Geometry+of+Lattices

Geometry of Crystals
Crystalline material such as metals and ceramics have atomic arrangements. Each crystal can be subdivided down to a unit cell. Some examples of unit cells are simple cubic, body-centered cubic, and face centered cubic. Ceramic unit cells include simple tetragonal, orthorhombic monoclinic, and triclinic.

X-ray diffraction of crstal produce specifc peaks related to the crystal plane and spacing. However, liquids or amorphous solids (such as glass) and liquids will not produce specific peaks.

Diffraction of Crystals, the Bragg Law and deBroglie wavelength
W.L. Bragg discovered that X-rays are diffracted by crystals and formulated the //**Bragg Law**//. where n=order of relection = 1,2,3. Only when the sine of the angle is less than one and d is the distance between planes will produce favorable conditions for diffraction. Lamda is the //**de Broglie wavelength**//, where e is charge of an electron, c the velocity of light, h is Planck's constant, m is the rest mass of an electron, and V is the potential difference applied to accelerate the electron. The //de Broglie wavelength (in angstroms) is plotted for acceleration voltages from 30kV to 400kV below.//







d is the distance betwen adjacent planes in (hkl) system and depends on the crystal type to relate to the spacing. For example, for a cubic crystal lattice d is related by the following equation. a is the lattice parameter.