settings

labeling

space groups

k points

images

irreps

isotropy subgroups

distortions

invariant polynomials

bushes

order parameters

**Q**: quit

**SC p1**: width of screen

**PAGE p1**: number of lines displayed at a time

**C V ...**: cancel a **V** command

**C V ALL**: cancel all previously used **V** commands

**C SH ...**: cancel a **SH** command

**C SH ALL**: cancel all previously used **SH** commands

**D V**: display all **V** commands in effect

**D SH**: display all **SH** commands in effect

**?**: help (can be inserted in place of any keyword)

**D SET**: display the current space-group setting

**SET p1**: change the setting (p1 = **I**, **I NEW**, **I OLD**, **MI**, **K**, **B**, **Z**)

**SET I p1 OR p2**: origin choice (p1 = space group or **ALL** and p2 = **1**, **2**)

**SET I p1 AX p2**: axis choice (p1 = space group or **ALL** and p2 = **B**, **C**, **HEX**, **RH**)

**SET I p1 CELL p2**: cell choice (p1 = space group or **ALL** and p2 = **1**, **2**, **3**)

**SET MAG**: magnetic space groups

**SET NOMAG**: return to Federov space groups

**L SP p1**: change the labeling of space groups (p1 = **SCH**, **I**, **I SHORT**, **I FULL**)

**L EL p1**: change the labeling of space group elements (p1 = **I**, **M**, **K**, **B**, **Z**)

**L VEC p1**: change the form of the vectors (p1 = **CON**, **PRIM**)

**L IM p1**: use image notation of Toledano and Toledano (p1 = **TOL**, **NOTOL**)

**L PO p1**: change the labeling of point groups (p1 = **SCH**, **I**)

**L LAT p1**: change the labeling of lattices (p1 = **SCH**, **P**)

**D PAR**: display data on parent space group

**V PAR p1 [p2]**: select space group(s)

**V LAT PAR p1...p6**: select lattice parameters a, b, c, alpha, beta, gamma

**V LAT p1 [p2]**: select lattice(s)

**V PO p1 [p2]**: select point group(s)

**V WY p1 [p2...]**: select wyckoff positions

**V WY IR p1 [p2...]**: select point-group irrep of wyckoff position

**V WY XYZ p1 p2 p3**: select parameters x,y,z of wyckoff position

**SH PAR**: show space group symbol

**SH CART**: show Cartesian coordinates

**SH GEN**: show generating elements of space group

**SH EL**: show coset representatives of space group

**SH LAT**: show lattice

**SH PO**: show point group

**SH BAS**: show basis vectors of lattice

**SH WY [p1 p2]**: show Wyckoff positions (p1 = **VEC**, **PO**, ELE, **CHAR**, p2 = **ALL**)

**D KP**: display data on **k** points

**V PAR p1 [p2]**: select space group(s)

**V IR p1**: select irrep

**V KP p1**: select **k** point

**V KDEG p1**: select degrees of freedom of **k** point

**SH PAR**: show space group symbol

**SH KP**: show coordinates of **k** point

**SH KDEG**: show degrees of freedom of **k** point

**SH STAR**: show the star of **k**

**D IM**: display data on images of irreps

**V IM p1**: select image

**V DIM p1 [p2]**: select dimension(s)

**V ORD p1 [p2]**: select order(s)

**V ACT p1**: select active or non-active images (p1 = **Y**, **N**)

**V LAN p1 [p2]**: select Landau frequency/frequencies

**V TYPE p1**: select type of irrep

**SH IM**: show image symbol

**SH GEN**: show generating matrices

**SH EL**: show all matrices

**SH DIM**: show dimension

**SH ORD**: show order

**SH ACT**: show whether image is active or not

**SH LAN**: show Landau frequency

**SH TYPE**: show type of irrep

**D IR**: display data on irreps

**V PAR p1 [p2]**: select space group(s)

**V IR p1**: select irrep

**V KP p1**: select **k** point

**V KDEG p1**: select degrees of freedom of **k** point

**V KVAL p1 [p2...]**: select parameters alpha, beta, gamma for the **k** point

**V IM p1**: select image of irrep

**V EL p1**: select space-group element (to display the character or matrix)

**V DIM p1 [p2]**: select dimension(s)

**V ACT p1**: select active or non-active irreps (p1 = **Y**, **N**)

**V LAN p1 [p2]**: select Landau frequency/frequencies

**V LIF p1 [p2]**: select Lifshitz frequency/frequencies

**V FEL p1 [p2]**: select Felix frequency/frequencies

**V TYPE p1**: select type of irrep

**V WY p1 [p2...]**: select wyckoff positions

**V WY IR p1**: select point-group irrep of wyckoff position

**V COMPAT p1**: select **k** point for compatibility relation

**SH PAR**: show space group

**SH IR [p1]**: show irrep (p1=other settings: **M**, **K**, **B**, **Z**, **P**)

**SH ACT**: show whether the irrep is active or not

**SH IM**: show image of irrep

**SH GEN**: show space-group elements that map onto the image generators

**SH EL**: show space-group element selected

**SH CH**: show character of selected space-group element

**SH MAT**: show matrix of selected space-group element

**SH COMPLEX**: show complex form of irrep matrix and character

**SH KER**: show generators of kernel

**SH DIM**: show dimension

**SH LAN**: show Landau frequency

**SH LIF**: show Lifshitz frequency

**SH FEL**: show Felix frequency

**SH TYPE**: show type of irrep

**SH FAINT**: show faintness index for linear coupling with other irreps

**SH FR**: show frequency and irreps of the Wyckoff-position point groups

**SH KP**: show coordinates of **k** point

**SH KDEG**: show degrees of freedom of **k** point

**SH STAR**: show the star of **k**

**SH COMPAT**: show compatibility relations

**D IS**: display data on isotropy subgroups

**D IS COUP**: display data on isotropy subgroups for coupled order parameters

**V PAR p1 [p2]**: select parent space group(s)

**V SUB p1 [p2]**: select isotropy subgroup(s)

**V LAT p1 [p2]**: select lattice(s) of subgroup

**V PO p1 [p2]**: select point group(s) of subgroup

**V IR p1**: select irrep

**V KP p1**: select **k** point

**V KVAL p1 [p2...]**: select parameters alpha, beta, gamma for the **k** point

**V IM p1**: select image of irrep

**V DIM p1 [p2]**: select dimension(s) of irrep

**V ACT p1**: select active or non-active irreps (p1 = **Y**, **N**)

**V CON p1**: select continuous or discontinuous transitions (p1 = **LAN**, **RG**, **NO**)

**V LAN p1 [p2]**: select Landau frequency/frequencies

**V LIF p1 [p2]**: select Lifshitz frequency/frequencies

**V FEL p1 [p2]**: select Felix frequency/frequencies

**V DIR p1 [p2...]**: select directions of order parameter

**V FREQ p1 [p2]**: select subduction frequency/frequencies

**V DOM p1**: select domain

**V DOM P p1 p2**: select domain pair

**V NORM p1 p2 p2**: select Miller indices (hkl) of plane between twin domains

**V POS p1 p2 p2**: select point on plane between twin domains

**V SIZ p1 [p2]**: select size of subgroup's primitive unit cell relative to parent group's

**V MAX p1**: select maximal or non-maximal subgroups (p1 = **Y**, **N**)

**V LAT PAR p1...p6**: select lattice parameters a, b, c, alpha, beta, gamma

**SH PAR**: show parent space group symbol

**SH SUB**: show isotropy subgroup symbol

**SH DIR [p1]**: show direction of order parameter (p1=**VEC** to show the vector)

**SH BAS**: show basis vectors of subgroup

**SH ORI**: show origin of subgroup

**SH XYZ**: show x,y,z in subgroup in terms of x,y,z in parent group

**SH WY SUBG**: show Wyckoff positions in subgroup

**SH GEN**: show elements of parent group which generate subgroup

**SH EL**: show elements of parent group which are elements of subgroup

**SH NEW**: show new fractionals in subgroup

**SH SIZ**: show relative size of subgroup's primitive unit cell to parent group's

**SH IND**: show index of subgroup in parent group

**SH DOM [p1]**: show domains (p1=**GEN** to show generators)

**SH DISTINCT**: show which domains are distinct

**SH PAIR**: show which pairs of domains are equivalent

**SH PAIR p1**: show pair intersection group (p1=**I**), pair group (p1=**GR**) and its basis vectors (p1=**B**),
its origin (p1=**O**), its generating elements (p1=**GE**), and its elements (p1=**E**).

**SH TWIN INT p1**: show twin intersection group: its label (p1=**GR**), its basis vectors (p1=**B**), its origin (p1=**O**),
its generating elements (p1=**GE**), and its elements (p1=**E**).

**SH TWIN p1**: show twin group: its label (p1=**GR**), its basis vectors (p1=**B**), its origin (p1=**O**),
its generating elements (p1=**GE**), and its elements (p1=**E**).

