The AFLOW Prototype Label

Every structural entry in the Encyclopedia of Crystallographic Prototypes has an AFLOW Prototype Label. This can be very simple, e.g., A_cF4_225_a-001 for copper in Fig. 1 or as complex as A108B24C11D24_cP334_222_h4i_i_bf_i-001 for Ti₆F₂₇(H₃O)₃, as shown in Fig. 2.

The AFLOW prototype label is designed to show the stoichiometry of the crystal structure, the shape and number of atoms in the unit cell, the structure's space group, and the distribution of each type of atom in the crystal. In this tutorial we'll look at each of these parts, show how to put them together in a consistent manner, and then use the prototype label to construct input files to run the latest AFLOW code (Divilov, 2025) or to use in another electronic structure program.

Deconstructing the AFLOW Prototype Label

Let's take apart a prototype label and look at the individual pieces. (The complete prototype label protocol was originally explained in Eckert, 2024.) Rather than looking at something as simple as copper or as complex as Ti₆F₂₇(H₃O)₃, we'll look at an intermediate structure, K₂AgSbS₄, shown in Fig. 3. If we look at the page for this structure in the Encyclopedia, we find that it has:

1. two potassium atoms and four sulfur atoms for each silver and antimony atom;
2. 32 atoms, or four formula units, in each unit cell;
3. an orthorhombic unit cell in space group Pnn2 #34;
4. and
   • silver (Ag) atoms on the (2a) and (2b) Wyckoff sites,
   • potassium (K) atoms on (2a), (2b) and (4c) sites,
   • sulfur atoms (S) on four separate (4c) sites, and
   • antimony atoms (Sb) on a (4c) site.

Each of these bullets forms a separate part of the prototype label. Let's dissect each one:

1. Stoichiometry
   The first part of the prototype label reveals the stoichiometry of the crystal. This is written in a generic form, so that we can describe different compounds. First we put the chemical formula in alphabetical order by element symbol, e.g., K₂AgSbS₄ → AgK₂S₄Sb   . We then replace the first element symbol by A, the second by B, and so on: K₂AgSbS₄ → AgK₂S₄Sb → AB₂C₄D   . Finally, we move the subscripted numbers onto the main line, giving the final symbol:

   

   K₂AgSbS₄ → AgK₂S₄Sb → AB₂C₄D → AB2C4D   .
2. Cell Size and Shape
   This is given by the Pearson symbol, here oP32. If we look ahead to the space group, we find that #34 is Pnn2, which has a simple (the P in the symbol) orthorhombic (the o) lattice. Adding up all the numbers in the Wyckoff positions we come up with 32 atoms per unit cell. This gives the symbol oP32.
3. Space Group
   This one is easy. We just use the number of the space group from the International Tables or the free Bilbao Crystallographic Server, where we find that space group Pnn2 is number 34.
4. Wyckoff Positions
   This is a little more complex. We want to write down occupied Wyckoff positions for each atomic species in the system, in alphabetical order by atomic symbol. Let's take all the information above and put it in a table, finishing up each entry with the AFLOW string for that atomic species:

   The occupied Wyckoff positions for each element in K₂AgSbS₄, arranged in alphabetical order by element symbol.

   Symbol	Name	Wyckoff Positions	AFLOW String
   Ag	Silver	(2a)   (2b)	a
   K	Potassium	(2a)   (2b)   (4c)	ab
   S	Sulfur	Four (4c) sites	4c
   Sb	Antimony	(4c)	c

Since the number of atoms of a Wyckoff position is solely determined by its letter, we don't need to put the Wyckoff number in the string, hence 2a → a. We do have to account for the same atom being on multiple sites with the same Wyckoff position. Here there are four unique (4c) Wyckoff sites for sulfur. We indicate this by putting a 4 in front of the c. We separate the atomic species by underscores, so the complete Wyckoff string is a_ab_4c_c.

Now we construct the AFLOW symbol by concatenating all of those pieces

1. Stoichiometry: AB2C4D
2. Cell Size: oP32
3. Space Group: 32
4. Wyckoff Positions: a_ab_4c_c

separating them by underscores, so that the final AFLOW prototype label is AB2C4D_oP32_34_ab_abc_4c_c   . You can use this technique to define an AFLOW prototype label for any compound with a known crystal structure.

