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Atomic diffusion within a crystalline lattice
condensed matter physics, lattice diffusion (also called bulk or volume diffusion) refers to atomic diffusion within a crystalline lattice, which occurs by either
Lattice_diffusion_coefficient
Diffusion coefficient through the pore space of a porous media
grain boundary diffusion coefficient and the lattice diffusion coefficient. Diffusion along both the grain boundary and in the lattice may be modeled
Effective diffusion coefficient
Effective_diffusion_coefficient
Proportionality constant in some physical laws
diffusivity or diffusion coefficient is usually written as the proportionality constant between the molar flux due to molecular diffusion and the negative
Mass_diffusivity
Net transport of atoms through a solid
combination of lattice, and grain boundary diffusion coefficients. In general, surface diffusion occurs much faster than grain boundary diffusion, and grain
Atomic_diffusion
Physical Process
of Fickian diffusion it is possible to extract both the ν and Ediff from an Arrhenius plot of the logarithm of the diffusion coefficient, D, versus 1/T
Surface_diffusion
Measure of voltage induced by change of temperature
The Seebeck coefficient (also known as thermopower, thermoelectric power, and thermoelectric sensitivity) of a material is a measure of the magnitude
Seebeck_coefficient
Class of computational fluid dynamics methods
The lattice Boltzmann methods (LBM), originated from the lattice gas automata (LGA) method (Hardy-Pomeau-Pazzis and Frisch-Hasslacher-Pomeau models), is
Lattice_Boltzmann_methods
Diffusion coefficient of a diffusant along a grain boundary
The grain boundary diffusion coefficient is the diffusion coefficient of a diffusant along a grain boundary in a polycrystalline solid. It is a physical
Grain boundary diffusion coefficient
Grain_boundary_diffusion_coefficient
Fick's law of diffusion into a more easily solved ordinary differential equation, which can then be applied to calculate the diffusion coefficient as a function
Boltzmann–Matano_analysis
Transport of dissolved species from the highest to the lowest concentration region
are used in two different scenarios ( D {\displaystyle D} is the diffusion coefficient, having dimensions area / time): Brownian motion of an impulsive
Diffusion
Material deformation mechanism
{\displaystyle n=2} , and the diffusion coefficient D {\displaystyle D} becomes D L {\displaystyle D_{L}} (the lattice diffusion coefficient). Thus, the minimum
Grain_boundary_sliding
Differential diffusion
the lower diffusion coefficient into the material with the higher diffusion coefficient—resulting in an overall translation of the lattice relative to
Kirkendall_effect
cases where a solid solution's two components do not have the same coefficient of diffusion. Darken's first equation is: ν = ( D 1 − D 2 ) ∂ N 1 ∂ x = ( D
Darken's_equations
Process forming a path from many random steps
to the position of the random walker, one obtains the equivalent diffusion coefficient to be considered for the asymptotic Wiener process toward which
Random_walk
Chemical properties of materials
approximations to the absolute temperatures at which atoms in a bulk crystal lattice (Tammann) or on the surface (Hüttig) of the solid material become sufficiently
Tammann temperature and Hüttig temperature
Tammann_temperature_and_Hüttig_temperature
Dynamical system
A coupled map lattice (CML) is a dynamical system that models the behavior of nonlinear systems (especially partial differential equations). They are
Coupled_map_lattice
Mechanism of crystalline solid deformation
\left(-{\tfrac {Q_{f}\,+\,Q_{m}}{k_{\rm {B}}T}}\right)} is the diffusion coefficient in the grain boundary, Q f {\displaystyle Q_{f}} is the vacancy
Coble_creep
Microscopic processes responsible for changes in a material's structure, shape and volume
effective diffusion coefficient in the strain rate equation depends on whether or not the system is dominated by core diffusion or lattice diffusion and can
Deformation_mechanism
Deformation mechanism in crystalline materials
of dislocations through the crystal lattice of the material, in contrast to diffusion creep, in which diffusion (of vacancies) is the dominant creep
Dislocation_creep
Study of motions and interactions of neutrons
transport code DRAGON – An open-source lattice physics code PHOENIX/ANC – A proprietary lattice-physics and global diffusion code suite from Westinghouse Electric
Neutron_transport
Convection with two density gradients
