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Structure factorIn physics, in the area of crystallography, the structure factor of a crystal is a mathematical description of how the crystal scatters incident radiation. The structure factor is a particularly useful tool in the interpretation of interference patterns obtained in Xray, electron and neutron diffraction experiments. Additional recommended knowledgeScattering from a crystalA crystal is a periodic arrangement of atoms in a particular pattern. Each of the atoms may scatter incident radiation such as Xrays, electrons and neutrons. Because of the periodic arrangement of the atoms, the interference of waves scattered from different atoms may cause a distinct pattern of constructive and destructive interference to form. This is the diffraction pattern caused by the crystal. In the kinematical approximation for diffraction, the intensity of a diffracted beam is given by: where is the wavefunction of a beam scattered a vector , and is the so called structure factor which is given by: Here, is the position of an atom j in the unit cell, and f_{j} is the scattering power of the atom, also called the atomic form factor. The sum is over all atoms in the unit cell. It can be shown that in the ideal case, diffraction only occurs if the scattering vector is equal to a reciprocal lattice vector . The structure factor describes the way in which an incident beam is scattered by the atoms of a crystal unit cell, taking into account the different scattering power of the elements through the term f_{i}. Since the atoms are spatially distributed in the unit cell, there will be a difference in phase when considering the scattered amplitude from two atoms. This phase shift is taken into account by the complex exponential term. The atomic form factor, or scattering power, of an element depends on the type of radiation considered. Because electrons interact with matter though different processes than for example Xrays, the atomic form factors for the two cases are not the same. Structure factors for specific lattice typesTo compute structure factors for a specific lattice, compute the sum above over the atoms in the unit cell. Since crystals are often described in terms of their Miller indices, it is useful to examine a specific structure factor in terms of these. Bodycentered cubic (BCC) As a convention, the bodycentered cubic system is described in terms of a simple cubic lattice with primitive vectors , with a basis consisting of and . The corresponding reciprocal lattice is also simple cubic with side 2π / a. In a monoatomic crystal, all the form factors f are the same. The intensity of a diffracted beam scattered with a vector by a crystal plane with Miller indices (hkl) is then given by: We then arrive at the following result for the structure factor for scattering from a plane (hkl):
This result tells us that for a reflection to appear in a diffraction experiment involving a bodycentered crystal, the sum of the Miller indices of the scattering plane must be even. If the sum of the Miller indices is odd, the intensity of the diffracted beam is reduced to zero due to destructive interference. This zero intensity for a group of diffracted beams is called a systematic absence. Since atomic form factors fall off with increasing diffraction angle corresponding to higher Miller indices, the most intense diffraction peak from a material with a BCC structure is typically the (110). The (110) plane is the most densely packed of BCC crystal structures and is therefore the lowest energy surface for a thin film to expose. Films of BCC materials like iron and tungsten therefore grow in a characteristic (110) orientation. Facecentered cubic (FCC) In the case of a monoatomic FCC crystal, the atoms in the basis are at the origin with indices (0,0,0) and at the three face centers , , with indices given by (1/2,1/2,0), (0,1/2,1/2), (1/2,0,1/2). An argument similar to the one above gives the expression with the result
The most intense diffraction peak from a material that crystallizes in the FCC structure is typically the (111). Films of FCC materials like silicon tend to grow in a (111) orientation with a triangular surface symmetry although the surfaces of wafers on which integrated circuits are grown instead have the (100) orientation with a square surface symmetry. Diamond Crystal Structure The Diamond cubic crystal structure is possessed by diamond (carbon), most semiconductors and tin. The basis cell contains 8 atoms located at cell positions:
The Structure factor then takes on a form like this:
h+k+l is odd then F^{2} will be 32f_{Si}^{2} h+k+l is an even multiple of 2 then F^{2} will be 64f_{Si}^{2} h+k+l is an odd multiple of 2 then F^{2} will be 0 See also

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Structure_factor". A list of authors is available in Wikipedia. 