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How to Prepare an Input File for Surface Calculations

Emre S. Tasci

Description

Tools

Procedure

Initial structural data

Constructing the Supercell

Lattice Planes

Trimming the new unit cell

Transforming into the new unit cell

A Word of caution

Final Touch

Alternative Ways

Conclusion

Acknowledgements

Appendix: Walkthru for PtC (111) Surface

1. Open VESTA, (“File→New Structure”)
   1. “Unit Cell”:
      1. Space Group: 225 (F m -3 m)
      2. Lattice parameter a: 4.5 Å
   2. “Structure Parameters”:
      1. New→Symbol:C; Label:C; x,y,z=0.0
      2. New→Symbol:Pt; Label:Pt; x,y,z=0.5
   3. “Boundary..”
      1. x(min)=y(min)=z(min)=-2
      2. x(max)=y(max)=z(max)=5
   4. “Edit→Lattice Planes…”
      1. (hkl)=(111); d(Å)=9.09327
      2. (hkl)=(111); d(Å)=1.29904
      3. (hkl)=(-110); d(Å)=3.18198
      4. (hkl)=(-110); d(Å)=-3.18198
      5. (hkl)=(11-2); d(Å)=3.67423
      6. (hkl)=(11-2); d(Å)=-4.59279
      (compare with Figure 10↑)
   5. Select (“Select tool” – shortcut “s” key) and delete (shortcut “Del” key) all the atoms lying out of the area designated by the lattice planes.
   6. 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
      1. o(1,0,-1/2)
      2. a(0,1,-1/2)
      3. b(1/2,-1/2,1/2)
      4. c(2,1,1/2)
   7. Subtract the origin-atom coordinates from the rest and construct the transformation matrix accordingly
      P = ⎡⎢⎢⎢⎣ − 1 − 121 1 − 121 011⎤⎥⎥⎥⎦
   8. Transform the initial unit cell with this matrix via TRANSTRU (http://www.cryst.ehu.es/cryst/transtru.html) (Figure 14↑)
   9. Save the resulting (low symmetry) structure as CIF, open it in VESTA, export it to VASP, select “Cartesian coordinates”
   10. Open the VASP file 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.

---

Recently, we are working on liquid alloys and for our work, we need the coordination number distribution. It’s kind of a gray area when you talk about coordination number of atoms in a liquid but it’s better than nothing to understand the properties and even more. I’d like to write a log on the tools I’ve recently coded/used in order to refer to in the future if a similar situation occurs. Also, maybe there are some others conducting similar research so, the tools introduced here may be helpful to them.

Recently, while searching recent publications on liquid alloys, I’ve found a very good and resourceful article on liquid Na-K alloys by Dr. J.-F. Wax (“Molecular dynamics study of the static structure of liquid Na-K alloys”, Physica B 403 (2008) 4241-48 | doi:10.1016/j.physb.2008.09.014). In this paper, among other properties, he had also presented the partial pair distribution functions. Partial-pair distribution functions is the averaged probability that you’ll encounter an atom in r distance starting from another atom. In solid phase, due to the symmetry of the crystal structure, you have discrete values instead of a continuous distribution and everything is crystal clear but I guess that’s the price we pay dealing with liquids. 8)

Partial-pair distribution functions are very useful in the sense that they let you derive the bond-length between constituent atom species, corresponding to the first minimums of the plots. Hence, one can see the neighborhood ranges by just looking at the plots.

I’ve sent a mail to Dr. Wax explaining my research topics and my interest and asking for his research data to which he very kindly and generously replied by providing his data.

He had sent me a big file with numerous configurations (coordinates of the atoms) following each other. The first -and the simplest- task was to split the file into seperate configuration files via this bash script:

#!/bin/bash
# Script Name: split_POS4.sh
# Splits the NaK conf files compilation POS4_DAT into sepearate
# conf files.
# Emre S. Tasci <e.tasci@tudelft.nl>
#                                              01/09/09

linestart=2
p="p"
for (( i = 1; i <= 1000; i++ ))
do
    echo $i;
    lineend=$(expr $linestart + 2047)
    confname=$(printf "%04d" $i)
    echo -e "3\n2048" > $confname
    sed -n "$linestart,$(echo $lineend$p)" POS4_DAT >> $confname
    linestart=$(expr $lineend + 1)
    cat $confname | qhull i TO $confname.hull
done

(The compilation was of 1000 configurations, each with 2048 atoms)

As you can check in the line before the “done” closer, I’ve -proudly- used Qhull software to calculate the convex hull of each configuration. A convex hull is the -hopefully minimum- shape that covers all your system. So, for each configuration I now had 2 files: “xxxx” (where xxxx is the id/number of the configuration set) storing the coordinates (preceded by 3 and 2048, corresponding to dimension and number of atoms information for the qhull to parse & process) and “xxxx.hull” file, generated by the qhull, containing the vertices list of each facet (preceded by the total number of facets).

