This paper provides a clearly defined procedure for the calculation of
the liberation spectrum that can be expected when any two-phase or po
rphyry three-phase ore is comminuted in a ball mill or an open-circuit
continuous mill. All the data that are required by the model are read
ily obtained by suitable image analysis of the original ore. The model
accommodates both random and non-random fracture patterns although, i
n the latter case, the model is not entirely predictive at present and
requires some measurements to be made on the comminuted ore. A linear
stochastic process is used to characterize the mineralogical texture
of the ore. This model of the ore texture can be used to predict the l
iberation spectrum in particles of any size after comminution of the o
re. The model is parameter-free and is not limited to textures having
convex grain structures nor to convex particles. The model is extended
to include the effects of different brittleness of the mineral compon
ents and fracture along the grain boundaries which lead to non-random
fracture patterns. The model predicts that modest amounts of grain-bou
ndary fracture will not increase liberation in minerals having exponen
tially distributed linear intercept lengths in each phase. The model i
s extended to multicomponent ores. Examples calculations are given for
a binary ore having exponentially distributed linear intercepts throu
gh both phases. An exponentially distributed porphyry ore with two val
uable mineral phases is analyzed up to the calculations of the linear
grade distribution as a function of particle size. The calculated dist
ribution of linear grades for this three-phase ore cannot be stereolog
ically transformed to the distribution of volumetric grades because no
suitable transformation kernel has yet been determined.