# Precipitation hardening

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Precipitation hardening, also called age hardening or particle hardening, is a heat treatment technique used to increase the yield strength of malleable materials, including most structural alloys of aluminium, magnesium, nickel, titanium, and some steels and stainless steels. In superalloys, it is known to cause yield strength anomaly providing excellent high-temperature strength.

## Contents

Precipitation hardening relies on changes in solid solubility with temperature to produce fine particles of an impurity phase, which impede the movement of dislocations, or defects in a crystal's lattice. Since dislocations are often the dominant carriers of plasticity, this serves to harden the material. The impurities play the same role as the particle substances in particle-reinforced composite materials. Just as the formation of ice in air can produce clouds, snow, or hail, depending upon the thermal history of a given portion of the atmosphere, precipitation in solids can produce many different sizes of particles, which have radically different properties. Unlike ordinary tempering, alloys must be kept at elevated temperature for hours to allow precipitation to take place. This time delay is called "aging". Solution treatment and aging is sometimes abbreviated "STA" in specifications and certificates for metals.

Note that two different heat treatments involving precipitates can alter the strength of a material: solution heat treating and precipitation heat treating. Solid solution strengthening involves formation of a single-phase solid solution via quenching. Precipitation heat treating involves the addition of impurity particles to increase a material's strength. [1]

## Kinetics versus thermodynamics

This technique exploits the phenomenon of supersaturation, and involves careful balancing of the driving force for precipitation and the thermal activation energy available for both desirable and undesirable processes.

Nucleation occurs at a relatively high temperature (often just below the solubility limit) so that the kinetic barrier of surface energy can be more easily overcome and the maximum number of precipitate particles can form. These particles are then allowed to grow at lower temperature in a process called ageing. This is carried out under conditions of low solubility so that thermodynamics drive a greater total volume of precipitate formation.

Diffusion's exponential dependence upon temperature makes precipitation strengthening, like all heat treatments, a fairly delicate process. Too little diffusion (under ageing), and the particles will be too small to impede dislocations effectively; too much (over ageing), and they will be too large and dispersed to interact with the majority of dislocations.

## Alloy design

Precipitation strengthening is possible if the line of solid solubility slopes strongly toward the centre of a phase diagram. While a large volume of precipitate particles is desirable, a small enough amount of the alloying element should be added that it remains easily soluble at some reasonable annealing temperature.

Elements used for precipitation strengthening in typical aluminium and titanium alloys make up about 10% of their composition. While binary alloys are more easily understood as an academic exercise, commercial alloys often use three components for precipitation strengthening, in compositions such as Al(Mg, Cu) and Ti(Al, V). A large number of other constituents may be unintentional, but benign, or may be added for other purposes such as grain refinement or corrosion resistance. In some cases, such as many aluminium alloys, an increase in strength is achieved at the expense of corrosion resistance.

The addition of large amounts of nickel and chromium needed for corrosion resistance in stainless steels means that traditional hardening and tempering methods are not effective. However, precipitates of chromium, copper, or other elements can strengthen the steel by similar amounts in comparison to hardening and tempering. The strength can be tailored by adjusting the annealing process, with lower initial temperatures resulting in higher strengths. The lower initial temperatures increase the driving force of nucleation. More driving force means more nucleation sites, and more sites means more places for dislocations to be disrupted while the finished part is in use.

Many alloy systems allow the ageing temperature to be adjusted. For instance, some aluminium alloys used to make rivets for aircraft construction are kept in dry ice from their initial heat treatment until they are installed in the structure. After this type of rivet is deformed into its final shape, ageing occurs at room temperature and increases its strength, locking the structure together. Higher ageing temperatures would risk over-ageing other parts of the structure, and require expensive post-assembly heat treatment because a high ageing temperature promotes the precipitate to grow too readily.

