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MONTE CARLO SIMULATIONS OF ELECTRON MOTION IN
MATERIALS AND AVAILABLE SOFTWARE. Michal
Zelechower Silesian University of Technology,
Katowice, Poland
Electronic version available at the web
site http//www.polsl.katowice.pl/pracownik.asp?Nr
Pracownika207 or http//www.polsl.katowice.pl?m
zelechower
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SOURCES AND REFERENCES
Chemical microanalysis by X-ray
spectroscopies Philippe-André Buffat, EPFL, CIME
GamBet Tutorials, Field Precision LLC (1989-2006)
The Electromagnetic Cascade Shower, S. H. Rokni
and W. R. Nelson, Stanford Linear Accelerator
Center, August 2, 2001
Fundamentals of Monte Carlo - particle transport,
Forrest B. Brown Los Alamos National Laboratory
Simulation Basics in CMS, H. W. K. Cheung
(Fermilab), All USCMS Meeting, 5/26/06
The EGSnrc Monte Carlo system, Iwan Kawrakow,
Ionizing Radiation Standards, NRC, Ottawa, Canada
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PENELOPE, a code system for Monte Carlo
simulation of electron and photon Transport,
Francesc Salvat, Jose M. Fernandez-Varea, Josep
Sempau
X-Ray Microanalysis of Real Materials Using Monte
Carlo Simulations, Raynald Gauvin and Eric
Lifshin, Microchim. Acta 145, 4147 (2004)
Pouchou J.-L., Deslile N., Henoc J., First
evaluation of HURRICANE software for Monte Carlo
simulation - Part I Computation principles and
basic applications to homogeneous and layered
targets, Proc. 9th EMAS Workshop, Florence,
Italy, 2005 Pouchou J.-L., First evaluation of
HURRICANE software for Monte Carlo simulation
Part II Applications to rough or porous
specimen, small particle and multiphase
specimen., Proc. 9th EMAS Workshop, Florence,
Italy, 2005
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Useful links
http//montecarlomodeling.mcgill.ca/
http//www.ioffe.rssi.ru/ES/
http//www.matter.org.uk/tem/electron_scattering.h
tm
http//www.geology.wisc.edu/courses/g777/777Softwa
re.html
http//dsa.dimes.tudelft.nl/usage/pattern_definiti
on/monte/monte.html
http//www.matsceng.ohio-state.edu/COLIJN/SEM.htm
l
http//www2.arnes.si/7Esgszmera1/
http//xdb.lbl.gov/
http//henke.lbl.gov/optical_constants/
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The first numerical Monte Carlo simulation of
photon transport is that of Hayward and Hubbell
(1954) who generated 67 photon histories using a
desk calculator. The simulation of photon
transport is straightforward since the mean
number of events in each history is fairly small.
Indeed, the photon is effectively absorbed after
a single photoelectric or pair-production
interaction or after a few Compton interactions
(of the order of 10). With present-day
computational facilities, detailed simulation of
photon transport is a simple routine task.
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The simulation of electron and positron transport
is much more diffcult than that of photons. The
main reason is that the average energy loss of an
electron in a single interaction is very small
(of the order of a few tens of eV). As a
consequence, high-energy electrons undergo a
large number of interactions before being
effectively absorbed in the medium. In practice,
detailed simulation is realistic only when the
average number of collisions per track is not too
large (up to a few hundred).
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The Monte Carlo simulation of a given
experimental arrangement (e.g. an electron beam,
coming from an accelerator or an electron gun and
impinging on a solid) consists of the numerical
generation of random histories. To simulate
these histories we need an interaction model,
i.e. a set of differential cross sections (DCS)
for the relevant interaction mechanisms.
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The DCS determines the probability distribution
function (PDF) of the random variables that
characterize a track 1) free path between
successive interaction events, 2) kind of
interaction taking place and 3) energy loss and
angular deflection in a particular event (and
initial state of emitted secondary particles, if
any). Once these PDFs are known, random histories
can be generated by using appropriate sampling
methods. If the number of generated histories is
large enough, quantitative information on the
transport process may be obtained by simply
averaging over the simulated histories.
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PSEUDO-RANDOM NUMBER GENERATORS 1. Multiplicative
congruential generators (Press and Teukolsky,
1992) produce a sequence of random numbers
uniformly distributed in (0,1). However, the
sequence is periodic, with a period of the order
of 109. 2. L'Ecuyer generator (1988) produces
32-bit floating point numbers uniformly
distributed in the open interval between zero and
one. Its period is of the order of 1018 3. The
cumulative distribution function is a
non-decreasing function and, therefore, it has an
inverse function. The inverse transformation
defines a new random variable that takes values
in the interval (0,1)
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The attempts to construct working Monte Carlo
codes were presented by Nelson et al. in 1985
(EGS4), Brun et al. in 1986 (GEANT3), Berger and
Seltzer in 1988 (ETRAN), Halbleib et al. in 1992
(ITS3), Joy in 1995 (MCS), Salvat et al. in 1996
(PENELOPE), Briesmeister in 1997 (MCNP4b) and
Kawrakow and Rogers in 2000 (EGSNRC). Currently
additional codes are available, of which the
HURRICANE by Pouchou is commercial while the
CASINO and the WINXRAY by Gauvin et al. are
freeware
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MC simulation of X-ray emission (C layer
deposited on Si substrate) D. Joy MC simulation
in DOS
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199 electron trajectories in air and their impact
into silicon substrate D. Joy MC simulation for
Win95
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199 electron trajectories in a multilayer
structure D. Joy MC simulation for Win95
Al
C
W
Si
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MC simulation of X-ray emission in Ag and ? ( ?
z) function for K, L, M series D. Joy MC
simulation for Win95
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MC simulation of ? ( ? z) function for Ag K, L, M
series D. Joy MC simulation for Win95
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200 electron trajectories in a multilayer
structure CASINO code by R. Gauvin et al.
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Simulated spectra of Cu-Fe alloy (PENELOPE code
by Salvat et al.)
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Simulated spectra of Cu-Fe alloy convoluted with
the Si(Li) detector efficiency function (PENELOPE
code)
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PENELOPE code
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Experimental and simulated X-ry spectra of
ettringite (WinXray by Gauvin et al.)
Experimental
WinXray simulation 10 000 trajectories
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Geometries available in PENELOPE code by Salvat
et al.
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C. Champion, Theoretical cross sections for
electron collisions in water structure of
electron tracks, Phys. Med. Biol. 48 (2003)
21472168
Figure 10. Two-dimensional plot of a 5 keV
electron track in gaseous water in taking a
density correction of ? 1 g cm-3 to take into
account the liquid-phase effect. The impact point
is at (X 0, Y 0, Z 0), and the initial
direction is (Y 0, Z 0). The primary and
secondary inelastic interactions are explicitly
marked (solid and open symbols, respectively),
and the ionization and excitation contributions
are differently represented circles for
ionization and diamonds for excitation.
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