Crystal Data Entry Example

Example 1: Crystal Data File Creation

On this page we explain how to generate a crystal structure input file using the command line program EMmkxtal.

Gathering all the necessary parameters

Before you can generate a crystal structure input file, you need to find the following pieces of information from the literature (for instance, from a .cif file) :

1. Chemical Formula: this will be useful to generate the filename.
2. Crystal system: cubic, tetragonal, hexagonal, orthorhombic, trigonal, monoclinic or anorthic (triclinic).
3. Lattice Parameters: depending on the crystal system, you may only need one parameter, or all six.
4. Space group number: a number between 1 and 230; EMsoft uses the International Tables for Crystallography, Volume A, for all crystallographic conventions. Only standard settings are available for the standard space group symbols (International Notation), but some space groups may have two origin settings. In addition, there is now support for the Hall Space Group Symbols; EMmkxtal supports 530 different space group strings using the Hall symbols (see this website for a detailed description of the Hall Space Group notation; see also example 3 at the end of this wiki.) The Hall Space Group Symbols should be used for all non-standard space group settings for monoclinic, orthorhombic and trigonal crystal systems.
5. Atomic numbers: this does not need any explanation.
6. Atom coordinates: these are fractional coordinates, and you will need one triplet for each atom in the asymmetric unit.
7. Site occupation parameters: in the range [0..1], these parameters describe the occupation of each lattice site. Generally, those numbers are set to 1.0.
8. Debye-Waller factors: for each atom in the asymmetric unit, we also need the value of the isotropic Debye-Waller factor in units of nm^2. If this factor is not known for your material, then you will need to set a reasonable value; experience has shown that a value in the range [0.004,0.006] is almost always resonable.

For this example, we will use the structure of Nickel, which has a lattice parameter of 0.35236 nm and belongs to space group 225 (Fm-3m). The asymmetric unit consists of only one atom, Ni, with atomic number 28, at position (0.0,0.0,0.0), full site occupation of 1, and a Debye-Waller factor of 0.0035 nm^2 at room temperature. [For a listing of DW factors for elemental crystals, a good reference is: L.-M. Peng, G. Ren, S.L. Dudarev, and M.J. Whelan. Debye–Waller Factors and Absorptive Scattering Factors of Elemental Crystals. Acta Crystall. A, 52:456–470, 1996 DOI]

It should be noted that EMsoft does not provide direct support for trigonal crystal structures in the rhombohedral unit cell; while EMmkxtal allows for such structures to be entered, they are automatically converted to the hexagonal setting before they are stored in the output .xtal file.

Below, we list three examples:

1. Entering the data using coordinate triplets
2. Entering the data using Wyckoff positions
3. Using the Hall Space Group symbols

Example 1: Entering the data using coordinate triplets

From the command line, start the EMmkxtal program. The program will print out a few messages and then asks for the crystal system:

 Select the crystal system :
  1. Cubic
  2. Tetragonal
  3. Orthorhombic
  4. Hexagonal
  5. Trigonal
  6. Monoclinic
  7. Triclinic

 Note about the trigonal system:
 -------------------------------
 Primitive trigonal crystals are defined with respect to a HEXAGONAL
 reference frame.  Rhombohedral crystals can be referenced with
 respect to a HEXAGONAL basis (first setting), or with respect to
 a RHOMBOHEDRAL basis (second setting).  The default setting for
 trigonal symmetry is the hexagonal setting.  When you select
 crystal system 5 above, you will be prompted for the setting.


  crystal system ---> 

In this case, we have a cubic crystal structure, so enter the value 1. Then the program will ask for the necessary lattice parameter(s), in this case only one:

Enter lattice parameters
     a [nm] = 

Enter the value 0.35236; then the program will list all the cubic space groups along with their sequential numbers for the cubic crystal system:

