Periodic Boundary Conditions (PBC)

Tutorial 6 - Transform a Face-Centered Unit Cell of Diamond Crystal to a Primitive Unit Cell, PBC/3D

6-1 Start a new file by selecting the Create New Molecule Group option from the File menu in the main window.

6-2 Show the PBC dialog for the molecule by selecting PBC from the Tools menu of the main window.

6-3 In the Symmetry tab of the PBC dialog, select Three from the Lattice Dimensions drop-down list.

6-4 In the Symmetry tab of the PBC dialog, check the Enable Space Group Symmetry checkbox, and then select 227 (F d -3 m:1) from the Constrain to Space Group drop-down list.

6-5 In the Contents tab of the PBC dialog, add a carbon atom at fractional coordinates (0, 0, 0) by first selecting C from the Symbol column (be sure to tab out of the Symbol field) and then selecting the Add button.

6-6 In the Cell tab of the PBC dialog, select Fix Contents’ Fractional Coordinates from the Cell Changes drop-down list, and then change the “a” cell length from 4 to the experimental value of 3.56 in the corresponding input field. Note that all of the cell lengths change to 3.56, and also the space group symmetry is preserved because of the Cell Changes option being used.

6-7 In the Contents tab of the PBC dialog, select Rebond All from the Bonds popup menu. Then, go to the the View tab and select Dull instead of Low Layer from the Replicate Contents Display drop-down list.

6-8 At this point, we have defined a Face-Centered Cubic unit cell for a PBC/3D model of a diamond crystal.

6-9 Then, do the following steps: (a) uncheck the Enable Space Group Symmetry box in the Symmetry tab; (b) select Fix Contents’ Cartesian Coordinates from the Cell Changes drop-down list of the Cell tab.

6-10 In the Cell tab of the PBC dialog, push down the Place button, and select a (1,0,0) instead of 0 (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 View window, click on atom 7.

6-11 In the Cell tab of the PBC dialog, push down the Place button, and 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 3.

6-12 In the Cell tab of the PBC dialog, push down the Place button, and 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 5.

6-13 In the Cell tab of the PBC dialog, select Delete All Atoms Outside Cell from the Trim Contents popup menu.

6-14 In the Contents tab of the PBC dialog, select Rebond All from the Bonds popup menu.

6-15 In the View tab of the PBC dialog, select Dull from the Replicate Contents Display drop-down list.

6-16 We now have a primitive unit cell for diamond crystal that gives the same crystal structure as that from the face-centered cubic unit cell we started with.

6-17 In the View tab of the PBC dialog, check the Show All Boundary Atoms checkbox.