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HOW TO PREPARE AN INPUT FILE FOR SURFACE CALCULATIONS
EMRE S. TASCI
etasci@metu.edu.tr
Physics Department, Middle East Technical University 06531 Ankara, Turkey
Abstract.
This how-to is intended to guide the reader during the preparation of the input le for
an intended surface calculation study. Mainly VESTA software is used to manipulate and transform
initial structure le along with some home brewed scripts to do simple operations such as translations.
Contents
1. Description 1
2. Tools 1
3. Procedure 2
3.1. Initial structural data 2
3.2. Constructing the Supercell 2
3.3. Lattice Planes 4
3.4. Trimming the new unit cell 7
3.5. Transforming into the new unit cell 7
3.6. Final Touch 8
4. Alternative Ways 9
5. Conclusion 11
6. Acknowledgements 11
7. Appendix: Walkthru for PtC (111) Surface 11
References 14
1.
Description
One of the questions I'm frequently being asked by the students is the preparation of input les
for surface calculations (or more accurately, a practical way for the purpose). In this text, starting
from a structural data le for bulk, the methods to obtain the input le t for structure calculations
will be dealt.
2.
Tools
VESTA
1
is a free 3D visualization program for structural models that also allows editing to some
extent. It is available for Windows, MacOS and Linux operating systems.
STRCONVERT
2
is a tool hosted on the Bilbao Crystallographic Server[1, 2, 3] (BCS) that oers
visualization and also basic editing as well as conversion between various common structural data
formats.
TRANSTRU
3
is an another BCS tool that transforms a given structure via the designated trans-
formation matrix.
1
http://jp-minerals.org/vesta/en/
2
http://www.cryst.ehu.es/cgi-bin/cryst/programs/mcif2vesta/index.php
3
http://www.cryst.ehu.es/cryst/transtru.html
1
HOW TO PREPARE AN INPUT FILE FOR SURFACE CALCULATIONS 2
225
4.50 4.50 4.50 90. 90. 90.
2
C 1 4a 0 0 0
Pt 1 4b 0.5 0.5 0.5
Table 1.
Structural data of
F m¯
3m
PtC
Figure 3.1.
VESTA's Unit cell interface
3.
Procedure
3.1.
Initial structural data.
We start by obtaining the structural data for the unit cell of the
material we are interested in. It should contain the unit cell dimensions and the atomic positions.
Some common formats in use are: CIF[4], VASP[5], VESTA[6] and BCS formats. Throughout this
text, we will be operating on the
F m¯
3m
phase of the platinum carbide (PtC), reported by Zaoui &
Ferhat[7] as reproduced in BCS format in Table 1.
These data can be entered directly into VESTA from the form accessed by selecting the File
New
Structure menu items and then lling the necessary information into the Unit cell and Structure
parameters tabs, as shown in Figures 3.1 and 3.2.
As a result, we have now dened the
F m¯
3m
PtC (Figure 3.3).
An alternative way to introduce the structure would be to directly open its structural data le
(obtained from various structure databases such as COD[8], ICSD[9] or Landolt-Bornstein[10] into
VESTA.
3.2.
Constructing the Supercell.
A supercell is a collection of unit cells extending in the a,b,c
directions. It can easily be constructed using VESTA's transformation tool. For demonstration
purposes, let's build a 3x3x3 supercell from our cubic PtC cell. Open the Edit
Edit Data
Unit
Cell... dialog, then click the Option... button in the Setting row. Then dene the transformation
matrix as 3a,3b,3c as shown in Figure 3.4.
HOW TO PREPARE AN INPUT FILE FOR SURFACE CALCULATIONS 3
Figure 3.2.
VESTA's Structure parameters interface
Figure 3.3.
F m¯
3m
platinum carbide
HOW TO PREPARE AN INPUT FILE FOR SURFACE CALCULATIONS 4
Figure 3.4.
Transformation matrix for the supercell
Figure 3.5.
A 3x3x3 supercell
Answer yes when the warning for the change of the volume of the unit cell appears, and again
click Yes to search for additional atoms. After this, click OK to exit the dialog. This way we
have constructed a supercell of 3x3x3 unit cells as shown in Figure 3.5.
