Diffusion creep

Last updated July 07, 2023

Diffusion creep refers to the deformation of crystalline solids by the diffusion of vacancies through their crystal lattice.^[1] Diffusion creep results in plastic deformation rather than brittle failure of the material.

Diffusion creep is more sensitive to temperature than other deformation mechanisms. It becomes especially relevant at high homologous temperatures (i.e. within about a tenth of its absolute melting temperature). Diffusion creep is caused by the migration of crystalline defects through the lattice of a crystal such that when a crystal is subjected to a greater degree of compression in one direction relative to another, defects migrate to the crystal faces along the direction of compression, causing a net mass transfer that shortens the crystal in the direction of maximum compression. The migration of defects is in part due to vacancies, whose migration is equal to a net mass transport in the opposite direction.

Principle

Crystalline materials are never perfect on a microscale. Some sites of atoms in the crystal lattice can be occupied by point defects, such as "alien" particles or vacancies. Vacancies can actually be thought of as chemical species themselves (or part of a compound species/component) that may then be treated using heterogeneous phase equilibria. The number of vacancies may also be influenced by the number of chemical impurities in the crystal lattice, if such impurities require the formation of vacancies to exist in the lattice.

A vacancy can move through the crystal structure when the neighbouring particle "jumps" in the vacancy, so that the vacancy moves in effect one site in the crystal lattice. Chemical bonds need to be broken and new bonds have to be formed during the process,^[2] therefore a certain activation energy is needed. Moving a vacancy through a crystal becomes therefore easier when the temperature is higher.

The most stable state will be when all vacancies are evenly spread through the crystal. This principle follows from Fick's law:

J_{x}=-D_{x}{\frac {\Delta C}{\Delta x}}

In which J_x stands for the flux ("flow") of vacancies in direction x; D_x is a constant for the material in that direction and ${\Delta C}/{\Delta x}$ is the difference in concentration of vacancies in that direction. The law is valid for all principal directions in (x, y, z)-space, so the x in the formula can be exchanged for y or z. The result will be that they will become evenly distributed over the crystal, which will result in the highest mixing entropy.

When a mechanical stress is applied to the crystal, new vacancies will be created at the sides perpendicular to the direction of the lowest principal stress. The vacancies will start moving in the direction of crystal planes perpendicular to the maximal stress.^[3] Current theory holds that the elastic strain in the neighborhood of a defect is smaller toward the axis of greatest differential compression, creating a defect chemical potential gradient (depending upon lattice strain) within the crystal that leads to net accumulation of defects at the faces of maximum compression by diffusion. A flow of vacancies is the same as a flow of particles in the opposite direction. This means a crystalline material can deform under a differential stress, by the flow of vacancies.

Highly mobile chemical components substituting for other species in the lattice can also cause a net differential mass transfer (i.e. segregation) of chemical species inside the crystal itself, often promoting shortening of the rheologically more difficult substance and enhancing deformation.

Types of diffusion creep

Diffusion of vacancies through a crystal can happen in a number of ways. When vacancies move through the crystal (in the material sciences often called a "grain"), this is called Nabarro–Herring creep . Another way in which vacancies can move is along the grain boundaries, a mechanism called Coble creep .

When a crystal deforms by diffusion creep to accommodate space problems from simultaneous grain boundary sliding (the movement of whole grains along grain boundaries) this is called granular or superplastic flow .^[4] Diffusion creep can also be simultaneous with pressure solution. Pressure solution is, like Coble creep, a mechanism in which material moves along grain boundaries. While in Coble creep the particles move by "dry" diffusion, in pressure solution they move in solution.

Flow laws

Each plastic deformation of a material can be described by a formula in which the strain rate ( ${\dot {\epsilon }}$ ) depends on the differential stress (σ or σ_D), the grain size (d) and an activation value in the form of an Arrhenius equation:^[5]

$\!{\dot {\epsilon }}=Ae^{\frac {-Q}{RT}}{\frac {\sigma ^{n}}{d^{m}}}$

In which A is the constant of diffusion, Q the activation energy of the mechanism, R the gas constant and T the absolute temperature (in kelvins). The exponents n and m are values for the sensitivity of the flow to stress and grain size respectively. The values of A, Q, n and m are different for each deformation mechanism. For diffusion creep, the value of n is usually around 1. The value for m can vary between 2 (Nabarro-Herring creep) and 3 (Coble creep). That means Coble creep is more sensitive to grain size of a material: materials with larger grains can deform less easily by Coble creep than materials with small grains.