driven by two different density gradients, which have different rates of diffusion. Convection in fluids is driven by density variations within them under
Double_diffusive_convection
Numerical analysis method
Where c1 is the constant coefficient for the principal direction in x axis, and c2 is the constant coefficient for the secondary direction in y
Nine-point_stencil
Mechanism of spontaneous phase separation
modulation in an initially homogeneous alloy implies uphill diffusion or a negative diffusion coefficient. Becker and Dehlinger had already predicted a negative
Spinodal_decomposition
Intentional introduction of impurities into an intrinsic semiconductor
has a small diffusion coefficient. Used for buried layers. Has diffusivity similar to arsenic, is used as its alternative. Its diffusion is virtually
Doping_(semiconductor)
Capacity of a material to conduct heat
whereas in dielectric materials such as diamond it is largely due to lattice vibrations. Materials with high thermal conductivity are used in heat sink
Thermal conductivity and resistivity
Thermal_conductivity_and_resistivity
Form of exhaust heat management
is cooled, a lattice mismatch strain arises between TGO and the top coat (TC) due to differing thermal expansion coefficients. Lattice mismatch strain
Thermal_barrier_coating
Material deformation mechanism
This equation can be greatly simplified. The lattice self-diffusion coefficient is given by: D L = D 0 ν exp ( − Q f + Q m k T ) {\displaystyle
Nabarro–Herring_creep
Pulse sequence during a medical test
(May 2011). "Signal evolution and infarction risk for apparent diffusion coefficient lesions in acute ischemic stroke are both time- and perfusion-dependent"
MRI_pulse_sequence
Computational model of cells and tissues
\\\end{aligned}}} where i, j are lattice sites, σi is the cell at site i, τ(σ) is the cell type of cell σ, J is the coefficient determining the adhesion between
Cellular_Potts_model
Quantity in solid-state physics
is the diffusion coefficient or diffusivity ∇ n {\displaystyle \nabla n} is the concentration gradient of electrons The diffusion coefficient for a charge
Electron_mobility
Medical imaging technique
diffusion coefficients D) of water protons in biological tissues. Namely, the image contrast in MRI is based on relaxation times (or spin diffusion)
Magnetic_resonance_imaging
Property of solid materials under mechanical stress
Nabarro–Herring creep, k is related to the diffusion coefficient of atoms through the lattice, Q = Q(self diffusion), m = 1, and b = 2. Therefore, Nabarro–Herring
Creep_(deformation)
Type of nuclear fusion that occurs at high densities & low temperatures
oscillations of nuclei around their equilibrium point bound in their crystal lattice. In quantum physics, the phenomenon can be interpreted as overlap of the
Pycnonuclear_fusion
of random motion, trajectory analysis can be used to measure the diffusion coefficient. In life sciences, single-particle tracking is broadly used to quantify
Single-particle_tracking
Paradigmatic model
}^{2}\theta _{i}\right\rangle ={\frac {1}{2}}K^{2}n} The classical diffusion coefficient in momentum direction is then given in first approximation by D
Kicked_rotator
Alloy
co-workers. Like most materials, the lattice parameter of GaInAs is a function of temperature. The measured coefficient of thermal expansion is 5.66×10−6 K−1
Indium_gallium_arsenide
Thin layer of material
parallel bulk lattice symmetry is preserved. This phenomenon can cause deviations from theoretical calculations of nucleation. Surface diffusion describes
Thin_film
Major stage of a crystallization process
{[quantity]}{[time]\cdot [area]}}} , D {\displaystyle \textstyle D} is the diffusion coefficient and ∇ c {\displaystyle \textstyle \nabla c} is the concentration
Crystal_growth
Movement of ions in an electrical field
activation energy of the thermal diffusion of metal atoms. The vacancy concentration represents availability of empty lattice sites, which might be occupied
Electromigration
Method of strengthening materials by changing grain size
prohibits dislocation pile-up and instead results in grain boundary diffusion. The lattice resolves the applied stress by grain boundary sliding, resulting
Grain_boundary_strengthening
variation Lattice Boltzmann methods Lattice constant Lattice density functional theory Lattice diffusion coefficient Lattice field theory Lattice gas automaton
Index_of_physics_articles_(L)
Materials engineered to have properties that have not yet been found in nature