**SH TWIN SW p1**: show switching elements in twin group (p1=**SIDE**, **NORMAL**, **BOTH**).

**SH MAX**: show whether or not the subgroup is maximal

**SH LAT**: show lattices of parent space group and of subgroup

**SH PO**: show point groups of parent space group and of subgroup

**SH IR [p1]**: show irrep (p1=other settings: **M**, **K**, **B**, **Z**, **P**)

**SH IM**: show image of irrep

**SH DIM**: show dimension

**SH ACT**: show whether the irrep is active or not

**SH CON**: show whether or not the phase transition is continuous

**SH LAN**: show Landau frequency

**SH LIF**: show Lifshitz frequency

**SH FEL**: show Felix frequency

**SH FR [p1]**: show frequencies and irreps that subduce the subgroup (p1=**DIR**, **GAM**, **CL**)

**SH CART**: show Cartesian coordinates

**D DIST**: display distortions

**V PAR p1**: select parent space group

**V IR p1**: select irrep

**V KP p1**: select **k** point

**V KVAL p1 [p2...]**: select parameters alpha, beta, gamma for the **k** point

**V RANK p1**: select rank and symmetries of macroscopic tensor

**V DIR p1 [p2...]**: select directions of order parameter

**V DOM p1**: select domain

**V CELL p1 p2 p3**: select super cell

**V LAT PAR p1...p6**: select lattice parameters a, b, c, alpha, beta, gamma

**V WY p1 [p2...]**: select wyckoff positions

**V WY IR p1 [p2...]**: select point-group irrep of wyckoff position

**V WY XYZ p1 p2 p3**: select parameters x,y,z of wyckoff position

**V POS p1 p2 p3**: select coordinates of point

**SH MAC [p1]**: show macroscopic distortion (p1=**PSEUDO**)

**SH MIC [p1] [p2]**: show microscopic distortion (p1=**SC**, **VEC**, p2=**PSEUDO**)

**SH LOC [p1] [p2]**: show local distortion (p1=**SC**, **VEC**, p2=**PSEUDO**)

**SH PAR**: show parent space group symbol

**SH IR [p1]**: show irrep (p1=other settings: **M**, **K**, **B**, **Z**, **P**)

**SH DIR**: show direction of order parameter

**SH DOM**: show domain

**SH WY [p1]**: show Wyckoff positions (p1=**IR**)

**SH POS IR**: show point group irrep of point about Wyckoff position

**SH UNIT**: show distortions in unit cell of parent

**SH CART**: show Cartesian coordinates

**D INV**: display invariant polynomials

**V PAR p1**: select parent space group

**V IR p1 [p2...]**: select irreps

**V KVAL p1 [p2...]**: select parameters alpha, beta, gamma for the **k** point

**V DIR p1 [p2...]**: select directions of order parameter

**V DOM p1 [p2...]**: select domains

**V DEG p1 [p2]**: select degree(s) of polynomials

**V GRAD p1**: select number of spatial derivatives

**SH PAR**: show parent space group symbol

**SH IR [p1]**: show irrep (p1=other settings: **M**, **K**, **B**, **Z**, **P**)

**SH DIM**: show dimension

**D BUSH**: display data on bush of modes

**V PAR p1**: select parent space group

**V IR p1**: select irrep

**V DIR p1**: select direction of order parameter

**V WY p1 [p2...]**: select Wyckoff positions

**V DEG p1 [p2]**: select degree(s) of invariant polynomials

**SH MODES**: show atomic displacements

**SH INV**: show invariant polynomials in free energy

**D DIR**: display directions of order parameters

**V PAR p1**: select parent space group

**V SUBG p1**: select subgroup

**V BASIS p1 p2 p3**: select basis vectors of subgroup lattice

**V ORIGIN p1**: select origin of subgroup

**SH KPOINT**: show **k** vectors

This software may be distributed without restriction, but if it is used in research that results in publications, the use of this program should be acknowledged with reference to both H. T. Stokes and D. M. Hatch.

ISOTROPY has access to six different space-group settings, found in the following references:

1.
*International Tables for Crystallography,* Vol. A, edited by T. Hahn
(Reidel, Boston, 1983).

2.
*International Tables for X-Ray Crystallography*, Vol. I, edited by
N. F. M. Henry and K. Lonsdale (Kynoch Press, Birmingham, 1965).

3.
S. C. Miller and W. F. Love, *Tables of Irreducible Representations
of Space Groups and Co-Representations of Magnetic Space Groups*
(Pruett, Boulder, 1967). This is essentially the same as A. P. Cracknell,
B. L. Davies, S. C. Miller, and W. F. Love, *Kronecker Product Tables,*
Vol. 1 (Plenum, New York, 1979).

4.
O. V. Kovalev, *Representations of the Crystallographic Space Groups:
Irreducible Representations, Induced Representations and Corepresentations*
(Gordon and Breach, Amsterdam, 1993).

5.
C. J. Bradley and A. P. Cracknell, *The Mathematical Theory of Symmetry
in Solids* (Clarendon, Oxford, 1972).

6.
*The Irreducible Representations of Space Groups,* edited by J. Zak
(Benjamin, New York, 1969).

These references will be referred to as International Tables (new ed.),
International Tables (old ed.), Miller-Love, Kovalev, Bradley-Cracknell,
and Zak, respectively. ISOTROPY has access to the irrep labeling of
Miller-Love, Kovalev, Bradley-Cracknell, and Zak for all physically
irreducible representations arising from **k** points of symmetry.
Also, ISOTROPY has access to the irrep labeling of Miller-Love for
all physically irreducible representations arising from *all* **k** points,
including **k** lines and **k** planes of symmetry and general **k** vectors.
When ISOTROPY starts, the default space-group setting is International
Tables (new ed.) and the default irrep labeling is Miller-Love.

If a question mark (**?**) is entered in place of one
of the keywords, all valid keywords that could be entered at the position
of the question mark will be displayed. For example, if a simple **?**
is entered in place of a command, ISOTROPY will indicate that the valid
keywords are **CANCEL**, **DISPLAY**, **LABEL**, **PAGE**, **QUIT**,
**SCREEN**, **SETTING**, **SHOW**, and **VALUE**.
This means that the first keyword
in a command must be one of these words. As another example, if
**LABEL ?** is entered as a command, ISOTROPY will indicate that the
valid keywords are **ELEMENT**, **IMAGE**, **LATTICE**,
**POINTGROUP**, **SPACEGROUP**, and **VECTOR**.
This means that if the
first keyword in a command is **LABEL**, then it must be followed
by one of those six words.

In the following material, each command is denoted by keywords and parameters (p1, p2) which may be a number or another keyword. A parameter in brackets (eg., [p2]) is optional and does not need to be present for a command to be valid.

**CANCEL p1 p2 [p3 ...]**

The keyword **CANCEL** can be put in front of any **SHOW** or
**VALUE** command below to cancel the effect of that command. These
cancel commands will not be explicitly listed here, except for a few commands
which require some additional explanation.

**CANCEL SHOW ALL**

Cancels the effect of all **SHOW** commands previously used.

**CANCEL SHOW ELEMENT**

This command also causes **CANCEL SHOW CHARACTER** and **CANCEL SHOW MATRIX** to be automatically executed.

**CANCEL SHOW IRREP [p1]**

Cancels the effect of **SHOW IRREP**. The parameter p1 is the name
of the one the settings (**MILLER-LOVE**, **KOVALEV**,
**BRADLEY-CRACKNELL**, or **ZAK**). If p1 is present, then
only the notation specified by p1 is removed from the display.
If p1 is not present, then all irrep symbols are removed from the
display. (Note that the irrep symbol in the current setting can only be
removed from the display by removing all irrep symbols with
**CANCEL SHOW IRREP**).

**CANCEL VALUE ALL**

Cancels the effect of all **VALUE** commands previously used.

**DISPLAY BUSH**

Data about a bush of vibrational modes are displayed. The parent space group,
irrep, direction of the order parameter, and Wyckoff positions of the atoms
must be selected. When used with **SHOW MODES**, the atomic displacements
in each mode is displayed. When used with **SHOW INVARIANTS**, the invariant
polynomials in the free-energy expansion of the bush of modes are displayed.

**DISPLAY DIRECTION**

The irreps and directions of order parameters are displayed, given the parent
space group, subgroup, basis vectors of the subgroup lattice, and origin of
the subgroup.

**DISPLAY DISTORTION**

Symmetry-allowed distortions are displayed.
The displayed data are controlled by
**VALUE**, **SHOW**, and **CANCEL** commands.

**DISPLAY IMAGE**

Data about images of the irreps are displayed.
The displayed data are controlled by
**VALUE**, **SHOW**, and **CANCEL** commands.

**DISPLAY INVARIANTS**

Invariant polynomials in the representation space of one or more coupled
irreps are displayed.
The displayed data are controlled by
**VALUE**, **SHOW**, and **CANCEL** commands.
A parent space group must be selected (using **VALUE PARENT**),
and one or more irreps must be selected (using **VALUE IRREP**).
Each invariant polynomial and its degree are displayed without needing to
use any **SHOW** commands.

**VALUE GRADIENT** may be used to display invariant polynomials containing
spatial derivatives. The value selected by this command determines the
number of derivatives each polynomial will contain. (Note that polynomials
which vanish in a volume integral are also displayed. The user must inspect
these himself and discard them by hand.) The degree of the polynomial must
be selected (using **VALUE DEGREE**).

**DISPLAY IRREP**

Data about irreps are displayed.
The displayed data are controlled by
**VALUE**, **SHOW**, and **CANCEL** commands.

**DISPLAY ISOTROPY**

Data about isotropy subgroups are displayed.
The displayed data are controlled by
**VALUE**, **SHOW**, and **CANCEL** commands.
Isotropy subgroups for irreps associated with **k** lines and **k** planes of
symmetry and general **k** vectors are not stored in the data base since they
depend on the parameters alpha, beta, gamma which define the exact location
of the **k** vector.
The data for these subgroups are read from a special file.
ISOTROPY looks for this file in the user's directory. If it is not found, the
user is prompted, and, if desired, ISOTROPY will then proceed to calculate
the requested subgroups and create the file.

