Reverse Monte Carlo - Revision history

Carl McBride: Added a recent publication

2015-05-25T16:57:05Z

Added a recent publication

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-'''Reverse Monte Carlo''' (RMC)  is a variation of the standard [[Metropolis Monte Carlo]] method. It is used to produce a 3 dimensional atomic [[models |model]] that fits a set of measurements (neutron diffraction, X-ray-diffraction, EXAFS etc.).
+'''Reverse Monte Carlo''' (RMC) <ref>[http://dx.doi.org/10.1080/08927028808080958 R. L. McGreevy and L. Pusztai, "Reverse Monte Carlo Simulation: A New Technique for the Determination of Disordered Structures", Molecular  Simulation, '''1''' pp. 359-367 (1988)]</ref> is a variation of the standard [[Metropolis Monte Carlo]] method. It is used to produce a 3 dimensional atomic [[models |model]] that fits a set of measurements (neutron diffraction, X-ray-diffraction, EXAFS etc.).
 In addition to measured data a number of constraints based on prior knowledge of the system (for example, chemical bonding etc.) can be applied. Some examples are:
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 #repeat from step 5.
 When <math>\chi^2</math> have reached an equilibrium the configuration is saved and can be analysed.
 [[Category:Monte Carlo]]

Nice and Tidy: Changed an internal link

2010-02-11T13:56:33Z

Changed an internal link

← Older revision		Revision as of 15:56, 11 February 2010
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	The algorithm for reverse Monte Carlo can be written as follows:		The algorithm for reverse Monte Carlo can be written as follows:

	#Start with a configuration of atoms with [[~~boundary conditions \|~~periodic boundary conditions]]. This can be a random or a crystalline configuration from a different simulation or model.		#Start with a configuration of atoms with [[periodic boundary conditions]]. This can be a random or a crystalline configuration from a different simulation or model.
	#Calculate the total [[radial distribution function]] <math>g_o^C(r)</math> for this old configuration (''C''=Calculated, ''o''=Old).		#Calculate the total [[radial distribution function]] <math>g_o^C(r)</math> for this old configuration (''C''=Calculated, ''o''=Old).
	#Transform to the total [[Structure factor \| structure factor]]:		#Transform to the total [[Structure factor \| structure factor]]:

Carl McBride: Changed internal link to boundary conditions.

2008-04-09T09:09:41Z

Changed internal link to boundary conditions.

← Older revision		Revision as of 11:09, 9 April 2008
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	The algorithm for reverse Monte Carlo can be written as follows:		The algorithm for reverse Monte Carlo can be written as follows:

	#Start with a configuration of atoms with [[periodic boundary conditions]]. This can be a random or a crystalline configuration from a different simulation or model.		#Start with a configuration of atoms with [[boundary conditions \|periodic boundary conditions]]. This can be a random or a crystalline configuration from a different simulation or model.
	#Calculate the total [[radial distribution function]] <math>g_o^C(r)</math> for this old configuration (''C''=Calculated, ''o''=Old).		#Calculate the total [[radial distribution function]] <math>g_o^C(r)</math> for this old configuration (''C''=Calculated, ''o''=Old).
	#Transform to the total [[Structure factor \| structure factor]]:		#Transform to the total [[Structure factor \| structure factor]]:

Carl McBride at 10:14, 2 August 2007

2007-08-02T10:14:27Z

← Older revision		Revision as of 12:14, 2 August 2007
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	'''Reverse Monte Carlo''' (RMC) ~~[1-4]~~ is a variation of the standard [[Metropolis Monte Carlo]] method. It is used to produce a 3 dimensional atomic model that fits a set of measurements (~~Neutron-~~, X-ray-diffraction, EXAFS etc.).		'''Reverse Monte Carlo''' (RMC) is a variation of the standard [[Metropolis Monte Carlo]] method. It is used to produce a 3 dimensional atomic [[models \|model]] that fits a set of measurements (neutron diffraction, X-ray-diffraction, EXAFS etc.).
	In addition to measured data a number of constraints based on prior knowledge of the system (~~like~~ chemical ~~bonds~~ etc.) can be applied. Some examples are:		In addition to measured data a number of constraints based on prior knowledge of the system (for example, chemical bonding etc.) can be applied. Some examples are:

	*Closest approach between atoms (hard sphere potential)		*Closest approach between atoms ([[hard sphere model \|hard sphere potential]])
	*Coordination numbers.		*Coordination numbers.
	*Angles in triplets of atoms.		*Angles in triplets of atoms.

	The 3 dimensional structure that is produced by ~~RMC~~ is not unique, it is a model consistent with the data and constraints provided.		The 3 dimensional structure that is produced by reverse Monte Carlo is not unique; it is a model consistent with the data and constraints provided.

