Materials Science and Engineering/Doctoral review questions/Definitions

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3.20

Phase
A homogeneous collection of material with one or more components
Fermi-Dirac Statistics

Fermi-Dirac statistics is a particular case of particle statistics that determines the statistical distribution of fermions over the energy states for a system in thermal equilibrium.

Distribution function of fermions that determines the probability of a level being occupied by a fermion
Maxwell-Boltzmann Statistics

In statistical mechanics, Maxwell–Boltzmann statistics describes the statistical distribution of material particles over various energy states in thermal equilibrium, when the temperature is high enough and density is low enough to render quantum effects negligible.

Distribution of energy states of non-interacting particles, including bosons and fermions
Bose-Einstein statistics

In statistical mechanics, Bose-Einstein statistics (or more colloquially B-E statistics) determines the statistical distribution of identical indistinguishable bosons over the energy states in thermal equilibrium.

Statistics of bosons
Statistical Mechanics

Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force.

Statistical mechanics is the quantum mechanical version of thermodynamics
Phase

In the physical sciences, a phase is a set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties (i.e. density, crystal structure, index of refraction, and so forth).

Chemical potential

The chemical potential of a thermodynamic system is the amount by which the energy of the system would change if an additional particle were introduced, with the entropy and volume held fixed.

Free energy changes upon the addition of one atom.
Heat capacity

Heat capacity (symbol: Cp) — as distinct from specific heat capacity — is the measure of the heat energy required to increase the temperature of an object by a certain temperature interval.

How a material stores thermal energy
Entropy

In physics, entropy, symbolized by S, is a measure of the unavailability of a system’s energy to do work.

Degree of randomness
Enthalpy

In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as H or ΔH, or rarely as χ) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the "useful" work obtainable from a closed thermodynamic system under constant pressure.

Inherent energy in a system from bonding
Gibb's free energy

In thermodynamics, the Gibbs free energy is a thermodynamic potential which measures the "useful" or process-initiating work obtainable from an isothermal, isobaric thermodynamic system.

The most real world relevant potential to determine what phases are in equilibrium
Work

In thermodynamics, work is the quantity of energy transferred from one system to another without an accompanying transfer of entropy.

The transfer of energy not in the form of heat
Fermion

In particle physics, fermions are particles with a half-integer spin, such as protons and electrons.

Particle with half-integer spin
Boson

In particle physics, bosons are particles with an integer spin, as opposed to fermions which have half-integer spin.

Particle with integer spin
Mean Field Theory

The main idea of MFT is to replace all interactions to any one body with an average or effective interaction, reducing any multi-body problem into an effective one-body problem.

Average force on a particle
Spinodal Decomposition

Spinodal decomposition is a method by which a mixture of two or more materials can separate into distinct regions with different material concentrations.

Barrierless phase transformation
Dulong-Petit

The Dulong-Petit law, a chemical law proposed in 1819, states the classical expression for the specific heat capacity of a crystal due to its lattice vibrations wherein regardless of the nature of the crystal, the specific heat capacity (measured in joule per kelvin per kilogram) is equal to 3R/M, where R is the gas constant (measured in joule per kelvin per mole) and M is the molar mass (measured in kilogram per mole).

The upper limit of heat capacity in a lattice
Nucleation and Growth

Nucleation is the onset of a phase transition in a small region.

Phase transition in a small region followed by a
Raoultian versus Henrian
In the case of Henrian solution, the different components demonstrate a preference of neighbors
Ideal versus regular solution
In the case of Henrian solution, the different components demonstrate a preference of neighbors

Using magnetization to absorb heat to minimize the energy

3.21

Fick's laws

Fick's laws of diffusion describe diffusion and can be used to solve for the diffusion coefficient D

1st law: flux is proportional to the conjugate gradient potential
2nd law: Conservation law
Diffusion

Diffusion is the spontaneous net movement of particles from an area of high concentration to an area of low concentration in a given volume of fluid (either liquid or gas) down the concentration gradient.

Displacement of a material to minimize total energy
Grain Boundary Schematic representations of a tilt boundary (top) and a twist boundary between two idealised grains.

A grain boundary is the interface between two grains in a polycrystalline material.

Region between grains with different crystallographic orientation

3.22

Tensor

A tensor is an object which extends the notion of scalar, vector, and matrix.

An object that organizes a collection of numbers (that may associated with properties of a crystallographic plane)
Diagonalized tensor

In linear algebra, a diagonal matrix is a square matrix in which the entries outside the main diagonal (↘) are all zero.

Diagonalized tensor is one set of eigenvalues

3.23

Paramagnetism

Paramagnetism is a form of magnetism which occurs only in the presence of an externally applied magnetic field, and paramagnetic materials are attracted to magnetic fields, hence have a relative magnetic permeability greater than one (or, equivalently, a positive magnetic susceptibility).