A facet is (in 3D) the plane formed by the vertice points. Imagine a cube, where an atom lies at each corner, 3 in the inside. So, we can say that our system consists of 11 atoms and the minimal shape that has edges selected from system’s atoms and covering the whole is a cube, with the edges being the 8 atoms at the corners. Now, add an atom floating over the face at the top. Now the convex hull that wraps our new system would no longer be a 6-faced, 8-edged cube but a 9-faced, 9-edged polygon. I need to know the convex hull geometry in order to correctly calculate the coordination number distributions (details will follow shortly).

The aforementioned two files look like:

sururi@husniya hull_calcs $ head 0001
3
2048
 0.95278770E+00 0.13334565E+02 0.13376155E+02
 0.13025256E+02 0.87618381E+00 0.20168993E+01
 0.12745038E+01 0.14068998E-01 0.22887323E+01
 0.13066590E+02 0.20788591E+01 0.58119183E+01
 0.10468218E+00 0.58523640E-01 0.64288678E+01
 0.12839412E+02 0.13117012E+02 0.79093881E+01
 0.11918105E+01 0.12163854E+02 0.10270868E+02
 0.12673985E+02 0.11642538E+02 0.10514597E+02
sururi@husniya hull_calcs $ head 0001.hull
180
568 1127 1776
1992 104 1551
956 449 1026
632 391 1026
391 632 1543
391 956 1026
966 632 1026
966 15 1039
632 966 1039

The sets of 3 numbers in the xxxx.hull file is the ids/numbers of the atoms forming the edges of the facets, i.e., they are the vertices.

To calculate the coordination number distribution, you need to pick each atom and then simply count the other atoms within the cut-off distance depending on your atom’s and the neighboring atom’s species. After you do the counting for every atom, you average the results and voilà! there is your CN distribution. But here’s the catch: In order to be able to count properly, you must make sure that, your reference atom’s cutoff radii stay within your system — otherwise you’ll be undercounting. Suppose your reference atom is one of the atoms at the corners of the cube: It will (generally/approximately) lack 7/8 of the neighbouring atoms it would normally have if it was to be the center atom of the specimen/sample. Remember that we are studying a continuous liquid and trying to model the system via ensembles of samples. So we should omit these atoms which has neighborhoods outside of our systems. Since neighborhoods are defined through bond-length, we should only include the atoms with a distance to the outside of at least cut-off radii. The “outside” is defined as the region outside the convex hull and it’s designated by the facets (planes).

From the xxxx.hull file, we have the ids of the vertice atoms and their coordinates are stored in the xxxx file. To define the plane equation

we will use the three vertice points, say p1, p2 and p3. From these 3 points, we calculate the normal n as:

then, the plane equation (hence the coefficients a,b,c,d) can be derived by comparing the following equation:

Here, (x0,y0,z0) are just the coordinates of any of the vertice points. And finally, the distance D between a point p1(x1,y1,z1) and a plane (a,b,c,d) is given by:

Since vector operations are involved, I thought it’s better to do this job in Octave and wrote the following script that calculates the coefficients of the facets and then sets down to find out the points whose distances to all the facets are greater than the given cut-off radius:

sururi@husniya trunk $ cat octave_find_atoms_within.m
DummyA = 3;
%conf_index=292;

% Call from the command line like :
%   octave -q --eval "Rcut=1.65;conf_index=293;path='$(pwd)';" octave_find_atoms_within.m
% hence specifying the conf_index at the command line.

% Emre S. Tasci <e.tasci@tudelft.nl>                    *
%
% From the positions and vertices file, calculates the plane
% equations (stored in "facet_coefficients") and then
% filters the atoms with respect to their distances to these
% facets. Writes the output to
% "hull_calcs/xxxx_insiders.txt" file
%                                              03/09/09 */

conf_index_name = num2str(sprintf("%04d",conf_index));;
%clock
clear facet_coefficients;
facet_coefficients = [];
global p v facet_coefficients
fp = fopen(strcat(path,"/hull_calcs/",conf_index_name));
k = fscanf(fp,"%d",2); % 1st is dim (=3), 2nd is number of atoms (=2048)
p = fscanf(fp,"%f",[k(1),k(2)]);
p = p';
fclose(fp);
%p = load("/tmp/del/delco");
fp = fopen(strcat(path,"/hull_calcs/",conf_index_name,".hull"));
k = fscanf(fp,"%d",1);% number of facets
v = fscanf(fp,"%d",[3,k]);
v = v';
fclose(fp);
%v = load("/tmp/del/delver");

function [a,b,c,d,e] = getPlaneCoefficients(facet_index)
    global p v
    % Get the 3 vertices
    p1 = p(v(facet_index,1)+1,:); % The +1s come from the fact 
    p2 = p(v(facet_index,2)+1,:); % that qhull enumeration begins
    p3 = p(v(facet_index,3)+1,:); % from 0 while Octave's from 1

    %printf("%d: %f %f %f %f %f %f %f %f %f\n",facet_index,p1,p2,p3);

    % Calculate the normal
    n = cross((p2-p1),(p3-p1));