The only problem with this label is that the Encyclopedia uses AB2C4D_oP32_34_ab_abc_4c_c-001 rather than AB2C4D_oP32_34_ab_abc_4c_c as the label for K₂AgSbS₄. The -001 extension is there because AB2C4D_oP32_34_ab_abc_4c_c could conceivably describe a completely different structure.

This is most easily shown by a different label, A_oC8_64_f, which is shared by three structures: α-gallium (Fig. 4), black phosphorous (Fig. 5), and crystallized molecular iodine (Fig. 6).

All of these structures are monatomic, in the same space group, Cmce #64, and all occupy one (8f) Wyckoff position. As can be seen from the figures, they are completely different structures. Assigning the exact same label to all of them would lead to confusion. However, we do want to keep the the A_oC8_64_f label, as it tells us a lot about the structure. The somewhat unsatisfactory answer is to add a three digit extension to the code, with the number arbitrarily chosen.

There are many labels with multiple entries. The worst case we have found so far is ABC_oP12_62_c_c_c where the extension goes from -001 to -017*.

Using AFLOW to determine the label

If a publication has provided a structure file^† in the form of a Crystallographic Information FILE (CIF) or the structure file for an electronic structure code, we can let AFLOW determine the label. For example, we can download the Encyclopedia CIF for K₂AgSbS₄ from the link

https://www.aflow.org/prototype-encyclopedia/AB2C4D_oP32_34_ab_abc_4c_c-001/aflow.cif or going to https://www.aflow.org/prototype-encyclopedia/AB2C4D_oP32_34_ab_abc_4c_c-001 scrolling down to the bottom, and clicking the button labeled “CIF Output”.

If the structure you want isn't in AFLOW, and the authors have not provided a structure file, you may still be able to get a CIF:

1. Go to the CCDC Access Structures Page
2. Enter the ICSD or CCSD number for the structure in the “Identifiers” box, or the paper's DOI into the “DOI” box.
3. Click search.

If the structure is registered with the ICSD or CSD you'll get the opportunity to download the CIF.^‼

The CIF for a given structure might also be available elsewhere. Our Crystallographic Information File lists some sources, some of which are free.

Once you have a CIF or another geometry file, feed it into AFLOW with the command

$ aflow --prototype --print_element_names < K2AgSbS4.cif and you will get the output
AFLOW label : AB2C4D_oP32_34_ab_abc_4c_c
params : a,b/a,c/a,z1,z2,z3,z4,x5,y5,z5,x6,y6,z6,x7,y7,z7,x8,y8,z8,x9,y9,z9,x10,y10,z10
params values : 10.348, 1.01681, 0.767878, 0.9519, 0.448, 0.2249, 0.758, 0.2468, 0.2349, 0.948, 0.55, 0.7051, 0.2672, 0.7104, 0.5518, 0.6322, 0.9238, 0.7208, 0.3037, 0.7201, 0.9228, 0.5872, 0.7272, 0.7254, 0.4485
element names : Ag,K,S,Sb
which not only shows you the label, but also the elements and geometric information for the structure, with the values a, b, c, z1, … corresponding to the coordinates found in the Encyclopedia page for K₂AgSbS₄.

Using the AFLOW Prototype Label

The AFLOW prototype label is the key to using AFLOW. Once we have the label we can use it to print out a CIF or the geometry file needed to run an electronic structure code and use it to to see the crystal structure. We can also modify the structure by changing the elements or the geometric input parameters. We can even set up an AFLOW input file to do a full calculation of electronic properties.

If the label is in AFLOW, then determining the structure is easy. As a simple example we'll use the sodium chloride structure, AFLOW label AB_cF8_225_a_b-001^‡ as an example. We can get a POSCAR (VASP) input file using the default command:

$ §
ClNa/AB_cF8_225_a_b-001 params=-1 SG=225 …
-2.000000
0.00000000000000 0.50000000000000 0.50000000000000
0.50000000000000 0.00000000000000 0.50000000000000
0.50000000000000 0.50000000000000 0.00000000000000
1 1
Direct(2) [A1B1]
0.00000000000000 0.00000000000000 0.00000000000000 A
0.50000000000000 0.50000000000000 0.50000000000000 B
where the params=-1 means “use what's in the AFLOW database.” (we truncated the first line of the output).