A material that enhances the applied field

Superparamagnetism

Superparamagnetism is a phenomenon by which magnetic materials may exhibit a behavior similar to paramagnetism even when at temperatures below the Curie or the Néel temperature.
Diamagnetism

Diamagnetism is a weak repulsion from a magnetic field, and it is a form of magnetism that is only exhibited by a substance in the presence of an externally applied magnetic field.

Magnetic response opposing magnetic force of a material with no paired electrons
Ferromagnetism

Ferromagnetism is defined as the phenomenon by which materials, such as iron, in an external magnetic field become magnetized and remain magnetized for a period after the material is no longer in the field.

Paramagnet with hysteretic temperature whose exchange energy causes neighboring spins to be oppositely aligned

Softness of hardness of ferromagnets based on remnance

Antiferromagnetism

In materials that exhibit antiferromagnetism, the spins of electrons align in a regular pattern with neighboring spins pointing in opposite directions.

Paramagnet with hysteretic temperature whose exchange energy causes neighboring spins to align
Ferrimagnetism

In physics, a ferrimagnetic material is one in which the magnetic moment of the atoms on different sublattices are opposed, as in antiferromagnetism; however, in ferrimagnetic materials, the opposing moments are unequal and a spontaneous magnetization remains.

A material with spins that are aligned in parallel but with a spins of different magnitudes
Curie temperature

The Curie point of a ferromagnetic material is the temperature above which it loses its characteristic ferromagnetic ability.

Transition temperature from ferromagnetism to paramagnetism
Neel temperatures

The Néel temperature, TN, is the temperature at which an antiferromagnetic material becomes paramagnetic — that is, the thermal energy becomes large enough to destroy the macroscopic magnetic ordering within the material.

Transition temperature between antiferromagnetism and paramagnetism
Bloch's theorem

A Bloch wave or Bloch state, named after Felix Bloch, is the wavefunction of a particle (usually, an electron) placed in a periodic potential.

Wavefunction same under discrete translation
Dispersion relation
Relationship between w, angular momentum, and k, the relevant wavenumber, in a system
Schrodinger equation

In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1926, describes the space- and time-dependence of quantum mechanical systems.

Conservation law of quantum mechanical system
Density of states

In statistical and condensed matter physics, density of states (DOS) is a property that quantifies how closely packed energy levels are in a quantum-mechanical system.

Number of possible states available in an increment of energy
Fermi function

In the case where $\mu$ is the fermi energy $E_{F}\$ and $g_{i}=1\$ , the function is called the Fermi function:

$F(E)={\frac {1}{e^{(\epsilon _{i}-E_{F})/kT}+1}}$ Probability of occupation of fermi particles
Hamiltonian

In quantum mechanics, the Hamiltonian H is the observable corresponding to the total energy of the system.

Describe total energy of the system
Raman spectroscopy

Raman spectroscopy is a spectroscopic technique used in condensed matter physics and chemistry to study vibrational, rotational, and other low-frequency modes in a system.

Spectroscopic technique using the inelastic interation of phonons and photons
Operator

In mathematics, an operator is a function, that operates on (or modifies) another function.

Quantum mechanical equivalence to an observable
Separation of variables

In mathematics, separation of variables is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to re-write an equation so that each of two variables occurs on a different side of the equation.

A method of solving equations by assume variables to be independent of one another
Constant of Motion

In mechanics, a constant of motion is a quantity that is conserved throughout the motion, imposing in effect a constraint on the motion.

A quantity that does not change with motion through space
Conserved Quantity

In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves.

Quantity that does not change with time under application of a symmetric operation
Commutators

In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative.

When two operators commute, they share a symmetry of the system.
Bravais lattice

In geometry and crystallography, a Bravais lattice, named after Auguste Bravais, is an infinite set of points generated by a set of discrete translation operations.

Points in space that can be translated to fill all space
Fourier series

In mathematics, the Fourier series is one of the specific forms of Fourier analysis and is a way of decomposing a function into a superposition of elementary waves.

Group velocity

The group velocity of a wave is the velocity with which the variations in the shape of the wave's amplitude (known as the modulation or envelope of the wave) propagate through space.

Free electron gas

A Fermi gas, or free electron gas, is a collection of non-interacting fermions and is the quantum mechanical version of an ideal gas, for the case of fermionic particles.

Metal

In chemistry, a metal is an element that readily loses electrons to form positive ions (cations) and has metallic bonds between metal atoms.

Semiconductor

A semiconductor is a solid material that has electrical conductivity in between that of a conductor and that of an insulator; it can vary over that wide range either permanently or dynamically.

Insulator

An insulator is a material that resists the flow of electric current.

Law of mass action

In chemistry, law of mass action is associated with two aspects: 1) the equilibrium aspect, concerning the composition of a reaction mixture at equilibrium and 2) the kinetic aspect concerning the rate equations for elementary reactions.

