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<title>GAMGI Tutorials: Calcite crystalline structure</title>
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<h1>Calcite crystalline structure</h1>
<div id="notebook">
<ul>
<li><span>Page 1</span></li>
</ul>
</div>
<div class="contents">
Calcite (CaCO3) is the stable form of calcium carbonate and is one of the most
widely available minerals, present in sedimentary (limestone) and metamorphic
(marble) rocks. Stalactites and stalagmites in caves are usually formed by calcite.
<p/>
First we create a cell with the calcite lattice parameters and space group,
then one atom of Ca, C and O, to model the atoms of the structure, and finally
link the cell with the atoms to build the crystal, using the Wyckoff positions
reported in the literature for calcite.
<p/>
A lateral view of the calcite structure, for a single conventional cell,
can be seen in the figure at
<a href="http://www.gamgi.org/images/screenshot10_4b.png">
http://www.gamgi.org/images/screenshot10_4b.png</a>.
<h3>Calcite</h3>
<ol>
<li>
Press <b>Cell->Create</b> and set <b>Group</b> to <b>167</b>, the R-3c
space group for calcite. As the lattice is rombohedral, <b>System</b>
and <b>Lattice</b> are automatically set to <b>h</b> and <b>R</b>,
respectively.
</li>
<li>
Set lattice parameters <b>a</b> and <b>c</b> to <b>4.9896</b> and
<b>17.0610</b>, respectively, the reported values for calcite. Entries
<b>b</b>, <b>ab</b>, <b>ac</b> and <b>bc</b> are automatically disabled,
as these parameters are known for the hexagonal system.
</li>
<li>
Press <b>Atom->Create</b> and set <b>Style</b> to <b>Solid</b>.
Write <b>Ca</b> in the <b>Element</b> entry and press the mouse
over the screen (outside the cell), to create a Ca atom. Repeat
the task to create C and O atoms. These three atoms will act as
models to create the structure.
</li>
<li>
Press <b>Cell->Link</b> and select the <b>Crystal</b> link method.
Initially, the <b>Wyckoff</b> menu (in <b>Position</b> page) only
has the option, <b>1 Basis 1</b>, which is the usual crystallographic
base or motif. The first "1" indicates the number of objects that will
be linked to each crystallographic node, and the last "1" the point symmetry.
</li>
<li>
Press the mouse over the cell to identify it. The cell belongs to space
group 167, so the <b>Wyckoff</b> menu is automatically updated to include
options for all the Wyckoff positions available for this space group:
<b>12 f 1</b>, <b>6 e .2</b>, <b>6 d -1</b>, <b>4 c 3.</b>, <b>2 b -3.</b>
and <b>2 a 32</b>.
</li>
<li>
Press the mouse over the Ca atom, to identify the atom used as a model
to create the Ca atoms of the crystal.
</li>
<li>
According to literature, Ca atoms occupy Wyckoff positions b, so select
these positions in the Wyckoff menu: <b>2 b -3.</b>. For these positions,
all coordinates are known in advance, so <b>x</b>, <b>y</b> and <b>z</b>
entries are all automatically disabled.
</li>
<li>
Press <b>Ok</b>. 2 atoms of Ca are added to each node of the
cell (and removed if they fall outside the cell volume).
</li>
<li>
Repeat the link procedure, to add the C atoms. Press the mouse first
over the cell, and then over the C atom. Carbon atoms occupy positions a,
so select these positions in the Wyckoff menu: <b>2 a 32</b>. For these
positions, all coordinates are known in advance, so <b>x</b>, <b>y</b>
and <b>z</b> entries are all automatically disabled.
</li>
<li>
Press <b>Ok</b>. 2 atoms of C are added to each node of the
cell (and removed if they fall outside the cell volume).
</li>
<li>
Repeat the link procedure, to add the O atoms. Press the mouse
first over the cell, and then over the O atom. Select positions e,
in the Wyckoff menu: <b>6 e .2</b>. For these positions, only the y,z
coordinates are fixed by symmetry. Enter <b>0.257</b> for <b>x</b>
and press <b>Ok</b>. 6 atoms of O are added to each node of the
cell (and removed if they fall outside the cell volume).
</li>
<li>
Select <b>Light->Create</b> and press <b>Ok</b>, to add a light
and give atoms a three dimensional look.
</li>
<li>
The atomic structure is now created. To remove the Ca,C,O atoms used
as models during the building process, press <b>Atom->Remove</b> and
click the mouse over them.
</li>
<li>
The conventional rombohedral cell thus created has 30 atoms inside.
For Ca: 4 x 1/6 + 4 x 1/12 (corners) + 2 x 1/3 + 2 x 1/6 (edges) + 4 (inside)
= 6 atoms. For C: 4 x 1/3 + 4 x 1/6 (edges) + 4 (inside) = 6 atoms.
For O: 8 x 1/2 (faces) + 14 (inside) = 18. As expected, the CaCO3
stoichiometry is obeyed.
</li>
<li>Rotate,move,scale the calcite cell with the mouse. Press
<b>Atom->Measure</b> to determine lengths and angles between atoms.
</li>
</ol>
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