In reflected light mineralogical studies involving opaque minerals, it is possible to section a composite particle so that the particle appears to be liberated. Clearly, a binary particle may be sectioned to appear liberated but a liberated particle cannot be sectioned to appear locked. The probability of this former occurrence depends upon the relative amounts of minerals and their structures which are contained within the composite particle.
A series of mathematical corrections to convert two dimensional estimates into three dimensional approximations for a specific mineral liberation characteristic have been proposed.* We have adopted a simplified version of some of these corrections based on our own measurements into some of our calculations. The general form of the correction is L3D = AL2D – B, where L3D and L-2D are the liberation values at three and two dimensions, and A and B are constants. However, some of the mineralogical data which are discussed in the text of this report are presented as uncorrected two dimensional observed liberation data.
In utilizing the three dimensional corrections, the difference between two dimensional observed, and three dimensional calculated liberation estimates
are proportionally redistributed between the other species present containing the target mineral. For example, 80 percent liberation of sphalerite in two dimensions, decreases to approximately 67 percent true sphalerite liberation in three dimensions after applying the simplified corrections. The percentage difference in liberation (80 – 67) of the sphalerite in the sample is then proportionally distributed between the other sphalerite-bearing composites present, effectively increasing their values.