We have built the supercell for a general task but at this stage, it's not convenient for preparing
the surface since we rst need to cleave with respect to the necessary lattice plane. So, revert to the
conventional unit cell (either by reopening the data le or undoing (CTRL-z) our last action).
Now, populate the space with the conventional cell using the Boundary setting under the Style
tool palette (Figure 3.6). In this case, we are building a 3x3x3 supercell by including the atoms
within the -fractional- coordinate range of [0,3] along all the 3 directions (Figure 3.7).
At this stage, the supercell formed is just a mode of display - we haven't made any solid changes
yet. Also, if preferred one can choose how the unit cells will be displayed from the Properties
setting's General tab.
3.3.
Lattice Planes.
To visualize a given plane with respect to the designated hkl values, open the
dialog shown in Figure 3.8 by selecting Edit
Lattice Planes... from the menu, then clicking on
New and entering the intended hkl values, in our example (111) plane.
The plane's distance to the origin can be specied in terms of Å or interplane distance, as well as
selecting 3 or more atoms lying on the plane (multiple selections can be realised by holding down
HOW TO PREPARE AN INPUT FILE FOR SURFACE CALCULATIONS 5
,
Figure 3.6.
Designating the boundaries for the construction of the supercell.
Figure 3.7.
(a)Single unit cell (conventional); (b) 3x3x3 supercell
Figure 3.8.
Selecting the (111) lattice plane
HOW TO PREPARE AN INPUT FILE FOR SURFACE CALCULATIONS 6
Figure 3.9.
Selecting the (111) lattice plane in the 3x3x3 supercell
Figure 3.10.
The new unit cell marked out by the lattice plane boundaries
SHIFT while clicking on the atoms) and then clicking on the Calculate the best plane for the selected
atoms button to have the plane passing from those positions to appear. This is shown in Figure
3.9, done within a 3x3x3 supercell.
The reason we have oriented our system so that the normal to the (111) plane is pointing up is to
designate this lattice plane as the surface, aligning it with the new c axis for convenience. Therefore
we also need to reassign a and b axes, as well. This all comes down to dening a new unit cell.
Preserving the periodicities, the new unit cell is traced out by introducing additional lattice planes.
These new unit cells are not unique,
as long as one preserves the periodicities in the 3 axial directions
,
they can be taken as large and in any convenient shape as allowed. A rectangular shaped such a
unit cell, along with the outlying lattice plane parameters is presented in Figure 3.10 (the boundaries
have been increased to [-2,5] in each direction for practicality).
HOW TO PREPARE AN INPUT FILE FOR SURFACE CALCULATIONS 7
Figure 3.11.
Filtered new unit cell with the original cell's lattice vectors
Figure 3.12.
The reference points for the new axe1s
3.4.
Trimming the new unit cell.
The next procedure is simple and direct: remove all the atoms
outside the new unit cell. You can use the Select tool from the icons on the left (the 2nd from
top) or the shortcut key s. The trimmed new unit cell is shown in Figure 3.11, take note of
the periodicity in each section. It should be noted that, this procedure is only for deducing the
transformation matrix, which we'll be deriving in the next subsection: other than that, since it's still
dened by the old lattice vectors, it's not stackable to yield the correct periodicity so we'll be xing
that.
3.5.
Transforming into the new unit cell.
Now that we have the new unit cell, it is time to
transform the unit cell vectors to comply with the new unit cell. For the purpose of obtaining the
transformation matrix (which actually is the matrix that relates the new ones with the old ones), we
will need the coordinates of the 4 atoms on the edges. Such a set of 4 selected atoms are shown in
Figure 3.12. These atoms' fractional coordinates are as listed in Table 2 (upon selecting an atom,
VESTA displays its coordinates in the information panel below the visualization).
Taking o' as our new origin, the new lattice vectors in terms of the previous ones become (as we
subtract the origin's coordinates):
a' = -a+b
b' = -1/2a-1/2b+c
c' = a+b+c
Therefore our transformation matrix is:
HOW TO PREPARE AN INPUT FILE FOR SURFACE CALCULATIONS 8
Label a' b' c' o'
a
0 1/2 2 1
b
1 -1/2 1 0
c
-1/2 1/2 1/2 -1/2
Table 2.
Reference atoms' fractional coordinates
Figure 3.13.