	The algorithm for ~~RMC~~ can be written:		The algorithm for reverse Monte Carlo can be written as follows:

	#Start with a configuration of atoms with periodic boundary conditions. This can be a random or a crystalline configuration from a different simulation or model.		#Start with a configuration of atoms with [[periodic boundary conditions]]. This can be a random or a crystalline configuration from a different simulation or model.
	#Calculate the total [[radial distribution function]] <math>g_o^C(r)</math> for this old configuration (''C''=Calculated, ''o''=Old).		#Calculate the total [[radial distribution function]] <math>g_o^C(r)</math> for this old configuration (''C''=Calculated, ''o''=Old).
	#Transform to the total [[Structure factor \| structure factor]]:		#Transform to the total [[Structure factor \| structure factor]]:

Carl McBride: Reverted edits by 62.231.243.138 (Talk); changed back to last version by 161.111.20.5

2007-07-04T13:43:22Z

Reverted edits by 62.231.243.138 (Talk); changed back to last version by 161.111.20.5

← Older revision		Revision as of 15:43, 4 July 2007
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	#[http://dx.doi.org/10.1088/0953-8984/13/46/201 R. L. McGreevy, "Reverse Monte Carlo modelling", Journal of Physics: Condensed Matter '''13''' pp. R877-R913 (2001)]		#[http://dx.doi.org/10.1088/0953-8984/13/46/201 R. L. McGreevy, "Reverse Monte Carlo modelling", Journal of Physics: Condensed Matter '''13''' pp. R877-R913 (2001)]
	#[http://dx.doi.org/10.1016/S1359-0286(03)00015-9 R. L. McGreevy and P. Zetterström, "To RMC or not to RMC? The use of reverse Monte Carlo modelling", Current Opinion in Solid State and Materials Science. '''7''' pp. 41-47 (2003)]		#[http://dx.doi.org/10.1016/S1359-0286(03)00015-9 R. L. McGreevy and P. Zetterström, "To RMC or not to RMC? The use of reverse Monte Carlo modelling", Current Opinion in Solid State and Materials Science. '''7''' pp. 41-47 (2003)]
	#[http://dx.doi.org/10.1088/0953-8984/17/5/001 G. Evrard, L. Pusztai, "Reverse Monte Carlo modelling of the structure of disordered materials with RMC : a new implementation of the algorithm in C ", Journal of Physics: Condensed Matter '''17''' pp. S1-S13 (2005)]		#[http://dx.doi.org/10.1088/0953-8984/17/5/001 G. Evrard, L. Pusztai, "Reverse Monte Carlo modelling of the structure of disordered materials with RMC++: a new implementation of the algorithm in C++", Journal of Physics: Condensed Matter '''17''' pp. S1-S13 (2005)]

	[[Category:Monte Carlo]]		[[Category:Monte Carlo]]

62.231.243.138 at 19:30, 3 July 2007

2007-07-03T19:30:13Z

← Older revision		Revision as of 21:30, 3 July 2007
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	#[http://dx.doi.org/10.1088/0953-8984/13/46/201 R. L. McGreevy, "Reverse Monte Carlo modelling", Journal of Physics: Condensed Matter '''13''' pp. R877-R913 (2001)]		#[http://dx.doi.org/10.1088/0953-8984/13/46/201 R. L. McGreevy, "Reverse Monte Carlo modelling", Journal of Physics: Condensed Matter '''13''' pp. R877-R913 (2001)]
	#[http://dx.doi.org/10.1016/S1359-0286(03)00015-9 R. L. McGreevy and P. Zetterström, "To RMC or not to RMC? The use of reverse Monte Carlo modelling", Current Opinion in Solid State and Materials Science. '''7''' pp. 41-47 (2003)]		#[http://dx.doi.org/10.1016/S1359-0286(03)00015-9 R. L. McGreevy and P. Zetterström, "To RMC or not to RMC? The use of reverse Monte Carlo modelling", Current Opinion in Solid State and Materials Science. '''7''' pp. 41-47 (2003)]
	#[http://dx.doi.org/10.1088/0953-8984/17/5/001 G. Evrard, L. Pusztai, "Reverse Monte Carlo modelling of the structure of disordered materials with RMC++: a new implementation of the algorithm in C++", Journal of Physics: Condensed Matter '''17''' pp. S1-S13 (2005)]		#[http://dx.doi.org/10.1088/0953-8984/17/5/001 G. Evrard, L. Pusztai, "Reverse Monte Carlo modelling of the structure of disordered materials with RMC : a new implementation of the algorithm in C ", Journal of Physics: Condensed Matter '''17''' pp. S1-S13 (2005)]

	[[Category:Monte Carlo]]		[[Category:Monte Carlo]]

161.111.20.5 at 16:12, 30 May 2007

2007-05-30T16:12:02Z

← Older revision		Revision as of 18:12, 30 May 2007
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	#:<math>S_o^C (Q)-1=\frac{4\pi\rho}{Q}\int\limits_{0}^{\infty} r(g_o^C(r)-1)\sin(Qr)\, dr</math>		#:<math>S_o^C (Q)-1=\frac{4\pi\rho}{Q}\int\limits_{0}^{\infty} r(g_o^C(r)-1)\sin(Qr)\, dr</math>
	#:where ''Q'' is the momentum transfer and <math>\rho</math> the number density.		#:where ''Q'' is the momentum transfer and <math>\rho</math> the number density.
	#Calculate the difference between the measured structure factor <math>S^E(Q)</math> and the one calculated from the configuration <math>S_o^C(Q)</math>:		#Calculate the difference between the measured structure factor <math>S^E(Q)</math> (''E''=Experimental) and the one calculated from the configuration <math>S_o^C(Q)</math>:
	#:<math>\chi_o^2=\sum_i(S_o^C(Q_i)-S^E(Q_i))^2/\sigma(Q_i)^2</math>		#:<math>\chi_o^2=\sum_i(S_o^C(Q_i)-S^E(Q_i))^2/\sigma(Q_i)^2</math>
	#:this sum is taken over all experimental points <math>\sigma</math> is the experimental error.		#:this sum is taken over all experimental points <math>\sigma</math> is the experimental error.