Variational principle

A variational principle is a principle in physics which is expressed in terms of the calculus of variations.

Hartree-Fock

In computational physics and computational chemistry, the Hartree-Fock (HF) method is an approximate method for the determination of the ground-state wavefunction and ground-state energy of a quantum many-body system

Slater Determinant

In quantum mechanics, a Slater determinant is an expression which describes the wavefunction of a multi-fermionic system that satisfies anti-symmetry (Φ = 0) requirements and subsequently the Pauli exclusion principle by changing sign upon exchange of fermions.

LCAO-MO

A linear combination of atomic orbitals or LCAO is a quantum superposition of atomic orbitals and a technique for calculating molecular orbitals in quantum chemistry.

Amorphous

An amorphous solid is a solid in which there is no long-range order of the positions of the atoms. (Solids in which there is long-range atomic order are called crystalline solids or morphous)

Van Hove Singularity

A Van Hove singularity is a kink in the density of states (DOS) of a solid. The wavevectors at which Van Hove singularities occur are often referred to as critical points of the Brillouin zone.

In computational mechanics and statistical mechanics, a radial distribution function (RDF), g(r), describes how the density of surrounding matter varies as a function of the distance from a distinguished point.

Bloch Wall

A Bloch wall is a narrow transition region at the boundary between magnetic domains, over which the magnetisation changes from its value in one domain to that in the next.

Spintronics

Spintronics (a neologism for "spin-based electronics"), also known as magnetoelectronics, is an emerging technology which exploits the quantum spin states of electrons as well as making use of their charge state.

Index of Refraction

The refractive index (or index of refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves) is reduced inside the medium.

Dielectric Constant

The relative static permittivity (or static relative permittivity) of a material under given conditions is a measure of the extent to which it concentrates electrostatic lines of flux.

GMR

Giant magnetoresistance (GMR) is a quantum mechanical effect, a type of magnetoresistance effect, observed in thin film structures composed of alternating ferromagnetic and nonmagnetic metal layers.

Non-linear optics

Nonlinear optics (NLO) is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the dielectric polarization P responds nonlinearly to the electric field E of the light.

Brewster's Angle

At one particular angle of incidence, the Brewster's angle, θB, light with one particular polarization cannot be reflected.

• Evanescent state
• Hartree
• Mobility edge
• Coordination defect
• Magnetostatic, magnetostriction, exchange, anisotropy
• TM/TE

3.42

Electronegativity

Electronegativity, symbol χ, is a chemical property that describes the ability of an atom (or, more rarely, a functional group) to attract electrons (or electron density) towards itself in a covalent bond.

Work function

The work function is the minimum energy (usually measured in electron volts) needed to remove an electron from a solid to a point immediately outside the solid surface (or energy needed to move an electron from the Fermi energy level into vacuum).

Schottky Defects

A Schottky defect is a type of point defect in a crystal lattice that forms when oppositely charged ions leave their lattice sites, creating vacancies

Frenkel Defects

A Frenkel defect, also called a Frenkel pair or Frenkel disorder, is a compound crystallographic defect in which an interstitial lies near a vacancy.

Polarizability

Polarizability is the relative tendency of a charge distribution, like the electron cloud of an atom or molecule, to be distorted from its normal shape by an external electric field, which may be caused by the presence of a nearby ion or dipole.

Band gap

In solid state physics and related applied fields, the band gap, also called an energy gap or stop band, is a region where a particle or quasiparticle is forbidden from propagating.

Varistor

A varistor is an electronic component with a significant non-ohmic current-voltage characteristic.

Effective mass

In solid state physics, a particle's effective mass is the mass it seems to carry in the semiclassical model of transport in a crystal.

Photoconductor

A photoresistor or LDR is an electronic component whose resistance decreases with increasing incident light intensity.

Photodiode

A photodiode is a type of photodetector capable of converting light into either current or voltage, depending upon the mode of operation.

LED

An LED is a semiconductor diode that emits incoherent narrow-spectrum light when electrically biased in the forward direction of the p-n junction, as in the common LED circuit.

Laser

A laser is an electronic-optical device that produces coherent radiation, and the term "laser" is an acronym meaning "Light Amplification by Stimulated Emission of Radiation".

Crystal Field Splitting

Crystal field theory (CFT) is a model that describes the electronic structure of transition metal compounds, all of which can be considered coordination complexes.

BJT

A bipolar junction transistor (BJT) is a type of transistor, a three-terminal device constructed of doped semiconductor material that may be used in amplifying or switching applications.

MOSFET

The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET) is by far the most common field-effect transistor in both digital and analog circuits.

Transconductance

Transconductance is the ratio of the current at the output port and the voltage at the input ports and is written as gm.

Attenuation

Attenuation is the reduction in amplitude and intensity of a signal.

