Evaluating the Recovery of Crystal Size Distributions from Computer Generated Microstructures

1. (1) data set identify-cation (2) number of crystals in chamber size of 1003 (mm3) (3) true volume of crystals (mm3) (4) ideal volume of crystals (mm3) (5) number of crystals measured in 2D slices (6) (5) minus crystals on boundaries (7) crystal size based on Intersection width/length Prisms 1:1:5 18869 914005 966057 1386 1216 width Prisms 1:1:3 11509 853394 910590 1543 1340 width Plates 1:5:5 18203 979694 1114570 2301 2017 length Plates 1:3:3 16438 900564 944237 2044 1825 length Cuboids 1:4:5 9018 958381 1128585 1298 1097 length Cuboids 1:3:5 11016 962449 1041728 1644 1423 length NSF REU DMR-0097449 Cuboids 1:2:5 16438 914045 966057 1973 1710 width Evaluating the Recovery of Crystal Size Distributions from Computer Generated Microstructures Roberts, Sarah M.; Wertz, Paxton D.; Amenta, Roddy V., Department of Geology and Environmental Science James Madison University Harrisonburg, VA 22807 CSD FOR ALL XLS VS. CSD WITH BOUNDARY XLS OMITTED Purpose The link between the kinetics of crystallization and the resulting ideal crystal size distribution (CSD) has been well established, but the microstructural and stereological problems related to the recovery of the CSDs from rocks needs to be further explored. These questions are addressed: (1) Does the rock microstructure modify the real (true) crystal sizes relative to their ideal sizes, (2) Can the CSD be recovered from slices? and (3) Do crystal aspect ratios affect the recovered CSDs. We used a computer crystallization model to simulate development of microstructures with known CSDs that were used as standards for comparing CSDs recovered from slices. PLATES PRISMS Crystallization Equations Used in Computer Model Nucleation equation (1) ) N= E(at) Crystal radius growth/time step equation (2) G=Δ L/ Δ t= (0.1mm)/1 Equation for CSD Charts Δ ln(n)/ Δ L = -a/G TRUE CRYSTAL SIZES VS. IDEAL SIZES CUBOIDS Where: N= Number of nuclei/time step a= nucleation rate constant (different for each crystallization experiment) Δt = 1 = time step unit t= cumulative number of time steps • Where: • n= population density • n0= population density as L->0 • G= growth rate constant= 0.1 • 2L= crystal diameter • CONCLUSIONS • The CSDs recovered from microstructures composed of prisms are linear, from plates weakly curvilinear and from cuboids moderately curvilinear. • We confirm the findings of others that intersection widths correlate with smallest diameters of tetragonal prisms and intersection lengths with intermediate diameters of tetragonal plates. • Results with cuboids are mixed. • In the class of orthorhombic plates the intersection lengths correlate with the intermediate crystal diameters. • In the class of orthorhombic prisms neither intersection widths nor lengths correlate with any crystal diameters. Acknowledgements Research funded by Donors of the American Chemical Society Petroleum Research Fund, Grant #39580-B2 and Microstructure formed by plates 1-5-5 North East Section GSA, Harrisburg, PA. 3/20-06