Wolfram Language
Paclet Repository
Community-contributed installable additions to the Wolfram Language
Primary Navigation
Categories
Cloud & Deployment
Core Language & Structure
Data Manipulation & Analysis
Engineering Data & Computation
External Interfaces & Connections
Financial Data & Computation
Geographic Data & Computation
Geometry
Graphs & Networks
Higher Mathematical Computation
Images
Knowledge Representation & Natural Language
Machine Learning
Notebook Documents & Presentation
Scientific and Medical Data & Computation
Social, Cultural & Linguistic Data
Strings & Text
Symbolic & Numeric Computation
System Operation & Setup
Time-Related Computation
User Interface Construction
Visualization & Graphics
Random Paclet
Alphabetical List
Using Paclets
Create a Paclet
Get Started
Download Definition Notebook
MaXrd
Guides
MaXrd – Mathematica X-ray diffraction package
Tech Notes
Applying crystal data
Basic computations
Computations on reflections
Formulas in crystallography
Importing crystal data
Quick guide to conditions
References
Symmetry calculations
The association structure of crystallographic data
Using the rotation options
Symbols
AttenuationCoefficient
BraggAngle
ConstructDomains
CrystalDensity
CrystalFormulaUnits
CrystalPlot
DarwinWidth
DistortStructure
DomainPlot
EmbedStructure
ExpandCrystal
ExportCrystalData
ExtinctionLength
FindPixelClusters
GetAtomCoordinates
GetAtomicScatteringFactors
GetCrystalMetric
GetElements
GetLatticeParameters
GetLaueClass
GetScatteringCrossSections
GetSymmetryData
GetSymmetryOperations
ImportCrystalData
InputCheck
InterplanarSpacing
MergeDomains
MergeSymmetryEquivalentReflections
MillerNotationToList
MillerNotationToString
ReciprocalImageCheck
ReciprocalSpaceSimulation
ReflectionList
RelatedFunctionsGraph
ResetCrystalData
ResizeStructure
SimulateDiffractionPattern
StructureFactor
StructureFactorTable
SymmetryEquivalentPositions
SymmetryEquivalentReflections
SymmetryEquivalentReflectionsQ
SynthesiseStructure
SystematicAbsentQ
ToStandardSetting
TransformAtomicDisplacementParameters
UnitCellTransformation
$CrystalData
$GroupSymbolRedirect
$LaueClasses
$MaXrdPath
$MaXrdVersion
$PeriodicTable
$PointGroups
$SpaceGroups
$TransformationMatrices
Quick guide to conditions
Say we have a list of reflections,
I
n
[
1
]
:
=
h
k
l
=
{
{
1
,
1
,
1
}
,
{
2
,
0
,
2
}
,
{
3
,
1
,
5
}
,
{
4
,
3
,
-
2
}
,
{
0
,
4
,
-
4
}
,
{
3
,
2
,
1
}
,
{
1
,
0
,
-
1
}
,
{
2
,
0
,
4
}
,
{
0
,
1
,
0
}
,
{
-
3
,
1
,
-
1
}
}
;
It may be that we want to look at a subset of reflections that fulfill some kind pattern. This filtering can easily be done with a
C
o
n
d
i
t
i
o
n
. We effectively run all the reflections through a test on the Miller
indices
h
,
k
and
l
. Here are some examples:
Keep the reflections where
h
=
0
and
k
is an even number:
I
n
[
2
]
:
=
C
a
s
e
s
[
h
k
l
,
{
h
_
,
k
_
,
l
_
}
/
;
h
0
&
&
E
v
e
n
Q
[
k
]
]
O
u
t
[
2
]
=
{
{
0
,
4
,
-
4
}
}
Keep the reflections where the indices add up to an even number (condition for body-centred cells):
I
n
[
3
]
:
=
C
a
s
e
s
[
h
k
l
,
{
h
_
,
k
_
,
l
_
}
/
;
E
v
e
n
Q
[
h
+
k
+
l
]
]
O
u
t
[
3
]
=
{
{
2
,
0
,
2
}
,
{
0
,
4
,
-
4
}
,
{
3
,
2
,
1
}
,
{
1
,
0
,
-
1
}
,
{
2
,
0
,
4
}
}
Keep the reflections that do not mix odd and even indices (reflection condition for face-centred cells):
I
n
[
4
]
:
=
C
a
s
e
s
[
h
k
l
,
{
h
_
,
k
_
,
l
_
}
/
;
A
l
l
T
r
u
e
[
{
h
,
k
,
l
}
,
O
d
d
Q
]
|
|
A
l
l
T
r
u
e
[
{
h
,
k
,
l
}
,
E
v
e
n
Q
]
]
O
u
t
[
4
]
=
{
{
1
,
1
,
1
}
,
{
2
,
0
,
2
}
,
{
3
,
1
,
5
}
,
{
0
,
4
,
-
4
}
,
{
2
,
0
,
4
}
,
{
-
3
,
1
,
-
1
}
}
Functions in the
MaXrd
package that allow conditions to be input in order to restrict the reflections include:
◼
R
e
f
l
e
c
t
i
o
n
L
i
s
t
◼
S
t
r
u
c
t
u
r
e
F
a
c
t
o
r
T
a
b
l
e
Some more examples of settings:
{
h
_
,
k
_
,
l
_
}
/
;
O
d
d
Q
[
h
]
I
n
d
e
x
k
h
a
s
t
o
b
e
o
d
d
{
h
_
,
k
_
,
l
_
}
/
;
E
v
e
n
Q
[
k
+
l
]
T
h
e
s
u
m
o
f
i
n
d
i
c
e
s
h
a
n
d
l
m
u
s
t
b
e
a
n
e
v
e
n
n
u
m
b
e
r
{
h
_
,
k
_
,
l
_
}
/
;
D
i
v
i
s
i
b
l
e
[
k
+
k
+
l
,
4
]
T
h
e
d
i
g
i
t
s
u
m
o
f
t
h
e
i
n
d
i
c
e
s
m
u
s
t
b
e
d
i
v
i
s
i
b
l
e
b
y
f
o
u
r
{
h
_
,
k
_
,
l
_
}
/
;
h
0
|
|
h
2
I
n
d
e
x
h
h
a
s
t
o
b
e
e
i
t
h
e
r
0
o
r
2
{
h
_
,
k
_
,
l
_
}
/
;
h
1
&
&
D
i
v
i
s
i
b
l
e
[
k
,
3
]
I
n
d
e
x
h
h
a
s
t
o
b
e
1
a
n
d
i
n
d
e
x
k
d
i
v
i
s
i
b
l
e
b
y
3
See
Mathematica'
s
g
u
i
d
e
o
n
p
a
t
t
e
r
n
s
for more on the topic.
"
"