This is rather generic, so let's decorate it with atomic species:

$
ClNa/AB_cF8_225_a_b-001 params=-1 SG=225 …
-58.208200
0.00000000000000 0.50000000000000 0.50000000000000
0.50000000000000 0.00000000000000 0.50000000000000
0.50000000000000 0.50000000000000 0.00000000000000
1 1
Direct(2) [A1B1]
0.00000000000000 0.00000000000000 0.00000000000000 Cl
0.50000000000000 0.50000000000000 0.50000000000000 Na
where AFLOW picks the volume of the unit cell (58.2Å) using Vegard's Law.
If we instead want to use the experimental lattice constant for table salt, the NaCl web page gives it as 5.639Å. We can add this to AFLOW using the --params flag:
$

ClNa/AB_cF8_225_a_b-001 params=5.639 SG=225 …
1.000000
0.00000000000000 2.81950000000000 2.81950000000000
2.81950000000000 0.00000000000000 2.81950000000000
2.81950000000000 2.81950000000000 0.00000000000000
1 1
Direct(2) [A1B1]
0.00000000000000 0.00000000000000 0.00000000000000 Cl
0.50000000000000 0.50000000000000 0.50000000000000 Na
If you want input for another electronic structure program, tags such as --abinit, --qe, and --elk will give you the appropriate data.
If instead of electronic structure input you want a CIF, you can use the command
$
which will also tell you everything you need to know about the structure, albeit in 200+ lines.

Suppose you want to do a full electronic calculation for NaCl, at another lattice constant, say 5.521Å. AFLOW can set that up using the command⁺

$
AFLOW V(4.0.5) creating
./AFLOWDATA/ClNa_sv/AB_cF8_225_a_b-001.AB:ANRL=421cf5e8d4a841cc62afc447c3a560ea/aflow.in
The aflow.in file has all the information you need to run the calculation, though you may want to throw in more flags to refine it. See the AFLOW Schools tutorials, the Encyclopedia Tutorials, and the README files in the AFLOW source code for more information.

The AFLOW Prototype Label Protocol

Now we know how to construct an AFLOW label using a published crystal structure. That might not be the label that AFLOW wants to use. That's because different sets of Wyckoff positions can describe the same crystal structure, depending on where you put the crystal origin and how you orient the lattice in Cartesian space. Space group Pmmm #47 is perhaps the worst offender in this regard. It is an orthorhombic structure with no screw axes or glide planes. This allows us to rename the axes in any order we want e.g., putting the shortest axis in the $\hat{x}$ direction and the longest in the $\hat{z}$ direction, or the middle axis in the $\hat{x}$ direction and the shortest in the $\hat{z}$ direction, or any other permutation. Each choice of axes changes the occupied Wyckoff positions of the structure. This is one reason why $Pmmm$ has 27 Wyckoff letters, the most of any space group.^¶

Fig. 7 shows an example of this. YBa₂Cu₃O_7-x, also known as (1212C), is a perovskite superconductor in space group $Pmmm$ #47. The original publication (David, 1987) places the longest axis in the $\hat{z}$ direction, while the Encyclopedia places it in the $\hat{x}$ direction. This gives the atoms completely different Wyckoff sites, as shown in this table:

The Wyckoff positions of each atom in YBa₂Cu₃O_7-x (1212C) as given in the original publication (David, 1987) and the Encyclopedia. The atom label is the one given in the Encyclopedia. The coordinates shown are the first set of coordinates given for each Wyckoff letter in the International Tables. Since this is in space group Pmmm #47 all sets of coordinates for a given Wyckoff letter can be obtained by mirroring each coordinate, e.g. x → -x.

Atom	(David, 1987)		Encyclopedia
	Wyckoff Letter	Coordinates	Wyckoff Letter	Coordinates
O I	(1e)	(0,½,0)	(1a)	(0,0,0)
Cu I	(1a)	(0,0,0)	(1c)	(0,0,½)
Y I	(1h)	(½,½,½)	(1f)	(½,½,0)
O II	(2r)	(0,½,z)	(2i)	(x,0,0)
Cu II	(2q)	(0,0,z)	(2j)	(x,0,½)
O III	(2q)	(0,0,z)	(2j)	(x,0,½)
Ba I	(2t)	(½,½,z)	(2k)	(x,½,0)
O IV	(2s)	(½,0,z)	(2l)	(x,½,½)

There is also an origin shift, with the origin moving from the Cu I atom in the original publication to the O I atom in the Encyclopedia. As a result the AFLOW label, which we would naively think would be A2BC7D_oP13_47_t_aq_eqrs_h^⁑ is now A2B3C7D_oP13_47_k_cj_aijl_f.

