#### Solid State Physics-I, Physics tutorial

Introduction to Solid State Physics:

Define: Solid state physics is the branch of condensed matter physics which deals by the physical properties of solids, particularly the thermodynamic, electromagnetic and structural properties of crystalline solids like semiconductors.

By statement or definition, solid state is that specific aggregation form of matter characterized through strong interaction forces between the constituent particles (that is, atoms, ions and molecules). As an outcome, a solid state material consists of an independent geometric form (in contrary to liquids, which take the form of the vessel) and an invariant volume (that is, in contrary to gases or vapors) in a particular temperature and pressure conditions. As temperature rises, a solid state material can grow into the other aggregation form (that is, liquid or gas). The solid state physics studies the mechanical, structural, thermodynamic, electrical, magnetic and optical properties of poly-crystalline and non-crystalline solids (for illustration: amorphous materials like glass).

Solid state physics is basically the study of how atoms arrange themselves to solids and what properties such solids have. By observing the arrangement of the atoms and considering how electrons move between the atoms, it is possible to comprehend most of the macroscopic properties of materials like their elasticity, electrical conductivity and optical properties.

Solid-state Physics is the stream of physics which deals by the structure and properties of the solids. Solid-state physicists do research in a diversity of regions ranging from technologically significant work on semiconductors and magnetic materials to work of academic interest only, like in the field of superconductivity. (The word 'solid state' as most usually employed in common speech signifies to electronic equipment employing the transistors and other semiconductor devices; however work in the company of semiconductors is only one phase of this extremely broad field.)

Solids comprises of atoms or molecules packed closely altogether - often in a very orderly manner. Most of the physical properties of solids based on the way in which the atoms or molecules are packed or arranged; that is, on the internal structure of the solid. For this cause the study of the structure of solids, termed as crystallography, is of fundamental significance to all other investigations in the solid-state physics.

The study of attractive forces among atoms or molecules in solids is the other fundamental characteristic; it has helped significantly in the understanding of most of the properties of solids. For illustration, as the attractive forces are electrical in nature, they play an extremely significant role in finding out such electrical properties of solids as conductivity. Such forces as well find out to a huge extent the optical and thermal properties of solids, like refractive power (that is, the capability to bend light waves) and the capability to conduct the heat.

Solids are seldom, if ever, pure. A pure substance comprises of one chemical element or compound only; impurities are traces of other elements mixed in by the main element or compound.) The study of influence of impurities on the properties of solids is a significant feature of solid-state physics. For illustration, devices like the solar battery and the transistor were made probable only after scientists had learned how to control the impurities in silicon and identical substances.

Often an atom or molecule is unexpectedly absent in the packing arrangement of the solid. The gap left in the structure is termed as a vacancy. Vacancies might deeply modify the mechanical properties of the materials. For illustration, a piece of cold-worked metal consists of many more vacancies than a comparable piece of the annealed metal, and is generally much harder and tougher. Therefore the study of vacancies through solid-state physicists is of considerable interest to the metallurgists.

The atoms and molecules at the surface of a solid are not packed in the similar manner as those in the interior; dissimilar to interior atoms or molecules, they are not totally surrounded by neighboring atoms or molecules. Therefore the surface behavior distinct substantially from that of the rest of the solid. The study of solid surfaces and of films (which is, extremely thin solids comprising mostly of surface) has led to the utilization in electronics of thin films having unusual electrical properties and to ways of raising the resistance of metal surfaces to the corrosion.

History of Solid State Physics:

However early experiments by ceramics and methods for tempering steel might be considered the forerunners of solid-state physics, it was not until the starting of the nineteenth century that the study of solids was approached in the scientific way. This was all through this period that Ren Just Hay, a French mineralogist, starts speculating concerning the internal structure of the crystalline materials and places the foundations for crystallography. Though, Hay's work and the work of some others who followed get little attention at the time.

The real starting of crystallography occurred in the year 1912 when Max von Laue, assisted through Walter Friedrich and Paul Knipping, introduced that crystals diffract X-rays. Instantly following this invention, William Henry Bragg and his son William Lawrence Bragg employed the diffraction method to find out the structure of solids. Von Laue gets the Nobel Prize in the year 1914 in physics for his work and the Braggs get the 1915 prize for theirs.

The invention of X-ray diffraction was the turning point in the growth of solid-state physics, giving a base for a theoretical understanding of the solids. Solid-state physics has grown quickly ever since-mainly since World War II. A great technical achievement of solid-state physics occurred in the year 1948 - the growth of the transistor via William Shockley, John Bardeen and Walter H. Brattain of the Bell Telephone Laboratories.

Crystal structure and properties:

Most of the properties of materials are influenced by their crystal structure. This structure can be investigated by employing a range of the crystallographic methods comprising X-ray crystallography, neutron diffraction and the electron diffraction.

The sizes of the individual crystals in a crystalline solid material differ based on the material involved and the conditions when it was made. Most of the crystalline materials encountered in daily life are polycrystalline having the individual crystals being microscopic in scale, however macroscopic single crystals can be generated either naturally (example: diamonds) or artificially.

Real crystals characteristic defects or irregularities in the ideal arrangements, and it are these defects which critically find out most of the electrical and mechanical properties of the real materials.