## Types of hardening

There are several ways by which a matrix can be hardened by precipitates, which could also be different for deforming precipitates and non-deforming precipitates. [2]

Deforming particles:

Coherency hardening occurs when the interface between the particles and the matrix is coherent, which depends on parameters like particle size and the way that particles are introduced. Small particles precipitated from supersaturated solid solution usually have coherent interfaces with the matrix. Coherency hardening originates from the atomic volume difference between precipitate and the matrix, which results in a coherency strain. The associated stress field interacts with dislocations leading to an increase in yield strength, similar to the size effect in solid solution strengthening.

Modulus hardening results from the different shear modulus of the precipitate and the matrix, which leads to an energy change of dislocation line tension when the dislocation line cuts the precipitate. Also, the dislocation line could bend when entering the precipitate, increasing the affected length of the dislocation line.

Chemical strengthening is associated with the surface energy of the newly introduced precipitate-matrix interface when the particle is sheared by dislocations. LIke modulus hardening, the analysis of interfacial area can be complicated by dislocation line distortion.

Order strengthening occurs when the precipitate is an ordered structure such that bond energy before and after shearing is different. For example, in an ordered cubic crystal with composition AB, the bond energy of A-A and B-B after shearing is higher than that of the A-B bond before. The associated energy increase per unit area is anti-phase boundary energy and accumulates gradually as the dislocation passes through the particle. However, a second dislocation could remove the anti-phase domain left by the first dislocation when traverses the particle. The attraction of the particle and the repulsion of the first dislocation maintains a balanced distance between two dislocations, which makes order strengthening more complicated.

Non-deforming particles:

In non-deforming particles, where the spacing is small enough or the precipitate-matrix interface is disordered, dislocation bows instead of shears. The strengthening is related to the effective spacing between particles considering finite particle size, but not particle strength, because once the particle is strong enough for the dislocations to bow rather than cut, further increase of the dislocation penetration resistance won't affect strengthening.

## Theory

The primary species of precipitation strengthening are second phase particles. These particles impede the movement of dislocations throughout the lattice. You can determine whether or not second phase particles will precipitate into solution from the solidus line on the phase diagram for the particles. Physically, this strengthening effect can be attributed both to size and modulus effects, and to interfacial or surface energy. [2] [3]

The presence of second phase particles often causes lattice distortions. These lattice distortions result when the precipitate particles differ in size and crystallographic structure from the host atoms. Smaller precipitate particles in a host lattice leads to a tensile stress, whereas larger precipitate particles leads to a compressive stress. Dislocation defects also create a stress field. Above the dislocation there is a compressive stress and below there is a tensile stress. Consequently, there is a negative interaction energy between a dislocation and a precipitate that each respectively cause a compressive and a tensile stress or vice versa. In other words, the dislocation will be attracted to the precipitate. In addition, there is a positive interaction energy between a dislocation and a precipitate that have the same type of stress field. This means that the dislocation will be repulsed by the precipitate.

Precipitate particles also serve by locally changing the stiffness of a material. Dislocations are repulsed by regions of higher stiffness. Conversely, if the precipitate causes the material to be locally more compliant, then the dislocation will be attracted to that region. In addition, there are three types of interphase boundaries (IPBs).

The first type is a coherent or ordered IPB, the atoms match up one by one along the boundary. Due to the difference in lattice parameters of the two phases, a coherency strain energy is associated with this type of boundary. The second type is a fully disordered IPB and there are no coherency strains, but the particle tends to be non-deforming to dislocations. The last one is a partially ordered IPB, so coherency strains are partially relieved by the periodic introduction of dislocations along the boundary.

In coherent precipitates in a matrix, if the precipitate has a lattice parameter less than that of the matrix, then the atomic match across the IPB leads to an internal stress field that interacts with moving dislocations.

