þ7‡´| jjjjjxŠŠŠš ¤´´(ÜxŠT tŠ*´jSuggested Exercises for CrystalView 1.0 T.H. Kosel, MSE 503 10/15/91 Please do not change any of the structures in the cells folder on the network, since other students will want to use them. If the program should hang (heaven forbid...), use Command-period to kill it, then restart. 1. Open the existing structures in the "cells" folder, and figure out the basis without reference to your notes. First, you need to figure out the Bravais lattice by searching for centering translations. You can view the cell from different orientations to help do this, using the Mouse or Crystal hkl orientation options. It may help to pick orientations near the low-index directions <100> or <110> using the mouse. It may also help to hide all but one type of basis atom using the Hide Atoms option - as long as you aren't tempted to just read the correct basis from the screen! (Remember, your'e trying to use the program to help learn, not to do the job for you....) You can check whether you are right about the centering by using the Centering option, picking the type of centering you think is correct, and finding out if the structure is unchanged. Once you know what centering translations exist, you know the Bravais lattice. (None of the stored structures are non-cubic.) Figure out how many atoms of each type there are per lattice point, and then choose a basis according to the rules in the previous handout. Now, use the New Basis option to redefine the structure, and see if it matches the original structure. 2. Use the Show All Atoms and Show Basis options with existing structures (or ones of your own definition) to help see how the basis group is repeated by adding it to all Bravais lattice points. Select Show All Atoms first; it will become checked in the menu, and you will see all atoms that are generated (inside and outside the cell) by adding the basis group to each lattice point. Now select Show Basis; it will become checked in the menu, and you will see only the basis group. You can then switch back and forth between views of only the basis and all atoms by turning the Show Basis option on and off. (This will be difficult if not impossible to visualize with complex structures like Spinel.) 3. Use the Show All Atoms option in conjunction with the Hide Atoms option to see the interpenetrating lattices in GaAs, NaCl, CsCl, etc. That is, use Hide Atoms to hide all but one basis atom, and note that it has the same arrangement in space as the Bravais lattice points which lie on the corners and any face or body center points. (This will be difficult if not impossible to visualize with complex structures like Spinel. It is a little hard to see with FCC strucutres since the atoms are disembodied from the cell. You may want to change the centering of a structure to make it base centered.) 4. Note that several different basis groups can be chosen that represent the same structure. For instance, for NaCl, if the Na+ atom is chosen as being at 000, you can put the Cl- ion 1/2 1/2 1/2, 1/2 0 0, 0 1/2 0, 0 0 1/2, 1 1/2 0, etc. and still have the same crystal structure. Similarly, the second atom of the GaAs basis could be chosen at 1/4 1/4 1/4 or at 3/4 3/4 1/4. Use Edit Basis to change the location of the second atom of the basis. (Versions later than 8.40 do not have the restriction on using 1 as a coordinate in the basis group.) 5. Use the Tetrahedra option of the Lines menu to install tetrahedra for the interior atoms of GaAs, and for the 4 interior tetrahedra of the high cristobalite structure. This makes a good exercise in visualization. 6. Use the About [hkl] option of the Rotate menu to investigate n-fold proper rotation axes. For instance, cubic crystals ussually have 4's along <100>, 2's along <110>, 3's along <111>. Diamond cubic has 4-fold rotation-inversion (improper) axes along <100> instead of proper 4's. (We need some more code for a rotation-inversion menu option.) € )<=G¸» — ˜ Ë Ì Ñ á é ì ô u € ‡ ’|~†‡Šüùüùöùñùíùíùêùêùêùêùêùçùä@ @€()=FG€ö÷ ¹ º   ÜCD |}~€‚ƒ„…ìììììÙÆÙÙƳ ÙÙzÙgÙÙÆÙÆYYTYYYYYT !ÀûxhÔ&G ÿ!À9ûxþ˜„L &G!À ûxþ˜„L &G!À ûxþ˜„L &G!À ûxþ˜„L &G ÿ!ÀYûxþ˜„L &G!À ûxþ˜„L &G!À ûxþ˜„L &G!À ûxþ˜„L &G …†‡ûè!À ûxþ˜„L &G o1o1*o2 tG þèýä88ûÈ8 8ýäÞ‡‡‡Pÿÿ Š …‡  –Èó&tHHÚ(ÿáÿâùFG(üHHÚ(d'@=à/Р  pÐR@H -:LaserWriter (ÕüàüÀ{{€€{