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**NOMENCLATURE, SYMBOLS AND CLASSIFICATION OF
THE SUBPERIODIC GROUPS**

This is a report presented to the Commission
on Crystallographic Nomenclature of the International Union of
Crystallography.
An announcement of this report is publication #62: "Nomenclature,
Symbols,
and Classification of the Subperiodic Groups," by V. Kopsky and D.B.
Litvin,
Acta Crystallographica A49 594 (1993).

This material is based on work supported by the
National Science Foundation under grant DMR-9100418.

Download IUCr
Report.pdf
(293 KB)

**TENSOR DISTINCTION OF NON-FERROELASTIC
MAGNETOELECTRIC
DOMAIN PAIR**

Of the 380 classes of magnetic completely
transposable
twin laws, 141 classes are non-ferroelastic completely transposable
magnetoelectric
twin laws. For each of these classes of domain pairs we give the
tensor distinction for physical property tensors of the type V,
aeV,
[V^{2}], aeV^{2},V[V^{2}], aeV[V^{2}],
V^{3} and ae[V^{3}] , where V denotes a polar
vector
tensor and "a" and "e" rank zero tensors that change sing,
respectively,
under time inversion and spatial inversion. The file is in PDF format.
See publication #64: "Non-ferroelastic Magnetoelectric Twin Laws" by
D.B.
Litvin, V. Janovec, and S.Y. Litvin, Ferroelectrics (1994) 162, 275-280.

This material is based on work supported by the
National Science Foundation under grants DMR-9100418, DMR-9305825.

Download TDNFMEDP.zip (249 KB)

**MAGNETIC COMPLETELY TRANSPOSABLE TWIN LAWS
AND TENSOR DISTINCTION**

PDF files of publication #66: "Magnetic
Completely Transposable Twin Laws and Tensor Distinction" by D.B.
Litvin, S.Y. Litvin, and V. Janovec, Acta Cryst. (1995) A51, 524-529.
along
with the unpublished tables of the 380 classes of magnetic completely
transposable
twin laws.

This material is based on work supported by the
National Science Foundation under grants DMR-9100418, DMR-9305825, and
INT-8922251.

Download MCTTWs.zip
(146 KB)

**NON-MAGNETIC TWIN LAWS**

For a phase transition between a high symmetry phase of non-magnetic
point group symmetry G and low symmetry phase of non-magnetic point
group
F, this program calculates:

The coset and double coset decomposition of the
point group G with respect to the point group subgroup F.

Indexes the domain states S(i) which arise in such
a transition.

Calculates the point group symmetry F(i) of each
domain state.

Calculates the permutations of the domain states
S(i) under the action of elements g of the point group G.

Calculates all domain pair {S(i),S(j)} in each class
of domain pairs.

Calculates a representative domain pair {S(1),S(j)}
from each class of domain pairs.

Calculates for each representative domain pair its
symmetry group J(1,j) and its twinning group K(1,j).

Calculates the domain pair {S(1), gS(1)} and its
symmetry and twinning groups.

Calculates the symmetry and twinning groups of an
arbitrary domain pair {S(i),S(j)}.

See publication #68: "Non-Magnetic Twin Laws" by J. Schlessman and
D.B. Litvin, Acta Cryst. (1995) A51, 947-949.

This material is based on work supported by the
National Science Foundation under grant DMR-9305825.

Download twinlaws.zip (63KB)

**BRIEF PRACTICAL GUIDE TO THE SCANNING TABLES**

If a crystal is transected by a plane then the subgroup of all elements
of the space group of the crystal which leaves the plane invariant is a
layer group. The layer groups corresponding to all planes of a
crystallographic
orientation for all space groups are tabulated in the scanning tables
to
be published in the forthcoming volume of the International Tables for
Crystallography: Volume E: Subperiodic Groups by V. Kopsky and D.B.
Litvin.
This is my personal guide to interpreting the information in the
scanning tables.

This material is based on work supported by the
National Science Foundation under grant DMR-9305825 and DMR-9510335.

Download
Guide.pdf(104
KB)

This program generates VRML General Position/Symmetry Diagrams of the 80 Layer Groups. See publication #74: "VRML General Position / Symmetry Diagrams of the 80 Layer Groups," by D.K. Tshudy and D.B. Litvin (Journal of Applied Crystallography, 31 973 (1998). Needed to view the diagrams are a web browser with a VRML viewer plug-in (e.g. Netscape with Cosmo). An Adobe Acrobat readable

This material is based on work supported by the National Science Foundation under grants DMR-9510335 and DMR-9722799.

