Input Data

ATOMS requires three types of input data, the dimensions of the unit cell and locations of the unique atoms, the space group symbol, and several operational parameters controlling the type and features of the output data. All versions of ATOMS require the same kinds of data, although the manner in which the user supplies the data varies between the versions. The stand-alone version reads data from an input file, the Tk version obtains the data from Tk widgets, and the CGI version obtains the data from an HTML form. Each of the versions is described in its own chapter. This chapter explains the data types and what ATOMS expects for each one.

Crystallographic Data

The basic unit of crystallographic data is the description of the unit cell. A unit cell is described by its three lattice constants, its three angles, the positions of representative atoms within the unit cell, and the space group of the crystal. The symbolism used to describe space groups is explained in Section

Lattice Constants and Angles

Lattice constants in ATOMS are specified in Ångstroms and angles are specified in degrees. Please note that ATOMS does not understand minutes and seconds of arc at this time. If you have an angle of, say, 87 degrees and 30 minutes, you must specify this in the input file as 87.5 degrees.

It is only necessary to specify the lattice constants and angles which are unique for a given crystal class. For example, in a cubic space group it is only necessary to specify the length of the a lattice constant, because b and c must be the same as a in a cubic space group and all three angles must be 90 degrees. There is a priority among the lattice constants. In the cubic example, if you only explicitly set on lattice constant, it must be a. Explicitly setting only b will confuse ATOMS. There is no harm in explicitly setting all three lattice constants to the same value in the cubic example, but it is unnecessary.

Crystal Classes

The class of a crystal is determined by the shape of its unit cell. The space group is thus the decoration of atoms within a cell of a particular class. There are seven crystal classes, triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. There is one other word used to describe a unit cell shape - rhombohedral. Rhombohedral cells are actually trigonal cells with additional symmetry.

The following table explains the shapes of the seven crystal classes in terms of the lattice constant and angles.

**Table:** Lattice constants for the crystal classes. See Section for details about alternate settings and unique angles besides beta for monoclinic groups, alternate settings of orthorhombic groups, and rotated settings of tetragonal groups. The rhombohedral settings of trigonal groups are explained below.
group	lattice constants and angles
triclinic	$a\ne b\ne c$	and	$\alpha\ne\beta\ne\gamma\ne90^\circ$
monoclinic	$a\ne b\ne c$	and	$\alpha=\beta=90^\circ$ , $\gamma\ne90^\circ$
orthorhombic	$a\ne b\ne c$	and	$\alpha=\beta=\gamma=90^\circ$
tetragonal	$a=b\ne c$	and	$\alpha=\beta=\gamma=90^\circ$
trigonal	$a=b\ne c$	and	$\alpha=\beta=90^\circ$ and $\gamma=120^\circ$
hexagonal	$a=b\ne c$	and	$\alpha=\beta=90^\circ$ and $\gamma=120^\circ$
cubic	a=b=c	and	$\alpha=\beta=\gamma=90^\circ$

Rhombohedral cells are a special case of the trigonal class. They can be specified using the rhombohedral parameters a and alpha or the trigonal parameters a and c. When a rhombohedral space group is specified, ATOMS will check the supplied lattice parameters and do the right thing. There is a functional relationship between the rhombohedral a and alpha and the trigonal a and c. Consult chapter 5 of the first volume of the International Tables of Crystallography (see Chapter

) for details.

Unique Positions

ATOMS requires a list of unique atom positions to fully describe the unit cell of a material. It is important to appreciate the difference between unique positions and the set of positions in the unit cell. In the example of sulphur given in Chapter

, the 'atoms.inp' file contains a list of four unique positions, whereas the unit cell of rhombic sulphur contains 128 atoms. The relationship between the four unique positions and the 128 actual positions is conceptually simple. The space group (see Section

) of the material implies a certain set of symmetry operations. These symmetry operations are applied to each of the unique positions to generate all the actual locations of atoms in the unit cell. The beauty of the notation using a space group symbol and the list of unique positions, and thus the beauty of ATOMS is that it is compact yet complete.

When structures are reported in the crystallographic literature or in a reference source like the Wyckoff tables, only the unique positions are given. And that is all the information needed by ATOMS. The manner in which the list of unique positions is entered is explained for ATOMS in Chapter

and for TkATOMS in Chapter

Shift Vectors

If you browse through the first volume of the International Tables of Crystallography in the part where the symmetry operations for the 230 space groups are spelled out in detail, you will see that there are 25 groups for which the symmetry operations are referenced to a choice of two origins. That is, there are two choices for which center of point symmetry is placed at the position (0,0,0). In the literature, you will find that some authors use one choice of origin and some use the other.