**DISPLAY ISOTROPY COUPLED**

Data about isotropy subgroups of coupled order parameters are displayed.
The displayed data are controlled by
**VALUE**, **SHOW**, and **CANCEL** commands.
A parent space group must be selected (using **VALUE PARENT**),
and two or more irreps must be selected (using **VALUE IRREP**).
The data for these subgroups are read from a special file.
ISOTROPY looks for this file in the user's directory. If it is not found, the
user is prompted, and, if desired, ISOTROPY will then proceed to calculate
the requested subgroups and create the file.

**DISPLAY KPOINT**

Data about **k** vectors in the first Brillouin zone are displayed.
The displayed data are controlled by
**VALUE**, **SHOW**, and **CANCEL** commands.

**DISPLAY PARENT**

Data about space groups are displayed. (The word **PARENT** refers
to ``parent space group''.) The displayed data are controlled by
**VALUE**, **SHOW**, and **CANCEL** commands.

**DISPLAY SETTING**

The current space-group setting being used is displayed.

**DISPLAY SHOW**

All **SHOW** commands currently in effect are shown.

**DISPLAY VALUE**

All **VALUE** commands currently in effect are shown.

**LABEL ELEMENT p1**

The notation for the space-group elements is changed.
This affects the label displayed whenever elements of a space
group are displayed. It also affects the way in which elements are to
be entered with the **VALUE ELEMENT** command. The parameter p1
indicates the notation to be used: **INTERNATIONAL**, **MILLER-LOVE**,
**KOVALEV**, **BRADLEY-CRACKNELL** and **ZAK** for the notations
of the international tables, Miller and Love, Kovalev, Bradley and Cracknell,
and Zak, respectively. See the **VALUE ELEMENT** command for an explanation
of these notations. Note that the **SETTING** command does not change
the notation of space-group elements. For example,
it is possible to show elements
of a space group in the setting of Zak using Bradley and Cracknell's
notation for the space-group elements.
When ISOTROPY is started, the default notation for elements is
**BRADLEY-CRACKNELL**.

**LABEL IMAGE p1**

**LABEL IMAGE TOLEDANO** adds the notation of Toledano and Toledano
for images whenever image symbols are displayed.
**LABEL IMAGE NOTOLEDANO** removes this notation.

**LABEL LATTICE p1**

The notation for Bravais lattices is changed. This affects the label
displayed when **SHOW LATTICE** is used.
The parameter p1 indicates the notation to be used: **SCHOENFLIES**
and **PEARSON**. See the **VALUE LATTICE** command for more
explanation about these notations.

**LABEL POINTGROUP p1**

The notation for point groups is changed. This affects the label
displayed when **SHOW POINTGROUP** is used.
The parameter p1 indicates the notation to be used: **INTERNATIONAL**
and **SCHOENFLIES**. See the **VALUE POINTGROUP** command for more
explanation about these notations.

**LABEL SPACEGROUP p1**

The notation for the space-group label is changed. This affects the label
displayed when **SHOW PARENT** or **SHOW SUBGROUP** are used.
The parameter p1 indicates the notation to be used: **INTERNATIONAL**
and **SCHOENFLIES**. Also the international notation can be changed
to the full symbol or the short symbol using
**LABEL SPACEGROUP INTERNATIONAL SHORT** or
**LABEL SPACEGROUP INTERNATIONAL FULL**, respectively.
The full symbol reflects the choice of cell and unique axis for the
monoclinic space groups, while the short symbol does not.
The **INTERNATIONAL** label also reflects the setting used. For example,
space group #12 is **C2/m**, **A2/m**, **B2/m**, **B2/m** for
the **INTERNATIONAL**, **MILLER-LOVE**, **BRADLEY-CRACKNELL**,
**ZAK** settings, respectively. When using the **KOVALEV** setting,
only the **SCHOENFLIES** labeling of space groups is shown.

**LABEL VECTOR p1**

**LABEL VECTOR PRIMITIVE** causes the components of vectors and coordinates
of points to be displayed in terms of primitive basis vectors.
**LABEL VECTOR CONVENTIONAL** causes the components of vectors and coordinates of
points to be displayed in terms of conventional basis vectors. For example,
a vector (1/2)**i**+(1/2)**j** in a face-centered cubic lattice
would be displayed as **(1/2,1/2,0)** using conventional basis vectors
and as **(0,0,1)** using primitive basis vectors. (This vector happens
to be chosen for the third primitive basis vector for that lattice.)
**LABEL VECTOR PRIMITIVE** cannot be used with the
**INTERNATIONAL** setting.

**PAGE p1**

This command sets the number of lines that can be displayed at one time.
When the output to a particular **DISPLAY** command
requires more lines than p1, only p1 lines are displayed at a time.
When ISOTROPY starts, the default number of lines is 22. If p1 is
**NOBREAK**, all lines are displayed at one time.

**QUIT**

The program ISOTROPY exits.

**SCREEN p1**

The width of the display is changed to p1 characters wide. The default
width is 80 characters. If the data to be displayed require
more than p1 characters in a line, ISOTROPY first tries to arrange
the last column of data to form more than one line on the screen. If this
cannot be done, the line is truncated and an asterisk
(*****) appears at the right edge of the screen.

**SETTING p1**

The current space-group setting is changed. The parameter p1 is
the name of the setting: **INTERNATIONAL NEW**,
**INTERNATIONAL OLD**, **MILLER-LOVE**, **KOVALEV**,
**BRADLEY-CRACKNELL**, and **ZAK** refer to the setting of
International Tables (new ed.), International Tables (old ed.),
Miller and Love, Kovalev, Bradley and Cracknell, and
Zak, respectively. The current setting can be displayed using the
**DISPLAY SETTING** command.
Additional options for the settings in International
Tables are discussed under the command, **SETTING INTERNATIONAL p1**.
If the **SETTING INTERNATIONAL** command is used (without the keywords
**NEW** or **OLD**), then the setting is returned to whichever edition
was used the last time the current setting
was **INTERNATIONAL**.
When ISOTROPY starts, the current setting is **INTERNATIONAL NEW**.
The **SETTING** command changes the notation used for irreps,
unless the setting is changed to **INTERNATIONAL**.

**SETTING INTERNATIONAL p1**

This command allows additional options for the setting of space groups
in International Tables.

Some space groups have two choices of origin. When ISOTROPY is started,
origin choice 2 is used. (This is the choice with the point of inversion
at the origin.) To change the origin choice for a particular space group,
use **SETTING INTERNATIONAL p1 ORIGIN p2**, where p1 is a space-group
number or symbol and p2 is **1** or **2**. The origin choice
for all space groups (with more than one origin choice) can be changed
by using **ALL** for p1. (Note that the origin choice is changed only for
the current setting, i.e., the new or old edition, not both.)
For example, **SETTING INTERNATIONAL 228 ORIGIN 1**
changes the setting to origin choice 1 for space group #228
Fd3c. **SETTING INTERNATIONAL ALL ORIGIN 1** changes the setting
of all space groups (which have two origin choices) to origin choice 1.

The monoclinic space groups have two choices for the unique axis. When
ISOTROPY is started, unique axis b is used for the new edition and
unique axis c is used for the old edition. To change the choice of
unique axis for a particular space group, use
**SETTING INTERNATIONAL p1 AXIS p2**,
where p1 is a space-group number or symbol and p2
is **B** or **C**. The choice of unique axis for all monoclinic
space groups can be changed by using **ALL** for p1. (Note that the
axis choice
is changed only for the current setting, i.e., the new or old edition,
not both.)
For example, **SETTING INTERNATIONAL 5 AXIS C**
changes the setting to unique axis c for space group #5
A2. **SETTING INTERNATIONAL ALL AXIS C** changes the setting
of all monoclinic space groups to unique axis c.

The base-centered monoclinic space groups in the new edition
have three cell choices. When
ISOTROPY is started, cell choice 1 is used. To change the cell choice
for a particular space group, use **SETTING INTERNATIONAL p1 CELL p2**,
where p1 is a space-group number or symbol and p2
is **1**, **2**, or **3**. The cell choice for all base-centered
monoclinic
space groups can be changed by using **ALL** for p1. (Note that the
cell choice is changed only if the current setting is the new edition.)
For example, **SETTING INTERNATIONAL 5 CELL 3**
changes the setting to cell choice 3 for space group #5
A2. **SETTING INTERNATIONAL ALL CELL 3** changes the setting
of all base-centered monoclinic space groups to cell choice 3.

The trigonal space groups have two choices for axes: hexagonal and
rhombohedral. When
ISOTROPY is started, the hexagonal axes are used.
To change the choice of
axes for a particular space group, use
**SETTING INTERNATIONAL p1 AXIS p2**,
where p1 is a space-group number or symbol and p2
is **HEXAGONAL** or **RHOMBOHEDRAL**.
The choice of axes for all trigonal
space groups can be changed by using **ALL** for p1. (Note that the
axis choice
is changed only for the current setting, i.e., the new or old edition,
not both.)
For example, **SETTING INTERNATIONAL 167 AXIS RHOMBOHEDRAL** changes the setting to rhombohedral axes
for space group #167
R-3c. **SETTING INTERNATIONAL ALL AXIS RHOMBOHEDRAL**
changes the setting
of all trigonal space groups to rhombohedral axes.

**SETTING MAGNETIC**

Data about the isotropy subgroups of the grey magnetic space groups are
displayed when **DISPLAY ISOTROPY** is used. All coordinates are expressed
in terms of the primitive basis vectors in the setting of Miller and Love.