Carl McBride at 13:11, 25 April 2007

2007-04-25T13:11:49Z

← Older revision		Revision as of 15:11, 25 April 2007
Line 1:		Line 1:
	'''Reverse Monte Carlo''' (RMC) [1-4] is a variation of the standard [[Metropolis Monte Carlo]] ~~(MMC)~~ method. It is used to produce a 3 dimensional atomic model that fits a set of measurements (Neutron-, X-ray-diffraction, EXAFS etc.).		'''Reverse Monte Carlo''' (RMC) [1-4] is a variation of the standard [[Metropolis Monte Carlo]] method. It is used to produce a 3 dimensional atomic model that fits a set of measurements (Neutron-, X-ray-diffraction, EXAFS etc.).
	In addition to measured data a number of constraints based on prior knowledge of the system (like chemical bonds etc.) can be applied. Some examples are:		In addition to measured data a number of constraints based on prior knowledge of the system (like chemical bonds etc.) can be applied. Some examples are:

Carl McBride at 09:27, 4 April 2007

2007-04-04T09:27:46Z

← Older revision		Revision as of 11:27, 4 April 2007
Line 1:		Line 1:
	Reverse Monte Carlo (RMC) [1-4] is a variation of the standard [[Metropolis Monte Carlo]] (MMC) method. It is used to produce a 3 dimensional atomic model that fits a set of measurements (Neutron-, X-ray-diffraction, EXAFS etc.).		'''Reverse Monte Carlo''' (RMC) [1-4] is a variation of the standard [[Metropolis Monte Carlo]] (MMC) method. It is used to produce a 3 dimensional atomic model that fits a set of measurements (Neutron-, X-ray-diffraction, EXAFS etc.).
	In addition to measured data a number of constraints based on prior knowledge of the system (like chemical bonds etc.) can be applied. Some examples are:		In addition to measured data a number of constraints based on prior knowledge of the system (like chemical bonds etc.) can be applied. Some examples are:

Carl McBride: /* References */

2007-03-19T12:11:00Z

References

← Older revision		Revision as of 14:11, 19 March 2007
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	== References ==		== References ==
	#[http://dx.doi.org/10.1080/08927028808080958 R. L. McGreevy and L. Pusztai, "Reverse Monte Carlo Simulation: A New Technique for the Determination of Disordered Structures", Molecular Simulation, '''1''' pp. 359-367 (1988)]		#[http://dx.doi.org/10.1080/08927028808080958 R. L. McGreevy and L. Pusztai, "Reverse Monte Carlo Simulation: A New Technique for the Determination of Disordered Structures", Molecular Simulation, '''1''' pp. 359-367 (1988)]
	#[http://dx.doi.org/10.1088/0953-8984/13/46/201 R. L. McGreevy, "Reverse Monte Carlo modelling", ~~J.Phys.~~:~~Cond.~~ Matter '''13''' pp. R877-R913 (2001)]		#[http://dx.doi.org/10.1088/0953-8984/13/46/201 R. L. McGreevy, "Reverse Monte Carlo modelling", Journal of Physics: Condensed Matter '''13''' pp. R877-R913 (2001)]
	#[http://dx.doi.org/10.1016/S1359-0286(03)00015-9 R. L. McGreevy and P. Zetterström, "To RMC or not to RMC? The use of reverse Monte Carlo modelling", Current Opinion in Solid State and Materials Science. '''7''' ~~no. 1 (2003)~~ pp. 41-47 ~~Elsevier Science~~]		#[http://dx.doi.org/10.1016/S1359-0286(03)00015-9 R. L. McGreevy and P. Zetterström, "To RMC or not to RMC? The use of reverse Monte Carlo modelling", Current Opinion in Solid State and Materials Science. '''7''' pp. 41-47 (2003)]
	#[http://dx.doi.org/10.1088/0953-8984/17/5/001 G. Evrard, L. Pusztai, "Reverse Monte Carlo modelling of the structure of disordered materials with RMC++: a new implementation of the algorithm in C++", ~~J.Phys.~~:~~Cond.~~ Matter '''17''' pp. S1-S13 (2005)]		#[http://dx.doi.org/10.1088/0953-8984/17/5/001 G. Evrard, L. Pusztai, "Reverse Monte Carlo modelling of the structure of disordered materials with RMC++: a new implementation of the algorithm in C++", Journal of Physics: Condensed Matter '''17''' pp. S1-S13 (2005)]

	[[Category:Monte Carlo]]		[[Category:Monte Carlo]]