 195: P 2 3      196: F 2 3      197: I 2 3      198: P 21 3    
 199: I 21 3     200: P m 3      201: P n 3      202: F m 3     
 203: F d 3      204: I m 3      205: P a 3      206: I a 3     
 207: P 4 3 2    208: P 42 3 2   209: F 4 3 2    210: F 41 3 2  
 211: I 4 3 2    212: P 43 3 2   213: P 41 3 2   214: I 41 3 2  
 215: P -4 3 m   216: F -4 3 m   217: I -4 3 m   218: P -4 3 n  
 219: F -4 3 c   220: I -4 3 d   221: P m 3 m    222: P n 3 n   
 223: P m 3 n    224: P n 3 m    225: F m 3 m    226: F m 3 c   
 227: F d 3 m    228: F d 3 c    229: I m 3 m    230: I a 3 d   
 --------------------------
  Enter space group number : 

Enter the value 225. If the selected space group has two origin settings, then this is the point where you would be asked to select setting 1 or 2. Then you will see a periodic table with the atomic numbers and chemical symbols. For each atom in the asymmetric unit, you will first be asked for the atomic number:

 Enter atoms in asymmetric unit

 ------------------------------------ Periodic Table of the Elements --------------------------------------

1:H                                                                                                    2:He
3:Li  4:Be                                                               5:B   6:C   7:N   8:O   9:F  10:Ne
11:Na 12:Mg                                                             13:Al 14:Si 15:P  16:S  17:Cl 18:Ar
19:K  20:Ca 21:Sc 22:Ti 23:V  24:Cr 25:Mn 26:Fe 27:Co 28:Ni 29:Cu 30:Zn 31:Ga 32:Ge 33:As 34:Se 35:Br 36:Kr
37:Rb 38:Sr 39:Y  40:Zr 41:Nb 42:Mo 43:Tc 44:Ru 45:Rh 46:Pd 47:Ag 48:Cd 49:In 50:Sn 51:Sb 52:Te 53: I 54:Xe
55:Cs 56:Ba ----- 72:Hf 73:Ta 74:W  75:Re 76:Os 77:Ir 78:Pt 79:Au 80:Hg 81:Tl 82:Pb 83:Bi 84:Po 85:At 86:Rn
87:Fr 88:Ra -----
57:La 58:Ce 59:Pr 60:Nd 61:Pm 62:Sm 63:Eu 64:Gd 65:Tb 66:Dy 67:Ho 68:Er 69:Tm 70:Yb 71:Lu
89:Ac 90:Th 91:Pa 92:U
 ----------------------------------------------------------------------------------------------------------
  ->  Atomic number : 

Enter 28 for Nickel. Then you will see:

 ->  Fractional coordinates, site occupation, and Debye-Waller Factor [nm^2] : 

Enter the five (floating point) numbers, separated by commas: 0.0,0.0,0.0,1.0,0.0035. The program then asks if you want to add another atom to the asymmetric unit:

  ->  Another atom ? (y/n) 

For fcc Nickel, there are no additional atoms, so enter n; if there were additional atoms, the program will prompt you for the next atomic number, then the coordinates, and so on until all atoms have been entered. Then you will see the following prompt:

Enter output file name (*.xtal)

Enter Ni.xtal; for more complex structures you should pick a file name that describes the chemical formula and perhaps the structure name. For instance, for TiO2 in the rutile form, you could select TiO2-rutile.xtal as the filename. Note that all the structure files are placed in a single location set by the EMsoftXtalFolderName configuration variable. Finally, the program will ask for a data source string which should be entered between single quotes; the source could be a DOI link to the paper where you found the structure data, or any other string (maximum length 512 characters).

Example 2: Entering the data using Wyckoff positions

From the command line, start the EMmkxtal program with the option -w; this will tell the program to use the Wyckoff special positions to enter atom coordinates. [Note that this option is not available through the EMsoftWorkbench GUI] Instead of asking for the atom coordinates, the program will list the available Wyckoff positions and ask you to pick one; for the space group 225, the program would list (after the Periodic Table):

