Title/Axes

Dialog Box: Title/Axes [ Input1 Menu]

The title may have up to 80 characters of identifying information.

The axial system determines the type of coordinate axes for crystal faces (if present) as well as atoms. If you are drawing a molecule you will probably want to choose Unit Cartesian axes unless the symmetry is trigonal or hexagonal - see sections 5 and IV-6 of the instructions.

If you choose a crystal system you must supply the axis lengths and interaxial angles appropriate to the crystal system you selected. Axis lengths should be in Angstroms, and angles in degrees and fractions (not minutes and seconds). If you are entering a new structure, the unique angle for the monoclinic system is always called beta at this point.

However, in the Symmetry options the selection of space or point group may change this, and if you return to the Title/Axes dialog the correct angle should be shown. If the angles are still incorrect you can use triclinic axes.

Although standard crystallographic nomenclature gives the same letter (usually a) to symmetry-equivalent axes, after the initial input ATOMS may call all axes, whatever the

system, "a, b, and c" and angles "Alpha", "Beta" and "Gamma".

If the Print title on plot box is checked, the title will be shown in the lower left on all display and output (of the structure, not the Powder or Precession patterns). If the Scale box is checked, the lettering on print and file output will be scaled to approximately the same relative size compared to the drawing as it is on the screen.

Use PostScript font. This allows you to enter a character string for PostScript fonts supported by a PostScript printer if such fonts do not appear in the standard system font dialog called up by the Font button. This character string usually specifies the weight (normal, bold) and slant (italic, oblique) of the font, but not the size, which is specified in the Font dialog. Certain PostScript typefaces are standard, and should be present on most PostScript printers.

3.2.2.2 Symmetry

Dialog Box: Symmetry [ Input1 Menu]

The authority and source of information for crystal symmetry is normally the

International Tables for X-ray Crystallography. However, any point- or space-group symmetry may be used for the atoms. There are several options for selecting or entering symmetry information.

Space group from table - Choose a space group by symbol or number.

Point group from table - Choose a crystallographic point group.

Cartesian matrices - Use non-standard or non-crystallographic point symmetry.

Custom point or space group - Enter all the individual operators.

Use no symmetry - Use no symmetry at all. Check Crystal to enable lattice translations - the space group will be P1.

Except for the last option, Use no symmetry, each choice calls up a sub-dialog.

3.2.2.2.1 Space-Group Symmetry, Basic Tab

Dialog Box: Symmetry - Space Group from Table: Basic Tab [ Symmetry dialog] Starting with V4.0 of ATOMS, space-group symmetry is obtained using licensed excerpts from the SGInfo program of Ralf Grosse-Kunstleve. This allows more complete selection of alternate orientations and origins than in previous versions of ATOMS, and also Shubnikov black-and-white symmetry.

You can specify the space group in any of three ways: 1) the Hermann-Maughin (H-M)

or International symbol; 2) the Hall symbol (S.R. Hall: Acta Cryst., A37, 517, 1981); or 3) the number of the group in the International Tables for X-ray Crystallography.

International Tables Volume. You have the option of using the older version of the Tables (called the Second Edition: various revisions and reprints from 1952 to 1979) in which the symmetry information was in Volume I, or the newer version (1983 onwards) in which it is in Volume A. The principal difference between the two versions is that in the older one the unique axis of a monoclinic group is assumed to be the c-axis, whereas in the newer one it is assumed to be the b-axis. Thus entering the symbol P2/m gives two different orientations depending on the volume selected. You can always specify the orientation by entering the long form of the symbol, i.e. P 2/m 1 1, P 1 2/m 1 or P 1 1 2/m.

The H-M symbol can be typed into the edit box in either short form or long form, with or without spaces between positions. However, it is usually safer to select the symbol from the list box at the bottom, which gives the standard-form symbols for all the space-groups. Clicking the Select button copies the relevant data to the edit boxes at the top; it does not actually generate the symmetry. Symmetry generation is done after you click OK - this may take a few seconds. If the space group you select does not appear to be

consistent with your choice of axes, a warning box appears, but in most cases consistency is not required. However, if you selected trigonal rhombohedral axes in the Title/Axes dialog, only a rhombohedral space group may be selected. This is done by adding :R to the end of the symbol in the case of H-M symbols, or asterisk (*) in the case of Hall symbols. This is a change from versions of ATOMS previous to V4.0, in which the orientation of the space group was automatically determined from the Title/Axes dialog.

