Primitive cubic unit cell

FIGURE 5.33 A primitive cubic unit cell has an atom at each corner. It is rarely found in metals. 

FIGURE 5.30 A primitive cubic unit cell. To count the number of nearest neighbors of an atom, we have to imagine the cell of interest with its neighbors stacked up around it. 

FIGURE 10.22 Geometries of (a) primitive-cubic and (b) body-centered cubic unit cells in both a skeletal view (top) and a space-filling view (bottom). Part (c) shows how eight primitive-cubic unit cells stack together to share a common corner. 

How many atoms are in one primitive-cubic unit cell of a metal ... 

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. 

Figure 2. PXD data for a phase A preparation containing a significant phase B component. The sets of vertical bars indicate computed reflection positions based on a C-centered orthorhombic unit cell with a = 7.94A, b = 10.34A and c = 11.59A (phase A - lower), and a primitive cubic unit cell with a = 12.44A (phase B - upper). The positions of additional impurity peaks are indicated by e.

The LTA structure (zeolite NaA) has a primitive cubic unit cell (a= 12.3 A) with one sodalite cage in each comer of the cube and a 4-4 unit in each edge of the cube[16,17] The total volume of these structures in each unit cell, using a T-0-T distance of 2.1 A. [16] and assuming that the sodalite cage is a sphere with radius of 4.4 A [16], is equal to 416 A. This corresponds to the 22.3% of the framework volume. 

Cr ions at the corners of a pc primitive cubic) unit cell [ one anion (radius ra ,on) per cell (edge length a) ]... 

By examining Figures 3.7 and 3.32, we note that the caesium cations sit on a primitive cubic unit cell (lattice type P) with chloride anion occupying the cubic hole in the body centre. Alternatively, one can view the structure as P-type lattice of chloride anions with caesium cation in cubic hole. Keep in mind that caesium chloride does not have a body centred cubic lattice although it might appear so at a first glance. The body centred lattice has all points identical, whereas in CsCl lattice the ion at fte body centre is different from those at the comers. 

S3.3 (1) Figures 3.3 and 3.23 show the primitive cubic unit cell. Each unit cell contains one sphere (equivalent to 8 x 1/8... 

However, this numbering sequence only holds for primitive cubic unit cells. Certain systematic absences occur for centered cells of which we need consider only I and F in the cubic system (the allowed Bravais Lattices). These absences arise in the following way. Let us assume that we have a cubic unit cell with a = 5.00 A. Normally we expect the 100 reflection to have riioo = 5.00 A for which 29 = 17.74°. The angle of incidence of the X-ray beam for this plane is 0, 8.87°. However, there is an exactly similar plane of atoms 200 at (5.00 A/2) = 2.50 A. When the angle of incidence is 8.87°... 

Consider the cubic unit cells (Figure 11.33) with an atom located at each lattice point. Calculate the net number of atoms in (a) a primitive cubic unit cell (b) a body-centered cubic unit cell (c) a face-centered cubic unit cell. 

F. 2 Schematic representation of the stmeture of A[B2]04 spinel lattices, a the smallest (primitive) cubic unit cell of normal spinel (Fcfim) and b the unit cell of the 1 3 ordered spinel (P4332). The structure is composed of alternating octants of AO4 tetrahedra and B4O4 cubes to build the fee unit cell [28]... 

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