philosophy by the Stoic school. Stoic epistemology emphasized that the mind starts blank, but acquires knowledge as the outside world is impressed upon it; the doxographer Aetius summarizes this view as "When a man is born, the Stoics say, he has the commanding part of his soul like a sheet of paper ready for writing upon." During the Middle Ages Aristotle's theory of tabula rasa was developed by Islamic philosophers starting with Al Farabi, developing into an elaborate theory by Avicenna and demonstrated as a thought experiment by Ibn Tufail. For Avicenna, for example, the tabula rasa is a pure potentiality, actualized through education, knowledge is attained through "empirical familiarity with objects in this world from which one abstracts universal concepts" developed through a "syllogistic method of reasoning in which observations lead to propositional statements which when compounded lead to further abstract concepts".
The intellect itself develops from a material intellect, a potentiality "that can acquire knowledge to the active intellect, the state of the human intellect in conjunction with the perfect source of knowledge". So the immaterial "active intellect", separate from any individual person, is still essential for understanding to occur. In the 12th century CE the Andalusian Muslim philosopher and novelist Abu Bakr Ibn Tufail included the theory of tabula rasa as a thought experiment in his Arabic philosophical novel, Hayy ibn Yaqdhan in which he depicted the development of the mind of a feral child "from a tabula rasa to that o
Reality is the sum or aggregate of all, real or existent, as opposed to that, imaginary. The term is used to refer to the ontological status of things, indicating their existence. In physical terms, reality is the totality of the universe and unknown. Philosophical questions about the nature of reality or existence or being are considered under the rubric of ontology, a major branch of metaphysics in the Western philosophical tradition. Ontological questions feature in diverse branches of philosophy, including the philosophy of science, philosophy of religion, philosophy of mathematics, philosophical logic; these include questions about whether only physical objects are real, whether reality is fundamentally immaterial, whether hypothetical unobservable entities posited by scientific theories exist, whether God exists, whether numbers and other abstract objects exist, whether possible worlds exist. A common colloquial usage would have reality mean "perceptions and attitudes toward reality", as in "My reality is not your reality."
This is used just as a colloquialism indicating that the parties to a conversation agree, or should agree, not to quibble over different conceptions of what is real. For example, in a religious discussion between friends, one might say, "You might disagree, but in my reality, everyone goes to heaven." Reality can be defined in a way that links it to worldviews or parts of them: Reality is the totality of all things, structures and phenomena, whether observable or not. It is what a world view attempts to describe or map. Certain ideas from physics, sociology, literary criticism, other fields shape various theories of reality. One such belief is that there and is no reality beyond the perceptions or beliefs we each have about reality; such attitudes are summarized in the popular statement, "Perception is reality" or "Life is how you perceive reality" or "reality is what you can get away with", they indicate anti-realism – that is, the view that there is no objective reality, whether acknowledged explicitly or not.
Many of the concepts of science and philosophy are defined culturally and socially. This idea was elaborated by Thomas Kuhn in his book The Structure of Scientific Revolutions; the Social Construction of Reality, a book about the sociology of knowledge written by Peter L. Berger and Thomas Luckmann, was published in 1966, it explained how knowledge is used for the comprehension of reality. Out of all the realities, the reality of everyday life is the most important one since our consciousness requires us to be aware and attentive to the experience of everyday life. Philosophy addresses two different aspects of the topic of reality: the nature of reality itself, the relationship between the mind and reality. On the one hand, ontology is the study of being, the central topic of the field is couched, variously, in terms of being, existence, "what is", reality; the task in ontology is to describe the most general categories of reality and how they are interrelated. If a philosopher wanted to proffer a positive definition of the concept "reality", it would be done under this heading.
As explained above, some philosophers draw a distinction between existence. In fact, many analytic philosophers today tend to avoid the term "real" and "reality" in discussing ontological issues, but for those who would treat "is real" the same way they treat "exists", one of the leading questions of analytic philosophy has been whether existence is a property of objects. It has been held by analytic philosophers that it is not a property at all, though this view has lost some ground in recent decades. On the other hand in discussions of objectivity that have feet in both metaphysics and epistemology, philosophical discussions of "reality" concern the ways in which reality is, or is not, in some way dependent upon mental and cultural factors such as perceptions and other mental states, as well as cultural artifacts, such as religions and political movements, on up to the vague notion of a common cultural world view, or Weltanschauung; the view that there is a reality independent of any beliefs, etc. is called realism.