    % Calculate the coefficients of the plane :
    % ax + by + cz +d = 0
    a = n(1);
    b = n(2);
    c = n(3);
    d = -(dot(n,p1));
    e = norm(n);
    if(e==0)
        printf("%f\n",p1);
        printf("%f\n",p2);
        printf("%f\n",p3);
        printf("%d\n",facet_index);
    endif
endfunction

function dist = distanceToPlane(point_index,facet_index)
    global p facet_coefficients
    k = facet_coefficients(facet_index,:);
    n = [k(1) k(2) k(3)];
    dist = abs(dot(n,p(point_index,:)) + k(4)) / k(5);
endfunction

for i = [1:size(v)(1)]
    [a,b,c,d,e] = getPlaneCoefficients(i);
    facet_coefficients = [ facet_coefficients ; [a,b,c,d,e]];
endfor

%Rcut = 1.65; % Defined from command line calling
% Find the points that are not closer than Rcut
inside_atoms = [];
for point = [1:size(p)(1)]
%for point = [1:100]
    inside=true;
    for facet = [1:size(v)(1)]
    %for facet = [1:10]
        %printf("%d - %d : %f\n",point,facet,dist);
        if (distanceToPlane(point,facet)<Rcut)
            inside = false;
            break;
        endif
    endfor
    if(inside)
        inside_atoms = [inside_atoms point-1];
    endif
endfor

fp = fopen(strcat(path,"/hull_calcs/",conf_index_name,"_insiders.txt"),"w");
fprintf(fp,"%d\n",inside_atoms);
fclose(fp);
%clock

This script is runned within the following php code which then takes the filtered atoms and does the counting using them:

<?PHP
/* Emre S. Tasci <e.tasci@tudelft.nl>                    *
 *
 * parse_configuration_data.php
 *
 * Written in order to parse the configuation files
 * obtained from J.F. Wax in order to calculate the 
 * Coordination Number distribution. Each configuration 
 * file contain 2048 atoms' coordinates starting at the 
 * 3rd line. There is also a convex hull file generated 
 * using qhull (http://www.qhull.com) that contains the 
 * indexes (starting from 0) of the atoms that form the 
 * vertices of the convex hull. Finally there is the 
 * IP.dat file that identifies each atom (-1 for K; 1 for 
 * Na -- the second column is the relative masses).
 *
 *                                              02/09/09 */

/*
# if present, remove the previous run's results file
if(file_exists("results.txt"))
    unlink("results.txt");
 */

error_reporting(E_ALL ^ E_NOTICE);

if(!file_exists("results.txt"))
{
    $fp = fopen("results.txt","w");
    fwrite($fp,"CONF#"."\tNa".implode("\tNa",range(1,20))."\tK".implode("\tK",range(1,20))."\n");
    fclose($fp);
}

# Support for command line variable passing:
for($i=1;$i<sizeof($_SERVER["argv"]);$i++)
{
        list($var0,$val0) = explode("=",$_SERVER["argv"][$i]);
        $_GET[$var0] = $val0;
}

if($_GET["configuration"])
    calculate($_GET["configuration"]);
else
    exit("Please specify a configuration number [php parse_configuration_data.php configuration=xxx]\n");

function calculate($conf_index)
{
    # Define the atoms array
    $arr_atoms = Array();

    # Get the information from the files
    parse_types($arr_atoms);
    $refs = get_vertices($conf_index);
    parse_coordinates($arr_atoms,$conf_index);

    # Define the Rcut-off values (obtained from partial parid distribution minimums)
    $Rcut_arr = Array();
    $Rscale = 3.828; # To convert reduced distances to Angstrom (if needed)
    $Rscale = 1; # To convert reduced distances to Angstrom
    $Rcut_arr["Na"]["Na"] = 1.38 * $Rscale;
    $Rcut_arr["Na"]["K"]  = 1.65 * $Rscale;
    $Rcut_arr["K"]["Na"]  = 1.65 * $Rscale;
    $Rcut_arr["K"]["K"]   = 1.52 * $Rscale;
    $Rcut = $Rcut_arr["Na"]["K"]; # Taking the maximum one as the Rcut for safety

    /*
    # We have everything we need, so proceed to check 
    # if an atom is at safe distance wrt to the vertices

    # Define all the ids
    $arr_test_ids = range(0,2047);
    # Subtract the ref atoms' ids
    $arr_test_ids = array_diff($arr_test_ids, $refs);
    sort($arr_test_ids);
    //print_r($arr_test_ids);

    $arr_passed_atom_ids = Array();
    # Check each atom against refs
    for($id=0, $size=sizeof($arr_test_ids); $id<$size; $id++)
    {
        //echo $id."\n";
        $arr_atoms[$arr_test_ids[$id]]["in"] = TRUE;
        foreach ($refs as $ref)
        {
            $distance = distance($arr_atoms[$arr_test_ids[$id]],$arr_atoms[$ref]);
            //echo "\t".$ref."\t".$distance."\n";
            if($distance < $Rcut)
            {
                $arr_atoms[$arr_test_ids[$id]]["in"] = FALSE;
                break;
            }
        }
        if($arr_atoms[$arr_test_ids[$id]]["in"] == TRUE)
            $arr_passed_atom_ids[] = $arr_test_ids[$id];
    }
     */