The transformed structure with missing atoms
−1−1
21
1−1
21
0 1 1
(i.e., -a+b,-1/2a-1/2b+c,a+b+c the coecients are read in columns)
Transforming the initial cell with respect to this matrix is pretty straight forward, in the same
manner we exercised in subsection 3.2, Constructing the supercell, i.e., Edit
Edit Data
Unit
Cell.., then Remove symmetry and Option... and introducing the transformation matrix. A
further translation (origin shift) of (0,0,1/2) is necessary (the transformation matrix being -a+b,-
1/2a-1/2b+c,a+b+c+1/2) if you want the transformed structure look exactly like the one shown in
Figure 3.11.
3.5.1.
A Word of caution.
Due to a bug, present in VESTA, you might end with a transformed
matrix with missing atoms (as shown in Figure - compare it to the middle and rightmost segments of
Figure 3.11). For this reason, always make sure you check your resulting unit cell thoroughly! (This
bug has recently been xed and will be patched in the next version (3.1.7)
4
)
To overcome this problem, one can conduct the transformation via the TRANSTRU
5
tool of the
Bilbao Crystallographic Server. Enter your structural data (either as a CIF or by denition into
the text box), select Transform structure to a subgroup basis, in the next window enter 1 as
the Low symmetry Space Group ITA number (1 corresponding to the P1 symmetry group) and
the transformation matrix either in abc notation (-a+b,-1/2a-1/2b+c,a+b+c+1/2) or by directly
entering the matrix form (both are lled in the screenshot taken in Figure 3.14).
In the result page export the transformed structure data (Low symmetry structure data) to CIF
format by clicking on the corresponding button and open it in VESTA. This way all the atoms in
the new unit cell will have been included.
3.6.
Final Touch.
The last thing remains is introducing a vacuum area above the surface. For this
purpose we switch from fractional coordinates to Cartesian coordinates, so when the cell boundaries
are altered, the atomic positions will
not
change as a side result. VASP format supports both
4
Personal communication with K. Momma
5
http://www.cryst.ehu.es/cryst/transtru.html
HOW TO PREPARE AN INPUT FILE FOR SURFACE CALCULATIONS 9
Figure 3.14.
TRANSTRU input form
notations so we export our structural data into VASP format (File
Export Data..., select VASP
as the le format, then opt for Write atomic coordinates as: Cartesian coordinates).
After the VASP le with the atomic coordinates written in Cartesian format is formed, open it
with an editor (the contents are displayed in Table 3).
Directly edit and increase the c-lattice length from the given value (7.7942 Å in our case) to a
suciently high value (e.g., 25.0000 Å) and save it. Now when you open it back in VESTA, the
surface with its vacuum should be there as in Figure 3.15.
At this point, there might be a couple of questions that come to mind: What are those Pt atoms
doing at the top of the unit cell? Why are the C atoms positioned above the batch instead of the Pt
atoms?
The answer to these kind of questions is simple: Periodicity. By tiling the unit cell in the c-direction
using the Boundary... option and designating our range of coordinates for the {x,y,z}-directions
from 0 to 3, we obtain the system shown in Figure 3.16.
From the periodicity, in fractional coordinates,
f|z=0 =f|z=1
, meaning the atoms at the base and
at the very top of the unit cell are the same (or equivalent from the interpretational side). If we had
wanted the Pt atoms to be the ones forming the surface, then we would have made the transformation
with the -a+b,-1/2a-1/2b+c,a+b+c matrix instead of -a+b,-1/2a-1/2b+c,a+b+c+1/2, so the half
shift would amount the change in the order, and
then
increase the c-lattice parameter size in the
Cartesian coordinates notation (i.e., in the VASP le). The result of such a transformation is given
in Figure 3.17.
4.