Download LG1-52.zip (1227 KB) Download LG53-80.zip (1392 KB) Download Symbols.pdf (43 KB)

**TENSOR DISTINCTION OF DOMAINS IN FERROIC
CRYSTALS**

This supplementary material contains (1) a listing of the 247
classes of non-magnetic ferroic phase transitions from G to F. For one
transition in each class we give G, F, gij, and the twinning group
Kij
(2) the distinct double coset classes of non-magnetic domain pairs (3)
the 137 tensor classes of non magnetic domain pairs and (4) for 22
tensor
types and each of the 139 tensor classes listed is if the tensor type
can
or can not distinguish between the domains of domain pairs belonging to
the tensor class. See publication #77: Tensor Distinction of Domains in
Ferroic Crystals," by D.B. Litvin, Acta Crystallographica A55 884-890
(1999).

This material is based on work supported by the
National Science Foundation under grant DMR-9722799.

Download the paper.pdf (102KB)

Download Supplementary
Material.pdf
(319 KB)

**MAGNETIC SUBPERIODIC GROUPS**

This file contains a short introduction to magnetic subperiodic groups.
Symbols for the types of these groups are constructed in analogy to the
Opechowski-Guccione symbols for magnetic space groups. Tables are
given that list one group from each type. Each group is specified not
only
by its symbol but also by explicitly listing the coset representatives
of the coset decomposition of the group with respect to its
translational
subgroup. See publication #78: "Magnetic Subperiodic Groups," by D.B.
Litvin,
Acta Crystallographica (1999) A55 963-964.

This material is based on work supported by the
National Science Foundation under grant DMR-9722799.

Download this
paper.pdf
(237 KB)

Download
Tables of Magnetic Subperiodic Groups.pdf(279
KB)

**SUBPERIODIC GROUPS ISOMORPHIC TO FACTOR
GROUPS
OF REDUCIBLE SPACE GROUPS**

This pdf file contains the listings of the
subperiodic
groups isomorphic to factor groups of reducible space groups. See
publication
#79 "Subperiodic Groups Isomorphic to Factor Groups of Reducible Space
Groups," D.B. Litvin and V. Kopsky, Acta Crystallographica (2000) A56
370-374.

This material is based on work supported by the
National Science Foundation under grant DMR-9722799.

Download the paper.pdf(244
KB)

Download
79 Supplementary Material.pdf (687 KB)

**PROPERTIES OF THE MAGNETIC POINT GROUPS**

This program gives the notation, elements, subgroups, centralizers,
normalizers, normal subgroups, and coset and double coset
decompositions
of the magnetic point groups. See publication #82 "Coset and Double
Decomposition
of the Magnetic Point Groups," by J. Schlessman and D.B. Litvin, Acta
Crystallographica
(2001) A57 114-115.

This material is based on work supported by the
National
Science Foundation under grant DMR-9722799.

Download the paper.pdf
(203KB)

Download the program.zip
(390
KB)

**MAGNETIC SPACE GROUP TYPES**

The interpretation of Opechowski-Guccione symbols for
magnetic space group types is based on coordinate triplets given in the
now
superceded *International Tables for
X-Ray Crystallography* (1952). Changes to coordinate triplets in the
*International
Tables for Crystallography* (1983) lead to misinterpretations of
these
symbols. We provide here a list of Opechowski-Guccione symbols for the
1651
magnetic space group types with their original definitions given
independent of
the *International Tables*. See publication #86
"Magnetic Space Group Types," Acta Crystallographica (2001) A57 729-730.

This material is based on work
supported by the National Science Foundation under grant DMR-0074550.

Download
the paper.pdf (204 KB)

Download Supplementary
Material.pdf ( 2.9 MB)

**SYMMETRY RELATIONS OF MAGNETIC DOMAIN PAIRS
( TWIN LAWS )**

Symmetry relationships between two simultaneously observed domain
states
(*domain pair*) are used to determine physical properties which
can
distinguish between the observed domains. A computer program
generates
these symmetry relationships, in terms of magnetic point groups,
i.e. we determine and tabulate all possible
*magnetic symmetry groups*
and *magnetic twinning groups* of domain pairs. See publication
#87
" Symmetry Relations of Magnetic Domain Pairs," by J. Schlessman and
D.B.
Litvin, Acta Crystallographica, A57 731 - 732 (2001).