There are two deformation paths, one is the coherency hardening, the lattice mismatch is

${\displaystyle \varepsilon _{coh}={\frac {a_{p}-a_{m}}{a_{m}}}}$
${\displaystyle \tau _{coh}=7G\left|\varepsilon _{coh}\right|^{\frac {3}{2}}\left({\frac {rf}{b}}\right)^{\frac {1}{2}}}$

Where ${\displaystyle G}$ is the shear modulus, ${\displaystyle \varepsilon _{coh}}$ is the coherent lattice mismatch, ${\displaystyle r}$ is the particle radius, ${\displaystyle f}$ is the particle volume fraction, ${\displaystyle b}$ is the burgers vector, ${\displaystyle rf/b}$ equals the concentration.

The other one is modulus hardening. The energy of the dislocation energy is ${\displaystyle U_{m}=G_{m}b^{2}/2}$, when it cuts through the precipitate, its energy is ${\displaystyle U_{p}=G_{p}b^{2}/2}$, the change in line segment energy is

${\displaystyle \bigtriangleup {U}=\left(U_{p}-U_{m}\right)2r=\left(G_{p}-G_{m}\right)b^{2}r}$.

The maximum dislocation length affected is the particle diameter, the line tension change takes place gradually over a distance equal to ${\displaystyle r}$. The interaction force between the dislocation and the precipitate is

${\displaystyle F={dU \over dr}=\left(G_{p}-G_{m}\right)b^{2}=G_{m}b^{2}{\frac {G_{p}-G_{m}}{G_{m}}}=G_{m}b^{2}\varepsilon _{Gp}}$ and ${\displaystyle \tau ={\frac {F}{bL}}}$.

Furthermore, a dislocation may cut through a precipitate particle, and introduce more precipitate-matrix interface, which is chemical strengthening. When the dislocation is entering the particle and is within the particle, the upper part of the particle shears b with respect to the lower part accompanies the dislocation entry. A similar process occurs when the dislocation exits the particle. The complete transit is accompanied by creation of matrix-precipitate surface area of approximate magnitude ${\displaystyle A=2\pi rb\,\!}$, where r is the radius of the particle and b is the magnitude of the burgers vector. The resulting increase in surface energy is ${\displaystyle E=2\pi rb\gamma _{s}\,\!}$, where ${\displaystyle \gamma _{s}}$ is the surface energy. The maximum force between the dislocation and particle is ${\displaystyle F_{max}=\pi r\gamma _{s}\,\!}$, the corresponding flow stress should be ${\displaystyle \Delta \tau =F_{max}/bL=\pi r\gamma _{s}/bL}$.

When a particle is sheared by a dislocation, a threshold shear stress is needed to deform the particle. The expression for the required shear stress is as follows:

${\displaystyle \tau =cG\varepsilon ^{\frac {3}{2}}\left({\frac {rf}{b}}\right)^{\frac {1}{2}}}$

When the precipitate size is small, the required shear stress ${\displaystyle \tau }$ is proportional to the precipitate size ${\displaystyle r^{1/2}}$, However, for a fixed particle volume fraction, this stress may decrease at larger values of r owing to an increase in particle spacing. The overall level of the curve is raised by increases in either inherent particle strength or particle volume fraction.

The dislocation can also bow around a precipitate particle through so-called Orowan mechanism.

Since the particle is non-deforming, the dislocation bows around the particles (${\displaystyle \phi _{c}=0}$), the stress required to effect the bypassing is inversely proportional to the interparticle spacing ${\displaystyle (L-2r)}$, that is, ${\displaystyle \tau _{b}=Gb/(L-2r)}$, where ${\displaystyle r}$ is the particle radius. Dislocation loops encircle the particles after the bypass operation, a subsequent dislocation would have to be extruded between the loops. Thus, the effective particle spacing for the second dislocation is reduced to ${\displaystyle (L-2r')}$ with ${\displaystyle r'>r}$, and the bypassing stress for this dislocation should be ${\displaystyle \tau _{b}'=Gb/(L-2r')}$, which is greater than for the first one. However, as the radius of particle increases, ${\displaystyle L}$will increase so as to maintain the same volume fraction of precipitates, ${\displaystyle (L-2r)}$ will increase and ${\displaystyle \tau _{b}}$ will decrease. As a result, the material will become weaker as the precipitate size increases.