transverse waves), and diffusion equations (pertaining to diffusion processes). Crafted to govern a range of diffusion activities, diffusion metamaterials prioritize
Metamaterial
with Si electronics as well as to overcome fundamental issues such as lattice mismatch in hetero-epitaxy, was developed and reported by Venkatasubramanian
Eutectic_bonding
American manufacturing company
concept of a "lattice" organization to Gore associates in 1967. He refined this to "culture principles" in a paper entitled "The Lattice Organization –
W._L._Gore_&_Associates
Seven mathematical problems with a US$1 million prize for each solution
variety. Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X. The official
Millennium_Prize_Problems
interdiffusion, hence most models of ion mixing involve an effective diffusion coefficient that is used to characterize thickness of the reacted layer as a
Ion_beam_mixing
Alloys with high proportions of several metals
of HEAs. The four core effects are high entropy, severe lattice distortion, sluggish diffusion, and cocktail effects. The high entropy effect is the most
High-entropy_alloy
Measuring timescales and/or temperatures of thermal events in the history of rock
\!C \over \operatorname {\partial } \!x}\right)} where D is the diffusion coefficient, or diffusivity (m2 s−1) of the element in the medium x is the position
Geospeedometry
Option pricing model
is thus a term used in quantitative finance to denote the set of diffusion coefficients, σ t = σ ( S t , t ) {\displaystyle \sigma _{t}=\sigma (S_{t},t)}
Local_volatility
Device that converts heat flux into electrical energy
gradient in a conducting material results in heat flow; this results in the diffusion of charge carriers. The flow of charge carriers between the hot and cold
Thermoelectric_generator
Form of wear caused by adhesion between sliding surfaces
diffusion-welded to the adjacent surface. This transfer can be enhanced if one or both metals form a thin layer of hard oxides with high coefficients
Galling
States of matter for water as a solid
In high pressure ices, protonic diffusion (movement of protons around the oxygen lattice) dominates molecular diffusion, an effect which has been measured
Phases_of_ice
Mathematical model of semiconductor oxidation
the first step, this means Henry's law; in the second, Fick's law of diffusion; in the third, a first-order reaction with respect to the oxidant. It
Deal–Grove_model
Gem variety of corundum
this color have appeared on the market as a result of artificial lattice diffusion of beryllium. A star sapphire is a type of sapphire that exhibits
Sapphire
American professor of chemistry
used PFG NMR to follow the diffusion of small molecules or ions and determine their self-diffusion coefficient. Diffusion in these systems was observed
Alan_A._Jones
Medical imaging technique
(May 2011). "Signal evolution and infarction risk for apparent diffusion coefficient lesions in acute ischemic stroke are both time- and perfusion-dependent"
Physics of magnetic resonance imaging
Physics_of_magnetic_resonance_imaging
Strong permanent magnet made from an alloy of a rare-earth element and cobalt
These samarium–cobalt magnets generally have a reversible temperature coefficient of -0.05%/°C. Saturation magnetization can be achieved with a moderate
Samarium–cobalt_magnet
Measure of temperature relative to absolute zero
(MgAl2O4). It has a face-centered cubic crystal lattice and no change in pressure can produce a lattice with a lower energy state. Nearly half of the 92
Thermodynamic_temperature
Alloy with higher durability than normal metals
bond coat due to oxidation and diffusion with substrate; Thermal stresses from mismatch in thermal expansion coefficient and growth stress due to the formation
Superalloy
Cryptographic hash function
SWIFFT is at least as difficult as finding short vectors in cyclic/ideal lattices in the worst case. By giving a security reduction to the worst case of
SWIFFT
Chemical process
adsorption. An inclusion (incorporation in the crystal lattice) occurs when the impurity occupies a lattice site in the crystal structure of the carrier, resulting
Coprecipitation
Electronic oscillator circuit
temperature-compensated cut – a cut oriented in a way that the temperature coefficients of the lattice are minimal; the FC and SC cuts are also temperature-compensated
Crystal_oscillator
Thermal engineering discipline concerning transfer of heat in physical systems
also called diffusion, is the direct microscopic exchanges of kinetic energy of particles (such as molecules) or quasiparticles (such as lattice waves) through