    # Run the octave script file to calculate the inside atoms
    if(!file_exists("hull_calcs/".sprintf("%04d",$conf_index)."_insiders.txt"))
    exec("octave -q --eval \"Rcut=".$Rcut.";conf_index=".$conf_index.";path='$(pwd)';\" octave_find_atoms_within.m");

    # Read the file generated by Octave
    $arr_passed_atom_ids = file("hull_calcs/".sprintf("%04d",$conf_index)."_insiders.txt",FILE_IGNORE_NEW_LINES);

    $arr_test_ids = range(0,2047);
    $arr_test_ids = array_diff($arr_test_ids, $refs);
    sort($arr_test_ids);
    for($i=0, $size=sizeof($arr_test_ids);$i<$size;$i++)
        $arr_atoms[$arr_test_ids[$i]]["in"]=FALSE;

    # Begin checking every passed atom
    foreach($arr_passed_atom_ids as $passed_atom_id)
    {
        $arr_atoms[$passed_atom_id]["in"] = TRUE;
        for($i=0, $size=sizeof($arr_atoms); $i<$size; $i++)
        {
            $distance = distance($arr_atoms[$passed_atom_id],$arr_atoms[$i]);
            //echo $passed_atom_id."\t---\t".$i."\n";
            if($distance < $Rcut_arr[$arr_atoms[$passed_atom_id]["id"]][$arr_atoms[$i]["id"]] && $distance>0.001)
                $arr_atoms[$passed_atom_id]["neighbour_count"] += 1;
        }
    }

    # Do the binning
    $CN_Na = Array();
    $CN_K  = Array();
    for($i=0, $size=sizeof($arr_atoms); $i<$size; $i++)
    {
        if(array_key_exists("neighbour_count",$arr_atoms[$i]))
        {
            ${"CN_".$arr_atoms[$i]['id']}[$arr_atoms[$i]["neighbour_count"]] += 1;
        }
    }

    ksort($CN_Na);
    ksort($CN_K);

    //print_r($arr_atoms);
    //print_r($CN_Na);
    //print_r($CN_K);

    # Report the results
    $filename = "results/".sprintf("%04d",$conf_index)."_results.txt";
    $fp = fopen($filename,"w");
    fwrite($fp, "### Atoms array ###\n");
    fwrite($fp,var_export($arr_atoms,TRUE)."\n");
    fwrite($fp, "\n### CN Distribution for Na ###\n");
    fwrite($fp,var_export($CN_Na,TRUE)."\n");
    fwrite($fp, "\n### CN Distribution for K ###\n");
    fwrite($fp,var_export($CN_K,TRUE)."\n");

    # Percentage calculation:
    $sum_Na = array_sum($CN_Na);
    $sum_K  = array_sum($CN_K);
    foreach($CN_Na as $key=>$value)
        $CN_Na[$key] = $value * 100 / $sum_Na;
    foreach($CN_K  as $key=>$value)
        $CN_K[$key]  = $value * 100 / $sum_K;
    //print_r($CN_Na);
    //print_r($CN_K);
    fwrite($fp, "\n### CN Distribution (Percentage) for Na ###\n");
    fwrite($fp,var_export($CN_Na,TRUE)."\n");
    fwrite($fp, "\n### CN Distribution (Percentage) for K ###\n");
    fwrite($fp,var_export($CN_K,TRUE)."\n");
    fclose($fp);

    # Write the summary to the results file
    $fp = fopen("results.txt","a");
    for($i=1;$i<=20;$i++)
    {
        if(!array_key_exists($i,$CN_Na))
            $CN_Na[$i] = 0;
        if(!array_key_exists($i,$CN_K))
            $CN_K[$i] = 0;
    }
    ksort($CN_Na);
    ksort($CN_K);
    fwrite($fp,sprintf("%04d",$conf_index)."\t".implode("\t",$CN_Na)."\t".implode("\t",$CN_K)."\n");
    fclose($fp);

}

function parse_types(&$arr_atoms)
{
    # Parse the types
    $i = 0;
    $fp = fopen("IP.DAT", "r");
    while(!feof($fp))
    {
        $line = fgets($fp,4096);
        $auxarr = explode(" ",$line);
        if($auxarr[0]==-1)
            $arr_atoms[$i]["id"] = "Na";
        else
            $arr_atoms[$i]["id"] = "K";
        $i++;
    }
    fclose($fp);
    array_pop($arr_atoms);
    return 0;
}

function get_vertices($conf_index)
{
    $arr_refs = Array();

    # Get the ids of the vertices of the convex hull
    $filename = "hull_calcs/".sprintf("%04d",$conf_index).".hull";
    $fp = fopen($filename, "r");

