Anti-phase domain

Order strengthening brought about from the interaction of dislocations with ordered precipitates, forming anti-phase boundaries as dislocations move throughout the crystal, can lead to significant increases in strength and creep resistance. For this reason, order strengthening is often exploited for high-temperature creep resistant superalloys used in turbine blades.^[2]

Antiphase domains carry with them a surface energy penalty when compared to the perfect lattice due to their chemical disorder, and the presence of these boundaries impedes dislocation motion throughout the crystal, leading to increased strength under shear stress. Figure 3 below shows the process of an edge dislocation propagating through an ordered particle. As the dislocation moves throughout the particle, lattice planes are displaced from their equilibrium configuration, and A-A bonds and B-B bonds are formed throughout the slip plane. This forms a higher energy state than when compared to the equilibrium A-B bonding configuration, and the change in energy is called the anti-phase boundary energy (APBE). This can increase the degree of strengthening created from precipitation hardening, making it more difficult for cutting to occur, and instead increasing the likelihood of Orowan bowing around the precipitate.^[1]

Figure 3: The process of an edge dislocation moving through an ordered precipitate. In (a), the perfectly ordered particle is shown. In (b), the dislocations has moved through part of the particle. In (c), the dislocation exits the precipitate, leading to an increase in surface energy from increased surface area and a higher-energy bonding configuration.^[1]

Order strengthening is often characterized by a ratio of the attractive anti-phase boundary energy (APBE) to the repulsive dislocation energy(Gb): ${\displaystyle \epsilon _{ord}={\frac {APBE}{Gb}}}$. The degree of order strengthening depends on both this ratio and whether the alloy is in the early or late stages of precipitation. When ${\displaystyle \epsilon _{ord}}$ is low, the trailing dislocation moves far behind the leading dislocations, leading to separate cutting of precipitates as seen in Figure 4a. Alternatively, when ${\displaystyle \epsilon _{ord}}$ is high, the trailing dislocation follows close behind the leading dislocation, leading to common cutting as seen in Figure 4b. During the early stages of precipitation, the increase in shear stress can be expressed as:

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

${\displaystyle \tau _{ord}\approx 0.7G[(\epsilon _{ord})^{3/2}({\frac {fr}{b}})^{1/2}-0.7\epsilon _{ord}f]}$ for high ${\displaystyle \epsilon _{ord}}$ where G is the shear modulus, f is the volume fraction of precipitates, r is the radius of the precipitate, and b is the burgers vector of the dislocation.

In the later stages of precipitation, the analogous expressions are:

${\displaystyle \tau _{ord}\approx 0.44G(\epsilon _{ord})f^{1/2}}$ for low ${\displaystyle \epsilon _{ord}}$ or

${\displaystyle \tau _{ord}\approx 0.44G(\epsilon _{ord})[f^{1/2}-0.92f]}$ for high ${\displaystyle \epsilon _{ord}}$.^[1]

Figure 4: Dislocation motion around precipitates.^[1]

Confusion between inversion domains and antiphase domains is common, even in the published literature, and particularly in the case of GaAs grown on silicon. (Similar defects form in GaN on silicon, where they are correctly identified as inversion domains). An example is illustrated in the diagram below.^[3]

Figure 4. Highlighted area showing an inversion domain, incorrectly called an antiphase domain, in GaAs on Si.^[4]

The shaded region, B, is an example of an APD. In the figure, GaAs is grown on a misoriented surface of Si (details are not discussed here). The misorientation causes the Ga and As atoms in region B to be on opposite sites compared to the crystal matrix. The presence of the APD results in Ga sites 1, 1’, 2, 2’, 3, 3’ being bonded to Ga atoms in the APD to form an APB.

In mixed oxidation state materials like magnetite, antiphase domains and antiphase domain boundaries can occur as a result of charge-ordering even though there are no changes in atom locations.^[4] For example, the reconstructed magnetite (100) surface contains alternating Fe^II pairs and Fe^III pairs in the first subsurface layer.^[4] An antiphase domain boundary can form if two subsurface Fe^II pairs meet when two terraces grow together.^[4]