For a fixed particle volume fraction, ${\displaystyle \tau _{b}}$ decreases with increasing r as this is accompanied by an increase in particle spacing.

On the other hand, increasing ${\displaystyle f}$ increases the level of the stress as a result of a finer particle spacing. The level of ${\displaystyle \tau _{b}}$ is unaffected by particle strength. That is, once a particle is strong enough to resist cutting, any further increase in its resistance to dislocation penetration has no effect on ${\displaystyle \tau _{b}}$, which depends only on matrix properties and effective particle spacing.

If particles of A of volume fraction ${\displaystyle f_{1}}$are dispersed in a matrix, particles are sheared for ${\displaystyle r and are bypassed for ${\displaystyle r>r_{c1}}$, maximum strength is obtained at ${\displaystyle r=r_{c1}}$, where the cutting and bowing stresses are equal. If inherently harder particles of B of the same volume fraction are present, the level of the ${\displaystyle \tau _{c}}$ curve is increased but that of the ${\displaystyle \tau _{b}}$ one is not. Maximum hardening, greater than that for A particles, is found at ${\displaystyle r_{c2}. Increasing the volume fraction of A raises the level of both ${\displaystyle \tau _{b}}$ and ${\displaystyle \tau _{c}}$ and increases the maximum strength obtained. The latter is found at ${\displaystyle r_{c3}}$, which may be either less than or greater than ${\displaystyle r_{c1}}$ depending on the shape of the ${\displaystyle \tau -r}$ curve.

## Governing equations

There are two main types of equations to describe the two mechanisms for precipitation hardening:

Dislocation cutting through particles: For most strengthening at the early stage, it increases with ${\displaystyle \epsilon ^{\tfrac {3}{2}}(fr/b)^{\tfrac {1}{2}}}$, where ${\displaystyle \epsilon }$ is a dimensionless mismatch parameter (for example, in coherency hardening, ${\displaystyle \epsilon }$ is the fractional change of precipitate and matrix lattice parameter), ${\displaystyle f}$ is the volume fraction of precipitate, ${\displaystyle r}$ is the precipitate radius, and ${\displaystyle b}$ is the magnitude of the Burgers vector. According to this relationship, materials strength increases with increasing mismatch, volume fraction, and particle size, so that dislocation is easier to cut through particles with smaller radius.

For different types of hardening through cutting, governing equations are as following.

For coherency hardening,

${\displaystyle \tau _{coh}=7G\left|\epsilon _{coh}\right|^{\frac {3}{2}}(fr/b)^{\frac {1}{2}}}$,

${\displaystyle \epsilon _{coh}=(a_{p}-a_{m})/a_{m}}$,

where ${\displaystyle \tau }$ is increased shear stress, ${\displaystyle G}$ is the shear modulus of the matrix, ${\displaystyle a_{p}}$ and ${\displaystyle a_{m}}$ are the lattice parameter of the precipitate or the matrix.

For modulus hardening,

${\displaystyle \tau _{G_{p}}=0.01G\epsilon _{G_{p}}^{\frac {3}{2}}(fr/b)^{\frac {1}{2}}}$,

${\displaystyle \epsilon _{G_{p}}=\left(G_{p}-G_{m}\right)/G_{m}}$,

where ${\displaystyle G_{p}}$ and ${\displaystyle G_{m}}$ are the shear modulus of the precipitate or the matrix.

For chemical strengthening,

${\displaystyle \tau _{chem}=2G\epsilon _{ch}^{\frac {3}{2}}(fr/b)^{\frac {1}{2}}}$,

${\displaystyle \epsilon _{ch}=\gamma _{s}/Gr}$,

where ${\displaystyle \gamma _{s}}$ is the particle-matrix interphase surface energy.