ATOMS has a preference between the two choices for each of these 25 space groups. In each case, ATOMS expects that you give the positions referenced to the origen at centre.^3.1 The unfortunate part of this is that, while ATOMS has a preference for which origin you choose, it has no way of knowing if you have, in fact, chosen the correct origin.

While ATOMS cannot know if you have chosen the correct origin, it does recognize when you use one of the 25 space groups and issues you a warning which includes the correct value of the shift vector that you should use if your data are referenced to the wrong origin. Figure

shows an example of this for a common space group. TkATOMS issues a pop-up dialog with a similar message. In WebATOMS, this message is written to the top of the page served upon output.

When you see the shift vector warning and the output data are, in fact, wrong, it usually suffices to rerun ATOMS with the correct shift vector. See Chapters

and

for instructions on how to specify the shift vector in the command line and Tk versions.

Sometimes a shift vector is needed even for a space group that is not in the list of 25. A common example is SiO₂ (GeO₂ is of the same structure). A nice study of the structure can be found in Acta Crystallographica B32 (1976) pages 2456-2459. In that article, the authors report the following structural data, which I reproduce as in input file for ATOMS.

The last two paragraphs are the answer to one of the most common questions I have received about ATOMS over the years. The moral of the story is, I think, to read your literature references carefully and not to trust authors to publish their data in the way that will be most convenient for your use!

Space Groups

Bravais Lattice Types

The Bravais type of space group specifies a particular translational symmetry. The easiest way to explain the Bravais translation is with an example. In FCC copper, you only need to specify one unique position, (0,0,0). In the copper unit cell, there are four atoms. They are at (0,0,0), (1/2,1/2,0), (1/2,0,1/2), and (0,1/2,1/2). If you examine the point symmetry operations indicated by the FCC space group, which is F m -3 m, you will find that each operation on the position (0,0,0) generates that same position. None of the point symmetry operations generate the other four positions. This is because those other positions are not related to (0,0,0) by point symmetry, but rather by the Bravais translation. Space groups whose Hermann-Maguin symbols begin with F all have three Bravais translation vectors, (1/2,1/2,0), (1/2,0,1/2), and (0,1/2,1/2) in addition to (0,0,0). So any positions generated by application of point symmetry are also translated by the Bravais vectors. In the case of an F group, the number of symmetry related positions in the unit cell is thus four times the number of positions generated by the point symmetry operations.

**Table:** Bravais lattice vectors. All Bravais types also have the default (0,0,0) vector.
`symbol`	vectors

`P`	none
`F`	$\big(\frac{1}{2},\frac{1}{2},0\big)$ , $\big(\frac{1}{2},0,\frac{1}{2}\big)$ , $\big(0,\frac{1}{2},\frac{1}{2}\big)$
`I`	$\big(\frac{1}{2},\frac{1}{2},\frac{1}{2}\big)$
`C`	$\big(\frac{1}{2},\frac{1}{2},0\big)$
`A`	$\big(0,\frac{1}{2},\frac{1}{2}\big)$
`B`	$\big(\frac{1}{2},0,\frac{1}{2}\big)$
`R`	$\big(\frac{2}{3},\frac{1}{3},\frac{1}{3}\big)$ , $\big(\frac{1}{3},\frac{2}{3},\frac{2}{3}\big)$

Space Groups Symbols

ATOMS is quite clever about interpreting space group symbols. The complete list of symbols recognized are listed in Appendix

. You can specify a space group by short or full Hermann-Maguin symbol, Schoenflies symbol, index from the International Tables, or (for some common groups) a nickname. As described in Section

, the best choice is to use the Hermann-Maguin symbol to avoid ambiguity of setting.

You can be fairly sloppy in how you enter the symbol. With only a few exceptions (see FAQ #

) whitespace is not important in the symbol. You can suppress whitespace or add extra and the symbol will be interpreted correctly. Similarly, the Schoenflies symbol can have the caret and underscore in either order. That is O_h^5 and O^5_h are the same. See Section

for a complete explanation of how space group symbols are determined.

The Symmetry Output File

One of the standard output file options as described in Chapter

and Appendix

is a file which describes the symmetry operations of a space group. Examining one of these files will help you understand how ATOMS turns crystallographic input data into a description of the unit cell. An example of this file is shown in Figure

for the orthorhombic space group, I m m 2.