    # Bypass the first line
    $line = fgets($fp,4096);

    while(!feof($fp))
    {
        $line = fgets($fp,4096);
        $auxarr = explode(" ",$line);
        array_pop($auxarr);
        $arr_refs = array_merge($arr_refs, $auxarr);
    }
    fclose($fp);
    // $arr_refs = array_unique($arr_refs); # This doesn't lose the keys
    $arr_refs = array_keys(array_count_values($arr_refs)); # But this does.
    return $arr_refs;
}

function parse_coordinates(&$arr_atoms, $conf_index)
{
    # Parse the coordinates
    $i = 0;
    $filename = "hull_calcs/".sprintf("%04d",$conf_index);
    $fp = fopen($filename, "r");

    # Bypass the first two lines
    $line = fgets($fp,4096);
    $line = fgets($fp,4096);

    while(!feof($fp))
    {
        $line = fgets($fp,4096);
        $arr_atoms[$i]["coords"] = explode(" ",$line);
        array_shift($arr_atoms[$i]["coords"]);
        $i++;
    }
    fclose($fp);
    array_pop($arr_atoms);
    return 0;
}

function distance(&$atom1,&$atom2)
{
    # Calculate the distance between the two atoms
    $x1 = $atom1["coords"][0];
    $x2 = $atom2["coords"][0];
    $y1 = $atom1["coords"][1];
    $y2 = $atom2["coords"][1];
    $z1 = $atom1["coords"][2];
    $z2 = $atom2["coords"][2];
    return sqrt(pow($x1-$x2,2) + pow($y1-$y2,2) + pow($z1-$z2,2));
}

?>

The code above generates a “results/xxxx_results.txt” file containing all the information obtained in arrays format and also appends to “results.txt” file the relevant configuration file’s CN distribution summary. The systems can be visualized using the output generated by the following plotter.php script:

<?PHP
/* Emre S. Tasci <e.tasci@tudelft.nl>                    *
 * Parses the results/xxxx_results.txt file and generates 
 * an XYZ file such that the atoms are labeled as the 
 * vertice atoms, close-vertice atoms and inside atoms..
 *                                              02/09/09 */

# Support for command line variable passing:
for($i=1;$i<sizeof($_SERVER["argv"]);$i++)
{
        list($var0,$val0) = explode("=",$_SERVER["argv"][$i]);
        $_GET[$var0] = $val0;
}

if($_GET["configuration"])
    $conf_index = $_GET["configuration"];
else 
    exit("Please specify a configuration number [php plotter.php configuration=xxx]\n");

$filename = sprintf("%04d",$conf_index);

# Get the atom array from the results file. Since results file 
# contains other arrays as well, we slice the file using sed for the 
# relevant part
$last_arr_line = exec('grep "### CN Distribution" results/'.$filename.'_results.txt -n -m1|sed "s:^\([0-9]\+\).*:\1:gi"');
exec('sed -n "2,'.($last_arr_line-1).'p" results/'.$filename.'_results.txt > system_tmp_array_dump_file');
$str=file_get_contents('system_tmp_array_dump_file');
$atom_arr=eval('return '.$str.';');
unlink('system_tmp_array_dump_file');

# Now that we have the coordinates, we itarate over the atoms to check 
# the characteristic and designate them in the XYZ file.
$fp = fopen("system_".$filename.".xyz","w");
fwrite($fp,sizeof($atom_arr)."\n");
fwrite($fp,"Generated by plotter.php\n");
for($i=0, $size=sizeof($atom_arr);$i<$size;$i++)
{
    if(!array_key_exists("in",$atom_arr[$i]))
        $atomlabel = "Mg";#Vertices
    elseif($atom_arr[$i]["in"]==TRUE)
        $atomlabel = $atom_arr[$i]["id"];#Inside atoms
    else
        $atomlabel = "O";#Close-vertice atoms
    fwrite($fp,$atomlabel."\t".implode("\t",$atom_arr[$i]["coords"]));
}
fclose($fp);
?>

which generates a “system_xxxx.xyz” file, ready to be viewed in a standard molecule viewing software. It designates the vertice atoms (of the convex hull, remember? 8)as “Mg” and the atoms close to them as “O” for easy-viewing purpose. A sample parsed file looks like this:

The big orange atoms are the omitted vertice atoms; the small red ones are the atoms critically close to the facets and hence also omitted ones. You can see the purple and yellow atoms which have passed the test sitting happilly inside, with the counting done using them.. 8)

Now that I’ve started to once again updating this scientific blog of mine, let me also talk about the things that occured since the last entry on October (or even going before that).

Meeting with Dr. Villars
The biggest event that occured to me was meeting with Dr. Pierre Villars, the person behind the Pauling File database which I have benefitted and still benefitting from. When I had registered to the “MITS 2008 – International Symposium on Materials Database”, an event hosted by the NIMS Materials Database, I had no idea that Dr. Villars would also be attending to the event, so it was a real surprise learning afterwards that I’d have a chance to meet him in person.

You can read the sheer happiness from my face on the occasion of meeting Dr. Villars

Dr. Villars is a very kind and a cheerful person, I had a greatest time knowing him and afterwards I had the privilege of visiting him in his home office in the lovely town of Vitznau, Switzerland where I enjoyed the excellent hospitality of the Villars family. Dr. Villars helped me generously in providing the data in my research project for finding transformation toughening materials through datamining which I’m indebted for.