Heat_transfer
Material of moderate electrical conductivity
quantum physics to explain the movement of charge carriers in a crystal lattice. Doping greatly increases the number of charge carriers within the crystal
Semiconductor
Phenomenon of surface adhesion
represent the impact of diffusion on monolayer formation and is proportional to the square root of the system's diffusion coefficient. The Kisliuk adsorption
Adsorption
Statistical mechanics model for ultrafast carrier relaxation
gas and the lattice is still far from being achieved. They also presented a way to calculate the electron-lattice heat transfer coefficient for arbitrary
Two_temperature_model
while the nonlinear lattice supplies momentum compensation. Conversion efficiency depends on the nonlinear tensor coefficient, modal overlap, interaction
Nonlinear_photonic_crystal
Power generation technology
stability[54]. The 3D micro lattice allows more pathways for gas flow; therefore, it promotes airflow toward membrane electrode and gas diffusion layer assembly (MEGA)
Proton-exchange membrane fuel cell
Proton-exchange_membrane_fuel_cell
Measure of solvency/solution
the mobility of the ions is determined it is possible to estimate diffusion coefficients and from those hydrodynamic radii. The hydrodynamic radii may be
Hydration_number
physical diffusion coefficient when trajectories consists of switching episodes for example alternating between free and confined diffusion. At low spatiotemporal
Single-particle_trajectory
Movement of entangled polymer chains
of dynamic phase transition. Due to the reptation motion the coefficient of self-diffusion and conformational relaxation times of macromolecules depend
Reptation
Overview of and topical guide to machine learning
Constructing skill trees Decision tree learning Dehaene–Changeux model Diffusion map Dominance-based rough set approach Dynamic time warping Error-driven
Outline_of_machine_learning
Portmanteau word for an atom adsorbed onto the surface of a solid material
a d s = s F {\displaystyle J_{ads}=sF} where s here is the sticking coefficient. Not only does this variable depend on the surface and on the energy
Adatom
Periodic optical nanostructure that affects the motion of photons
"Flory–Huggins Photonic Sensors for the Optical Assessment of Molecular Diffusion Coefficients in Polymers". ACS Applied Materials & Interfaces. 11 (18): 16872–16880
Photonic_crystal
Movement of a drug into the bloodstream or lymph
concentration of the solid in the diffusion layer surrounding the solid. D is the diffusion coefficient. L is the diffusion layer thickness. As can be inferred
Absorption_(pharmacology)
Solar power cell with multiple band gaps from different materials
resulting crystal quality, the crystal lattice constant a of each material must be closely matched, resulting in lattice-matched devices. This constraint has
Multi-junction_solar_cell
conductors. The classical theory of diffusion and migration in solids is based on the notion of a diffusion coefficient, activation energy and electrochemical
Nanoionics
Model of intermolecular interactions
Also transport properties (viscosity, heat conductivity, and self diffusion coefficient) of the Lennard-Jones fluid have been studied, but the database
Lennard-Jones_potential
Compounds consisting of sodium, oxygen and cobalt
allow their quasi-unidimensional diffusion. The sodium lattice "melts" at about 370 K, allowing two-dimensional diffusion. As x increases, the conductivity
Sodium_cobalt_oxide
Materials whose temperature variance leads to voltage change
{\displaystyle \Xi } is the deformation potential coefficient, κ L {\displaystyle \kappa _{\rm {L}}} is the lattice thermal conduction, and T {\displaystyle T}
Thermoelectric_materials
LEDs are limited to 660 nm by this. Lattice constants of the compounds also tend to be different, and the lattice mismatch against the substrate, dependent
List of semiconductor materials
List_of_semiconductor_materials
Form of matter
factors such as surface tension, the Marangoni effect, drainage, and gas diffusion. Foams have numerous applications, including thermal insulation, packaging
Foam
Alloy of zirconium and hydrogen
doi:10.1016/0022-5088(84)90254-6. Kearns, J. J (1972-06-01). "Diffusion coefficient of hydrogen in alpha zirconium, Zircaloy-2 and Zircaloy-4". Journal
Zirconium_hydride
hydrogen diffusion via H+ can occur on the timescales of minutes to hours at temperatures as low as 800-1000 °C within the olivine crystal lattice (e.g.