Suppose that an atom has the unique position (0.5, 0, 0.5053)^3.3. The symmetry properties are applied to this unique position as stated in Figure

. Since there are two Bravais vectors and four symmetry related positions, the one unique position yields eight possible positions. These are

Settings of Low Symmetry Groups

For monoclinic and orthorhombic space groups, the crystal symmetries in one direction are not necessarily the same in the three directions. In a right-handed coordinate system, there may be several possibilities for how to orient the crystal. These different possibilities are the settings of the crystal. Each setting has a different Hermann-Maguin symbol and so a different way of interpreting a set of unique atom coordinates. For several monoclinic groups there are three possible settings (of which only two are commonly used in the literature) and for many orthorhombic groups there are as many as six possible settings. ATOMS has no way of knowing which setting is appropriate to a particular list of unique coordinates. Thus it is essential that you, the user use the correct symbol for the setting corresponding to your list of coordinates. In this case, you must use the Hermann-Maguin symbol. The Schoenflies symbols do not distinguish among the various possible settings. See App.

for a complete list of symbols for the various settings.

There is a related problem of interpretation for tetragonal and rhombohedral groups. For tetragonal groups a 45 $^\circ$ rotation will transform a primitive (P-type) Bravais lattice into a c-face centered (C-type) one or a body centered (I-type) Bravais lattice into a face-centered (F-type) one. ATOMS will handle all four types of tetragonal cell descriptions transparently. You can use symbols and unique coordinates appropriate to any of the four descriptions and ATOMS will correctly fill the unit cell.

For rhombohedral groups, the unit cell can be described by a hexagonal or a rhombohedral shape. Either shape uses the same Hermann-Maguin symbol, but different cell axis lengths and angles. With the hexagonal shape, the a and c axis lengths must be specified and the gamma angle is set by ATOMS to be 120 $^\circ$ . With the rhombohedral shape, the a axis length and alpha angle must be specified and ATOMS sets the other cell parameters appropriately. For either shape the list of unique coordinates must be appropriate to that shape.

Operational Parameters

In general there a few more pieces of information that you must feed to ATOMS in order for it to correctly build a cluster or perform some other calculation. For example, you may wish to specify a radial dimension for a cluster or specify a particular absorption edge. For many such operational parameters there are sensible default values. There are situations, though, where either it is desirable or necessary to explicitly specify non-crystallographic parameters. These operational parameters are explained for ATOMS in Chapter

and for TkATOMS in Chapter

Dopants

The manner in which ATOMS handes dopants is complicated and possibly confusing. Of course, the manner in which dopants must be considered in EXAFS analysis is also complicated and possibly confusing. That vindicates the fact that dopants in ATOMS are confusing, but certainly doesn't justify it!

There is an important distinction you must keep in mind while reading this section of the document. This is between how dopants are specified among the input data to ATOMS and how the dopant data is used by ATOMS to generate its output. In some situations you can specify dopants more thoroughly in the input data than ATOMS can use them to generate certain kinds of output data. Also keep in mind that I am not a crystallographer and I never intend that ATOMS be used to solve tough crystallography problems such as Rietveld refinements or superlattice detemination.

Specifying Dopants

The simplest form of dopant is a vacancy, so I will start by explaining how to tell ATOMS about a vacancy. By a vacancy I mean that a crystallographic site is incompletely occupied, i.e. that some positions in real space generated by that crystallographic site are not occupied by any atom. You tell ATOMS about this by specifying an occupancy for a site of less than 1.

In TkATOMS, this is done by manipulating the occupancy slider in the lower panel of the TkATOMS window. You can click on the slider and drag to set the value. Clicking mouse-1 in the trough will increment or decrement the slider value by 0.01. In this way you can specify occupancies between 0 and 1.

In an input file, occupancies can be specified in the sixth column of the atoms list. As explained in Sec.

, the first column is used for the atomic symbol, the next three for the fractional coordinates, and the fifth for the optional site tag. A number between 0 and 1 can be specified in the sixth column. If a site does not have a tag and the fifth column can be interpreted as a number, then ATOMS assumes that the number is an occupancy. Thus it is prudent to use at least one non-numeric character in your site tags.

Now we consider a simple substitution, i.e. the replacement of a fraction of the atoms occupying a crystallographic site with an atom of another species. This is handled in a manner very similar to a vacancy. First specify an occupancy of less than 1 for the host atom. Next, create a new crystallographic site which has the same fractional coordinates as the host atom. In TkATOMS this is done by repeating the coordinates in the subsequent row of the site table in the bottom panel. In an input file, this is done by replicating the coordinates in the next line of the atoms list. For the dopant site, specify the appropriate atomic symbol and an appropriate tag. Then specify the doping fraction using the occupancy slider in TkATOMS or the sixth column in the input file. IN this manner you may specify any number of dopants. The occupancies of the host and its dopants must sum to a number less than 1. ATOMS will flag an error if the occupancies sum to greater than 1.