The MITS 2008 – Int’l Symposium on Materials Database
I was frequently using the databases on the NIMS’ website and had the honour to participate in the last year’s event together with my dear supervisor Dr. Marcel Sluiter. On that occasion, I presented two talks – a materials based one, and another about database query&retrieval methods- titled “Inference from Various Material Properties Using Mutual Information and Clustering Methods” and “Proposal of the XML Specification as a Standard for Materials Database Query and Result Retrieval”, respectively.

I have an ever growing interest on the Japanese Culture since I was a youngster and due to this interest, my expectations from this trip to Japan was high enough for me to be afraid of the fact that I may have disappointed since it was next-to-impossible for anything to fulfill the expectations I had built upon. But, amazingly, I was proved false: the experience I had in Japan were far more superior to anything I had anticipated. The hospitality of the organizing commitee was incredible: everything had been taken care of and everyone was as kind as one could be. I had the chance to meet Dr. Villars as I’ve already wrote about above, and also Dr. Xu, Dr. Vanderah, Dr. Dayal and Dr. Sims and had a great time. It was also due to this meeting, I met a dear friend.

Ongoing Projects
During my time here, I still don’t have anything published and that’s the number one issue that’s bothering me. Apart from my research on the transformation toughening materials, I worked for a time on a question regarding to a related phenomenon, namely about the martensitic transformation mechanism on some transition-metal alloy types. We were able to come up with a nice equation and adequate coefficients that caught the calculation results but couldn’t manage to transfer it to -so to say- a nicely put theory and that doomed the research to being an “ad-hoc” approach. I’ll be returning to it at the first chance I get, so currently, it’s been put on ice (and now remembering how, in the heat of the research I was afraid that someone else would come up with the formula and it would be too late for me.. sad, so sad..). One other (side) project was related to approximate a specific amorphous state in regards with some basis structures obtained using datamining. This project was really exciting and fun to work on because I got to use different methods together: first some datamining, then DFT calculations on the obtained structures and finally thermodynamics to extrapolate to higher temperatures. We’re at the stage of revising the draft at the moment (gratefully!).

Life in the Netherlands & at the TUDelft
It has been almost one and a half year since I started my postdoc here in TUDelft. When we first came here, my daughter was still hadn’t started speaking (yet she had been practicing walking) and now she approximately spent the same amount of time in the Netherlands as she had spent in Turkey (and thankfully, she can speak and also running to everywhere! 8).

When I had come here, I was a nano-physicist, experienced in MD simulations and -independently- a coder when the need arouse. Now, I’m more of a materials guy and coding for the purpose.. 8) I enjoy the wide variety of the jobs & disciplines people around me are working on and definitely benefitting from the works of my friends in our group. I couldn’t ask for more, really. (OK, maybe I’d agree if somebody would come up with an idea for less windy and more sunny weather here in Delft. That’s the one thing I couldn’t still get used to. Delft is a marvelous city with bikes and kind people everywhere, canals full of lillies in the spring, historical buildings everywhere, Amsterdam, Den Haag and Rotterdam just a couple of train stations away and if you wish, Antwerpen, Brussels and Brugges (Belgium) is your next-door neighbour but this dark and closed weather can sometimes be a little mood lowering.) TUDelft is really a wonderful place to be with all the resources and connections that makes you feel you can learn anything and meet anyone that is relevant to the work you’re doing without worrying about the cost. And you’re being kept informed about the events taking place about you through the frequent meetings in your group, in your section, in your department, in your field. I’ve learned a lot and I’m really happy I was accepted here.

(And just when you think I was out of photos!.. 8)

So that’s about the things I’ve enjoyed experiencing and living through.. And I promise, I’ll be posting more regularly and frequently from now on..

Yours the chatty.

It’s of great importance to have sufficient number of k-points when doing DFT calculations. The most practical (but CPU time costly) way is to check energies for different number of k-points until some kind of "convergence" is reached.

Here are the two scripts I’ve recently written for VASP to check for suitable k-point values.

The first code runs the calculation with increasing k-points (I have a cubic cell, so using same number of k-points for the 3 lattice axes).

Before running this code, make sure that the essential files (KPOINTS POSCAR POTCAR INCAR) are in the directory, also copy your KPOINTS file to a file named "KP" which has KPOINTS mesh defined as 2x2x2:

sururi@husniya Al3Li $ cat KP
Automatic
0
Gamma
2 2 2
0 0 0

The following script will then run the calculations, incrementing the number of K-Points by 1 per each axis. It will store the output (and the 4 input files) in archive files in the format k{%03d}.tar.bz2 where the value in the curly brackets is actually the number of k-points per axis. As you can easily see, it runs from k= 1x1x1 (silly but since this is tutorial) to k=13x13x13.