Melt_inclusion
Iterative method for solving the Sylvester matrix equations
each iteration is determined by parameters such as the timestep, diffusion coefficient, and grid spacing. The connection to ADI on matrix equations can
Alternating-direction implicit method
Alternating-direction_implicit_method
Substance-specific relation between two physical quantities
at a point of contact between two interfaces through a dimensionless coefficient of friction μf, which depends on the pair of materials: F f = μ f R
Constitutive_equation
Physical law in electrochemistry
dissolved species, its chemical activity (a) is the product of its activity coefficient (γ) by its molar (mol/L solution), or molal (mol/kg water), concentration
Nernst_equation
Crystal growth process relative to the substrate used as seed
to the seed layer is defined in terms of the orientation of the crystal lattice of each material. For most epitaxial growths, the new layer is usually
Epitaxy
Method for discovering interesting relations between variables in databases
Transformation) is a backtracking algorithm, which traverses the frequent itemset lattice graph in a depth-first search (DFS) fashion. Whereas the breadth-first
Association_rule_learning
Device for measuring a physical quantity
depends on elastic properties, density, geometry, and inner structures (lattice or fissures). Cam plastometer Plastometer Universal testing machine Grindometer
List_of_measuring_instruments
Law of electrical current and voltage
{R}}} is the resistance of the test wire per unit length. Thus, Ohm's coefficients are, a = E R , b = r R . {\displaystyle a={\frac {\mathcal {E}}{\mathcal
Ohm's_law
Heat from a current in an electric conductor
quantized, ionic lattice oscillations in the harmonic approximation of a crystal), energy is being transferred from the electrons to the lattice (by the creation
Joule_heating
Ceramic material
31±4 GPa, a modulus of elasticity of 550±50 GPa, a thermal expansion coefficient of 9.35×10−6 K−1, and a superconducting transition temperature of 5.6 K
Titanium_nitride
Academic field
Watts–Strogatz model begins as a non-random lattice structure, it has a very high clustering coefficient along with a high average path length. Each rewire
Network_science
Topics referred to by the same term
optical power of a lens or curved mirror (also in Medicine) D, Diffusion coefficient (D), in molecular physics D, Electric displacement field (D) D meson
D_(disambiguation)
Capacity of a substance to dissolve in a homogeneous way
the dissolving substance and the solvent D {\displaystyle D} = diffusion coefficient d {\displaystyle d} = thickness of the boundary layer of the solvent
Solubility
Diagram used to represent quantum field theory calculations
group G and a connection form. This is actually an exact duality over a lattice. Over a manifold however, assumptions like diffeomorphism invariance are
Spin_network
Translucent polycrystalline solid
[m/m] crystallinity, the two coefficients balance such that the glass-ceramic as a whole has a thermal expansion coefficient that is very close to zero
Glass-ceramic
Probabilistic problem-solving algorithm
(January 1993). "Insertion of peptide chains into lipid membranes: an off-lattice Monte Carlo dynamics model". Proteins. 15 (1): 10–25. doi:10.1002/prot
Monte_Carlo_method
State of matter
are tightly bound to each other in one of two ways: regular geometric lattices called crystalline solids (e.g. metals, water ice), or irregular arrangements
Solid
LATTICE DIFFUSION-COEFFICIENT
LATTICE DIFFUSION-COEFFICIENT
Biblical
effusion; inclination; theft
Girl/Female
Latin
Joy. Popular medieval British form of the name Letitia.
Boy/Male
Biblical
Diffusion; inclination; theft.
Female
English
Variant spelling of English Patty, PATTIE means "patrician; of noble birth."
Female
French
French form of Latin Viatrix, BÉATRICE means "voyager (through life)."
Girl/Female
British, Christian, English, French, Latin
Joy; Popular Medieval Form of the Name Letitia; Gladness; Happiness
Male
French
Medieval French form of Latin Patricius, PATRICE means "patrician; of noble descent."
Girl/Female
Biblical
Effusion of blood.
Girl/Female
American, Australian, British, English, Greek
Modern Blend of Catrina and Patrice
Boy/Male
Biblical
Diffusion; inclination; theft.
