text: Coherent grain boundaries are those in which the crystal lattice of adjacent grains is continuous across the boundary. In other words, the crystallographic orientation of the grains on either side of the boundary is related by a small rotation or translation. Coherent grain boundaries are typically observed in materials with small grain sizes or in highly ordered materials such as single crystals. Because the crystal lattice is continuous across the boundary, there are no defects or dislocations associated with coherent grain boundaries. As a result, they do not act as barriers to the motion of dislocations and have little effect on the strength of a material. However, they can still affect other properties such as diffusion and grain growth.
  When solid solutions become supersaturated and precipitation occurs, tiny particles are formed. These particles typically have interphase boundaries that match up with the matrix, despite differences in interatomic spacing between the particle and the matrix. This creates a coherency strain, which causes distortion. Dislocations respond to the stress field of a coherent particle in a way similar to how they interact with solute atoms of different sizes. It is worth noting that the interfacial energy can also influence the kinetics of phase transformations and precipitation processes. For instance, the energy associated with a strained coherent interface can reach a critical level as the precipitate grows, leading to a transition from a coherent to a disordered (non-coherent) interface. This transition occurs when the energy associated with maintaining the coherency becomes too high, and the system seeks a lower energy configuration. This happens when particle dispersion is introduced into a matrix. Dislocations pass through small particles and bow between large particles or particles with disordered interphase boundaries. The predominant slip mechanism determines the contribution to strength, which depends on factors such as particle size and volume fraction.