Magnetic space groups are displayed in the following format: (1) the
number of the associated Fedorov space group in parentheses, (2) the Belov
number, and (3) the symbol given in Miller and Love.
Magnetic space groups are selected using the number or
symbol of the corresponding Fedorov space group.
For example, **VALUE PARENT 155**
or **VALUE PARENT R32** selects the grey magnetic space group R321'.
The command **VALUE SUBGROUP 155** selects any of the four space
groups associated with R32, i.e., R32, R321', R32', R_{I}32.

**SETTING NOMAGNETIC**

The command, **SETTING MAGNETIC**, is cancelled.

**SHOW ACTIVE**

Active images are indicated when **DISPLAY IMAGE** is used. Active irreps
are indicated when **DISPLAY IRREP** or **DISPLAY ISOTROPY** is used. An irrep is active when
both its Landau and Lifshitz frequencies are zero (the Landau and
Lifshitz conditions). An image is active when at least one
active irrep is mapped onto it. Note that not all irreps mapped onto
active images are active irreps. Some of them may fail the Lifshitz
condition.

**SHOW BASIS**

The basis vectors are shown. When **DISPLAY PARENT** is used, the primitive
basis
vectors of the parent space group are shown. If **LABEL VECTOR CONVENTIONAL**
is used, primitive basis vectors with
respect to the conventional unit cell are shown.

When **DISPLAY ISOTROPY** or **DISPLAY ISOTROPY COUPLED**
is used, the basis vectors of the isotropy subgroup are shown. When used with
**LABEL VECTOR PRIMITIVE**, the primitive basis vectors of the subgroup
are given in terms of the primitive basis vectors of the parent space group.
When used with
**LABEL VECTOR CONVENTIONAL**, the conventional basis vectors of the subgroup
are given in terms of the conventional basis vectors of the parent space group.

**SHOW CARTESIAN**

Cartesian coordinates are displayed. The cartesian coordinates are
defined by the **VALUE LATTICE PARAMETER** command. This is only implemented
a few places in ISOTROPY: (1) **DISPLAY PARENT**: basis vectors of the
primitive lattice (**SHOW BASIS**), space-group elements, displayed
as a rotation matrix followed by a translation (**SHOW GENERATORS** and
**SHOW ELEMENT**), and Wyckoff positions (**SHOW WYCKOFF VECTOR**).
(2) **DISPLAY ISOTROPY**: basis vectors of the
primitive lattice (**SHOW BASIS**) and space-group elements
(**SHOW GENERATORS** and **SHOW ELEMENT**).
(3) **DISPLAY DISTORTION**: Wyckoff positions and displacement vectors
(**SHOW MICROSCOPIC**).
In the case of Wyckoff positions, the values of the parameters x,y,z
must be selected by **VALUE WYCKOFF XYZ** if needed.
Vectors must be given in terms of conventional basis vectors, not primitive.

**SHOW CHARACTER**

The irrep character for an element of the parent space group is
shown when **DISPLAY IRREP** is used. The **SHOW ELEMENT** command is
also automatically executed. The element is selected with
the **VALUE ELEMENT** command.
(The character is the trace of the
matrix onto which the irrep maps the element of the space group.)

**SHOW COMPATIBILITY**

The compatibility relations for an irrep is shown when **DISPLAY IRREP**
is used. The irrep of the little group of **k** is decomposed into
irreps of the little group of **k**', where **k**' is some **k** vector
with more degrees of freedom than **k** and contains **k** as a subspace
of its domain. For example, if **k** is a point of symmetry, then **k**'
may be a line of symmetry which contains that point. **k**' may be
selected by the **VALUE COMPATIBILITY** command. If not selected, then
relations for every possible **k**' with one degree of freedom less than
that of **k** are shown.

**SHOW COMPLEX**

The complex form of an irrep is shown when **DISPLAY IRREP** is used.

**SHOW CONTINUOUS**

The phase transitions allowed to be continuous in Landau theory or in RG
theory are indicated when **DISPLAY ISOTROPY** is used.
In Landau theory, a phase transition to a particular subgroup is allowed
to be continuous if the irrep is active and the order parameter is
a possible minimum of the free energy expanded to fourth degree.
RG theory imposes the additional constraint that
the coefficients of the free-energy expansion lie within the attractor
basin of a stable fixed point.

**SHOW DIMENSION**

The dimension of the image of the irrep is shown when **DISPLAY IMAGE**,
**DISPLAY INVARIANTS**,
**DISPLAY IRREP**, **DISPLAY ISOTROPY**, or **DISPLAY ISOTROPY COUPLED** is used. In the cases of **DISPLAY INVARIANTS** and
**DISPLAY ISOTROPY COUPLED**, the
dimension of the *reducible* representation is shown (the sum of the
dimensions of each of the irreps selected).

**SHOW DIRECTION [p1]**

The symbol for the direction of the order parameter is shown when
**DISPLAY ISOTROPY**, **DISPLAY ISOTROPY COUPLED**, or
**DISPLAY DISTORTION** is used.
If p1 is **VECTOR**, then the
vector form of the order parameter is also shown.

When **DISPLAY DISTORTION** is used, the direction is shown only when one
has been selected by **VALUE DIRECTION**. Also, the parameter p1 is
ignored.

When **DISPLAY ISOTROPY COUPLED** is used,
the symbol for the order parameter direction of each
irrep is shown followed by a number in parentheses indicating which domain
of the uncoupled isotropy subgroup is involved. For example, suppose we
display the isotropy subgroups for the coupled order parameters of irreps
X_{3}^{+} and P_{5} of space group
D_{4h}^{17}.
We would find that one of the subgroups is D_{2d}^{4} with
order parameter direction **P1(1)P4(3)**. This means that this subgroup
is an intersection of the first domain of D_{4h}^{16} [irrep X_{3}^{+},
direction P_{1}=(a,0)] and the third domain of D_{2d}^{11} [irrep P_{5},
direction P_{4}=(a,0,- a,0)]. The direction of the order parameter for
D_{2d}^{4} is denoted **(a,0,b,0,-b,0)**, the first two components
associated with irrep X_{3}^{+} and the remaining four components associated
with irrep P_{5}. The irreps associated with each part of the order parameter
may be seen by using **SHOW IRREP**.

**SHOW DISTINCT**

The domains for distinct subgroups are shown when **DISPLAY ISOTROPY** is
used.

**SHOW DOMAINS [GENERATORS]**

The possible domains arising from the phase transition are shown when
**DISPLAY ISOTROPY** or **DISPLAY ISOTROPY COUPLED** is used.
The number of possible domains is
equal to the index of the isotropy subgroup in the parent space group.
When the parameter **GENERATORS** is present,
the element of the parent space group which
generates the domain is also shown.

When **DISPLAY DISTORTIONS** is used, **SHOW DOMAINS** will cause the
domain selected by **VALUE DOMAIN** to be shown.

**SHOW ELEMENTS**

When used with **DISPLAY PARENT**, the coset representatives of the parent
space group with respect to its translation subgroup are shown.

When used with **DISPLAY IMAGE**, all of the matrices of the image are shown.

When used with **DISPLAY IRREP**, the element of the parent space group
selected by **VALUE ELEMENT** is shown.

When used with **DISPLAY ISOTROPY**, the coset representatives of the
subgroup with respect to its translation subgroup are shown.

**SHOW FAINTNESS**

The nonzero faintness indices for all of the other irreps of the parent
space group are shown when **DISPLAY IRREP** is used.
Invariant polynomials exist which linearly couple these irreps to the
selected irrep. The minimum degree of the part of the polynomial associated
with the selected irrep is the faintness index. For example, if the
selected irrep is **R4+**, we find a faintness index 3 for irrep **R2+**.
The form of the invariant polynomial in this case is
q_{1}n_{1}n_{2}n_{3}
where q_{1} is the order parameter associated with **R2+** and
n_{1},n_{2},n_{3} are components of the order parameter **n**
associated with
**R4+**. The coupling is linear in q_{1}, and the degree of the part of
the polynomial containing components of **n** is 3, the faintness index.

**SHOW FELIX**

The Felix frequency of the image
is shown when **DISPLAY IRREP** or **DISPLAY ISOTROPY** is used.
The Felix frequency is the number of anisotropic gradient terms in the LGW
Hamiltonian.

**SHOW FREQUENCY [p1]**

When **DISPLAY IRREP** is used, the point-group irreps of the Wyckoff
positions which induce the space-group irrep are shown, along with the
subduction frequency.
If p1 is **VECTOR**, only the point-group irreps which induce vector
irreps of the space-group irrep are shown, along with the number
vector irreps which can be induce. This number will be some multiple of
the subduction frequency, since there may be more than one independent
set of vector basis functions for the point group irrep.

When **DISPLAY ISOTROPY** or **DISPLAY ISOTROPY COUPLED** is used,
the irreps which subduce the isotropy subgroup are shown, along with the
subduction frequency.
For each irrep, there is a direction of an order
parameter which remains invariant under the operation of each element in
the isotropy subgroup. If p1 is **DIR**, the
direction of that order parameter is shown. In parentheses is
shown the domain number where you can find that direction if you display
the isotropy subgroups for that irrep. If p1 is **GAMMA**, only
the gamma (**k**=0) irreps are shown. If p1 is **CLASSIFICATION**,
the symbol **F** (for ``full'') is shown when the distortions associated
with the irrep fully classify the domains of the subgroup. Otherwise, the
symbol **P** (for ``partial'') is shown.