#!/bin/bash

# A script file to run the system for various k-points in order to find the optimal setting
# Emre S. Tasci, 20/10/2008

for (( i = 1; i <= 13; i++ )) 
do  
    date
    echo $i

    # change the KPOINTS (KP is a copy of the KPOINTS with k=2:
    cat KP|sed s/"2 2 2"/"$i $i $i"/ > KPOINTS

    # run the vasp
    vasp > vasp.out

    # archive the existing files (except the archive files):
    tar -cvjf $(printf "k%02d.tar.bz2" $i) $(ls |grep -v "\(.bz2\)\|\(runrunrun.sh\)\|\(KP$\)\|\(work\)")

    # remove the output files:
    rm $(ls *|grep -v "\(.bz2\)\|\(KPOINTS\)\|\(POSCAR\)\|\(POTCAR\)\|\(INCAR\)\|\(runrunrun.sh\)\|\(KP$\)") -f
    date
    echo "=================================================="
done

After it ends, you should see something like

-rw-r----- 1 sururi users 299K 2008-10-20 10:14 POTCAR
-rw-r--r-- 1 sururi users  283 2008-10-20 10:14 POSCAR
-rw-r--r-- 1 sururi users  604 2008-10-20 10:14 INCAR
-rw-r--r-- 1 sururi users   31 2008-10-20 11:06 KP
-rw-r--r-- 1 sururi users   34 2008-10-20 14:33 KPOINTS
-rw-r--r-- 1 sururi users 195K 2008-10-20 11:08 k01.tar.bz2
-rw-r--r-- 1 sururi users 196K 2008-10-20 11:08 k02.tar.bz2
-rw-r--r-- 1 sururi users 193K 2008-10-20 11:08 k03.tar.bz2
-rw-r--r-- 1 sururi users 195K 2008-10-20 11:08 k04.tar.bz2
-rw-r--r-- 1 sururi users 195K 2008-10-20 11:08 k05.tar.bz2
-rw-r--r-- 1 sururi users 197K 2008-10-20 11:09 k06.tar.bz2
-rw-r--r-- 1 sururi users 197K 2008-10-20 11:09 k07.tar.bz2
-rw-r--r-- 1 sururi users 200K 2008-10-20 11:10 k08.tar.bz2
-rw-r--r-- 1 sururi users 201K 2008-10-20 11:10 k09.tar.bz2
-rw-r--r-- 1 sururi users 205K 2008-10-20 11:11 k10.tar.bz2
-rw-r--r-- 1 sururi users 205K 2008-10-20 11:12 k11.tar.bz2
-rw-r--r-- 1 sururi users 211K 2008-10-20 11:13 k12.tar.bz2
-rw-r--r-- 1 sururi users 211K 2008-10-20 11:14 k13.tar.bz2
-rwxr--r-- 1 sururi users  732 2008-10-20 14:02 runrunrun.sh

Now, it’s time for the second script. Create a new directory (say “work”) and then type the following into a script file (don’t forget to set it as executable (or you can also always “sh ” 😉 ) )

#!/bin/bash
 
# Script name: energy_extract_from_OUTCAR.sh
# Emre S. Tasci, 20/10/2008
 
# Reads the OUTCAR files from the archive files in the parent directory
# Stores the energies in corresponding ENE files.
 
# (Assuming filenames are given like "k05.tar.bz2")
 
k=00
 
for i in ../k*.bz2
do
    kpre=$k
    enepre="0.00000000"
 
    # Extract OUTCAR
    tar -xjf $i OUTCAR
 
    # Parse file counter from filename 
    k=$(echo $(basename $i)|sed "s:k\([0-9]*\).*:\1:")
 
    # write the energies calculated in this run 
    cat OUTCAR | grep "energy without"|awk '{print $8}' > $(printf "%s_ENE" $k)
 
    #calculate the energy difference between this and the last run
    if [ -e "$(printf "%s_ENE" $kpre)" ] 
    then
        enepre=$(tail -n1 $(printf "%s_ENE" $kpre));
    fi
 
    enethis=$(tail -n1 $(printf "%s_ENE" $k));
 
    # Using : awk '{ print ($1 >= 0) ? $1 : 0 - $1}' : for absolute value
 
    echo -e $(printf "%s_ENE" $kpre) " :\t" $enepre "\t" $(printf "%s_ENE" $k) ":\t" $enethis "\t" $(echo $(awk "BEGIN { print $enepre - $enethis}") | awk '{ print ($1 >= 0) ? $1 : 0 - $1}')
 
    rm -f OUTCAR
done;

when runned, this script will produce an output similar to the following:

sururi@husniya work $ ./energy_extract_from_OUTCAR.sh
00_ENE  :        0.00000000      01_ENE :        -6.63108952     6.63109
01_ENE  :        -6.63108952     02_ENE :        -11.59096452    4.95988
02_ENE  :        -11.59096452    03_ENE :        -12.96519853    1.37423
03_ENE  :        -12.96519853    04_ENE :        -13.20466179    0.239463
04_ENE  :        -13.20466179    05_ENE :        -13.26411934    0.0594576
05_ENE  :        -13.26411934    06_ENE :        -13.26528991    0.00117057
06_ENE  :        -13.26528991    07_ENE :        -13.40540825    0.140118
07_ENE  :        -13.40540825    08_ENE :        -13.35505746    0.0503508
08_ENE  :        -13.35505746    09_ENE :        -13.38130280    0.0262453
09_ENE  :        -13.38130280    10_ENE :        -13.36356457    0.0177382
10_ENE  :        -13.36356457    11_ENE :        -13.37065368    0.00708911
11_ENE  :        -13.37065368    12_ENE :        -13.37249683    0.00184315
12_ENE  :        -13.37249683    13_ENE :        -13.38342842    0.0109316