If you select the rhombohedral setting and then switch to the Custom symmetry option, the lattice type will be P; it will be R if the axes are hexagonal.

Origin of coordinates. In the International Tables, 24 space groups in the

orthorhombic, tetragonal and cubic systems are given with a choice of origin: 1) not on a center of inversion or 2) on a center of inversion. These two origins are selected by adding :1 or :2 respectively to the end of the H-M symbol or the number. Although the origin on the center is second in the Tables and in the list, if the number is omitted this will be the default. This difference in origin is explicit in the Hall symbol, and other choices of origin may be specified for any space group with the Hall symbol.

---Shubnikov Symmetry. You can use ---Shubnikov black-and-white symmetry to show

magnetic or other properties of crystals. If you choose this option you must enter at least some of the relevant parameters in the Shubnikov Tab. You enter the Shubnikov space-group symmetry using modified versions of either the H-M or Hall symbols. After entering the Shubnikov symmetry in the Basic Tab, you can check the Shubnikov lattice type and basis operations in the Shubnikov Tab after clicking OK or Apply. The H-M symbol is modified in the standard way, by a) adding a subscript (actually a postscript) to

the lattice symbol; or b) adding a prime or apostrophe to the individual "positions" or basis operations in the symbol. To enter a Shubnikov symbol you must separate the lattice symbol and the individual positions by at least one space or underscore. The entries in the list box already have these separations, so it is advisable to select one of these and then edit it. The Hall symbol is modified in a similar way, but instead of using a prime you must use the "^" character. An initial minus sign on the Hall symbol signifies a center of inversion - if you want to assign Shubnikov inversion to this center, add "^" to the lattice symbol, not to the minus sign.

Standard H-M Shubnikov lattice symbols use both lower- and upper-case subscripts A, B, C for "color" face centering, and a, b, c for edge centering. In ATOMS a capital letter will always indicate face centering, and either lower-case a, b, c or x, y, z (or X, Y, Z) will indicate edge centering. Note that there is little checking for self-consistency, either for input through the symbol or explicit operators in the Shubnikov Tab. The user is responsible for entering a valid Shubnikov space group.

Shubnikov inversion is considered to apply to the spin of a magnetic atom, rather than directly to the vector which shows the magnetic direction. This means that improper operations, including a center of inversion, planes of symmetry and improper (bar) axes, result in inversion or reversal of the magnetic spin vector when the operation is not primed or Shubnikov, and no inversion when the operation is primed or Shubnikov. Of course, the resulting spin-vector orientation depends also on the orientation of the spin with respect to the symmetry operator - when the vector is parallel to an axis or plane the result is completely different from when it is perpendicular. ATOMS can apply Shubnikov symmetry in this way, or in certain other ways - see the Shubnikov Tab.

Magnetic or other Shubnikov symmetry normally involves entries in three different places:

1) The Space Group from Table symmetry option (this dialog), including the Shubnikov Tab;

2) The Atomic Vectors dialog (Input1 menu), to set the display parameters of the vectors; and

3) the Revise Atom dialog, Vector Tab for individual input atoms, to set the orientation of the vectors on the atoms.

---Molecules. It may sometimes be desirable to use the Space Group symmetry option for a molecule rather than the Point Group option because in some point groups you can select different orientations of the symmetry operators with respect to the coordinate axes by choosing the operations from different space groups. Space-group operations are applicable to point groups, provided there are no translations - that is, you cannot use space groups with screw axes, glide planes, or non-primitive lattices. For example, in number 111, P42m - D2d1 the mirror planes are 45 degrees from the structure axes,

whereas in no. 115, P4m2 - D2d5, the mirror planes are parallel to the axes. If you choose the Point Group symmetry option and enter the point group 4m2 - D2d, the first of these orientations, as in number 111, will always be used. These two space groups actually differ in other ways than the 45 degree rotation, but this is irrelevant if the

operations are used without lattice translations. The choice between the two space groups depends on the relative orientation of coordinate axes and symmetry elements. In this case, if an atom lies on a 2-fold axis it will belong to a set of four (rather than eight if it does not lie on any symmetry elements). For no. 111, such atoms will have coordinates like x,0,0, whereas for no. 115 they will be like x,x,0.

