The development of outgrowths or pits of various shapes on coated grains is explained via a quantitative model of grain growth/dissolution kinetics coupled to evolving grain geometry (morphological dynamics). Grain-coating thinning or fracturing occurring due to nonplanar growth (and consequent grain surface area increase) is shown to underlie an instability to the formation of bumps, or in the case of undersaturated systems, to pitting. Examples of diagenetic outgrowth phenomena on clay-coated quartz are presented. A quantitative model of coupled quartz growth and coating dynamics is shown to imply many features observed in natural systems. Crystal growth anisotropy is shown to strongly influence the morphology of the outgrowths. The creation of inclusions is shown to be closely related to the present morphological instability. These morphological instability phenomena are interesting examples of geochemical self-organization.