Primitive cubic

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

Self-Test 5.4A How many atoms are there in a primitive cubic cell (see Fig. 5.33) ... 

The metal polonium (which was named by Marie Curie after her homeland, Poland) crystallizes in a primitive cubic structure, with an atom at each corner of a cubic unit cell. The atomic radius of polonium is 167 pm. Sketch the unit cell and determine (a) the number of atoms per unit cell (b) the coordination number of an atom of polonium (c) the length of the side of the unit cell. 

The structure of PuB,qq is not yet clear. A satisfactory indexing can be made for a primitive cubic cell with a = 23.42 A, but with 10 reflections not characteristic of space group Fm3c . ... 

For additional symbols of further packings cf. [38, 156], T (triangular) refers to hexagonal layers, Q to layers with a periodic pattern of squares. The packing Qs yields a primitive cubic lattice (Fig. 2.4), Qf a body-centered cubic lattice (cf. Fig. 14.3, p. 153). Sometimes the symbols are set as superscripts without the angular brackets, for example Ti[Ca03]c. 

Primitive cubic crystal lattice. One unit cell is marked... 

Sb LSb, yields the primitive-cubic polonium-type structure, which is S / known as a high-pressure modification of arsenic. Therefore, five electrons... 

Fig. 6 The structure of Mg2Cu6Gas, emphasizing the primitive cubic packing of Cu6 octahedra and three-shell 45-atom clusters. One of the latter is cut open to show its inner shells...

ACs. Moreover, the glue atoms beyond triacontahedra, in fact, center prolate rhombohedron (a cube elongated along a threefold axis), the recognized interstitial cavity among primitive cubic packed triacontahedra (also shown in Fig. 18). 

Figure 9.31 Some varients of allocation of PBUs fora primitive cubic packing (Pc) (a) PBU/C (b) PBU as a 3D graph and (c) as 2D planar graph (d) PBU/P black circles (b) and (c) are the sites of the lattice, that correspond to the centers of particles (or atoms), the solid lines are the bonds between them, the dotted lines are the bonds with the sites from the neighbor cells.

All the formal expressions involve the Fourier transform lu of the function q(j = l/47ri i3-. We consider the case wrhere i and j are defects on one of the primitive cubic lattices. Rj denotes the vector from defect i at the origin to defect j in unit cell number l. Born and Bradburn10 have shown that for an infinite lattice we can write... 

The structure-dependent coefficients have been calculated for the three primitive cubic lattices.4 For the sodium chloride lattice we have A — 2a3, where a denotes the anion-cation lattice spacing, and if we define a parameter bi by the equation... 

An example where, due to ordering, we observe perhaps in a more immediate way, the increase of the unit cell size (formation of a multiple cell) is the MnCu2Al-type structure (representative of the so-called Heusler alloys) which can be considered a derivative structure (superstructure) of the cP2-CsCl type, which in turn is a superstructure of the W-type structure, corresponding to a non-primitive cubic cI2... 

The simplest of the cubic structures is the primitive cubic structure. This is built by placing square layers like the one shown in Figure 1.1 (a), directly on top of one another. Figure 1.9(a) illustrates this, and you can see in Figure 1.9(b) that each atom sits at the corner of a cube. The coordination number of an atom in this structure is six. The majority of metals have one of the three basic structures hep, cep, or bcc. Polonium alone adopts the primitive structure. The distribution of the packing types among the most stable forms of the metals at 298 K is shown in Figure 1.10. As we noted earlier, a very few metals have a mixed hcp/ccp structure of a more complex type. The structures of the actinides tend to be rather complex and are not included. 

FIGURE 1.9 (a) Two layers of a primitive cubic array (b) a cube of atoms from this array. 

The same structure redrawn as a primitive cubic array of anions, (d)... 

First, consider a primitive cubic system. From equation 2.4, we see that the planes giving rise to the reflection with the smallest Bragg angle will have the largest dtu spacing. In the primitive cubic system the 100 planes have the largest separation... 

For the primitive cubic class all integral values of the indices h, k, and 1 are possible. Table 2.1 lists the values of M7in order of increasing value of (1 +1 + f) and therefore of increasing sin0 values. 

Taking Equation 2.5, if we plot the intensity of diffraction of the powder pattern of a primitive cubic system against sin OMi we would get six equi-spaced lines with the 7th, 15th, 23rd, etc., missing. Consequently, it is easy to identify a primitive cubic system and by inspection to assign indices to each of the reflections. 

What is the sequence of the following reflections in a primitive cubic crystal 220, 300, and 2117... 

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