What's going on? There are six possible axes orientations in Pmmm, leading to six possible AFLOW labels for YBa₂Cu₃O_7-x. In addition, all of the first eight Wyckoff positions in Pmmm have the full mmm symmetry of the lattice so we can use any of them as the origin, giving 6 × 8 = 48 possible labels. For programming ease we would like to fix settle on one label per AFLOW prototype. To do that, we standardize the labels by defining the AFLOW Prototype Label Protocol. This updates the original AFLOW label construction method described above.

1. Select a compound to represent all the compounds with this structure. This is usually the first such compound we found in the literature, which we often (though not always) choose as structure class representative in the ICSD.
2. Alphabetize the elements by atomic symbol and derive the stoichiometry as described previously, and add the Pearson symbol and the space group number. This part of the label is always the same.
3. Scroll through all possible combinations of Wyckoff positions that describe this structure (48 for YBa₂Cu₃O_7-x). Give each Wyckoff letter a number: a = 1, b = 2, c = 3, etc and add up all the Wyckoff values.
4. Use the orientation with the smallest Wyckoff sum.
5. In the quite possible case that two or more labels have the same score, chose the case with the smallest Wyckoff letter on the first atom.
6. If that still results in a tie, chose the case with the smallest label on the second atom.
7. Repeat as necessary until there is one unique label.

If done by hand this would be a lot of work for a label as complicated as the one for YBa₂Cu₃O_7-x, but fortunately AFLOW does it automatically, and you can see the result using the aflow --prototype command.

Using AFLOW: the --params string

Given a structural reference we can often find a CIF or a POSCAR file that represents the structure in the literature^♦, but sometimes we can't, especially with older literature and with computational predictions. In that case we can use AFLOW to produce a CIF or POSCAR from the published data.

As an example, let's look at YBa₂Cu₃O_7-x again, starting with the original publication of (David, 1987). When this was published CIFs did not exist. Fortunately we now have a CIF for this structure, so we can check our work.

Table 1 of (David, 1987) gives all the crystallographic information needed for YBa₂Cu₃O_7-x. We produce this below:

The Wyckoff positions, including data, for YBa₂Cu₃O_7-x from Table 1 of (David, 1987). The structure is in space group Pmmm #47, with a = 3.8187Å, b = 3.8833Å, and c = 11.6687Å. x, y, and z are given as lattice coordinates, that is, (x,y,z) corresponds to Cartesian coordinates (ax,by,cz).

Atom Number	Atom	Wyckoff Letter	x	y	z
1	Cu I	(1a)	0	0	0
2	O I	(1e)	0	½	0
3	Y I	(1h)	½	½	½
4	Cu II	(2q)	0	0	0.3554
5	O II	(2q)	0	0	0.1579
6	O III	(2r)	0	½	0.3771
7	O IV	(2s)	½	0	0.3788
8	Ba I	(2t)	½	½	0.1844

We'll use the published Wyckoff positions rather than the rotated AFLOW positions. That's a lot easier, since there are 48 possible orientations plus origin choices and we can let AFLOW find the standard orientation when we're done.

The next thing to notice is that we reordered the structure. Now the structure is ordered by

• Wyckoff letter, in alphabetical order, followed by
• Elements in symbolic alphabetical order, if two or more elements share the same Wyckoff order.
• If there are multiple instances of one element occupying the same Wyckoff letter, the you write them is up to you, but it will be written in stone once you've made your choice.

This is the order AFLOW requires for its input. It may seem strange, but it agrees with the historical ordering of an Encyclopedia structure page, which always starts with the smallest Wyckoff letter.

To get all of this into AFLOW, we enter all of the data in the format

a,b/a,c/a,x1,y1,z1, x2,y2,z2, x3,y3,z3, … with the caveat that we only enter the information necessary to reproduce the structure. You can see from Table 2 that some Wyckoff coordinates are fixed by symmetry at zero or ½. We don't enter those values. Similarly, if we had a cubic structure, then b/a = c/a = 1 and we do not entry those values. If you don't know which values are fixed, it is best to look up the space group in the International Tables or the freely available Bilbao Crystallographic Server, as a coordinate can sometimes be zero even if it is not required by symmetry.