Wyckoff positions for space group 225
-------------------------------------
4a ( 0, 0, 0 )
4b ( 1/2, 1/2, 1/2 )
8c ( 1/4, 1/4, 1/4 )
24d ( 0, 1/4, 1/4 )
24e ( x, 0, 0 )
32f ( x, x, x )
48g ( x, 1/4, 1/4 )
48h ( 0, y, y )
48i ( 1/2, y, y )
96j ( 0, y, z )
96k ( x, x, z )
192l ( x, y, z )
 WPstring : DaaaDbbbFcccKaccKxaaLxxxNxccNayyNbyyPayzPxxzQ
  ->  Atomic number, site occupation, Debye-Waller factor : 

Enter the values 28, 1.0, 0.0035; then you will see the prompt:

->  Wyckoff position : 

and you should enter 4a for Nickel. In this case, no coordinate values need to be entered, but in other cases, the program will prompt for any necessary fractional coordinates (for instance the y value for the 48h Wyckoff position). Note that the WPstring listed above is just informational; this is how all the Wyckoff positions are encoded in the program (one such string for each space group). The remainder of the program execution is similar to the description in the previous section.

Example 3: Using the Hall Space Group symbols

The Hall Space Group symbols offer an alternative notation for space groups that includes origin information; the symbols encode lattice centering and inversion in the first portion, and the rotational operators with axis and translation information (see the citation at the top of this wiki for details). There are 530 Hall symbols that unambiguously encode all possible space group settings for monoclinic and orthorhombic space groups as well as an unambiguous description of hexagonal vs. rhombohedral settings for the trigonal space groups.

To create a crystal structure using the Hall symbols, start the program with the -H command line option. Data entry is identical to that in Example 1, except for the fact that after the entry of the space group number, a list of available Hall symbols is produced; in many cases there will be only one single Hall symbol, so one should select 1. In other cases, more than one option is available (for some monoclinic groups there are 18 Hall symbols).

As an example, consider the structure of the mineral forsterite; this mineral is nearly always described in the non-standard orthorhombic Pbnm space group. The standard setting for this space group # 62 is Pnma, which is the only option available when the International Space Group notation is used (as in example 1). When using the Hall symbols, the program will list six available Hall Space Group symbols:

...
  16: P 2 2 2          17: P 2 2 21         18: P 21 21 2        19: P 21 21 21
  20: C 2 2 21         21: C 2 2 2          22: F 2 2 2          23: I 2 2 2   
  24: I 21 21 21       25: P m m 2          26: P m c 21         27: P c c 2   
  28: P m a 2          29: P c a 21         30: P n c 2          31: P m n 21  
  32: P b a 2          33: P n a 21         34: P n n 2          35: C m m 2   
  36: C m c 21         37: C c c 2          38: A m m 2          39: A b m 2   
  40: A m a 2          41: A b a 2          42: F m m 2          43: F d d 2   
  44: I m m 2          45: I b a 2          46: I m a 2          47: P m m m   
  48: P n n n          49: P c c m          50: P b a n          51: P m m a   
  52: P n n a          53: P m n a          54: P c c a          55: P b a m   
  56: P c c n          57: P b c m          58: P n n m          59: P m m n   
  60: P b c n          61: P b c a          62: P n m a          63: C m c m   
  64: C m c a          65: C m m m          66: C c c m          67: C m m a   
  68: C c c a          69: F m m m          70: F d d d          71: I m m m   
  72: I b a m          73: I b c a          74: I m m a   

 --------------------------
  Enter space group number : 62
 ------------------------------------
 This program will use the Hall Space Group symbols;
 please select the correct Hall Space Group entry from
 the list below
 ------------------------------------
   SG label Int. Symbol  Hall Symbol
 1 : 62      P n m a     -P 2ac 2n
 2 : 62:ba-c P m n b     -P 2bc 2a
 3 : 62:cab  P b n m     -P 2c 2ab
 4 : 62:-cba P c m n     -P 2n 2ac
 5 : 62:bca  P m c n     -P 2n 2a
 6 : 62:a-cb P n a m     -P 2c 2n

 Enter Hall space group selection : 

To use the Pbnm setting, one should enter 3. From then on, the atom coordinates should be entered in this setting, not in the Pnma setting. All subsequent EMsoftOO program runs will then be performed in the Pbnm setting, including EBSD master pattern computations and dictionary indexing.