Dispersed particles can impart significant obstacles to the dislocation motion, thus increasing the strength of the material. Particle hardening is a much stronger mechanism than the solid solution hardening. This type of strengthening could be effective even at higher temperatures based on the stability of the precipitates.

There are two types of fine particle strengthening mechanism: precipitation hard­ening and dispersion strengthening.

• For precipitation hardening (or age hardening) to happen, the second phase needs to be soluble at elevated temperatures and should have decreasing solubil­ity with decreasing temperatures. However, in dispersion hardening, the second phases have very little solubility in the matrix (even at higher temperatures).

• Generally, there is atomic matching (i. e., coherency) between the precipitates and the matrix. However, in dispersion hardening system, there is no coherency between the second-phase particles and the matrix.

• The number of precipitation hardening systems is limited, whereas it is theoreti­cally possible to create an almost infinite number of dispersion hardening systems.

As the particles are central to these kinds of strengthening mechanisms, the fol­lowing particle characteristics are important: (a) particle volume fraction,

(b) particle shape, (c) particle size, (d) nature of the particle-matrix interface, and (e) particle structure. Note that particle volume fraction can be related to the parti­cle size through the interparticle spacing (l):

4(1 — f)r

3f

where f is the volume fraction of spherical particles of radius r. There are other similar relations also, depending on the assumptions of derivation.