Primitive cubic crystal structure

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. 

Definitive x-ray diffraction data on structure I was obtained by McMullan and Jeffrey (1965) for ethylene oxide (EO) hydrate, as presented in Table 2.2a. The crystal consists of a primitive cubic lattice, with parameters as given in Table 2.2a. The common pictorial view of structure I is presented in Figure 1.5a. In that figure, the front face of a 12 A cube is shown, with two complete 51262 (emphasizing hydrogen bonds) connecting four 512. 

Cl-. The lattice type is reduced from face-centered cubic to primitive cubic, and the space group of CsCl is 0 - Pm3m. Figure 10.3.3(a) shows a unit cell in the crystal structure of CsCl. 

Below 249 K, the molecules are orientated in an ordered fashion, and the symmetry of the crystal is reduced from a face-centered cubic lattice to a primitive cubic lattice. At 5 K, the crystal structure determined by neutron diffraction yielded the following data space group Pa3 (no. 205), a = 1404.08 (1) pm C-C bond lengths (6/6) 139.1 pm, (6/5) 144.4 pm, and 146.6 pm (mean 145.5 pm). 

Crystal structure of MOF-5. (a) Z114O tetrahedra joined by benzenedicarboxylate linkers. H atoms are omitted for clarity, (b) The topology of the framework (primitive cubic net) shown as an assembly of i/iu (>)()— clusters (represented as truncated tetrahedra) andp-phenylene (-CgFLj-) links (represented by rods). From O. M. Yaghi, M. O Keeffe, N. W. Ockwig, H. K. Chae, M. Eddaoudi, and J. Kim, Nature 423, 705-14 (2003). 

The rocksalt crystal structure belongs to the cubic system with space group 0 (Pm3m). It consists of two face-centered cubic (fee) sublattices, which are occupied by one atom species each. The two sublattices are shifted along one half of the diagonal of the primitive unit cell against each other. The rocksalt lattice is sixfold coordinated. 

L. Pauling, Icosahedral quasicrystals are twins of cubic crystals containing large icosa-hedral clusters of atoms The 1012-atom primitive cubic structure of Al6CuLi3, the C-phase of Al37Cu3Li2iMg3, and GaMg2Zn3. Proc. Natl. Acad. Sd. (USA) 85, 3666-3669 (1988). 

Figure 2.t. The crystal structure of CeO> (a) unii celt as cep array of cerium atoms The cep layers are parallel to the [Ml] planes of the fe e. unit cell, (b) and (c) the same stniclure redrawn as a primitive cubic array of oxygens. 

As a first example, consider the growth of a cubic lattice about the origin. For the simple primitive lattice , most familiar as the structure of the model crystal cubium , the cubic array... 

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