Most of the solids and some crystalline liquids encompass a regular, repeating, three-dimensional arrangement of atoms termed as a crystal structure or crystal lattice. In contrary, an amorphous solid is a kind of solid material, like glass, which lacks such a long-range repeating structure. Most of the physical, optical and electrical properties of the crystalline solids or liquids are closely associated to the crystal structure. The repeating units of a crystalline structure that are build up of small boxes or other three-dimensional shapes, are termed to as cells. Most of these cells are grouped altogether in a repeating, orderly structure to build up the entire structure.

The crystal structure of a given crystalline material can influence most of that material's entire properties. It is one of the main defining factors influencing the optical properties of the material, for illustration. Crystal structure as well significantly influences the reactivity of the crystalline material, as it finds out the arrangement of reactive atoms on the outside edges and faces of the crystalline liquid or solid. Other significant material traits, comprising electrical and magnetic properties of certain materials, are as well determined largely through crystal structure.

Defects in solids: Point defects and line defects

Imperfections or defects: Any divergence from the perfect atomic arrangement in a crystal is stated to have imperfections or defects. However, by employing the term defect is sort of a misnomer as these characteristics are generally intentionally employed to manipulate the mechanical properties of the material.

Adding alloying elements to a metal is one approach of introducing a crystal defect. Crystal imperfections encompass strong influence on many properties of crystals, like strength, electrical conductivity and hysteresis loss of ferromagnetism. Therefore a few significant properties of crystals are regulated by as much as by imperfections and by the nature of the host crystals.

- The conductivity of certain semiconductors is due completely to trace the amount of chemical impurities.

- Color, luminescence of most of the crystals occurs from impurities and imperfections.

- Atomic diffusion might be accelerated extremely through impurities or imperfections.

- Mechanical and plastic properties are generally regulated through imperfections.

Imperfections in the crystalline solids are generally categorized according to their dimension as:

1) Point imperfections (or Zero dimensional defects)

2) Line imperfections (or one dimensional defects)

3) Plane or surface imperfections (or two dimensional defects)

4) Volume imperfections (or three dimensional defects)

Bonds in solid:

A solid comprises of atoms, ions and molecules packed closely altogether and forces which hold them in place give mount to the characteristic properties of the different type of solids. The covalent bonds which can link a fixed number of atoms to make a certain molecule can as well link an unlimited number of molecules to form a solid. Addition of Ionic solids, Van der Waals, and metallic bonds give the cohesive forces in solids, whose structural elements are correspondingly ion, molecules and metal atoms.

Therefore on the basis of bonding type, we have five groups of solids:

1) Ionic solids (NaCl, NaOH and so on)

2) Covalent solids (Diamond and Silicon)

3) Metallic solids (various metals and alloys)

4) Van der Waals bonded solids or molecules (O2, H2, Solid He, Kr, Xe)

5) Hydrogen bonded solids (Ice and Some fluorides)

Electronic properties:

The properties of materials like electrical conduction and heat capacity are investigated through solid state physics. An early model of electrical conduction was the Drude model that applied kinetic theory to the electrons in a solid. By supposing that the material includes immobile positive ions and an electron gas of classical, non-interacting electrons, the Drude model was capable to describe electrical and thermal conductivity and the Hall Effect in metals, however it greatly overestimated the electronic heat capacity.

Arnold Sommerfeld joined the classical Drude model by quantum mechanics in the free electron model (or Drude-Sommerfeld model). In this, the electrons are modeled as a Fermi gas, a gas of particles that follow the quantum mechanical Fermi-Dirac statistics. The free electron model gave enhanced predictions for the heat capacity of metals; though, it was not able to describe the existence of the insulators.

The nearly free electron model is an alteration of the free electron model that comprises a weak periodic perturbation meant to model the interaction among the conduction electrons and the ions in the crystalline solid. By introducing the idea of electronic bands, the theory describes the existence of conductors, semi-conductors and insulators.

The nearly free electron model rewrites the Schrodinger equation for the case of a periodic potential. The solutions in this case are termed as Bloch states. As Bloch's theorem applies merely to periodic potentials, and as unceasing random movements of atoms in a crystal disturb the periodicity, this use of Bloch's theorem is just an approximation, however it has proven to be a tremendously valuable approximation, devoid of which most solid-state physics analysis would be intractable. Deviations from the periodicity are treated through quantum mechanical perturbation theory.

X-Ray Diffraction:

X-rays are the electromagnetic radiation of wavelength around1 Å (10-10 m) that is about the similar size as an atom.

The discovery of X-rays in the year 1895 enabled scientists to probe crystalline structure at the atomic level. X-ray diffraction has been in utilization in two main regions, for the finger-print characterization of crystalline materials and the determination of their structure. Each and every crystalline solid consists of its unique feature X-ray powder pattern that might be employed as a finger-print for its recognition. Once the material has been recognized, X-ray crystallography might be employed to find out its structure, that is, how the atoms pack altogether in the crystalline state and what the interatomic distance and angle are and so on. X-ray diffraction is one of the most significant characterization tools employed in the solid state chemistry and materials science.

We can find out the size and shape of the unit cell for any compound most simply by employing the X-ray diffraction.

X-ray diffraction can be employed to characterize the crystalline materials and metals because very small distances separate the crystal structure. The energy of an x-ray consists of wavelengths which are alike to the inter-crystal spacing. As an outcome, the crystal structures will bend the x-ray energy in measurable and reliable patterns.

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