the maximum pinning force, Fmax, the total pinning pressure exerted by the particle distribution per unit area of the boundary is This is referred to as the Zener pinning pressure. It follows that large pinning pressures are produced by: Increasing the volume fraction of particles Reducing the particle size The Zener pinning pressure is orientation dependent, which means that the exact pinning pressure depends on the amount of coherence at the grain boundaries. Computer Simulation Particle pinning has been studied extensively with computer simulations. Monte Carlo and phase field simulations have been used in 3D to model the phenomenon. Complex shape of interface can be captured in the computer models. It can provide better approximation for the pinning force. Notes According to Current issues in recrystallization: a review, R.D. Doherty et al., Materials Science and Engineering A238 (1997), p 219-274 For information on zener pinning modeling see: - "Contribution à l'étude de la dynamique du Zener pinning: simulations numériques par éléments finis", Thesis in French (2003). by G. Couturier. - "3D finite element simulation of the inhibition of normal grain growth by particles". Acta Materialia, 53, pp. 977–989, (2005). by G. Couturier, R. Doherty, Cl. Maurice, R. Fortunier. - "3D finite element simulation of Zener pinning dynamics". Philosophical Magazine, vol 83, n° 30, pp. 3387–3405, (2003). by G. Couturier, Cl. Maurice, R. Fortunier. Materials science