xnd 1.2: encoding of variables in the standard blocks.

Introduction

The program is structured in order to have a starting input file of a simple form containing only a limited number of foundamental blocks having a simple form. Nevertheless, it is possible, as the refinement progresses, to add some more blocks or to modify the existent. This actually leads to an increased complexity of the block structures and to a growing number of blocks. We have already said that it is possible to introduce a depence on an external variable Temp in all the cristallographic parameters.

A new structure associated with a key takes place of the previous numerical code in xnd_1.1 which are still recognised.

Each variable has two parameters. The first is its order, it characterizes the allowed expansion along an internal parameter; it is the number of term in the polynomial expansion : if the variable does not depend on this parameter, its order is one. The second parameter is the size of the expansion, its allows complex linear dependance to be written. In this file, the name of the variable will be @VARIABLE, in the real file it should be @LAMBDA, @BACKGROUND, @CELL, @COORD, ... according to the real name of the variable. In the other files of this document all blocks the parameter of each variable will not be specified but the variable block has always the following structure.

@VARIABLE		key identifier for a variable named "VARIABLE"
ORDER	d	1	number of term in the polynomial expansion
SIZE	d	1	size of the parameter space

Order and size expansion

order	size		example
0		The bloc is empty : used to read some blocks in which you can have no data (eg if no points are specified in the background)
1	1	No Dependance of Temp, that is a classical parameter	a=a(0)
>1	1	Polynomial expansion with Temp of power order(eg cell paramters with thermal expansiond)	a=a(0)+a(1)*Temp+a(2)*Temp^2
1	n	No Dependance of Temp but a multidimensional linear expansion using internal parameters b, c ...	a=b(0)+c(0)
>1	n	Polynomial expansion with Temp of power -order and multidimensional linear expansion	a=b(0)+c(0)+Temp*(b(1)+c(1))

Caution, the value of order is limited when reading the file to the value given in the MaxOrder parameter specified in the file header. This has be done to detect some mistakes reading the file avoiding some nosense data.

Content of the value field

• the value;
• RefCode, the refinement code which can include a coupling coefficient.

Codeword and coupling coefficient

• the codeword value;
• an optional coupling coefficient.

CodeWord	Coupling Coef.		meaning
0			fixed
1..9	1	not read	adjusted
11..999	f	to be read
-1..-9	1	not read	fixed
-11..-999	f	to be read

For the codewords between 11 and 999, the program creates an internal parameter with CodeWord as reference number and all the values refering the parameter are moved from this parameter multiplied by their coupling coefficient. Some specific rules appear in case where the ValidRef value in the general header is non zero, they will be described with alternate refinement.

Examples

The following example is a fixed size block corresponding to the setting of the instrument. There are 4 variables to read, only the first will be adjusted.

@SETTING
   0.002   1    1.0  0
   0.0     0    .20  -1

@COORD
   0.123   1    0.25  0    0.432  1
   1.0     0    0.70  1

Example of usage of codewords in xnd.

Contents

• orthorhombic cell
• quadratic cell
• cubic cell
• thermal expansion of hexagonal cell
• chemical substitution of atoms
• alternate refinement of parameters

Variables block for an orthorhombic cell

@CELL
     0.000   0
     5.375   1      6.375  1       7.789   1       
     90.0    0     90.0    0      90.0    0

Variables block for a quadratic cell

@CELL
    0.000    0            
    5.1234  12 1.0     
    5.1234  12 1.0    
    8.2345   1           
    90       0            
    90       0     
    90       0     

Variables block for an cubic cell

@CELL
     0.000   0
     1.234  11    1.0     1.234  11    1.0
     1.234  11    1.0     90.0    0
     90.0    0            90.0    0

Variables block for a hexagonal cell with thermal expansion

@CELL ORDER=2                                   
    0.000    0       0.0    0        
    5.1234  12 1.0   0.002 13 1.0    
    5.1234  12 1.0   0.002 13 1.0    
    8.2345   1       0.004  1        
    90       0       0      0        
    90       0       0      0
    120      0       0      0

@CELL ORDER=3                                   
    0.000    0       0.0    0       0.0     0        
    5.1234  12 1.0   0.002 13 1.0   0.0001 14 1.0    
    5.1234  12 1.0   0.002 13 1.0   0.0001 14 1.0    
    8.2345   1       0.004  1       0.0002  1        
    90       0       0      0       0       0        
    90       0       0      0       0       0
    120      0       0      0       0       0

chemical substitution of atoms

 
 At1 FE 0                           
@COORD SIZE=2                               
    0.25     0       0              X and Y are on special position
    0.25     0       0
    0.413   14  1.0  0 0            Z has to be the same for all atoms
    0.700   15  0.5 16 1.0          t11 = p15 / 2 + p16
    1.0      7  1.0  0              B common thermal factor
 At2 CO 0                           
@COORD SIZE=2                               
    0.413   14  1.0  0 0            Z is the same for all atoms
    0.100   15  0.5 16 -1.0         t12 = p15 / 2 - p16
    ...
 At3 NI 0                           
@COORD SIZE=2                               
    0.200   15 -1.0  0 0            t13 = -p15
    ...

 
 At1 FE 0                           
 -2 2                               
    0.25   0      0      0      0      0
    0.25   0      0      0      0      0
    0.413 14 1.0  0 0    0.001 17 1.0  0
    0.700 15 0.5 16 1.0  0.010 18 0.5 19 1.0
    1.0   17 1.0  0      0.10  20 1.0  0

alternate refinement of parameters

ValidRef	code	coupling	refined if
1	1		always used
	2 .. 9
	10 .. 199	read
	200 ..999	read
2..9	1		always used
	2		PrtNew % ValidRef == 0
	3		PrtNew % ValidRef == 1
	9		PrtNew % ValidRef == 7
	10 .. 199	read	always used
	200 ..299	read	PrtNew % ValidRef == 0
	300 ..399	read	PrtNew % ValidRef == 1
	400 ..499	read	PrtNew % ValidRef == 2

The following table represent the inside of a block and what append for ValidRef = 4. Note that ValidRef is restricted to values between 2 and 9 and that codeword are always lower than 1000.

value	code	coupling	refined if PrtNew is
0.105	1		always used
0.251	2		0, 4, 8, ...
0.249	3		1, 5, 9, ...
0.413	11	1.0	always used
0.413	199	1.0	always used
0.700	200	1.0	0, 4, 8, ...
0.700	201	1.0	0, 4, 8, ...
0.700	300	1.0	1, 5, 9, ...