Traces of diffusion creep

It is difficult to find clear microscale evidence for diffusion creep in a crystalline material, since few structures have been identified as definite proof. A material that was deformed by diffusion creep can have flattened grains (grains with a so called shape-preferred orientation or SPO). Equidimensional grains with no lattice-preferred orientation (or LPO) can be an indication for superplastic flow.^[6] In materials that were deformed under very high temperatures, lobate grain boundaries may be taken as evidence for diffusion creep.^[7]

Diffusion creep is a mechanism by which the volume of the crystals can increase. Larger grain sizes can be a sign that diffusion creep was more effective in a crystalline material.

Related Research Articles

In physics and materials science, plasticity is the ability of a solid material to undergo permanent deformation, a non-reversible change of shape in response to applied forces. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the material itself. In engineering, the transition from elastic behavior to plastic behavior is known as yielding.

A crystallite is a small or even microscopic crystal which forms, for example, during the cooling of many materials. Crystallites are also referred to as grains.

In materials science, creep is the tendency of a solid material to undergo slow deformation while subject to persistent mechanical stresses. It can occur as a result of long-term exposure to high levels of stress that are still below the yield strength of the material. Creep is more severe in materials that are subjected to heat for long periods and generally increase as they near their melting point.

In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to slide over each other at low stress levels and is known as glide or slip. The crystalline order is restored on either side of a glide dislocation but the atoms on one side have moved by one position. The crystalline order is not fully restored with a partial dislocation. A dislocation defines the boundary between slipped and unslipped regions of material and as a result, must either form a complete loop, intersect other dislocations or defects, or extend to the edges of the crystal. A dislocation can be characterised by the distance and direction of movement it causes to atoms which is defined by the Burgers vector. Plastic deformation of a material occurs by the creation and movement of many dislocations. The number and arrangement of dislocations influences many of the properties of materials.

In geology, a shear zone is a thin zone within the Earth's crust or upper mantle that has been strongly deformed, due to the walls of rock on either side of the zone slipping past each other. In the upper crust, where rock is brittle, the shear zone takes the form of a fracture called a fault. In the lower crust and mantle, the extreme conditions of pressure and temperature make the rock ductile. That is, the rock is capable of slowly deforming without fracture, like hot metal being worked by a blacksmith. Here the shear zone is a wider zone, in which the ductile rock has slowly flowed to accommodate the relative motion of the rock walls on either side.

In chemical physics, atomic diffusion is a diffusion process whereby the random, thermally-activated movement of atoms in a solid results in the net transport of atoms. For example, helium atoms inside a balloon can diffuse through the wall of the balloon and escape, resulting in the balloon slowly deflating. Other air molecules have lower mobilities and thus diffuse more slowly through the balloon wall. There is a concentration gradient in the balloon wall, because the balloon was initially filled with helium, and thus there is plenty of helium on the inside, but there is relatively little helium on the outside. The rate of transport is governed by the diffusivity and the concentration gradient.

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In materials science and engineering, the yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible and is known as plastic deformation.

In metallurgy and materials science, annealing is a heat treatment that alters the physical and sometimes chemical properties of a material to increase its ductility and reduce its hardness, making it more workable. It involves heating a material above its recrystallization temperature, maintaining a suitable temperature for an appropriate amount of time and then cooling.

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<span class="mw-page-title-main">Coble creep</span>

Coble creep, a form of diffusion creep, is a mechanism for deformation of crystalline solids. Contrasted with other diffusional creep mechanisms, Coble creep is similar to Nabarro–Herring creep in that it is dominant at lower stress levels and higher temperatures than creep mechanisms utilizing dislocation glide. Coble creep occurs through the diffusion of atoms in a material along grain boundaries. This mechanism is observed in polycrystals or along the surface in a single crystal, which produces a net flow of material and a sliding of the grain boundaries.

Cleavage, in structural geology and petrology, describes a type of planar rock feature that develops as a result of deformation and metamorphism. The degree of deformation and metamorphism along with rock type determines the kind of cleavage feature that develops. Generally, these structures are formed in fine grained rocks composed of minerals affected by pressure solution.

A deformation mechanism, in geology, is a process occurring at a microscopic scale that is responsible for changes in a material's internal structure, shape and volume. The process involves planar discontinuity and/or displacement of atoms from their original position within a crystal lattice structure. These small changes are preserved in various microstructures of materials such as rocks, metals and plastics, and can be studied in depth using optical or digital microscopy.

<span class="mw-page-title-main">Grain boundary strengthening</span> Method of strengthening materials by changing grain size

In materials science, grain-boundary strengthening is a method of strengthening materials by changing their average crystallite (grain) size. It is based on the observation that grain boundaries are insurmountable borders for dislocations and that the number of dislocations within a grain has an effect on how stress builds up in the adjacent grain, which will eventually activate dislocation sources and thus enabling deformation in the neighbouring grain as well. By changing grain size, one can influence the number of dislocations piled up at the grain boundary and yield strength. For example, heat treatment after plastic deformation and changing the rate of solidification are ways to alter grain size.