In the trigonal, hexagonal and tetragonal systems several space groups have alternate orientations at 30 or 45 degrees from each other as in the case of D2d. If the symmetry for a molecule is specified with the Point Group option, the "standard" orientation is generated. One may access the alternate orientation by the Space Group option and giving the alternate space group as follows (a B before a number indicates a "bar" or inversion axis:

Standard Orientation Alternate Orientation

42m - D2d PB42M (no. 111) PB4M2 (no. 115)

32 - D3 P321 (no. 150) P312 (no. 149)

3m - C3v P3M1 (no. 156) P31M (no. 157)

32/m - D3d PB3M1 (no. 164) PB31M (no. 162)

6m2 - D3h PB6M2 (no. 187) PB62M (no. 189)

You can also use this symmetry option to select a non-standard setting for monoclinic or orthorhombic point groups as

discussed in the previous section. For example, you can cause the unique axis of groups 2 - C2, m - Cs or 2/m - C2h to be either a, b or c (the standard setting for ATOMS is unique axis b). You can also cause the 2-fold axis of mm2 - C2v to be parallel to any of the three structure axes. If you do choose this option, using space-group operations for a molecule, be sure that the space group has no screw axes or glide planes, and has a primitive Bravais lattice.

3.2.2.2.2 Space-Group Symmetry, Shubnikov Tab

Dialog Box: Space-Group Symmetry: Shubnikov Tab [ Symmetry Dialog]

ATOMS uses several tools for description and depiction of magnetic structures, loosely gathered in the "Shubnikov" tab.

These tools include 1) constant vector orientation for all atoms in a site; 2) full Shubnikov symmetry in that the vectors themselves obey the full specified symmetry; 3) Shubnikov

symmetry with vector orientations remaining constant except for inversion; and 3) lattice inversion or magnetic supercells independent of Shubnikov symmetry.

Magnetic or other Shubnikov symmetry may involve entries in three different places: 1) The Space Group from Table symmetry option, including the Shubnikov Tab (this dialog); 2) The Atomic Vectors dialog (Input1 menu), to set the display parameters of the vectors; and 3) the Revise Atom dialog, Vector Tab for individual input atoms, to set the orientation of the vectors on the atoms.

In the upper part of this dialog, the methods of Display and Application of the Shubnikov symmetry are selected.

Display:

1) Labels +/-. In this mode, only the two "colors", signified by the +/- symbols, are shown. Select the size and other properties of the symbols with the dialog called up by the Labels button. Caution : this option may not be suitable for showing Shubnikov magnetic symmetry. Whether or not an atomic vector is reversed or inverted by the combination of ordinary and Shubnikov symmetry depends on the orientation of that vector with respect to the symmetry operator. Most published diagrams of magnetic structure using black and white or + and - atoms are not actually showing the Shubnikov inversions, they are showing symbolically the reversals of spin vectors which are typically in special orientations. If you want to show arbitrary black/white inversion which does not conform to Shubnikov symmetry, you can simple draw up a normal structure, convert

Generated to Input (Transform menu) and recolor individual atoms as desired.

2) Vectors - reversal only. In this mode, each input atom has a vector, but the orientation is constant except that the direction may be reversed by the Shubnikov operators. This is not what most workers seem to understand by Shubnikov symmetry applied to atomic spin vectors, but it can be useful in illustrating many magnetic

structures or in non-magnetic applications. Especially, it can be used to align all atoms in a particular site in the same direction, regardless of space-group symmetry. To do this, you should also uncheck the Shubnikov box in the Space-Group Symmetry: Basic Tab.

Virtually any commensurate magnetic structure can then be illustrated by converting Generated to Input (Transform menu) and reversing or otherwise reorienting the vectors manually. When in the Input=generated mode, clicking on a magnetic atom brings up a dialog which has a button for vector reversal or inversion.

3) Vectors - full symmetry. In this mode, the orientation of the vector on each generated atom is subject to all symmetry operations, both standard and Shubnikov reversal.