In this particular case all of the values of zero and ½ are fixed, so we need to enter the values

a,b/a,c/a,z4,z5,z6,z7,z8 To get a POSCAR for this structure, we feed all of this information into AFLOW using the --params string. Combined with the AFLOW label, Pearson symbol, space group and composition we have
$ aflow --proto=A2B3C7D_oP13_47_t_aq_eqrs_h:Ba:Cu:O:Y --params=3.8187,1.01692,3.05567,0.3554,0.1579,0.3771,0.3788,0.1844
By default, this gives the output as a POSCAR file:
BaCuOY/A2B3C7D_oP13_47_t_aq_eqrs_h.ABCD params=3.8187,1.01692,3.05567,0.3554,0.1579,0.3771,0.3788,0.1844 SG=47 …
1.000000
3.81870000000000 0.00000000000000 0.00000000000000
0.00000000000000 3.88331240400000 0.00000000000000
0.00000000000000 0.00000000000000 11.66868702900000
2 3 7 1
Direct(13) [A2B3C7D1]
0.50000000000000 0.50000000000000 0.18440000000000 Ba
0.50000000000000 0.50000000000000 0.81560000000000 Ba
0.00000000000000 0.00000000000000 0.00000000000000 Cu
0.00000000000000 0.00000000000000 0.35540000000000 Cu
0.00000000000000 0.00000000000000 0.64460000000000 Cu
0.00000000000000 0.50000000000000 0.00000000000000 O
0.00000000000000 0.00000000000000 0.15790000000000 O
0.00000000000000 0.00000000000000 0.84210000000000 O
0.00000000000000 0.50000000000000 0.37710000000000 O
0.00000000000000 0.50000000000000 0.62290000000000 O
0.50000000000000 0.00000000000000 0.37880000000000 O
0.50000000000000 0.00000000000000 0.62120000000000 O
0.50000000000000 0.50000000000000 0.50000000000000 Y
This gives the structure in the published coordinates. If, however, we ask for a CIF file,
$ aflow --proto=A2B3C7D_oP13_47_t_aq_eqrs_h:Ba:Cu:O:Y --params=3.8187,1.01692,3.05567,0.3554,0.1579,0.3771,0.3788,0.1844 --cif

we get a 42 line file which you can download here as aflow.cif. If we look at the relevant parts of the CIF we find the lattice constants^⁌
_cell_length_a 11.6686870290
_cell_length_b 3.8187000000
_cell_length_c 3.8833124040
and the Wyckoff positions
Ba1 1.0000000000 0.8156000000 0.5000000000 0.0000000000 Biso 1.0 Ba 2 k
Cu2 1.0000000000 0.0000000000 0.0000000000 0.5000000000 Biso 1.0 Cu 1 c
Cu3 1.0000000000 0.6446000000 0.0000000000 0.5000000000 Biso 1.0 Cu 2 j
O4 1.0000000000 0.0000000000 0.0000000000 0.0000000000 Biso 1.0 O 1 a
O5 1.0000000000 0.8421000000 0.0000000000 0.5000000000 Biso 1.0 O 2 j
O6 1.0000000000 0.6229000000 0.0000000000 0.0000000000 Biso 1.0 O 2 i
O7 1.0000000000 0.6212000000 0.5000000000 0.5000000000 Biso 1.0 O 2 l
Y8 1.0000000000 0.5000000000 0.5000000000 0.0000000000 Biso 1.0 Y 1 f
This is obviously the preferred AFLOW orientation.

The structures are equivalent, as you can see by running the commands
$
and
$
both of which produce the result
AFLOW label : A2B3C7D_oP13_47_k_cj_aijl_f
params : a,b/a,c/a,x4,x5,x6,x7,x8
params values : 11.6687,0.32726,0.332796,0.6229,0.6446,0.8421,0.8156,0.6212
Alternatively, you can let AFLOW do the comparison
$
which produces a lot of information ending with
CCCCC COMPLETE compare::compareInputStructures(): 4.44089e-16 : MATCH - [dir=/var/www/html/Encyclopedia/Tutorials/AFLOW_Prototype_Label/DATA/] - [user=mike] - [host=mycroft] - [PID=403003] - [date=Sat Jul 26 17:23:16 2025] - [/home/runner/_work/AFLOW4/AFLOW4/src/modules/COMPARE/aflow_compare_structure.cpp:485]
with the value 4.44089e-16 indicating that the structures are identical.

