The model for the RMC method is usually described with the P1 space group and the cell (generally a cube) is large,
otherwise no acceptable fit can be expected.
 

The model for the RDM method has generally to be much smaller in volume and can use space groups with any symmetry.

RMC
 

RMCA version 3.04 adapted for MS Windows 95/98/NT

Three files are necessary :
cubig.dat containing the input data
cusq.dat the experimental structure factor
cubig.cfg the starting model configuration
 

cubig.dat :

cusq.dat

cubig.cfg

1000 atoms instead of 250 in the original test file

The PC RMCA program starts by :
 

a double click on its name in the Windows Explorer,
or typing 'rmca' in a DOS box opened in the directory containing rmca.exe and the data files.

The PC version shows some minor differences with the original RMCA software :

The .his (histogram) file is not created,
and the timelim and timesav parameters have different significations.
Instead of being the time the program should run for, in minutes, timelim is now the total number of moves generated before the program will stop. Timesav is the interval number or generated moves at which the results should be saved to the output file.

Also the file containing the experimental data (cusq.dat here) is given without the .dat extension in the main data file (cubig.dat here).

Get the manual RMCA.ps and the Fortran source code at the
RMCA FTP server :
 ftp://www.studsvik.uu.se/pub/rmc/rmca/
 

Running the test file, you should see at the end :

the Chi**2 oscillates around 5 after 15000 accepted moves

LIVE DEMONSTRATION

The resulting fit of S(Q) is the following :

 

Some hints and tips

What is the main function acting in RMCA :
 

RAN (in Fortran language)
the random number generator

used for selecting the moving atom
as well as
for deciding of the x,y,z moves
 
 

Why the calculation may be so fast ?
 

Many elements needed for calculating the interference function
are stored in memory
 

Only are recalculated those corresponding to the moving atom
 
 
 
 
 
 
 

RDM

In order to apply the RDM method to glasses, one should dispose of crystalline-based starting models presenting the same composition or at least the same formulation as the material to be modelled.

The disorder is statistically introduced by microstrain effects leading to line broadening on the diffraction pattern.

The cell volume may be adjusted for corresponding to
the measured glass density.

A preliminary test consists in looking at the starting agreement between observed and calculated S(2q) selecting some standard line broadening parameters (they can be easily adjusted by hand) and refining the scale factors.

In case of non ideal composition, for instance modelling a NaPbFe₂F₉ glass starting from coordinates of KCaAl₂F₉, after cell adaptation, the best would be to refine first the F atom coordinates, expecting adjustment of Pb-F (~2.50 Å), Na-F (~2.35 Å) and Fe-F (~1.93 Å) distances replacing respectively the K-F (~2.80 Å), Ca-F (~2.40 Å) and Al-F (~1.81 Å) ones (one should try Pb/Na permutation too and also some statistical disorder). The next step, if some convergence has been obtained, is to refine all atomic coordinates. This supposes that a maximum of independent diffraction data have been collected. Testing a model with this complexity would require the largest possible number of oscillations on diffraction data, say at least a total of 25 bumps which could correspond to 3 independent structure factors exhibiting 8 or 9 oscillations each of them. Finally, the line-broadening parameters could be refined and even the cell parameters. The process converges, or not, with agreement factors specific to the models.

Which model can we use for molten Cu ?
 

Certainly first the Cu crystal structure
 

If you possess CRYSTMET, it is readily obtained
 
 

LIVE DEMONSTRATION

Cubic Close Packed (CCP)
= face centered cubic

Fm3m

a = 3.6144 A

Cu in (4a) Wyckoff position at x = 0, y = 0, z = 0
 
 
 
 

But, the liquid density corresponds to 0.0721 atom/ų

and Cu solid at room temperature has :
V = a³ = 47.22 ų
with 4 Cu atoms per cell :
4 / 47.22 = 0.0847

We need a cell volume of
4 / 0.0721 =55.478 ų
 

Corresponding to a = 3.8139 Å

ARITVE version 2000 for MS Windows 95/98/NT
 

ARITVE is simply a Rietveld method program allowing :

- a huge limit of reflection number (60000 on each pattern)
- 3 interference functions maximum fitted simultaneously
- a huge limit of reflections overlapping at the same angle (20000)
- a small number of parameters to be refined (max = 75)
- only Gaussian peak shape
- line broadening following the Caglioti law
 

Two files are necessary :

cuCCP.dat containing the input data
cust.nor the experimental structure factor
 
 
 
 
 

cuCCP.dat :

cust.nor

Same as cusq.dat from RMCA, but with constant 2q step
and x1000 (arbitrary scale)

The PC ARITVE program starts by :
 

a double click on its name in the Windows Explorer,
or typing 'aritve' in a DOS box opened in the directory containing aritve.exe and the data files.
 
 

A window is opened.
You are prompted to give the entry filename
(here cuCCP, the test file) :

Live Demonstration

At the end of the calculation, you should have :

And the fit looks like :

Not as good as the RMC fit, but remember the small cell containing only 4 Cu atoms. Nevertheless, similitudes are there. One can imagine that a better fit would be obtained if the model size was extended.

Combining some aspects
of both methods, is that possible ?
 

Some directions to explore :

A powder diffraction pattern from the RMC result could be calculated exactly in the same way as by the RDM method.

The problem is to build a special program for the simulation of powder patterns in case of P1 space group with cell parameters of 30 Å or more.

The reflection number for Q up to 25 Å^-1
would be probably larger than 10⁶.

There is no serious difficulty to code a program doing that, but this was not realized up to now.
60000 reflections maximum are allowed per pattern, and 20000 which could overlap at a given diffracting angle, in the present RDM ARITVE software. This is already considerable !

Using the Rietveld method for glass modelling supposes that one accepts the idea that a selected crystal structure may represent a mean model for a glass, or a nanocrystalline material.

The disorder is statistically introduced by microstrain effect, leading to strong line broadening on the diffraction pattern.

If the mean RDM small models were physically sound, then they should be able to represent good starting configurations for RMC modelling, that would really introduce locally the disorder treated statistically in RDM modelling.

It was thus decided to enlarge some previously established RDM models, so as to build starting RMC configurations to be tested. In all cases presented hereafter, some initial coordinations were constrained during the Monte Carlo process (SiO₄ and ZnCl₄ tetrahedra; MF₆ octahedra), so that the final RMC models were obtained from small random atom moves, keeping essentially the crystal structure features of the RDM starting models.

Which interference functions were modelled ?

With the RMC method, the neutron and X-ray data were simulated as F(Q) data, the total coherent scattering functions (TSF) :

F(Q) = [I_coh(Q)-<f²>] / <f>²,

where the <f²> and <f>² terms are the usual mean diffusion factors, depending on Q (X-ray) or not (neutron).
 
 
 
 
 
 
 

The RDM final models were selected among many possibilities as those providing the best Rp reliability factor.

Testing a model by the RDM method, the data fitted become :

S(2q) = I_coh(2q)/<f²>.

Q = 4psinq/l
 
 
 
 

Characterizing the fit quality

A reliability Rp factor was calculated as :
 

100*å |Iobs-kIcalc|/å |Iobs| (%)
 

(according to the definition I(Q) = F(Q)+1, k being a scale factor).