**SHOW GENERATORS**

When used with **DISPLAY PARENT**, the generators of the parent space group
are shown. (Generators of the lattice are actually not shown explicitly.)

When used with **DISPLAY IMAGE**, the generating matrices of the image
are shown.

When used with **DISPLAY IRREP**, elements of the parent space group
which are mapped onto the generating matrices of the irrep's image are shown.

When used with **DISPLAY ISOTROPY** or **DISPLAY ISOTROPY COUPLED**,
the elements of the parent space
group which generate the isotropy subgroup are shown.

**SHOW IMAGE**

The symbol of the image of the irrep is shown when **DISPLAY IMAGE**,
**DISPLAY IRREP**, or **DISPLAY ISOTROPY** is used.

**SHOW INDEX**

The index of the isotropy subgroup in the parent space group is shown
when **DISPLAY ISOTROPY** or **DISPLAY ISOTROPY COUPLED**
is used. The index is the size of the parent
space group relative to the subgroup.

**SHOW IRREP [p1]**

The symbol of the irrep is shown when **DISPLAY INVARIANTS**,
**DISPLAY DISTORTION**, **DISPLAY IRREP**, **DISPLAY ISOTROPY**, or **DISPLAY ISOTROPY COUPLED** is used.
The symbol shown uses the irrep notation of the
current space-group setting. The parameter p1 allows the irrep
symbol to also be shown in other notations. p1 can be **MILLER-LOVE**,
**KOVALEV**, **BRADLEY-CRACKNELL**, or **ZAK**, referring to the
irrep notations of Miller and Love, Kovalev, Bradley and Cracknell, and
Zak, respectively. p1 can also be **POINTGROUP**, in which case the
conventional labels for point-group irreps are shown for irreps at the
gamma point (**k**=0).
Even when p1 is present, this command causes the
irrep to be shown in the notation of the current setting in addition
to the setting specified by p1. When **DISPLAY INVARIANTS** or
**DISPLAY ISOTROPY COUPLED** is
used, the symbols of all irreps selected are shown in sequence on the same
line.

**SHOW INVARIANTS**

The invariant polynomials in the free-energy expansion of a bush of modes are
displayed when **DISPLAY BUSH** is used.

**SHOW KDEGREE**

The degrees of freedom of the **k** vector are shown. For example, a
**k** point of symmetry has 0 degrees of freedom, and a **k** line of symmetry
has 1 degree of freedom.

**SHOW KERNEL**

The generating elements of the kernel of the irrep are shown when
**DISPLAY IRREP** is used. (The kernel is the set of all elements
in the parent space group which map onto the unit matrix in the image.)

**SHOW KPOINT**

The coordinates of the **k** vector are shown when **DISPLAY KPOINT**,
**DISPLAY IRREP** or **DISPLAY DIRECTION** is used.
The coordinates are given in terms of the
reciprocal lattice vectors derived from the basis vectors of the direct lattice.
The form depends on the space-group setting as well as the form of the vectors
used, primitive or conventional.

**SHOW LANDAU**

The Landau frequency of the image
is shown when **DISPLAY IMAGE**, **DISPLAY IRREP**, or **DISPLAY ISOTROPY** is used. The Landau frequency is
the number of independent third-degree invariants.

**SHOW LATTICE**

When **DISPLAY PARENT** is used, the Bravais lattice of the space
group is shown. When **DISPLAY ISOTROPY** or **DISPLAY ISOTROPY COUPLED**
is used, the Bravais lattices
of both the parent space group and isotropy subgroup are shown.

**SHOW LIFSHITZ**

The Lifshitz frequency of the irrep
is shown when **DISPLAY IRREP** or **DISPLAY ISOTROPY** is used.
The Lifshitz frequency is
the number of times that the vector representation is contained
in the antisymmetrized cube of the irrep.

**SHOW LOCAL [p1] [p2]**

The local microscopic distortions at a point about a Wyckoff position
are displayed when **DISPLAY DISTORTION** is
used. The coordinates of the point must be selected with the command
**VALUE POSITION**.
If p1 is not present, then the distortions are shown as linear
combinations of basis functions of the irrep of the point group associated
with the point. The command **SHOW LOCAL SCALAR** displays
distortions of scalar functions, such as occupation probabilities.
The command **SHOW LOCAL VECTOR** displays vector
distortions, such as atomic displacements. The command **SHOW LOCAL VECTOR PSEUDO** displays pseudo vector distortions, such as molecular rotations
or magnetic moments.

**SHOW MACROSCOPIC [PSEUDO]**

The macroscopic distortions (tensor components) are displayed when
**DISPLAY DISTORTION** is used. The type of tensor must be specified by
the **VALUE RANK** command. The parameter **PSEUDO** indicates a
pseudo-tensor, such as a magnetic moment.

**SHOW MATRIX**

The irrep matrix for an element of the parent space group is
shown when **DISPLAY IRREP** is used. The command **SHOW ELEMENT**
is also automatically executed.
The element is selected with
the **VALUE ELEMENT** command.

**SHOW MAXIMAL**

Maximal isotropy subgroups are indicated when **DISPLAY ISOTROPY** is
used.
An isotropy subgroup is maximal when it is not a subgroup of any other
isotropy subgroup for the same irrep.

**SHOW MICROSCOPIC [p1] [p2]**

The microscopic distortions are displayed when **DISPLAY DISTORTION** is
used. If p1 is not present, then the distortions are shown as linear
combinations of basis functions of the irrep of the point group associated
with the Wyckoff position. The command **SHOW MICROSCOPIC SCALAR** displays
distortions of scalar functions, such as occupation probabilities.
The command **SHOW MICROSCOPIC VECTOR** displays vector
distortions, such as atomic displacements. The command **SHOW MICROSCOPIC VECTOR PSEUDO** displays pseudo vector distortions, such as molecular rotations
or magnetic moments.

**SHOW MODES**

The atomic displacements in each vibration mode of a bush are displayed when
**DISPLAY BUSH** is used.

**SHOW NEWFRACTIONALS**

The new fractionals in the unit cell of the isotropy subgroup are shown
when **DISPLAY ISOTROPY** or **DISPLAY ISOTROPY COUPLED**
is used. These new fractionals are vectors
which are lattice vectors in the parent space group but are not lattice
vectors in the isotropy subgroup.

**SHOW ORDER**

The order of the image is shown when **DISPLAY IMAGE** is used.

**SHOW ORIGIN**

The origin of the isotropy subgroup with respect to the parent space
group is shown when **DISPLAY ISOTROPY** or **DISPLAY ISOTROPY COUPLED**
is used. When used with
**LABEL VECTOR PRIMITIVE**, the coordinates of the origin
are given in terms of the primitive basis vectors of the parent space group.
When used with
**LABEL VECTOR CONVENTIONAL**, the coordinates of the origin
are given in terms of the conventional basis vectors of the parent space group.

**SHOW PAIRS [p1]**

This command shows information about pairs of domains of isotropy subgroups
when **DISPLAY ISOTROPY** is used.
We denote a pair of domains by (P_{i},P_{j}), where
P_{i} is the ith domain of an isotropy subgroup.
The pair to be considered can be selected by the **VALUE DOMAIN PAIRS**
command.
If the pair has not been selected, then the pair (P_{1},P_{j}) is considered
for each domain j.

When the pair has not been selected,
equivalence classes of domain pairs are displayed.
Any class of pairs has an element of the form
(P_{1},P_{j}). Each pair is considered for every domain j.
The number in the pair column numbers the class of pairs to which the pair
belongs. For example, domain 3, pair 2 means the pair (1,3) is in the second
equivalence class of pairs.

If p1 is **INTERSECT**, the intersection of the isotropy groups belonging
to the two domains in the domain pair is displayed. We call this the
pair intersection group. This group is always one of the other isotropy
subgroups belonging to the same irrep. Therefore, we display simply the
direction of that isotropy subgroup. The domain of that subgroup is also
shown in parentheses if it is not the first domain.

If p1 is **SWITCH**, an element of the space group which switches
the two domains in the pair is displayed.
For the domain pair (P_{i},P_{j}), this element
takes P_{i} to P_{j} and it also takes P_{j} to P_{i}. When the two domains
are identical, we consider the switching element to not exist.

If p1 is **GROUP**, the space group label of the
pair group is displayed. This group consists of
all elements in the pair intersection group plus all elements that switch
the two domains in the pair. If p1 is **BASIS**, **ORIGIN**,
**GENERATORS**, or **ELEMENTS**, then the basis vectors of the lattice,
the origin of the space group, the generating elements, or the complete
list of elements of the pair group are displayed, respectively. These commands
are very similar to the **SHOW BASIS**, **SHOW ORIGIN**,
**SHOW GENERATORS**, and **SHOW ELEMENTS** commands used with the
**DISPLAY ISOTROPY** command.

**SHOW PARENT**

The parent space group is displayed when **DISPLAY PARENT**,
**DISPLAY INVARIANTS**, **DISPLAY DISTORTION**,
**DISPLAY IRREP**, **DISPLAY ISOTROPY**, **DISPLAY ISOTROPY COUPLED**, or
**DISPLAY KPOINT** is used.

**SHOW POINTGROUP**

When **DISPLAY PARENT** is used, the point group of the space group
is displayed. When **DISPLAY ISOTROPY** or **DISPLAY ISOTROPY COUPLED**
is used, the point groups of
both the parent space group and isotropy subgroup are shown.

**SHOW POSITION IRREP**

The irrep of the point group associated with a point about a Wyckoff
position is shown when **DISPLAY DISTORTION** is used with **SHOW LOCAL**.