Capacitance

Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential.

Brillouin Zone

In mathematics and solid state physics, the first Brillouin zone is a uniquely defined primitive cell of the reciprocal lattice in the frequency domain.

Rayleigh Scattering

Rayleigh scattering (named after Lord Rayleigh) is the scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the light.

Waveguide

A waveguide is a structure which guides waves, such as electromagnetic waves, light, or sound waves.

Nernst Equation

In electrochemistry, the Nernst equation is used to calculate equilibrium reduction potential (electromotive force), E, of an electrochemical cell (or half-cell) from its standard reduction potential (or standard electrode potential), E0, and the activities (effective concentrations) of its components.

Punchthrough

When the base–collector voltage reaches a certain (device specific) value, the base–collector depletion region boundary meets the base–emitter depletion region boundary, and in this state the transistor effectively has no base, the device thus losing all gain when in this state.

Base-Width Modulation

As the applied collector–base voltage ($V_{BC}$ ) varies, the collector–base depletion region varies in size.

• Avalance Breakdown
• Brouwer approximation
• Avalanche, zener breakdown
• Base-width modulation
• Inversion

3.44

Evaporation

Evaporation is the process by which molecules in a liquid state (e.g. water) spontaneously become gaseous (e.g. water vapor).

Molecular Beam Epitaxy

Molecular beam epitaxy (MBE), requires high vacuum or ultra high vacuum and is one of several methods of depositing single crystals.

CVD

Chemical vapor deposition (CVD) is a chemical process used to produce high-purity, high-performance solid materials.

LOCOS

LOCOS, short for LOCal Oxidation of Silicon, is a microfabrication process where silicon dioxide is formed in selected areas on silicon wafer with the Si-SiO2 interface at a lower point than the rest of the silicon surface.

SOI

Silicon on insulator technology (SOI) refers to the use of a layered silicon-insulator-silicon substrate in place of conventional silicon substrates in semiconductor manufacturing, especially microelectronics, to reduce parasitic device capacitance and thereby improve performance.

SIMOX

One prominent method to prepare silicon on insulator (SOI) substrates from conventional silicon substrates is the SIMOX (Separation by IMplantation of OXygen) process, wherein a buried high dose oxygen implant is converted to silicon oxide by a high temperature annealing process.

Evaporative Deposition

Evaporation is a common method of thin film deposition, wherein the source material is evaporated in a vacuum and the vacuum allows vapor particles to travel directly to the target object (substrate), where they condense back to a solid state.

RIE

Reactive ion etching (RIE) is an etching technology used in microfabrication wherein a chemically reactive plasma removes material deposited on wafers.

Ion Implantation

Ion implantation is a materials engineering process by which ions of a material can be implanted into another solid, thereby changing the physical properties of the solid.

Atomic Layer Deposition

Atomic Layer Deposition (ALD) is a gas phase chemical process used to create extremely thin coatings.

• Segregation coefficient, effective segregation coefficient.
Lithography

Microlithography and nanolithography refer specifically to lithographic patterning methods capable of structuring material on a fine scale.

Plasma

In physics and chemistry, a plasma is typically an ionized

Electroplating

Electroplating is the process of using electrical current to reduce metal cations in a solution and coat a conductive object with a thin layer of metal.

Anodization

Anodizing, or anodising, is an electrolytic passivation process used to increase the thickness of the natural oxide layer on the surface of metal parts.

Sputter Deposition

Sputter deposition is a physical vapor deposition (PVD) method of depositing thin films by sputtering, i.e. ejecting, material from a "target," i.e., source, which then deposits onto a "substrate," e.g., a silicon wafer.

Knudsen Cell

In crystal growth, knudsen cells are often used as sources evaporators for relatively low partial pressure elementary sources, e.g., Ga, Al, Hg, As, etc. It is easy to control the temperature of evaporating content and commonly used in molecular-beam epitaxy.

Depth of Field

In optics, particularly film and photography, the depth of field (DOF) is the distance in front of and beyond the subject that appears to be in focus.

Boundary Layer

In physics and fluid mechanics, a boundary layer is that layer of fluid in the immediate vicinity of a bounding surface. In the Earth's atmosphere, the planetary boundary layer is the air layer near the ground affected by diurnal heat, moisture or momentum transfer to or from the surface.

Lithography

Microlithography and nanolithography refer specifically to lithographic patterning methods capable of structuring material on a fine scale.

• Ion Milling
• Elingham diagram
• Cellular, dendritic growth
• Frank van der Merwe, Volmer Weber, Stranski Krastanov
• Commensurate pseudomorphic growth
• e-beam source
• Boundary layer
• Hot electron
• Ion implantation
• Emitter-push effect
• Straggle, range
• Ion milling
• Bank-end processing
• Normal versus abnormal growth
• Superfill
• Modulation transfer function
• Source coherency