For order strengthening,

${\displaystyle \tau _{ord}=0.7G\epsilon _{ord}^{\frac {3}{2}}(fr/b)^{\frac {1}{2}}}$

(low ${\displaystyle \epsilon _{ord}}$, early stage precipitation), where the dislocations are widely separated;

${\displaystyle \tau _{ord}=0.7G\left(\epsilon _{ord}^{\tfrac {3}{2}}(fr/b)^{\tfrac {1}{2}}-0.7\epsilon _{ord}f\right)}$

(high ${\displaystyle \epsilon _{ord}}$, early stage precipitation), where the dislocations are not widely separated; ${\displaystyle \epsilon _{ord}={\frac {APBE_{s}}{Gb}}}$, where ${\displaystyle APBE_{s}}$ is anti-phase boundary energy.

Dislocations bowing around particles: When the precipitate is strong enough to resist dislocation penetration, dislocation bows and the maximum stress is given by Orowan equation. Dislocation bowing, also called Orowan strengthening, [4] is more likely to occur when the particle density in the material is lower.

${\displaystyle \tau ={\frac {Gb}{L-2r}}\,\!}$

where ${\displaystyle \tau }$ is the material strength, ${\displaystyle G}$ is the shear modulus, ${\displaystyle b}$ is the magnitude of the Burgers vector, ${\displaystyle L}$ is the distance between pinning points, and ${\displaystyle r}$ is the second phase particle radius. This governing equation shows that for dislocation bowing the strength is inversely proportional to the second phase particle radius ${\displaystyle r}$, because when the volume fraction of the precipitate is fixed, the spacing ${\displaystyle L}$ between particles increases concurrently with the particle radius ${\displaystyle r}$, therefore ${\displaystyle L-2r}$ increases with ${\displaystyle r}$.

These governing equations show that the precipitation hardening mechanism depends on the size of the precipitate particles. At small ${\displaystyle r}$, cutting will dominate, while at large ${\displaystyle r}$, bowing will dominate.

Looking at the plot of both equations, it is clear that there is a critical radius at which max strengthening occurs. This critical radius is typically 5-30 nm.

The Orowan strengthening model above neglects changes to the dislocations due to the bending. If bowing is accounted for, and the instability condition in the Frank-Read mechanism is assumed, the critical stress for dislocations bowing between pinning segments can be described as: [5]

${\displaystyle \tau _{c}=A(\theta ){\frac {Gb}{2\pi L^{'}}}ln\left({\frac {L^{'}}{r}}\right)}$

where ${\displaystyle A}$ is a function of ${\displaystyle \theta }$, ${\displaystyle \theta }$ is the angle between the dislocation line and the Burgers vector, ${\displaystyle L^{'}}$is the effective particle separation, ${\displaystyle b}$ is the Burgers vector, and ${\displaystyle r}$ is the particle radius.

## Computational discovery of new alloys

While significant effort has been made to develop new alloys, the experimental results take time and money to be implemented. One possible alternative is doing simulations with Density functional theory, that can take advantage of, in the context of precipitation hardening, the crystalline structure of precipitates and of the matrix and allow the exploration of a lot more alternatives than with experiments in the traditional form.

One strategy for doing these simulations is focusing on the ordered structures that can be found in many metal alloys, like the long-period stacking ordered (LPSO) structures that have been observed in numerous systems. [6] [7] [8] The LPSO structure is long packed layered configuration along one axis with some layers enriched with precipitated elements. This allows to exploit the symmetry of the supercells and it suits well with the currently available DFT methods. [9]

