Building crystals from atoms

Another example has to do with the mechanical properties of solids. Solids are classified as ductile when they yield plastically when stressed, or brittle when they do not yield easily, but instead break when stressed. A useful measure of this behavior is the yield stress ay, which is the stress up to which the solid behaves as a linear elastic medium when stressed, that is, it returns to its original state when the external stress is removed. Yield stresses in solids, measured in units of MPa, range from 40 in Al, a rather soft and ductile metal, to 5 x 10 in diamond, the hardest material, a brittle insulator. The yield stresses of common steels range from 200-2000 MPa. Again we see an impressive range of more than three orders of magnitude in how a solid responds to an external agent, in this case a mechanical stress. 

The structure of crystals can be understood to some extent by taking a close look at the properties of the atoms from which they are composed. We can identify several broad categories of atoms, depending on the nature of electrons that participate actively in the formation of the soUd. The electrons in the outermost shells of the isolated atom are the ones that interact strongly with similar electrons in neighboring atoms as already mentioned these are called valence electrons. The remaining electrons of the atom are tightly bound to the nucleus, their wavefunctions (orbitals) 

Selected shapes of the corresponding crystal unit cells are shown in Fig. 1.1. 

The natural units for various physical quantities in the context of the structure of solids and the names of unit multiples are collected in two tables at the end of the hook (see Appendix I). 

Potassium Calcium Scandium Titanium Vanadium Chromium Manganese Iron Cobalt 

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The various types of point defect found in pure or almost pure stoichiometric solids are summarized in Figure 1.17. It is not easy to imagine the three-dimensional consequences of the presence of any of these defects from two-dimensional diagrams, but it is important to remember that the real structure of the crystal surrounding a defect can be important. If it is at all possible, try to consult or build crystal models. This will reveal that it is easier to create vacancies at some atom sites than others, and that it is easier to introduce interstitials into the more open parts of the structure. 

A crystal can be characterized both by the unit cell (the carrier of the chemical composition and atomic structure), and by three translation vectors a, b and c the latter can be used to build the whole crystal from original cells. Each of these three vectors corresponds to a symmetry operation, since these operations superpose a crystal with itself each atom (supposed to be a point) moves over to a similar atom in the nearby unit cell. Any point (atom, including) can be transferred to another crystal point, identical to the first, by operation of a translation t, which is... 

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