Author: N. Dragan "I.Gh.Murgulescu" Physical-Chemistry Institute,
* XRAY-1.0 program estimates the <D> mean Crystallite Size and <S> mean Lattice
Strain. Maximum 14 consecutive or selected X-Ray lines represent data sources for one compound. The original algorithm has got two steps:
(1) Pearson-VII functions and Least Squares fitting method; it contains the limitation of the variance range fitted parameters, the stabilisation method of the iterations, and the conditions of solution precision.
(2) Size and Strain Analysis using the Cauchy-Cauchy approximation for small Strains and adapted Langford's Integral Breadth Method with Voigt functions for Pearson's functions. The <D>, <S> values for a given direction can be easily found in multiple-lines Williamson-Hall diagrams.
* XRAY-1.0 is an interactive program. Initial solution, some of the setups or options are available by marking them on the graphics, or by activating the windows. The diffraction recorded lines are organised in data (ASCII) files. The results of the program are represented by graphics or tables (they include the estimated errors). The results can be Hard Disk or Printer (A4 paper format) saved.
* If XRAY-1.0 program receives the
necessary ASCII files (xray_ETL.mat or xray_PRO.mat file for
example), external sources Data for Profile Analysis and Size
& Strain Separation can be used by avoiding the
fitting part.
1. FIT parameters
BkR: Background Residue; int:
Background intercept; Itr: Iterations number;
Io: Maximum
Intensity; Low: Lower angle of fit range; mP7:
Pearson's function exponent;
MEP: Maximum_Error of Parameters; PME:
Parameter of Maximum_Error;
Res: Profile Residue; slo :
Background slope; T1: XR-Ka1 peak position;
T2: XR-Ka2 peak position;
Upp: Upper angle of fit range;
eI0 = I0
error; emP7= mP7
error; eT1= T1 error;...
2. Profile Analysis and SIZE-STRAIN parameters
Dsh: Crystallite Size
(sh=Scherrer, Dsh=L/(IB.cosT) or IB=5.Sw.tanT);
Dp,Dcc: Crystallite Size
(p7=Pearson-VII, IB.cosT=L/<Dcc>+5<Scc>sinT);
FWHMx: Full Width at the Io/2 of the
x-profile [x=g:STanDard,f:SAMple];
IBx: Total Integral Breadth of the x=g
(f:corrected) profile;
IBCx: Integral Breadth Cauchy component of
the x-profile (Convolution);
IBGx: Integral Breadth Gauss component of
the x-profile (Convolution);
Sw,Sp7: Lattice Strain
(w=Stokes-Wilson model, p7=Convolution model);
SFx: Shape Factor of the x-profile
(SFx=2Wx/IBx Convolution model).
2W: Full Width at the Io/2; eIB = IB
error; e2W = 2W error;...
* Xray-1.0 works under
Matlab-3.5 (MS-DOS 6.2) control. The program has about 750 KB
(unpacked). It can be used at X-ray Diffractometers without
Monochromator and Crystallized Powders Analysis;
* PC 486-DX2/100MHz (mathematical coproccesor),
4MB RAM, 100MB HDD;
* VGA/EGA color display (video card:
512MB);
* Printers: Oki ML-390 or Canon BJC-250 (A4
paper); Select Emulation Mode, set on Epson-LQ
(USA);
Use Matlab-3.5 (DOS) device:
/dlqf/fprn/p/cc (cc = complex character font);
* Data Editor: NC 4.0, Wp51 (ASCII file)...
* Load Matlab-3.5 for
MS-DOS;
* Copy XMOVE.M file from Xray-1.0 to
Matlab;
* Type: Matlab, press Enter, Xmove, press
Enter;
xHELP (80KB), xDEMO (170KB), XRAY (500KB)
directories will be automatically copied to Matlab;
*Type to Start: xHELP, xDEMO, XRAY or XR10.
1) X-Ray Ka 1 -Ka 2
Doublet Separation by Fit on the (311)
line of the sample NiO (500° C);
2) Size-Strain Separation uses
data typed in J.Appl.Cryst. 21, (1988), 430-437 by D.Louer
and J.I.Langford. In this application the sample is BaF2
crystallized powder.