Alternative Ways
In this work, a complete treatment of preparing a surface
in silico
is proposed. There are surely
more direct and automated tools that achieve the same task. It has been brought to our attention
HOW TO PREPARE AN INPUT FILE FOR SURFACE CALCULATIONS 10
generated_by_bilbao_crystallographic_server
1.0
6.3639612198 0.0000000000 0.0000000000
0.0000000000 5.5113520622 0.0000000000
0.0000000000 0.0000000000 7.7942290306
C Pt
12 12
Cartesian
0.000000000 3.674253214 6.495164688
0.000000000 1.837099013 1.299064110
3.181980610 1.837099013 1.299064110
1.590990305 0.918577018 6.495164688
4.772970915 4.592774880 1.299064110
1.590990305 4.592774880 1.299064110
4.772970915 0.918577018 6.495164688
0.000000000 0.000000000 3.897114515
3.181980610 0.000000000 3.897114515
4.772970915 2.755676031 3.897114515
1.590990305 2.755676031 3.897114515
3.181980610 3.674253214 6.495164688
0.000000000 3.674253214 2.598050405
1.590990305 0.918577018 2.598050405
4.772970915 0.918577018 2.598050405
1.590990305 4.592774880 5.196178858
3.181980610 1.837099013 5.196178858
0.000000000 1.837099013 5.196178858
4.772970915 4.592774880 5.196178858
0.000000000 0.000000000 0.000000000
3.181980610 3.674253214 2.598050405
3.181980610 0.000000000 0.000000000
4.772970915 2.755676031 0.000000000
1.590990305 2.755676031 0.000000000
Table 3.
The constructed (111) oriented VASP le's contents
that the commercial software package Accelrys Materials Studio
6
has an integrated tool called Cleave
Surface which exactly serves for the same purpose discussed in this work. Since it is propriety
software, it will not be further described here and we encourage the user to benet from freely
accessible software whenever possible.
Also, it is always to compare your resulting surface with that of an alternate one obtained using
another tool. In this sense, Surface Explorer
7
is very useful in visualizing how the surface will look,
eventhough its export capabilities are limited.
Chapter 4 (DFT Calculations for Solid Surfaces) of Zhang's Ph.D. thesis[11] contains very fruitful
discussions on possible ways to incorporate the surfaces in computations.
It is the author's intention to soon implement such an automated tool for constructing surfaces
from bulk data, integrated within the Bilbao Crystallographic Server's framework of tools.
6
http://accelrys.com/products/materials-studio/
7
http://surfexp.fhi-berlin.mpg.de
HOW TO PREPARE AN INPUT FILE FOR SURFACE CALCULATIONS 11
Figure 3.15.
Prepared surface with vacuum
5.
Conclusion
Preparing a surface t for atomic & molecular calculations can be tedious and tiresome. In this
work, we have tried to guide the reader in a step-by-step procedure, sometimes wandering o from
the direct path to show the mechanisms and reasons behind the usually taken on an as-it-is basis,
without being pondered upon. This way, we hope that the techniques acquired throughout the text
will be used in conjunction with other related problems in the future. A walkthru for the case
studied ((111) PtC surface preparation) is included as Appendix to provide a quick consultation in
the future.
6.
Acknowledgements
This work is the result of the inquiries by the Ph.D. students M. Gökhan ensoy and O. Karaca
Orhan. If they hadn't asked a practical way to construct surfaces, I wouldn't have sought a way.
Since I don't have much experience with surfaces, I turned to my dear friends Rengin Peköz and O.
Bar³ Malco§lu for help, whom enlightened me with their experiences on the issue.
7.
Appendix: Walkthru for PtC (111) Surface
(1) Open VESTA, (File
New Structure)
HOW TO PREPARE AN INPUT FILE FOR SURFACE CALCULATIONS 12
Figure 3.16.
New unit cell with periodicity applied
(a) Unit Cell:
(i) Space Group: 225 (F m -3 m)
(ii) Lattice parameter a: 4.5 Å
(b) Structure Parameters:
(i) New
Symbol:C; Label:C; x,y,z=0.0
(ii) New
Symbol:Pt; Label:Pt; x,y,z=0.5
(c) Boundary..
(i) x(min)=y(min)=z(min)=-2
(ii) x(max)=y(max)=z(max)=5
(d) Edit
Lattice Planes...
(i) (hkl)=(111); d(Å)=9.09327
(ii) (hkl)=(111); d(Å)=1.29904
(iii) (hkl)=(-110); d(Å)=3.18198
(iv) (hkl)=(-110); d(Å)=-3.18198
(v) (hkl)=(11-2); d(Å)=3.67423
(vi) (hkl)=(11-2); d(Å)=-4.59279
HOW TO PREPARE AN INPUT FILE FOR SURFACE CALCULATIONS 13
Figure 3.17.
