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- https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Online_Dictionary_of_Crystallography_(IUCr_Commission)/01%3A_Fundamental_Crystallography/1.113%3A_Wigner-Seitz_cellThe Wigner-Seitz cell of a body-centered cubic lattice I is a cuboctahedron (Figure 2) and the Wigner-Seitz cell of a face-centered cubic lattice F is a rhomb-dodecahedron (Figure 3). Since the recipr...The Wigner-Seitz cell of a body-centered cubic lattice I is a cuboctahedron (Figure 2) and the Wigner-Seitz cell of a face-centered cubic lattice F is a rhomb-dodecahedron (Figure 3). Since the reciprocal lattice of body-centered lattice is a face-centered lattice and reciprocally, the first Brillouin zone of a body-centered cubic lattice is a rhomb-dodecahedron and that of a face-centered cubic lattice is a cuboctahedron.
- https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Online_Dictionary_of_Crystallography_(IUCr_Commission)/04%3A_Crystal_Chemistry/4.02%3A_Isomorphous_CrystalsTwo crystals are said to be isomorphous if (a) both have the same space group and unit-cell dimensions and (b) the types and the positions of atoms in both are the same except for a replacement of one...Two crystals are said to be isomorphous if (a) both have the same space group and unit-cell dimensions and (b) the types and the positions of atoms in both are the same except for a replacement of one or more atoms in one structure with different types of atoms in the other (isomorphous replacement), such as heavy atoms, or the presence of one or more additional atoms in one of them (isomorphous addition). Isomorphous crystals can form solid solutions.
- https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Online_Dictionary_of_Crystallography_(IUCr_Commission)/05%3A_Structure_Determination/5.06%3A_Heavy-Atom_MethodFor a compound containing a heavy atom (i.e. one with a significantly higher atomic scattering factor than the others present) the diffraction phases calculated from the position of the heavy atom are...For a compound containing a heavy atom (i.e. one with a significantly higher atomic scattering factor than the others present) the diffraction phases calculated from the position of the heavy atom are used to compute a first approximate electron density map. Further portions of the structure are recognizable as additional peaks in the map. Successive approximate electron density maps may then be calculated to solve the entire structure.
- https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Online_Dictionary_of_Crystallography_(IUCr_Commission)/10%3A_Biological_Crystallography/10.02%3A_Isomorphous_replacementFigure: Principle of the isomorphous replacement method for structure solution. F 1 and F 2 represent the total structure factor from two isomorphous crystals for a given reflection, ΔF is their diffe...Figure: Principle of the isomorphous replacement method for structure solution. F 1 and F 2 represent the total structure factor from two isomorphous crystals for a given reflection, ΔF is their difference. The angles φ 1 and φ ΔF are the phases of F 1 and ΔF, they are related via φ.
- https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Online_Dictionary_of_Crystallography_(IUCr_Commission)/03%3A_X-rays/3.12%3A_Ewald_sphereA reflected direction, of unit vector s h , will satisfy the diffraction condition if the diffraction vector OH = IH – IO = s h /λ – s o /λ (s o unit vector in the direction IO) is a reciprocal lattic...A reflected direction, of unit vector s h , will satisfy the diffraction condition if the diffraction vector OH = IH – IO = s h /λ – s o /λ (s o unit vector in the direction IO) is a reciprocal lattice vector, namely if H is a node of the reciprocal lattice (see Diffraction condition in reciprocal space) . If other reciprocal lattice nodes, such as G, lie also on the sphere, there will be reflected beams along IG, etc.
- https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Online_Dictionary_of_Crystallography_(IUCr_Commission)/01%3A_Fundamental_Crystallography/1.88%3A_Priority_ruleFor orthorhombic space groups, the priority rule is applied only to the ‘standard symbol’. The symbols for the other five settings are obtained from the standard symbol by the appropriate transformati...For orthorhombic space groups, the priority rule is applied only to the ‘standard symbol’. The symbols for the other five settings are obtained from the standard symbol by the appropriate transformations, without invoking the priority rule again. In I222, the three rotation axes and the three screw axes intersect, whereas in I2 1 2 1 2 1 neither the three rotation axes nor the three screw axes intersect.
- https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Online_Dictionary_of_Crystallography_(IUCr_Commission)/01%3A_Fundamental_Crystallography/1.53%3A_Group_isomorphismIt is a mapping between two groups that sets up a one-to-one correspondence between the elements of the groups in a way that respects the respective group operations. Let (G, *) and (H, #) be two grou...It is a mapping between two groups that sets up a one-to-one correspondence between the elements of the groups in a way that respects the respective group operations. Let (G, *) and (H, #) be two groups, where "*" and "#" are the binary operations in G and H, respectively. A group isomorphism from (G, *) to (H, #) is a bijection from G to H, i.e. If H = G and the binary operations # and * coincide, the bijection is an automorphism.
- https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Online_Dictionary_of_Crystallography_(IUCr_Commission)/09%3A_Twinning/9.12%3A_Twinning(effects_of)
- https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Online_Dictionary_of_Crystallography_(IUCr_Commission)/09%3A_Twinning/9.22%3A_Twin_elementThe direct lattice element about which a twin operation is performed.
- https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Online_Dictionary_of_Crystallography_(IUCr_Commission)/01%3A_Fundamental_Crystallography/1.80%3A_Patterson_vectorA real-space vector representing the difference between two position vectors locating scattering centers in a diffracting crystal lattice .
- https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Online_Dictionary_of_Crystallography_(IUCr_Commission)/10%3A_Biological_Crystallography/10.04%3A_Molecular_ReplacementThe probe may be a different crystal form of the same protein; or it may be a different protein with a high level of sequence identity, which correlates well with structural resemblance. As a rule of ...The probe may be a different crystal form of the same protein; or it may be a different protein with a high level of sequence identity, which correlates well with structural resemblance. As a rule of thumb, molecular replacement is often straightforward if the probe is well characterized and shares at least 40% sequence identity with the target. The translation function T is then determined to shift the now correctly orientated probe model to the correct coordinates within the asymmetric unit.
