A new Monte Carlo application for complex sample geometries

Nicholas W. M. Ritchie

Purpose: Performing quantitative microanalysis on micron-sized particles has always
been a challenge. The volume of the particle is typically smaller than the electron beam
excitation volume and x-ray absorption corrections are complicated by surface topology.
Some researchers have approached this problem by approximating the particle as a simple
geometric shape such as a cylinder, a rectangular or triangular prism [1]. While this
approach is better than applying bulk correction methods, it may be possible to combine
topological measurements from multiple imaging detectors to build a more accurate threedimensional
model of the unknown particle. This model could then become the input
sample structure for a Monte Carlo simulation. The Monte Carlo simulation could be
compared to Monte Carlo simulations of bulk references and the result could be iterated in
a manner similar to the iterative correction processed used by the standard ZAF correction
scheme. The result is likely to be more accurate quantitative results. However, this
scheme relies on the availability of a Monte Carlo model that can handle complex sample
geometries.

This work involved developing a library of Monte Carlo simulation routines capable of
handling samples of arbitrary geometric complexity.

Major Accomplishments: We have developed and tested a Monte Carlo simulation
implemented in platform independent Java code. We have evaluated various different
algorithms for electron elastic [2,3] (see figure 1) and inelastic scattering cross section,
electron energy loss, fluorescence yield and mass absorption coefficient. For each
algorithm class, we have selected the one that we have determined produces the most
realistic results. These algorithms have been implemented into a model in which the
sample is represented by instances of a generic Shape interface*. The Shape interface
represents samples of arbitrary complexity with sufficient detail for the purposes of this
model. Implementations of the Shape interface have been created for basic shapes such as
spheres, blocks and the volume defined by the intersection of an arbitrary number of
directed planes. In addition, implementations of the Shape interface have been created to
represent the union of two or more Shapes and the difference of two Shapes (the volume of
Shape A minus the intersection between Shape A and Shape B). By combining these
Shapes programmatically, samples of arbitrary complexity can be built from primitive
Shapes.

Impact: Assigning particles to a descriptive class through quantitative microanalysis is
hampered by morphologically induced particle-to-particle variance. It is anticipated that
by better modeling the shape of the particle we will be able to reduce particle-to-particle
variance and thereby improve our ability to differentiate particles of similar but different
materials.

Plans: We plan to use the results from this Monte Carlo simulation to develop and
evaluate more computationally efficient analytical expressions for quantifying particulate
samples.

References:
1. J. T. Armstrong in Electron Probe Quantitation, K. F. J. Heinrich and D. E.
Newbury, eds., Plenum Press, New York (1991) pp 261-315
2. Z. Czyzeweski Z, D.O. MacCallum, A. Romig, D. Joy, J Appl. Phys. 68, 7 (1990)
pp 3066-3072
3. A. Jablonksi, F. Salvat, C. J. Powell NIST Electron Elastic-Scattering Cross-
Section Database – Version 3.1. National Institute of Standards and Technology,
Gaithersburg, MD (2003)
4. K. Heinrich in X-ray Optics and Microanalysis, R. Castaing, P. Deschamps, J.
Philibert, eds. Hermann, Paris (1966) pp 159-167

Figure 1: The modeled backscatter yield for various different implementations of the
electron elastic scattering cross section compared with measured values from Heinrich [4].
Rutherford corresponds to a simple screened Rutherford cross-section; NIST-Mott [3] and
Czyzeweski [3] are different implementations of the Mott cross-section. The Czyzewski
cross-section reproduces the experimental results most accurately across the full range of
atomic numbers.

* Shape refers to a Java interface (a contract between a classes’ user and
implementer).

Web Contact micro@nist.gov