More philosophers are given to speaking about "realism about" this and that, such as realism about universals or realism about the external world. Where one can identify any class of object, the existence or essential characteristics of, said not to depend on perceptions, language, or any other human artifact, one can speak of "realism about" that object. One can speak of anti-realism about the same objects. Anti-realism is the latest in a long series of terms for views opposed to realism; the first was idealism, so called because reality was said to be in the mind, or a product of our ideas. Berkeleyan idealism is the view, propounded by the Irish empiricist George Berkeley, that the objects of perception are ideas in the mind. In this view, one might be tempted to say that reality is a "mental construct". By the 20th century, views similar to Berkeley's were called phenomenalism. Phenomenalism differs from Berkeleyan idealism in that Berkeley believed that minds, or souls, are not ideas nor made up of ideas, whereas varieti
Effective mass (solid-state physics)
In solid state physics, a particle's effective mass is the mass that it seems to have when responding to forces, or the mass that it seems to have when interacting with other identical particles in a thermal distribution. One of the results from the band theory of solids is that the movement of particles in a periodic potential, over long distances larger than the lattice spacing, can be different from their motion in a vacuum; the effective mass is a quantity, used to simplify band structures by modeling the behavior of a free particle with that mass. For some purposes and some materials, the effective mass can be considered to be a simple constant of a material. In general, the value of effective mass depends on the purpose for which it is used, can vary depending on a number of factors. For electrons or electron holes in a solid, the effective mass is stated in units of the rest mass of an electron, me. In these units it is in the range 0.01 to 10, but can be lower or higher—for example, reaching 1,000 in exotic heavy fermion materials, or anywhere from zero to infinity in graphene.
As it simplifies the more general band theory, the electronic effective mass can be seen as an important basic parameter that influences measurable properties of a solid, including everything from the efficiency of a solar cell to the speed of an integrated circuit. At the highest energies of the valence band in many semiconductors, the lowest energies of the conduction band in some semiconductors, the band structure E can be locally approximated as E = E 0 + ℏ 2 k 2 2 m ∗ where E is the energy of an electron at wavevector k in that band, E0 is a constant giving the edge of energy of that band, m* is a constant, it can be shown that the electrons placed in these bands behave as free electrons except with a different mass, as long as their energy stays within the range of validity of the approximation above. As a result, the electron mass in models such as the Drude model must be replaced with the effective mass. One remarkable property is that the effective mass can become negative, when the band curves downwards away from a maximum.
As a result of the negative mass, the electrons respond to electric and magnetic forces by gaining velocity in the opposite direction compared to normal. This explains the existence of valence-band holes, the positive-charge, positive-mass quasiparticles that can be found in semiconductors. In any case, if the band structure has the simple parabolic form described above the value of effective mass is unambiguous; this parabolic form is not valid for describing most materials. In such complex materials there is no single definition of "effective mass" but instead multiple definitions, each suited to a particular purpose; the rest of the article describes these effective masses in detail. In some important semiconductors the lowest energies of the conduction band are not symmetrical, as the constant-energy surfaces are now ellipsoids, rather than the spheres in the isotropic case; each conduction band minimum can be approximated only by E = E 0 + ℏ 2 2 m x ∗ 2 + ℏ 2 2 m y ∗ 2 + ℏ 2 2 m z ∗ 2 where x, y, z axes are aligned to the principal axes of the ellipsoids, mx*, my* and mz* are the inertial effective masses along these different axes.
The offsets k0,x, k0,y, k0,z reflect that the conduction band minimum is no longer centered at zero wavevector. In this case, the electron motion is no longer directly comparable to a free electron. Still, in crystals such as silicon the overall properties such as conductivity appear to be isotropic; this is because there are multiple valleys, each with effective masses rearranged along different axes. The valleys collectively act together to give an isotropic conductivity, it is possible to average the different axes' effective masses together in some way, to