text: 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.
  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.
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  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.
  Order strengthening is often characterized by a ratio of the attractive anti-phase boundary energy (APBE) to the repulsive dislocation energy(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  is low, the trailing dislocation moves far behind the leading dislocations, leading to separate cutting of precipitates as seen in Figure 4a. Alternatively, when 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:
   for low  or
  for high 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:
   for low or
  for high .
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  Figure 4: Dislocation motion around precipitates.