**SHOW SIZE**

The relative sizes of the primitive unit cells of the parent space group
and the isotropy subgroup is shown when **DISPLAY ISOTROPY** or
**DISPLAY ISOTROPY COUPLED** is used.

**SHOW STAR**

When **DISPLAY KPOINT** or **DISPLAY IRREP** is used, the star of **k** is
displayed.

**SHOW SUBGROUP**

The space-group symbol of the
isotropy subgroup is shown when **DISPLAY ISOTROPY** or **DISPLAY ISOTROPY COUPLED** is used.

**SHOW TWIN p1 [p2]**

This command displays information about twin intersection groups and twin
groups when **DISPLAY ISOTROPY** is used. This information is
shown for a particular domain pair if one has been selected by the
**VALUE DOMAIN PAIR** command. Otherwise, the pair (P_{1},P_{j}) for
each domain j will be used. In order to display information about twins,
a plane must be specified by selecting its normal position using the
**VALUE NORMAL** command and a point on the plane using the
**VALUE POSITION** command.

If p1 is **INTERSECT**, then information about the twin intersection
group is displayed. Each element in this group must obey the following
requirements: It must be a member of each of the two
isotropy subgroups associated with the two domains in the pair. (This means
that this group is a subgroup of the pair intersection group.)
If the element operates on a point in the specified plane, the point must
stay in the plane. (This means that the group must be diperiodic.)
If the point operator part of the element operates on a vector perpendicular
to the specified plane, the direction of the vector must stay the same.
To display information about twin intersection groups, an additional keyword
(p2) must also be present.
If p2 is **GROUP**, **BASIS**, **ORIGIN**,
**GENERATORS**, or **ELEMENTS**, then the diperiodic space group label,
the basis vectors of the lattice,
the origin of the space group, the generating elements, or the complete
list of elements of the twin intersection
group are displayed, respectively. These commands
are very similar to the **SHOW SUBGROUP**, **SHOW BASIS**, **SHOW ORIGIN**,
**SHOW GENERATORS**, and **SHOW ELEMENTS** commands used with the
**DISPLAY ISOTROPY** command.

Information which is displayed about the twin group is is controlled by p1.
Each element in the twin group must obey the following requirements:
It must either keep both domains in the pair invariant or switch them.
(This means
that this group is a subgroup of the pair group.)
If the elements operates on a point in the specified plane, the point must
stay in the plane. (This means that the group must be diperiodic.)
If the point operator part of the element operates on a vector perpendicular
to the specified plane, the direction of the vector either stays the same
or reverses its direction.
If p1 is **GROUP**, **BASIS**, **ORIGIN**,
**GENERATORS**, or **ELEMENTS**, then the diperiodic space group label,
the basis vectors of the lattice,
the origin of the space group, the generating elements, or the complete
list of elements of the twin group are displayed, respectively. These commands
are very similar to the **SHOW SUBGROUP**, **SHOW BASIS**, **SHOW ORIGIN**,
**SHOW GENERATORS**, and **SHOW ELEMENTS** commands used with the
**DISPLAY ISOTROPY** command.

If p1 is **SWITCH**, then a ``switching'' element is displayed.
If p2 is **SIDE**, then the element switches the two domains but does
not change the direction of the vector normal to the plane.
If p2 is **NORMAL**, then the element reverses the direction of
the vector normal to the plane but does not switch the two domains.
If p2 is **BOTH**, then the element switches both the two domains and
the direction of the vector normal to the plane.

**SHOW TYPE**

The irrep type (1,2,3) are shown when **DISPLAY IMAGE** or **DISPLAY IRREP** is used. A type-1 irrep is real. A type-2 irrep is complex but its
characters are real. A type-3 irrep is complex and its characters are also
complex.

**SHOW UNITCELL**

Only distortions in the unit cell of the parent are shown when **DISPLAY DISTORTIONS** is used with **SHOW MICROSCOPIC**.

**SHOW WYCKOFF [p1,p2]**

When **DISPLAY PARENT** is used,
the symbol for the Wyckoff position is shown.
If p1 is **VECTOR**, the coordinates of the Wyckoff position
are shown. In addition, if p2 is **ALL**, the coordinates of all
of the points associated with the Wyckoff position are shown.
If p1 is **POINTGROUP**, the point group
of the Wyckoff position is shown.
If p1 is **ELEMENTS**, the space-group elements which belong to the
point group of the Wyckoff position are shown.
If p1 is **CHARACTER**, the characters of the point-group irreps are
shown for each space-group element which belongs to the point group of the
Wyckoff position.

When **DISPLAY DISTORTION** is used,
the symbol for the Wyckoff position is shown.
If p1 is **IRREP**, the irrep of the point group of the Wyckoff position
is shown.

**SHOW WYCKOFF SUBGROUP**

When **DISPLAY ISOTROPY** or **DISPLAY ISOTROPY COUPLED** is used, the Wyckoff positions of the atoms in the subgroup
are shown.

**SHOW XYZ**

The x,y,z coordinates of a point in the unit cell of the isotropy subgroup
are given in terms of the x,y,z coordinates of a point in the unit cell
of the parent space group when **DISPLAY ISOTROPY** or **DISPLAY ISOTROPY COUPLED** is used.
The coordinates are given with respect to the origins of
the space groups.
When used with
**LABEL VECTOR PRIMITIVE**, the coordinates
are given in terms of primitive basis vectors.
When used with
**LABEL VECTOR CONVENTIONAL**, the coordinates
are given in terms of conventional basis vectors.
(In the case of centered Bravais lattices, the conventional basis vectors
are not primitive.)

**VALUE ACTIVE p1**

When **DISPLAY IMAGE** is used, **VALUE ACTIVE YES** selects active
images and **VALUE ACTIVE NO** selects images which are not active.
When **DISPLAY IRREP** or **DISPLAY ISOTROPY** is used,
**VALUE ACTIVE YES** selects active
irreps and **VALUE ACTIVE NO** selects irreps which are not active.
An irrep is active when
both its Landau and Lifshitz frequencies are zero (the Landau and
Lifshitz conditions). An image is active when at least one
active irrep is mapped onto it. Note that not all irreps mapped onto
active images are active irreps. Some of them may fail the Lifshitz
condition.

**VALUE BASIS p1 p2 p3**

The basis vectors of a subgroup are selected. This command affects the data
displayed by **DISPLAY DIRECTION**. p1,p2,p3 are the three vectors.
Each vector is denoted by three numbers separated by commas. The
three numbers are components of the vector in terms of the basis
vectors of the lattice of the parent space group. See **VALUE CELL**
below for examples.

**VALUE CELL p1 p2 p3**

The basis vectors of a super cell are selected. This command affects the data
displayed by **DISPLAY DISTORTION**. p1,p2,p3 are the three vectors.
Each vector is denoted by three numbers separated by commas. The
three numbers are components of the vector in terms of the basis
vectors of the lattice. For example, **2,0,0** denotes a vector which is
two times the first basis vector of the lattice. Components may be fractions
if the conventional form of the vector has been chosen with **LABEL VECTOR CONVENTIONAL**. Each vector must be a vector of the primitive lattice.
For example, **1/2,1/2,0** would be a vector
of a face-centered lattice. When a super cell has been selected,
**DISPLAY DISTORTION** shows all atoms in the super cell.

**VALUE COMPATIBILITY p1**

The compatibility relations to be shown by **DISPLAY IRREP** are selected.
p1 is the label of a **k** vector. See the **SHOW COMPATIBILITY**
command.

**VALUE CONTINUOUS p1**

Phase transitions which may or may not be allowed to be continuous in
Landau theory or in RG theory
are selected when **DISPLAY ISOTROPY** is used.
**VALUE CONTINUOUS RG** selects isotropy
subgroups to which a phase transition
is allowed to be continuous in RG theory, **VALUE CONTINUOUS LANDAU**
selects isotropy subgroups to which a phase transition is also allowed to
be continuous in Landau theory and
**VALUE CONTINUOUS NO** selects isotropy
subgroups to which a phase transition is
not allowed to be continuous in either theory.
In Landau theory, a phase transition to a particular subgroup is allowed
to be continuous if the irrep is active and the order parameter is
a possible minimum of the free energy expanded to fourth degree.
RG theory imposes the additional constraint that
the coefficients of the free-energy expansion lie within the attractor
basin of a stable fixed point.

**VALUE DEGREE p1 [p2]**

The degrees of invariant polynomials are selected.
This command affects the data displayed by **DISPLAY INVARIANTS**.
The parameters, p1 and p2, are numbers representing the degree of the
polynomial. If they are both present,
then degrees p1 through p2 are selected. If only p1 is
present, then only degree p1 is selected. If this command has not been used
yet, or if the **CANCEL VALUE DEGREE** command has been used, ISOTROPY
displays the invariant polynomials of degrees 1 through 4 by default.

**VALUE DIMENSION p1 [p2]**

The dimensions of matrices in the irrep's
image are selected. This command affects the data displayed
by **DISPLAY IMAGE**, **DISPLAY IRREP**, and **DISPLAY ISOTROPY**.
The parameters, p1 and p2, are numbers representing the dimension
of matrices in an image. If they are both present,
then dimensions p1 through p2 are selected. If only p1 is
present, then only dimension p1 is selected.