Application :

1) Magnetic. Shubnikov inversion is considered to apply to the spin or electric current loop of a magnetic atom, rather than directly to the vector which shows the magnetic direction. This means that improper operations, including a center of inversion, planes of symmetry and improper (bar) axes, result in inversion or reversal of the magnetic spin vector when the operation is not primed or Shubnikov, and no inversion when the operation is primed or Shubnikov. Of course, the resulting spin-vector orientation depends also on the orientation of the spin with respect to the symmetry operator - when the vector is parallel to an axis or plane the result is completely different from when it is perpendicular.

2) Dipole or Black/White. In this case the inversions are applied directly to the vectors, not to the spin or electric current loops. Thus improper operations result in no inversion or reversal of the vector when the operation is not primed, and inversion when the operation is primed. This type of symmetry could be applied to atomic dipoles, or to displacements, for example.

See the table below for the various combinations of Display and Application.

Set the overall properties of atomic vectors with the Vectors dialog called up by the Vectors button; set the orientation of the vector for each input atom in the

Revise Atom: Vector Tab. Whether each input atom has a Shubnikov reversal at all is also set in the Revise Atom: Basic Tab. In general, not every input atom is Shubnikov or even can be Shubnikov in display modes 1) and 3). The orientation of vectors in special positions may be restricted. Black-white reversal itself may be forbidden in some special positions. Such positions should be identified during the calculation and marked as non-Shubnikov.

Shubnikov Operators. This section of the dialog summarizes the information obtained from the Shubnikov symbol in the Basic Tab. The possibilities for the Shubnikov lattice type or Lattice centering are lower-case a, b, or c, indicating translation reversal in the respective axis direction, or S, indicating reversal on all three directions; or upper-case A, B, or C indicating a Shubnikov centering of the respective faces, or I, indicating

Shubnikov body centering.

For non-translational Shubnikov symmetry, the possibilities are Inversion, and either Rotation parallel to, or Reflection perpendicular to any of the three axis directions. If present, rotation and reflection are indicated by capital letters A, B and/or C. The face diagonal [110] direction, indicated by AB, is also possible in high-symmetry crystals. The body diagonal [111] direction is not a possible Shubnikov operator orientation as it can only have a three-fold axis.

Note that there is little checking for self-consistency of Shubnikov operators. The user is responsible for entering a valid Shubnikov space group.

Table showing possibilities for Display and Application of Shubnikov symmetry

+/- Reversal Only Full Symmetry

Magnetic bc bc abc

Dipole bd bd abd

a) Operate on vector with ordinary space-group symmetry

b) Proper operators (lattice and non-bar axes) - reverse if primed, do not reverse if unprimed

c) Improper operators (inversion, reflection, bar axes) - reverse if unprimed, do not reverse if primed

d) Improper operators (inversion, reflection, bar axes) - do not reverse if unprimed, reverse if primed

Reverse means to change vector direction by 180 degrees, or to change + to - or vice-versa. The ordinary space-group symmetry operations are always applied to the positions of the atoms.

Lattice Inversions or Magnetic Supercell. This option is not actually part of Shubnikov symmetry, but it offers a simple means of describing many magnetic structures, either by itself or in combination with Shubnikov operators, often without changing the unit cell and overall symmetry from what describes the non-magnetic structure.

Checking one of the boxes causes all magnetic vectors to reverse with each translation on that axis. This normally results in a doubled magnetic axis or cell edge in that direction.

When more than one lattice inversion is selected, the operations are applied successively.

For example if there is inversion on a and b axes, the 100 and 010 unit cells have inversion, but the 110 unit cell does not.

If the unit cell is non-primitive you can use inversion on either the Bravais axes or the primitive axes, but not both.

Note that the Default Unit Cell boundary option uses the non-magnetic Bravais axes, not the doubled magnetic axes. To show the reversals adequately it may be necessary to select the -1 to 1 inclusive option in the Default Unit Cell boundary option, or to use the

Translation Limits boundary option.

This option is definitely not the same as using non-primitive Shubnikov lattices, and is apparently equivalent to specifying a magnetic "wave vector". Compare the samples FCCMAG, FCCMAGR, and FCCFULL_II for different ways of showing Type II FCC (MnO) magnetic structure - the most concise is FCCFULL_II which uses inversions on all three primitive (face-centering) lattice translations, with the full Fm3m X-ray

symmetry of MnO.

symmetry of MnO.

Im Dokument ATOMS for Windows and Macintosh (Seite 62-74)