Periodic Boundary Conditions (PBC)

Tutorial 3 - Build a Primitive Unit Cell of Diamond Crystal From Methane, PBC/3D

3-1 Create a new molecule and corresponding view window by clicking on the "New" toolbar button.

3-2 Make the "Carbon Tetrahedral" fragment the "Current Fragment" by double-clicking on the "Element Fragment" tool button and then clicking on the "Carbon" button and then the "Carbon Tetrahedral" button in the "Select Element Fragment" dialog.

3-3 Click anywhere in the empty view window to create a methane molecule.

3-4 Center the molecule in the view window by clicking on the "Center" toolbar button and then position the molecule so all atoms are visible.

3-5 Turn on atom labels for the view window by checking "Labels" from the "View" menu of the main window.

3-6 Show the "Point Group" dialog for the molecule by selecting "Point Group" from the "Edit" menu of the main window. In the "Point Group" dialog, check the "Enable Point Group Symmetry" box and then select the "Td" item from the "Constraint to Subgroup" combobox.

3-7 Change the CH bond lengths to match the experimental values for the diamond CC bond length. Click on the "Modify Bond" toolbar button and then click on atoms 1 and 2 in the the view window. In the corresponding "Semichem Smartslide" dialog, change the bond length value from 1.07 to 1.54 in the input field and then click on the OK button. Note that all of the CH bond lengths have increased to 1.54 to preserve the Td symmetry. In the Point Group dialog, uncheck the "Enable Point Group Symmetry" box and then click the "OK" button.

3-8 Show the PBC dialog for the molecule by selecting "PBC" from the "Edit" menu of the main window.

3-9 In the "Symmetry" tab of the PBC dialog, select "Three" from the "Lattice Dimensions" combobox.

3-10 In the "Cell" tab of the PBC dialog, push down the "Place" button to enable placement of the cell origin ("O (0,0,0)") vertex at any atom selected in the view window using the mouse. In the combobox to the immediate right of the "Place" button, select "Cell" instead of "Vertex" so that the whole cell will be translated rather than just the cell origin vertex. In the view window, click on atom 3.

3-11 In the "Cell" tab of the PBC dialog, select "a (1,0,0)" instead of "O (0,0,0)" to enable placement of the head of the "a" lattice vector at any atom selected in the view window using the mouse. In the combobox to the immediate right of the "Place" button, select "Vertex" instead of "Cell" so that just the "a" vertex will be translated rather than the whole cell. In the view window, click on atom 5.

3-12 In the "Cell" tab of the PBC dialog, select "b (0,1,0)" instead of "a (1,0,0)" to enable placement of the head of the "b" lattice vector at any atom selected in the view window using the mouse. In the view window, click on atom 4.

3-13 In the "Cell" tab of the PBC dialog, select "c (0,0,1)" instead of "b (0,1,0)" to enable placement of the head of the "c" lattice vector at any atom selected in the view window using the mouse. In the view window, click on atom 2.

3-14 In the "Contents" tab of the PBC dialog, select the "Delete Atoms | Redundant" item from the "Edit" menu of the Atom List editor.

3-15 In the "Contents" tab of the PBC dialog, change the hydrogen atom to a carbon atom atom by editing the second row of the "Symbol" column in the atom list editor.

3-16 In the "Contents" tab of the PBC dialog, select "Rebond All" from the "Bonds" popup menu.

3-17 The bonds between reference unit cells atoms and replicate cell atoms are shown in the replicate format, which is "Low Layer" by default. In the "View" tab of the PBC dialog, select "Dull" from the "Replicate Contents Format" combobox in order to better see the bonds in this case.

3-18 At this point we have defined a primitive unit cell for a PBC/3D model of a diamond crystal.

3-19 In the "View" tab of the PBC dialog, check the "Show All Boundary Atoms" checkbox to show all atoms in or on the boundary of the cell.

3-20 In the "View" tab of the PBC dialog, show two cells along each of the "a", "b" and "c" axes using the corresponding spin boxes in the "Cell Replication" section.

3-21 In the "View" tab of the PBC dialog, click on the "Combine" button in the "Cell Replication" section. This will cause the reference unit cell and the replicate unit cells shown on screen to be combined into a larger "super" unit cell which is 8 times the primitive unit cell. Note the atom number changes. Note also that the number of cells being viewed is automatically reduced to one to avoid potential confusion.