Biblical
effusion of blood
Female
English
Pet form of Middle English Lettice, LETTIE means "happiness."
Male
English
Pet form of English Matthew, MATTIE means "gift of God." Compare with feminine Mattie.
Female
English
Middle English form of Latin Lætitia, LETTICE means "happiness."
Female
English
Pet form of English Harriet, HATTIE means "little home-ruler."
Boy/Male
Indian, Telugu
Radiance; Diffusing Light
Female
English
Pet form of French Charlotte, LOTTIE means "man."
Girl/Female
Latin
From Attica.
Female
English
Pet form of English Matilda, MATTIE means "mighty in battle." Compare with masculine Mattie.
Girl/Female
Latin
From Attica.
LATTICE DIFFUSION-COEFFICIENT
LATTICE DIFFUSION-COEFFICIENT
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Mythological, Oriya, Telugu
Spring
Boy/Male
Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Ceremonial Rites to God
Surname or Lastname
English
English : variant of Pask, from the byform pasche, Latin pascha.Americanized spelling of German Pasch.
Boy/Male
Gaelic Irish
Black-haired.
Female
Italian
Feminine form of Italian Cosimo, COSIMA means "order, beauty."
Surname or Lastname
Irish
Irish : reduced Anglicized form of Gaelic Mac ToimÃn ‘son of ToimÃn’, a pet form of Tomás, Gaelic form of Thomas.Irish : Anglicized form of Gaelic Ó Tiomáin ‘descendant of Tiomán’, a personal name from a diminutive of tiom ‘pliant’, ‘soft’.Irish : reduced Anglicized form of Gaelic Ó Tiománaigh (see Timoney).English : patronymic from a pet form of the personal name Timm.
Girl/Female
American, Bengali, Gujarati, Hebrew, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
Understanding; Wisdom and Knowledge; Truth
Boy/Male
French
Form of Leander. 'Lionlike man.
Boy/Male
American, Anglo, Australian, British, Christian, English, Irish
From the Birch Tree Meadow; Place Name; Where Birches Grow
Boy/Male
English Greek
Dusty one; servant.
LATTICE DIFFUSION-COEFFICIENT
LATTICE DIFFUSION-COEFFICIENT
LATTICE DIFFUSION-COEFFICIENT
LATTICE DIFFUSION-COEFFICIENT
LATTICE DIFFUSION-COEFFICIENT
n.
Any work of wood or metal, made by crossing laths, or thin strips, and forming a network; as, the lattice of a window; -- called also latticework.
n.
The language of the Lettic race, including Lettish, Lithuanian, and Old Prussian.
v. t.
A lattice or grating.
v. i.
To close, as an opening, with latticework; to furnish with a lattice; as, to lattice a window.
a.
Of or pertaining to milk; procured from sour milk or whey; as, lactic acid; lactic fermentation, etc.
imp. & p. p.
of Lattice
n.
The act of diffusing, or the state of being diffused; a spreading; extension; dissemination; circulation; dispersion.
a.
Having the quality of diffusing; capable of spreading every way by flowing; spreading widely; widely reaching; copious; diffuse.
a.
Having power to diffuse itself; diffusing itself.
v. t.
The act of infusing, pouring in, or instilling; instillation; as, the infusion of good principles into the mind; the infusion of ardor or zeal.
n.
The act of passing by osmosis through animal membranes, as in the distribution of poisons, gases, etc., through the body. Unlike absorption, diffusion may go on after death, that is, after the blood ceases to circulate.
a.
Latticed. See Lattice, n., 2.
n.
The representation of a piece of latticework used as a bearing, the bands being vertical and horizontal.
v. i.
To make a lattice of; as, to lattice timbers.
a.
Shaped like a lattice; cancellate.
n.
A composite plant of the genus Lactuca (L. sativa), the leaves of which are used as salad. Plants of this genus yield a milky juice, from which lactucarium is obtained. The commonest wild lettuce of the United States is L. Canadensis.
p. pr. & vb. n.
of Lattice
n.
The act of pouring out; as, effusion of water, of blood, of grace, of words, and the like.
n.
Same as Lattice, n., 1.
n.
The act or process of making a lattice of, or of fitting a lattice to.