**VALUE DIRECTION p1 [p2 ...]**

The direction of the order parameter is selected. This command affects
the data displayed by **DISPLAY ISOTROPY**, **DISPLAY DISTORTION**,
**DISPLAY INVARIANTS**, **DISPLAY BUSH**, and **DISPLAY DIRECTION**.
The parameters p1,p2,... each represent the direction of an order
parameter. If more than one direction is selected, then corresponding
irreps must be selected first, and the number of directions selected must
equal the number of irreps selected.

The direction of an order parameter can be represented in several ways.
The most usual way is to simply enter for the parameter the symbol of
the direction (for example **VALUE DIRECTION P1** to selecte the direction
P1).
**VALUE DIRECTION KERNEL** selects the order parameter in the most
general direction.
**VALUE DIRECTION ONEARM** selects order parameters which arise from only
one arm of the star of **k**. These are implemented only for non **k** points
of symmetry. In addition, **VALUE DIRECTION ONEARM,P1** selects the
order parameter P1 among those which arise from only one arm of the star
of **k**.
**VALUE DIRECTION VECTOR,A,0,0** selects the order parameter (a,0,0),
and **VALUE DIRECTION VECTOR,0.5A,0.866A** selects the order parameter
(1/2a,1/2sqrt(3)a). Note that irrational coefficients
(and sometimes rational coefficients such as 1/3) must be given to
three decimal places.

**VALUE DOMAIN p1 [p2 ...]**

The domain of the isotropy subgroup is selected.
This command affects the data displayed by **DISPLAY ISOTROPY** when used with
**SHOW DOMAIN**, by
**DISPLAY DISTORTION** when
a subgroup has been selected with **VALUE DIRECTION**,
and by **DISPLAY INVARIANTS** when the direction of an order parameter
has been selected with **VALUE DIRECTION**.
p1 is a number indicating the domain. (The numbering of domains may
be obtained by using **SHOW DOMAINS** with **DISPLAY ISOTROPY**.)
Normally, **DISPLAY ISOTROPY** used with **SHOW DOMAIN** causes all domains
to be displayed. **VALUE DOMAIN** causes only one domain to be displayed.
Normally, **DISPLAY DISTORTION** uses the direction
of the order parameter in the first domain.
**VALUE DOMAIN** along with **VALUE DIRECTION** uses the direction
of the order parameter in selected domain. When used with
**DISPLAY INVARIANTS**, the number of domains selected
must be equal to the number of irreps selected by the
**VALUE IRREP** command.

**VALUE DOMAIN PAIR p1 p2**

A pair of domains of the isotropy subgroup is selected.
This command affects the data displayed by **DISPLAY ISOTROPY** when used with
**SHOW PAIRS** or **SHOW TWIN** commands.

**VALUE ELEMENT p1**

The element of the parent space group is selected.
This command affects the data displayed by **DISPLAY IRREP**.
p1 is a space-group element.
The element is denoted by a symbol, using the notation of International Tables,
Miller and Love, Kovalev, Bradley and Cracknell, or Zak.
For example, **X 1/2-Y -Z**,
**2 0 1/2 0**, **H2 0 1/2 0**,
**C2X 0 1/2 0**, and **UX 0 1/2 0**
all refer to the same element (using each of the notations, respectively).
In the notation of the International Tables,
the x,y,z parts are separated by
a space character. In the other notations, the point operation comes first,
followed by the fractional, each part separated by a space character.
The notation used for p1 must agree with the point-operation notation
selected for elements. The
**LABEL ELEMENT** command changes the notation selected.

**VALUE FELIX p1 [p2]**

The Felix frequency of the image
is selected. This command affects the data displayed
by **DISPLAY IRREP** and **DISPLAY ISOTROPY**.
The parameters, p1 and p2, are numbers representing the Felix frequency
of an irrep (the number of anisotropic gradient terms in the LGW Hamiltonian).
If they are both present,
then Felix frequencies p1 through p2 are selected. If only p1 is
present, then only Felix frequency
p1 is selected.

**VALUE FREQUENCY p1 [p2]**

The subduction frequency of the isotropy subgroup
is selected. This command affects the data displayed
by **DISPLAY ISOTROPY**.
The parameters, p1 and p2, are numbers representing the subduction
frequency.
If they are both present,
then subduction frequencies p1 through p2 are selected. If only p1 is
present, then only subduction frequency
p1 is selected.

**VALUE GRADIENT p1**

The number of spatial derivatives in invariant polynomials is selected.
This command affects the data displayed by **DISPLAY INVARIANTS**.
The parameter p1 is a number representing the number of derivatives to
appear in each invariant polynomial.

**VALUE IMAGE p1**

The image of the irrep is selected. This command affects the data displayed
by **DISPLAY IMAGE**, **DISPLAY IRREP**, and **DISPLAY ISOTROPY**.
The parameter p1 is an image to be selected.
The image is denoted by a symbol, using either
the notation of Stokes and Hatch or the notation of Toledano and Toledano.

**VALUE IRREP p1 [p2 ...]**

The irreps are selected. This command affects the data displayed
by **DISPLAY INVARIANTS**, **DISPLAY DISTORTION**,
**DISPLAY IRREP**, **DISPLAY ISOTROPY**, **DISPLAY ISOTROPY COUPLED**, and **DISPLAY KPOINT**.
The parameters p1,p2,... are irreps to be selected.
Only the first irrep listed (p1) is used by **DISPLAY DISTORTIONS**,
**DISPLAY IRREP**, and
**DISPLAY ISOTROPY**. This command cancels the
effect of any **VALUE KPOINT** command previously used.
The irrep is denoted by a symbol, using either
the notation of Miller and Love, Kovalev, Bradley and Cracknell, or Zak.
For example, **Y1+**, **K8T1**, **Z1+**, and **Z1** all refer
to the same irrep (using each of the notations, respectively)
in space group #12 A2/m. Note that **Z1** and **A1** are the
same irrep in the Zak notation for this space group. When there are
more than one symbol for the same irrep, any of them may be used for
p1. **GM** is used for gamma. When a physically irreducible
representation is constructed from two complex conjugate irreps, the
notation indicates this (for example, **Z1Z2** or **K22T1T2**
in space group #30 Pnc2/mc2).

The irrep notation used for p1 must agree with the current
space-group setting. The
**SETTING** command changes the current setting. When **SETTING INTERNATIONAL** is used, the current irrep notation does not
change. When ISOTROPY is first started, the irrep notation
is Miller and Love. See the **SETTING** command for an explanation
of how the command affects the irrep selected by **VALUE IRREP**.

**VALUE KDEGREE p1**

The degrees of freedom of the **k** vector are selected.
This command affects the data displayed
by **DISPLAY IRREP** and **DISPLAY KPOINT**.

**VALUE KPOINT p1**

Irreps which arise from a given **k** point are selected.
This command affects the data displayed
by **DISPLAY IRREP**, **DISPLAY ISOTROPY** and **DISPLAY DISTORTION**.
This command also selects the **k** vector displayed by **DISPLAY KPOINT**.
The parameter p1 is the **k** point to be selected. This command cancels the
effect of any **VALUE IRREP** command previously used.
The **k** point is denoted by a symbol, using either
the notation of Miller and Love, Kovalev, Bradley and Cracknell, or Zak.
For example, **Y**, **K8**, **Z**, and **Z** all refer
to the same **k** point (using each of the notations, respectively)
in space group #12 A2/m. Note that **Z** and **A** are equivalent
**k** points in the Zak notation for this space group. When there are
equivalent **k** points, any of them may be used for
p1. **GM** is used for gamma.
As with irrep notation,
the **k**-point notation used for p1 must agree with the current
space-group setting. See the **VALUE IRREP** command for a further
discussion of this point.

**VALUE KVALUE p1 [p2 ...]**

The values of the parameters alpha,beta,gamma defining the **k** vectors
are selected. The parameters p1,p2,... each represent a set of parameters
for a **k** vector. The number of sets selected must
equal the number of irreps selected. These parameters need only be selected
if one or more of the irreps are associated with **k** vectors
which are not at **k** points of symmetry. For example, a **k** vector on
a **k** line of symmetry is defined by a single parameter alpha which gives
the position of the vector on the line. In that case,
**VALUE KVALUE 1,1/4** would select one value, alpha=1/4. **VALUE KVALUE 2,1/4,3/8** selects two values, alpha=1/4 and beta=3/8.
**VALUE KVALUE 0 1,1/4** selects values for two **k** vectors, the first
one at a **k** point of symmetry and the second one at a **k** line of
symmetry.
Each value must be given as a ratio of two integers, as shown in the examples.

**VALUE LANDAU p1 [p2]**

The Landau frequency of the image
is selected. This command affects the data displayed
by **DISPLAY IMAGE**, **DISPLAY IRREP**, and **DISPLAY ISOTROPY**.
The parameters, p1 and p2, are numbers representing the Landau frequency
of an image (the number of independent third-degree invariants).
If they are both present,
then Landau frequencies p1 through p2 are selected. If only p1 is
present, then only Landau frequency
p1 is selected.

**VALUE LATTICE p1 [p2]**

When **DISPLAY PARENT** is used, the Bravais lattices of the space group
are selected. When **DISPLAY ISOTROPY** or **DISPLAY ISOTROPY COUPLED**
is used, the Bravais lattices
of the isotropy subgroup are selected.
The parameters, p1 and p2 are lattices. If they are both present, then
lattices p1 through p2 are selected (using the order shown in the
table below). If only p1 is present,
then only lattice p1 is selected.
The lattices are denoted by a symbol, using either
the Schoenflies notation or the Pearson notation (see table below).
For example, **VALUE LATTICE TI** and **VALUE LATTICE Q-V** both
select the body-centered tetragonal lattice.