Wrapping Up

In this tutorial we've explained the construction of the AFLOW Prototype Label, how to use it to construct a Crystallographic Information File or an electronic structure input, and looked at the protocol we use to construct a “standard” label. If you've got any questions, please contact us.

Footnotes

* At the moment (summer 2025) only two of these entries are in the Encyclopedia, but all seventeen are available in the AFLOW database. Space group Pnma #62 has more inorganic crystal structures than any other high symmetry (orthorhombic and above) space group and only four Wyckoff positions, so there are many labels with large extensions.

^† As they should.

^‼ The CCDC only allows a limited number of downloads per day for non-subscribers, so use this sparingly. In addition, some CCDC CIFs are not compatible with AFLOW, although they can usually be edited to work if you know the proper format — compare the CCDC CIF to an AFLOW CIF from the same space group.
Or write to the authors of the paper and ask for a structure file. If enough readers do this consistently maybe authors will always include a structure file in their paper's supplementary information.

^‡ For historic reasons the tag AB_cF8_225_a_b, without the extension, will work here. Each structural entry in the Encyclopedia will tell you which labels will work with a given structure.

^§ Click on the clipboard icon to copy the string on the left to the clipboard.

⁺ There is a big difference between --proto and --aflow_proto.

^¶ The 27^th site is represented by A.

^⁑ This was the original label in the Encyclopedia. As with all of the legacy labels you can still access this structure using that label.

^♦ Some repositories which make CIF files available are listed in our Crystallographic Information File page.

^⁌ The exact values of the lattice constants are different because of the precision used when we set values for b/a and c/a to constructed the CIF.

References

• W. I. F. David, W. T. A. Harrison, J. M. F. Gunn, A. K. S. O. Moze, P. Day, J. D. Jorgensen, D. G. Hinks, M. A. Beno, L. Soderholm, D. W. C. Ii, I. K. Schuller, C. U. Segre, K. Zhang, and J. D. Grace, Structure and crystal chemistry of the high-T_c superconductor YBa₂Cu₃O_7-x, Nature 327, 310–312 (1987). DOI: 10.1038/327310a0
• Simon Divilov, Hagen Eckert, Scott D. Thiel, Sean D. Griesemer, Rico Friedrich, Nicholas H. Anderson, Michael J. Mehl, David Hicks, Marco Esters, Nico Hotz, Xiomara Campilongo, Arrigo Calzolari, and Stefano Curtarolo AFLOW4: Heading Toward Disorder, High Entropy Alloys & Materials 3, 178 (2025). DOI: 10.1007/s44210-025-00058-2 (arXiv link)
• Hagen Eckert, Simon Divilov, Michael J. Mehl, David Hicks, Adam C. Zettel, Marco Esters, Xiomara Campilongo, and Stefano Curtarolo, The AFLOW library of crystallographic prototypes: part 4, Computational Materials Science 240, 112988 (2024). DOI: 10.1016/j.commatsci.2024.112988 (arXiv link)
• T. Hahn, ed., International Tables of Crystallography. Volume A: Spacegroup symmetry (Kluwer Academic publishers, International Union of Crystallography, Chester, England, 2002).
  For a free version of most of this information see the Bilbao Crystallographic Server

Resources

This is a list of resources mentioned in the text:

• All things AFLOW (Automatic - FLOW for Materials Discovery) can be found on the AFLOW Home Page. Details about the current version of the program are found in (Divilov, 2025) and references therein.
• The Bilbao Crystallographic Server is a center for all things related to the symmetry of crystals. It is free, and contains much of the information found in the International Tables.
  The list of crystal structures can be found at this link. AFLOW, Bilbao, and the International Tables all agree on the default or standard choice of a space group representation.
• Cambridge Crystallographic Data Centre (CCDC) search engine allows a free, if somewhat restricted, search of both the CSD and ICSD databases.
• Cambridge Structural Database (CSD) contains three-dimensional structural data for organic and metal organic systems. Annually they publish a table showing the frequency distribution of CSD structures by space group. We used the 2024 version for our data.
• Inorganic Crystal Structure Database (ICSD) has structural data for inorganic systems.
• Section 2 of our paper The AFLOW library of crystallographic prototypes: part 3 contains a history of the development of Strukturbericht symbols.
• The history and information discussed here appears in another form in our AFLOW library of crystallographic prototypes: part 4 paper.
• The (Vienna Ab initio Simulation Package is a full-scale program for calculating the electronic structure, total energy, forces, pressure, etc., for a periodic solid.