In this way, some researchers have developed strategies to screen the possible strengthening precipitates that allow decreasing the weight of some metal alloys. [10] For example, Mg-alloys have received progressive interest to replace Aluminum and Steel in the vehicle industry because it is one of the lighter structural metals. However, Mg-alloys show issues with low strength and ductility which have limited their use. To overcome this, the Precipitation hardening technique, through the addition of rare earth elements, has been used to improve the alloy strength and ductility. Specifically, the LPSO structures were found that are responsible for these increments, generating an Mg-alloy that exhibited high-yield strength: 610 MPa at 5% of elongation at room temperature. [11]

In this way, some researchers have developed strategies to Looking for cheaper alternatives than Rare Elements (RE) it was simulated a ternary system with Mg-Xl-Xs, where Xl and Xs correspond to atoms larger than and shorter than Mg, respectively. Under this study, it was confirmed more than 85 Mg-Re-Xs LPSO structures, showing the DFT ability to predict known LPSO ternary structures. Then they explore the 11 non-RE Xl elements and was found that 4 of them are thermodynamically stable. One of them is the Mg-Ca-Zn system that is predicted to form an LPSO structure. [12]

Following the previous DFT predictions, other investigators made experiments with the Mg-Zn-Y-Mn-Ca system and found that at 0.34%at Ca addition the mechanical properties of the system were enhanced due to the formation of LPSO-structures, achieving “a good balance of the strength and ductibility”. [13]

## Related Research Articles

A composite material is a material which is produced from two or more constituent materials. These constituent materials have notably dissimilar chemical or physical properties and are merged to create a material with properties unlike the individual elements. Within the finished structure, the individual elements remain separate and distinct, distinguishing composites from mixtures and solid solutions.

Shear stress, often denoted by τ, is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. Normal stress, on the other hand, arises from the force vector component perpendicular to the material cross section on which it acts.

In materials science, creep is the tendency of a solid material to move slowly or deform permanently under the influence of 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 increases 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.

Work hardening, also known as strain hardening, is the strengthening of a metal or polymer by plastic deformation. Work hardening may be desirable, undesirable, or inconsequential, depending on the context.

Hardening is a metallurgical metalworking process used to increase the hardness of a metal. The hardness of a metal is directly proportional to the uniaxial yield stress at the location of the imposed strain. A harder metal will have a higher resistance to plastic deformation than a less hard metal.

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.

Critical resolved shear stress (CRSS) is the component of shear stress, resolved in the direction of slip, necessary to initiate slip in a grain. Resolved shear stress (RSS) is the shear component of an applied tensile or compressive stress resolved along a slip plane that is other than perpendicular or parallel to the stress axis. The RSS is related to the applied stress by a geometrical factor, m, typically the Schmid factor:

Solid solution strengthening is a type of alloying that can be used to improve the strength of a pure metal. The technique works by adding atoms of one element to the crystalline lattice of another element, forming a solid solution. The local nonuniformity in the lattice due to the alloying element makes plastic deformation more difficult by impeding dislocation motion through stress fields. In contrast, alloying beyond the solubility limit can form a second phase, leading to strengthening via other mechanisms.

The neutral axis is an axis in the cross section of a beam or shaft along which there are no longitudinal stresses or strains. If the section is symmetric, isotropic and is not curved before a bend occurs, then the neutral axis is at the geometric centroid. All fibers on one side of the neutral axis are in a state of tension, while those on the opposite side are in compression.

Methods have been devised to modify the yield strength, ductility, and toughness of both crystalline and amorphous materials. These strengthening mechanisms give engineers the ability to tailor the mechanical properties of materials to suit a variety of different applications. For example, the favorable properties of steel result from interstitial incorporation of carbon into the iron lattice. Brass, a binary alloy of copper and zinc, has superior mechanical properties compared to its constituent metals due to solution strengthening. Work hardening has also been used for centuries by blacksmiths to introduce dislocations into materials, increasing their yield strengths.

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, too. So, 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.