Alternative surface with the Pt atoms on the top (Left: prior to vacuum
introduction; Center: with vacuum; Right: tiled in periodicity)
(compare with Figure 3.10)
(e) Select (Select tool - shortcut s key) and delete (shortcut Del key) all the atoms
lying out of the area designated by the lattice planes.
(f) Select an origin-atom of a corner and the 3 axe-atoms in the edge of each direction
of the unit cell, write down their fractional coordinates
(i) o(1,0,-1/2)
(ii) a(0,1,-1/2)
(iii) b(1/2,-1/2,1/2)
(iv) c(2,1,1/2)
(g) Subtract the origin-atom coordinates from the rest and construct the transformation
matrix accordingly
HOW TO PREPARE AN INPUT FILE FOR SURFACE CALCULATIONS 14
P=
−1−1
21
1−1
21
0 1 1
(h) Transform the initial unit cell with this matrix via TRANSTRU (http://www.cryst.ehu.es/cryst/transtru.html)
(Figure 3.14)
(i) Save the resulting (low symmetry) structure as CIF, open it in VESTA, export it to
VASP, select Cartesian coordinates
(j) Open the VASP le in an editor, increase the c-lattice parameter to a big value (e.g.
25.000) to introduce vacuum. Save it and open it in VESTA.
References
[1] Mois Ilia Aroyo, Juan Manuel Perez-Mato, Cesar Capillas, Eli Kroumova, Svetoslav Ivantchev, Gotzon Madariaga,
Asen Kirov, and Hans Wondratschek. Bilbao crystallographic server: I. databases and crystallographic computing
programs.
Zeitschrift für Kristallographie
, 221(1):1527, 01 2006. doi: 10.1524/zkri.2006.221.1.15.
[2] Mois I. Aroyo, Asen Kirov, Cesar Capillas, J. M. Perez-Mato, and Hans Wondratschek. Bilbao crystallographic
server. ii. representations of crystallographic point groups and space groups.
Acta Crystallographica Section A
,
62(2):115128, Mar 2006.
[3] M I Aroyo, J M Perez-Mato, D Orobengoa, E Tasci, G De La Flor, and A Kirov. Crystallography online: Bilbao
crystallographic server.
Bulg Chem Commun
, 43(2):183197, 2011.
[4] S. R. Hall, F. H. Allen, and I. D. Brown. The crystallographic information le (cif): a new standard archive le
for crystallography.
Acta Crystallographica Section A
, 47(6):655685, Nov 1991.
[5] G. Kresse and J. Furthmüller. Ecient iterative schemes for
ab initio
total-energy calculations using a plane-wave
basis set.
Phys. Rev. B
, 54:1116911186, Oct 1996.
[6] Koichi Momma and Fujio Izumi.
VESTA3 for three-dimensional visualization of crystal, volumetric and morphol-
ogy data
.
Journal of Applied Crystallography
, 44(6):12721276, Dec 2011.
[7] A Zaoui and M Ferhat. Dynamical stability and high pressure phases of platinum carbide.
Solid State Communi-
cations
, 151(12):867869, 6 2011.
[8] Saulius Graºulis, Adriana Da²kevi£, Andrius Merkys, Daniel Chateigner, Luca Lutterotti, Miguel Quirós,
Nadezhda R. Serebryanaya, Peter Moeck, Robert T. Downs, and Armel Le Bail. Crystallography open data-
base (cod): an open-access collection of crystal structures and platform for world-wide collaboration.
Nucleic
Acids Research
, 40(D1):D420D427, 2012.
[9] Alec Belsky, Mariette Hellenbrandt, Vicky Lynn Karen, and Peter Luksch. New developments in the inorganic
crystal structure database (icsd): accessibility in support of materials research and design.
Acta Crystallographica
Section B
, 58(3 Part 1):364369, Jun 2002.
[10] Springer, editor.
The Landolt-Boernstein Database (http://www.springermaterials.com/navigation/)
. Springer
Materials.
[11] Yongsheng Zhang.
First-principles statistical mechanics approach to step decoration at solid surfaces
. PhD thesis,
Frei Universitat Berlin, 2008.