Which shows the final energies of the sequential runs as well as the difference of them. You can easily plot the energies in the gnuplot via as an example “plot “12_ENE”“. You can also plot the evolution of the energy difference with help from awk. To do this, make sure you first pipe the output of the script to a file (say “energies.txt”):

./energy_extract_from_OUTCAR.sh > energies.txt

And then, obtaining the last column via awk

cat energies.txt |awk '{print $7}' > enediff.txt

Now you can also easily plot the difference file.

Hope this scripts will be of any help.

Still saddened by the loss of Randy Pausch whom I knew about from his famous "Last Lecture", while working on the Miedema’s Model, I came across this article by him:

Dr. Villars had already mentioned Miedema’s passing at a young age but still it was really tragic to find such a sad detail on a scientific article.

I checked the web for a Miedema biography but couldn’t find any. The only information I could find was from H. Bakker’s book which I’m quoting the preface below:

PREFACE

   Andries Miedema started developing his rather unconventional model in the sixties as a professor at the University of Amsterdam and continued this work from 1971 at Philips Research Laboratories. At first he encountered scepticism in these environments, where scientists were expecting all solutions from quantum- mechanics. Of course, Miedema did not deny that eventually quantum mechanics could produce (almost) exact solutions of problems in solid-state physics and materials science, but the all-day reality he experienced was, – and still is -, that most practical problems that are encountered by researchers are too complex to allow a solution by application of the Schr6dinger equation. Besides, he believed in simplicity of nature in that sense that elements could be characterised by only a few fundamental quantities, whereby it should be possible to describe alloying behaviour. On the basis of a comparison of his estimates of the heat of formation of intermetallic compounds with ample experimental data, he was gradually able to overcome the scepticism of his colleagues and succeeded in convincing the scientific world that his model made sense. This recognition became distinct by the award of the Hewlett Packard prize in 1980 and the Hume-Rothery decoration in 1981. At that time, Miedema himself and many others were successfully using and extending the model to various questions, of course realising that the numbers obtained by the model have the character of estimates, but estimates that could not be obtained in a different fast way. It opened new perspectives in materials science. Maybe the power of the model is best illustrated by a discussion, the present author had with Jim Davenport at Brookhaven National Laboratory in 1987. Dr Davenport showed him a result that was obtained by a one-month run on a Gray 1 supercomputer. This numerical result turned out to be only a few kilo Joules different from the outcome by Miedema’s model, obtained within a few minutes by use of a pocket calculator. Andries Miedema passed away in 1992 at a much too young age of 59 years. His death came as a bad shock not only for the scientific community in The Netherlands, but for scientists all over the world. However, for his family, friends and all the people, who knew him well, it is at least some consolation that he lives on by his model, which is being used widely and which is now part of many student programmes in physics, chemistry and materials science.

   It is the aim of the present review to make the reader familiar with the application of the model, rather than to go in-depth into the details of the underlying concepts. After studying the text, the reader should be able, with the aid of a number of tables from Miedema’s papers and his book, given in the appendix, to make estimates of desired quantities and maybe even to extend the model to problems that, so far, were not handled by others. Beside, the reader should be aware of the fact that not all applications could be given in this review. For obvious reasons only part of all existing applications are reported and the reader will find further results of using the model in Miedema’s and co-worker’s papers, book and in literature.

   Dr Hans Bakker is an associate professor at the Van der Waals-Zeeman Institute of the University of Amsterdam. In 1970 Andries Miedema was the second supervisor of his thesis on tracer diffusion. He inspired him to subsequent work on diffusion and defects in VIII-IIIA compounds at a time, when, – as Bakker’s talk was recently introduced at a conference -, these materials were not yet relevant’ as they are now. Was it again a foreseeing view of Andries Miedema? Was it not Miedema’s standpoint that intermetallic compounds would become important in the future?

   Rather sceptic about the model as Bakker was at first like his colleagues, his scepticism passed into enthusiasm, when he began using the model with success in many research problems. In 1984 Bakker’s group started as one of the first in the world ball milling experiments. Surprisingly this seemingly crude technique turned out to be able to induce well-defined, non-equilibrium states and transformations in solids. Miedema’s model appeared again to be very helpful in understanding and predicting those phenomena.

Hans Bakker
Mauro Magini

Preface from Enthalpies in Alloys : Miedema’s Semi-Emprical Model
H. Bakker
Trans Tech Publications 1998 USA
ISSN 1422-3597