In materials science, a Frank–Read source is a mechanism explaining the generation of multiple dislocations in specific well-spaced slip planes in crystals when they are deformed. When a crystal is deformed, in order for slip to occur, dislocations must be generated in the material. This implies that, during deformation, dislocations must be primarily generated in these planes. Cold working of metal increases the number of dislocations by the Frank–Read mechanism. Higher dislocation density increases yield strength and causes work hardening of metals.

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A fiber-reinforced composite (FRC) is a composite building material that consists of three components:

1. the fibers as the discontinuous or dispersed phase,
2. the matrix as the continuous phase, and
3. the fine interphase region, also known as the interface.

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.

An antiphase domain (APD) is a type of planar crystallographic defect in which the atoms within a region of a crystal are configured in the opposite order to those in the perfect lattice system. Throughout the entire APD, atoms sit on the sites typically occupied by atoms of a different species. For example, in an ordered AB alloy, if an A atom occupies the site usually occupied by a B atom, a type of crystallographic point defect called an antisite defect is formed. If an entire region of the crystal is translated such that every atom in a region of the plane of atoms sits on its antisite, an antiphase domain is formed. In other words, an APD is a region formed from antisite defects of a parent lattice. On either side of this domain, the lattice is still perfect, and the boundaries of the domain are referred to as antiphase boundaries. Crucially, crystals on either side of an antiphase boundary are related by a translation, rather than a reflection or an inversion.

Toughening is the improvement of the fracture resistance of a given material. The material's toughness is described by irreversible work accompanying crack propagation. Designing against this crack propagation leads to toughening the material.

## References

1. W.D. Callister. Fundamentals of Materials Science and Engineering, 2nd ed. Wiley & Sons. pp. 252.
2. Thosmas H. Courtney. Mechanical Behavior of Materials, 2nd ed. Waveland Press, Inc.. pp. 198-205.
3. Orowan Bowing Archived 2011-09-28 at the Wayback Machine
4. Soboyejo, Wole O. (2003). "8.6.1 Dislocation/ Orowan Strengthening". Mechanical properties of engineered materials. Marcel Dekker. ISBN   0-8247-8900-8. OCLC   300921090.
5. "Long-period ordered structure in a high-strength nanocrystalline Mg-1 at% Zn-2 at% Y alloy studied by atomic-resolution Z-contrast STEM". Acta Materialia. 50 (15): 3845–3857. 2002-09-03. doi:10.1016/S1359-6454(02)00191-X. ISSN   1359-6454.
6. "Long period stacking order in close packed structures of metals". Journal of Physics and Chemistry of Solids. 28 (2): 137–160. 1967-02-01. doi:10.1016/0022-3697(67)90104-7. ISSN   0022-3697.
7. Nie, Jian-Feng (2012-11-01). "Precipitation and Hardening in Magnesium Alloys". Metallurgical and Materials Transactions A. 43 (11): 3891–3939. doi:. ISSN   1543-1940.
8. Neugebauer, Jörg; Hickel, Tilmann (2013). "Density functional theory in materials science". WIREs Computational Molecular Science. 3 (5): 438–448. doi:10.1002/wcms.1125. ISSN   1759-0884. PMC  . PMID   24563665.
9. "High-throughput computational search for strengthening precipitates in alloys". Acta Materialia. 102: 125–135. 2016-01-01. doi:. ISSN   1359-6454.
10. "Vol.42 No.07 pp.1172-1176". www.jim.or.jp. Retrieved 2021-05-14.
11. "Thermodynamic stability of Mg-based ternary long-period stacking ordered structures". Acta Materialia. 68: 325–338. 2014-04-15. arXiv:. doi:10.1016/j.actamat.2013.10.055. ISSN   1359-6454.
12. "Effects of Ca on the formation of LPSO phase and mechanical properties of Mg-Zn-Y-Mn alloy". Materials Science and Engineering: A. 648: 37–40. 2015-11-11. doi:10.1016/j.msea.2015.09.046. ISSN   0921-5093.
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