Lattice | Symbols | Lattice | Symbols | ||
---|---|---|---|---|---|

1. triclinic | T | AP | 8. primitive tetragonal | Q | TP |

2. primitive monoclinic | M | MP | 9. body-centered tetragonal | Q-V | TI |

3. base-centered monoclinic | M-B | MC | 10. Trigonal | RH | HR |

4. primitive orthorhombic | O | OP | 11. Hexagonal | H | HP |

5. base-centered orthorhombic | O-B | OC | 12. primitive cubic | C | CP |

6. body-centered orthorhombic | O-V | OI | 13. face-centered cubic | C-F | CF |

7. face-centered orthorhombic | O-F | OF | 14. body-centered cubic | C-V | CI |

**VALUE LATTICE PARAMETER p1 p2 p3 p4 p5 p6**

The lattice parameters are selected. The parameters p1 through p6
are the values of a,b,c,alpha,beta,gamma, respectively. a,b,c
are the lengths of the 3 basis vectors **a**,**b**,**c** of the conventional
lattice, alpha is the angle between **b** and **c**, beta is the angle
between **a** and **c**, and gamma is the angle between **a** and **b**.

**VALUE LIFSHITZ p1 [p2]**

The Lifshitz frequency of the irrep
is selected. This command affects the data displayed
by **DISPLAY IRREP** and **DISPLAY ISOTROPY**.
The parameters, p1 and p2, are numbers representing the Lifshitz frequency
of an irrep (the number of times that the vector representation is contained
in the antisymmetrized cube of the irrep).
If they are both present,
then Lifshitz frequencies p1 through p2 are selected. If only p1 is
present, then only Lifshitz frequency
p1 is selected.

**VALUE MAXIMAL p1**

When **DISPLAY ISOTROPY** is used, **VALUE MAXIMAL YES** selects maximal
isotropy
subgroups and **VALUE MAXIMAL NO** selects subgroups which are not maximal.
An isotropy subgroup is maximal when it is not a subgroup of any other
isotropy subgroup for the same irrep.

**VALUE NORMAL p1 p2 p3**

This command affects the data displayed by **DISPLAY ISOTROPY** when
one of the **SHOW TWIN** commands is used.
This command selects the orientation of the plane between a domain pair.
p1 p2 p3 are the Miller indices (hkl) of the plane. All three
numbers must be integers. Note that if the primitive labeling of vectors
is selected by the **LABEL VECTORS PRIMITIVE** command,
these Miller indices may not have
their usual meaning.

**VALUE ORDER p1 [p2]**

The orders of the image
are selected. This command affects the data displayed
by **DISPLAY IMAGE**.
The parameters, p1 and p2, are numbers representing the order of an image
(number of distinct matrices in the image group). If they are both present,
then orders p1 through p2 are selected. If only p1 is
present, then only order p1 is selected.

**VALUE ORIGIN p1**

The origin of a subgroup is selected. This command affects the data
displayed by **DISPLAY DIRECTION**. p1 is the position of the origin,
denoted by three numbers separated by commas. The
three numbers are coordinates in terms of the basis
vectors of the lattice of the parent space group.

**VALUE PARENT p1 [p2]**

The parent space groups are selected. This command affects the
data displayed by **DISPLAY PARENT**, **DISPLAY INVARIANTS**,
**DISPLAY DISTORTION**,
**DISPLAY IRREP**, **DISPLAY ISOTROPY**, **DISPLAY ISOTROPY COUPLED**,
and **DISPLAY KPOINT**.
The parameters, p1 and p2, are space groups.
If they are both present, then space groups p1 through p2
are selected. If only p1 is present, then only space group p1
is selected. The space groups can be denoted by a number or by a symbol,
using either the Schoenflies or international notation (either short or full
symbol). For example,
**VALUE PARENT 124** refers to space group #124 (D^{2}_{4h} or
P4/mcc or P4/m2/c2/c). This command could have also been
entered as **VALUE PARENT D4H-2** or **VALUE PARENT P4/MCC** or
**VALUE PARENT P4/M2/C2/C**. Note that since parameters are delimited
by space characters, they should not contain any space characters themselves.
In the international notation, bars over
numbers are denoted by a preceding minus sign (eg., **P-3C1** for P-3c1)
and subscripts are denoted by a preceding underline character (eg.,
**P4_2/MCM** for P4_{2}/mcm).

**VALUE POINTGROUP p1 [p2]**

When **DISPLAY PARENT** is used, the point groups of the space group
are selected. When **DISPLAY ISOTROPY** or **DISPLAY ISOTROPY COUPLED**
is used, the point groups of
the isotropy subgroup are selected.
The parameters, p1 and p2 are space groups. If they are both present,
then point groups p1 through p2 are selected (using the order shown in
the table below). If only p1 is present, then only point group p1 is
selected.
The point groups are denoted by a symbol, using either the Schoenflies
or international notation (see table below). For example, **VALUE POINTGROUP OH** and **VALUE POINTGROUP M-3M** both refer to the
point group O_{h} or m-3m. A bar over a number is denoted by a preceding
minus sign (eg., **-4** for "4 bar").

1. C1 | 1 | 9. C4 | 4 | 17. C3I | -3 | 25. C6V | 6MM |

2. CI | -1 | 10. S4 | -4 | 18. D3 | 32 | 26. D3H | -62M |

3. C2 | 2 | 11. C4H | 4/M | 19. C3V | 3M | 27. D6H | 6/MMM |

4. CS | M | 12. D4 | 422 | 20. D3D | -3M | 28. T | 23 |

5. C2H | 2/M | 13. C4V | 4MM | 21. C6 | 6 | 29. TH | M3 |

6. D2 | 222 | 14. D2D | -42M | 22. C3H | -6 | 30. O | 432 |

7. C2V | MM2 | 15. D4H | 4/MMM | 23. C6H | 6/M | 31. TD | -43M |

8. D2H | MMM | 16. C3 | 3 | 24. D6 | 622 | 32. OH | M-3M |

**VALUE POSITION p1 p2 p3 **

The coordinates of a point are selected.
This command affects the data displayed
by **DISPLAY DISTORTION** when **SHOW LOCAL** is used.
The coordinates are assumed to be in terms of the basis vectors of the lattice,
using the setting chosen at the time when **DISPLAY DISTORTION** is used.
Each coordinate must be given in terms of rational numbers. For example,
**1/2 1/2 1/2** would denote the coordinates at
(1/2,1/2,1/2).
Also, irrational coordinates can be denoted by **x**, **y**, or **z**.
For example, **x 1/2-x 0** would denote coordinates at
(x,1/2-x,0), where x is an arbitrary irrational number.
The coordinates **x y z** would denote a general point.

The command **VALUE POSITION** also affects the data displayed by
**DISPLAY ISOTROPY** when one of the **SHOW TWIN** commands are used.
In this case, a point on the plane between the pair of domains is selected.

**VALUE RANK p1**

The rank of a macroscopic
tensor is selected. This command affects the data displayed
by **DISPLAY DISTORTION** when **SHOW MACROSCOPIC** is used.
p1 shows the indices of the tensor in numerical order. For example,
p1=**1234** indicates a tensor of rank 4. Indices to be symmetrized are
enclosed by square brackets. For example, p1=**[12]** indicates
a totally-symmetrized tensor of rank 2. Indices to be antisymmetrized are
enclosed by curly brackets. For example,
p1=**1{23}** indicates a tensor of rank 3 which is
antisymmetric with respect to the 2nd and 3rd indices.
The value of the rank cannot exceed 6.

**VALUE SIZE p1 [p2]**

The relative sizes of the primitive unit cells of the parent space group
and the isotropy subgroup
are selected. This command affects the data displayed
by **DISPLAY ISOTROPY** and **DISPLAY ISOTROPY COUPLED**.
The parameters, p1 and p2, are numbers representing relative size.
If they are both present,
then sizes p1 through p2 are selected. If only p1 is
present, then only size p1 is selected.

**VALUE SUBGROUP p1 [p2]**

The isotropy subgroup space groups are selected. This command affects the
data displayed by
**DISPLAY ISOTROPY** and **DISPLAY ISOTROPY COUPLED**.
The parameters, p1 and p2, are space groups.
If they are both present, then space groups p1 through p2
are selected. If only p1 is present, then only space group p1
is selected. The space groups can be denoted by a number or by a symbol.
See **VALUE PARENT** for an explanation of the symbols
used.

**VALUE TYPE**

The irrep type (1,2,3) is selected. This command affects the data displayed by
**DISPLAY IRREP** and **DISPLAY IMAGE**.
A type-1 irrep is real. A type-2 irrep is complex but its
characters are real. A type-3 irrep is complex and its characters are also
complex.

**VALUE WYCKOFF p1 [p2 ...]**

Wyckoff positions are selected. This command affects the data displayed by
**DISPLAY PARENT**, **DISPLAY IRREP**, and **DISPLAY DISTORTION**.
The parameters p1,p2,... are the single-letter
symbols of the positions, as given in International Tables.

**VALUE WYCKOFF IRREP p1 [p2 ...]**

Irreps of the point group of a Wyckoff position are selected. This command
affects the data displayed by **DISPLAY PARENT**, **DISPLAY IRREP**,
and **DISPLAY DISTORTION**.
The parameters p1,p2,... are the irrep symbols, using the convention of
Bradley and Cracknell.

**VALUE WYCKOFF XYZ p1 p2 p3**

The parameters x,y,z of the Wyckoff position are selected. p1,p2,p3
are the values of x,y,z, respectively.