This material is based on work supported by the
National Science Foundation under grants DMR-9722799 and No.
DMR-0074550.

Download this paper.pdf (226 KB)

Download this program.zip (203
KB)

**DOMAIN AVERAGE ENGINEERING**

In a domain average engineered sample of a multidomain
ferroic, the sample is divided into a very large number of domains,
representing
m domain states where m is less than the theoretically allowed maximum
number n of domain states. The response to external fields is described
by tensorial properties averaged over all the involved domain states.
We
have developed a program to classify subsets of m < n domain states
which can arise in a ferroic phase transition. We calculate properties
of these subsets of domain states, including the symmetry of the
subset,
the subset domain polarizations and magnetizations, and, if they exist,
the poling directions which gives rise to the subsets of domain states.
See Publication #90 " Domain Average Engineering in Ferroics," by B.
Shaparenko,
J. Schlessman, and D.B. Litvin, Ferroelectrics, 269 9 - 14 (2002).

This material is based on work supported by the
National Science Foundation under grant No. DMR-0074550.

Download this paper.pdf (40 KB)

Download this program.zip (390 KB)

**MAGNETIC SUBPERIODIC GROUPS: VRML GENERAL
POSITION
DIAGRAMS**

VRML general position diagrams for the 31 magnetic frieze groups,
394 magnetic rod groups, and 528 magnetic layer groups are
given.
These diagrams are viewable in a web brouser with a VRML plug-in,
e.g. Cortona
VRML Client or a VRML viewer, e.g. VRMLview
. (The NIST
website
lists many plug-ins, applets, and programs to view VRML files on
Windows,
Linux, and Mac operating systems.)

This material is based on work supported by the
National Science Foundation under grant No. DMR-0074550.

Download Frieze and Rod.zip (10.4
MB)

Download Layer.zip (11.2 MB)

Download Documentation (260
KB)

SPACE-GROUP SCANNING TABLES

Due to page
limitations, in Volume E: "Subperiodic Groups" of the International
Tables for Crystallography not all scanning tables were explicitly
given. Instead,
auxiliary tables were given providing information from which to
construct the additional
tables. We have constructed these additional tables and present them here

This material is
based on work supported by the
National Science Foundation under grant No. DMR-0074550.

Download
the paper (101KB)

Download the additional
scanning tables (11.1MB)

MAGNETIC SUBPERIODIC
GROUPS (Electronic Book)

Tables of properties of the magnetic subperiodic groups: The content
and format is similar to that on non-magnetic subperiodic groups and
space groups given in the International Tables for Crystallography.
Additional content for each group type includes a diagram of
general positions with corresponding general magnetic moments, Seitz
notation used as a second notation for symmetry operations, and General
and Special Positions listed with the corresponding magnetic moments
allowed by symmetry.

This material is based on work supported by the National Science Foundation under grants DMR-9722799 and DMR-0074550.

Download the paper (645 K)

Download
Read Me.pdf ( 81KB)

Download Magnetic
Subperiodic Groups.pdf ( 14.6MB)

Download The Rod Groups.pdf (13.2MB)

Download The Layer Groups.pdf
(13.9MB)

VRML general position diagrams for the 1502 non-cubic magnetic space groups are given. These diagrams are viewable in a web brouser with a VRML plug-in, e.g. Cortona VRML Client or a VRML viewer, e.g. VRMLview . (The NIST website lists many plug-ins, applets, and programs to view VRML files on Windows, Linux, and Mac operating systems.) Examples of individual magnetic space group VRML General Position Diagrams are given below. The complete set of diagrams, on CD, is available on request, or can be downloaded from the Non-Cubic Magnetic Space Group General Position Diagram download page.

This material is based on work supported by the National Science Foundation under grant No. DMR-0074550.

Individual Examples:

Download VRML diagram 57.10.467 P2abcm (363 KB)

Download VRML diagram 72.6.635 Iba'm' (561 KB)

Download VRML diagram 89.9.755 P2c4'22' (588 KB)

Download VRML diagram 130.8.1095 P4'/n'cc' (549 KB)

Download VRML diagram 169.1.1344 P61 (293 KB)

Download VRML diagram 193.5.1489 P63'/mcm' (1.2 MB)