Unit cell atoms belong

PETN, [C(CH20N02)4] is a molecular crystal with 29 atoms per molecule, with two molecules per unit cell, and belongs to the tetragonal P42,c space group. The internal co-ordinates used were from Kitaigorodskii [23]. RDX,... 

CH2NN02 ] has 21 atoms per molecule, 8 molecules per unit cell, and belongs to the orthorhombic Pbca space group, with internal co-ordinates from Choi and Prince [24], This results in 1176 atomic orbitals for the 168 atoms per unit cell and for this size of a system, it becomes especially important to utilize efficient numerical techniques and accurate physical models in order to obtain results in a reasonable time-frame. 

Atoms can also reside on centers of inversion. Since there is no inversion center in the space group Cmm2, which was considered in Table 1.18, we turn our attention to the distribution of the centers of inversion in the unit cell that belongs to the triclinic space group symmetry P1 Figure 1.45). 

Number of atoms per unit cell. Keep in mind that a huge number of unit cells are in contact with each other, interlocking to form a three-dimensional crystal This means that several of the atoms in a unit cell do not belong exclusively to that cell Specifically—... 

The number of atoms in a unit cell is counted by noting how they are shared between neighboring cells. For example, an atom at the center of a cell belongs entirely to that cell, but one on a face is shared between two cells and counts as one-half an atom. As noted earlier for an fee structure, the eight corner atoms contribute 8 X 1/8 = 1 atom to the cell. The six atoms at the centers of faces contribute 6x1/2 = 3 atoms (Fig. 5.37). The total number of atoms in an fee unit cell is therefore 1 + 3=4, and the mass of the unit cell is four times the mass of one atom. For a bcc unit cell (like that in Fig. 5.34b), we count 1 for the atom at the center and 1/8 for each of the eight atoms at the vertices, giving 1 + (8 X 1/8) = 2 overall. 

In addition to the two structures already discussed, another arrangement of atoms in a cubic unit cell is possible. Atoms of a metal are identical, so the ratio of atomic sizes is 1.000, which allows a coordination number of 12. One structure that has a coordination number of 12 is known as face-centered cubic fee), and it has one atom on each comer of the cube and an atom on each of the six faces of the cube. The atoms on the faces are shared by two cubes, so one-half of each atom belongs in each cube. With there... 

Fortunately, the known superconductors belong to a broad class of inorganic compounds in which the atoms have a layered configuration. Therefore, they can be classified and compared to one another by specifying the composition, the type and the sequence of the layers contained in the unit cell of the structure. This approach is... 

In some circumstances the magnitudes of the translation vectors must be taken into account. Let us demonstrate this with the example of the trirutile structure. If we triplicate the unit cell of rutile in the c direction, we can occupy the metal atom positions with two kinds of metals in a ratio of 1 2, such as is shown in Fig. 3.10. This structure type is known for several oxides and fluorides, e.g. ZnSb20g. Both the rutile and tlie trirutile structure belong to the same space-group type PAjmnm. Due to the triplicated translation vector in the c direction, the density of the symmetry elements in trirutile is less than in rutile. The total number of symmetry operations (including the translations) is reduced to... 

X-ray crystallographic studies have been carried out on four compounds belonging to three different pseudoazulene systems.9-61129 All studied compounds crystallized in monoclinic or orthorhombic space groups, a situation requiring Cs symmetry of each molecule. The size of the unit cells of the crystal lattice strongly depends upon the pseudoazulene system. The atoms of the pseudoazulene skeleton are all coplanar to within <5 ... 

Atoms that belong to more iff than one unit cell are classified as corner, edge, or face atoms, which contribute, respectively, 1 /8,1 /4,1 /2 atom per unit cell. 

As shown in Figure 10.22a, there is an atom at each of the eight corners of the primitive-cubic unit cell. When unit cells are stacked together, each corner atom is shared by eight cubes, so that only 1 / 8 of each atom "belongs" to a given unit cell. Thus there is 1/8 X 8 = 1 atom per unit cell. 

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