Dislocation creep is a deformation mechanism in crystalline materials. Dislocation creep involves the movement of dislocations through the crystal lattice of the material, in contrast to diffusion creep, in which diffusion is the dominant creep mechanism. It causes plastic deformation of the individual crystals, and thus the material itself.

Crystallization of polymers is a process associated with partial alignment of their molecular chains. These chains fold together and form ordered regions called lamellae, which compose larger spheroidal structures named spherulites. Polymers can crystallize upon cooling from melting, mechanical stretching or solvent evaporation. Crystallization affects optical, mechanical, thermal and chemical properties of the polymer. The degree of crystallinity is estimated by different analytical methods and it typically ranges between 10 and 80%, with crystallized polymers often called "semi-crystalline". The properties of semi-crystalline polymers are determined not only by the degree of crystallinity, but also by the size and orientation of the molecular chains.

In Earth science, ductility refers to the capacity of a rock to deform to large strains without macroscopic fracturing. Such behavior may occur in unlithified or poorly lithified sediments, in weak materials such as halite or at greater depths in all rock types where higher temperatures promote crystal plasticity and higher confining pressures suppress brittle fracture. In addition, when a material is behaving ductilely, it exhibits a linear stress vs strain relationship past the elastic limit.

<span class="mw-page-title-main">Grain boundary sliding</span> Material deformation mechanism

Grain boundary sliding (GBS) is a material deformation mechanism where grains slide against each other. This occurs in polycrystalline material under external stress at high homologous temperature and low strain rate and is intertwined with creep. Homologous temperature describes the operating temperature relative to the melting temperature of the material. There are mainly two types of grain boundary sliding: Rachinger sliding, and Lifshitz sliding. Grain boundary sliding usually occurs as a combination of both types of sliding. Boundary shape often determines the rate and extent of grain boundary sliding.

Nabarro–Herring creep is a mode of deformation of crystalline materials that occurs at low stresses and held at elevated temperatures in fine-grained materials. In Nabarro–Herring creep, atoms diffuse through the crystals, and the creep rate varies inversely with the square of the grain size so fine-grained materials creep faster than coarser-grained ones. NH creep is solely controlled by diffusional mass transport. This type of creep results from the diffusion of vacancies from regions of high chemical potential at grain boundaries subjected to normal tensile stresses to regions of lower chemical potential where the average tensile stresses across the grain boundaries are zero. Self-diffusion within the grains of a polycrystalline solid can cause the solid to yield to an applied shearing stress, the yielding being caused by a diffusional flow of matter within each crystal grain away from boundaries where there is a normal pressure and toward those where there is a normal tension. Atoms migrating in the opposite direction account for the creep strain. The creep strain rate is derived in the next section. NH creep is more important in ceramics than metals as dislocation motion is more difficult to effect in ceramics.

Geometrically necessary dislocations are like-signed dislocations needed to accommodate for plastic bending in a crystalline material. They are present when a material's plastic deformation is accompanied by internal plastic strain gradients. They are in contrast to statistically stored dislocations, with statistics of equal positive and negative signs, which arise during plastic flow from multiplication processes like the Frank-Read source.

References

↑ Passchier & Trouw 1998; p. 257
↑ Twiss & Moores 2000, p. 391
↑ Twiss & Moores 2000; p. 390-391
↑ Twiss & Moores 2000, p. 394
↑ Passchier & Trouw 1998; p. 54
↑ Passchier & Trouw 1998; p. 42
↑ Gower & Simpson 1992

Literature

Gower, R.J.W. & Simpson, C.; 1992: Phase boundary mobility in naturally deformed, high-grade quartzofeldspatic rocks: evidence for diffusion creep, Journal of Structural Geology 14, p. 301-314.
Passchier, C.W. & Trouw, R.A.J., 1998: Microtectonics, Springer, ISBN 3-540-58713-6
Twiss, R.J. & Moores, E.M., 2000 (6th edition): Structural Geology, W.H. Freeman & co, ISBN 0-7167-2252-6

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[1] Passchier & Trouw 1998; p. 257

[2] Twiss & Moores 2000, p. 391

[3] Twiss & Moores 2000; p. 390-391

[4] Twiss & Moores 2000, p. 394

[5] Passchier & Trouw 1998; p. 54

[6] Passchier & Trouw 1998; p. 42

[7] Gower & Simpson 1992

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