ATOMS uses a simple scheme to distinguish between host and dopant atoms in the case of simple substitution. Whichever atomic species is enountered first is taken as the host species. In TkATOMS this means that the host is closer to the top of the sites table in the bottom panel. In an input file, the host is the earlier line in the atoms list. To switch host and dopant, simply change the order in which they appear.

ATOMS is also able to consider a complex substitutional dopant in which the substitute atom replaces the host atom, but not in exactly the same position. This is specified in the manner described above, except that the dopant need not have the same coordinates as the host. There are two important caveats to using ATOMS in this manner. The first is if you use ATOMS to make an input file for FEFF. As explained in Sec.

, this will result in a very unsatisfactory input file. The second is that the check made by ATOMS that the occupancies sum to less than 1 will not be made correctly, thus it is easy to specify nonsensical input data.

There are, of course, other phenomena which may be lumped under the term ``dopant''. For example, one might consider interstitial or grain boundary intrusions as dopants. ATOMS makes no attempt to consider these sorts of phenomena in any of its calculations.

Dopants in ATOMS

The primary purpose of ATOMS is to generate input data for FEFF. These data are finite lists of real-space atomic coordinates. For the sake of a FEFF calculation there is no point in generating a list of a radial extent about the central atom that is much larger than a small multiple of the photo-electron mean free path. Typically a cluster containing all atoms no farther than 10 Å from the central atoms quite suffices. A list of that size contains no more than a few hundred atoms. In EXAFS analysis, it is rare to consider atoms farther than about 6 Å from the central atoms, i.e. no more than a few tens of atoms. While the concept of ``fractional occupancy'' is quite well defined in crystallography, its meaning is much more ambiguous when considering only a few tens of atoms.

Consider, for example, analyzing EXAFS data taken on metallic copper doped with 8.3% silver. Since copper is an FCC metal and the first coordination shell contains 12 atoms, it might be sensible to replace one of the first shell atoms with a silver atom. However the second shell contains only six atoms. There is no way in the FEFF input file to replace a half an atom. Suppose that there was 10% silver in the copper. Thus 1.2% of the first coordination shell is silver, on the avarage, but again there is no way to specify a fractional atom in FEFF's input file. This is not say that you cannot use FEFF to analyze data taken on a doped material. Quite the opposite! FEFF is an excellent tool for doing so, but the techniques are more complicated than simply choosing atoms from the atoms list to replace with dopants. A more detailed discussion of those techniques is given elsewhere. (See Chapter 10 of EXAFS Analysis Using FEFF and FEFFIT at http://leonardo.phys.washington.edu/~ravel/course/notes.pdf.)

The bottom line is that there is no simply stated algorithm for constructing a finite sized atom list in the 'feff.inp' file which properly considers dopants. Any consideration of dopants in EXAFS analysis using FEFF requires that the FEFF user expend effort that cannot be coded into ATOMS.

When ATOMS writes a list of atomic coordinates of the sort used in a 'feff.inp', it ignores the dopant atoms. All sites are occupied by the host atoms.

However, ATOMS does not completely discard the information about dopants when writing 'feff.inp' files. That information is used in a variety of ways. A dopant atoms may be chosen as the central atom. In that case, the first item in the atoms list and the first item in the potentials list is the dopant atom. If an edge symbol is not specified. ATOMS will select a default edge appropriate to the dopant core. Finally the results of the absorption calculations, which may be written in the output file, will consider all dopants (not merely the central atom dopant) specified in the atoms list.

Dopants in Other Calculations

There are other output file types available to 'atoms.pl' or to the ATOMS notecard in TkATOMS. Most of these handle dopants in a more natural manner. For example the unit cell and P1 cell output options (see Chapter

) report the host and all dopants along with their occupancies.

The other calculations available in TkATOMS (and other programs in the ATOMS distribution) make use of dopants in a much more straight-forward manner than is true of the creation of 'feff.inp' files. The absorption calculations, the DAFS simulation, and the powder diffraction simulation all make use of the dopant data exactly as stated in the sites table or atoms list. For example, the contribution of an atoms to an absorption calculation is multiplied by its occupancy. Similarly, the contribution of an atom to the DAFS scattering factor is multiplied by its occupancy.