Closure in crystal size distributions (CSD), verification of
CSD calculations, and the significance of CSD fans


American Mineralogist 2002, 87: 171-175

Crystal Size Distribution (CSD) measurements are susceptible to the closure problem, just like chemical compositions. In its simplest form this means that the total crystal content of a rock cannot exceed 100%. Where chemical or thermal effects limit the total quantity of a single phase, closure can occur at lower volumetric phase proportions. This means that parts of the CSD diagram [ln(population density) versus size] are not accessible. If the volumetric phase proportion is constant, then straight CSDs will appear to rotate around a point at small sizes giving a fan of CSDs. These fans are significant and do show changes in crystal sizes that can be interpreted in terms of magmatic processes. However, the correlation between the slopes (or characteristic lengths) and intercepts of individual CSDs in a family is not significant, but just a consequence of the constant phase proportion effect. Many other graphs, such as characteristic length versus volumetric phase proportion, can give more information on magmatic processes.
 
 

 

(a) The closure problem in CSDs, illustrated for cubic crystals. A straight CSD with a slope of -0.57 (characteristic length 1.73 mm) and an intercept of -8.6 has a volumetric phase proportion of 1%. If the intercept is increased to -4.0, for example by crystal growth and exponential increase in nucleation rate, then the crystal content will reach 100% and textural changes will stop. At 100% crystals the CSD is locked and cannot move into the grey area of the diagram. (b) A fan of straight-line CSDs with 100% crystals are tangential to a concave-up curve. Straight CSDs cannot exist in the grey part of the diagram. (c) Straight CSDs can be represented by a point on a graph of characteristic length (-1/ slope) versus intercept. Possible CSDs for 100% crystals proscribe a curve. CSDs can exist below, but not above this line. The position of the line differs for different shapes, here indicated by the aspect ratios of rectangular parallelepipeds and spheres. It is assumed here that the crystals completely fill the volume.