Primitive cubic 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. 

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. 

Many metals have close-packed structures, with the atoms stacked in either a hexagonal or a cubic arrangement close-packed atoms have a coordination number of 12. Some metals have body-centered cubic structures, but primitive cubic structures are rare. 

Self-Test 5.5B What is the coordination number of an atom in a primitive cubic structure (Hint Take into account the atoms in the neighboring cubes shown in Fig. 5.30.)... 

Natural gas clathrate hydrates normally form either in the primitive cubic structure I, in the face-centered cubic structure II, or in the hexagonal structure H. 

Metallic compositions are primarily encountered for stoichiometries A3C60. These salts are superconducting and they adopt, in general, either fee or primitive cubic structures, in which the three cations occupy the available octahedral and tetrahedral interstitial sites. Charge transfer is essentially complete and the... 

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). 

Show that atoms occupy only 52.4% of the total volume in a primitive cubic structure in which all the atoms are identical. 

Show that a sphere of radius 0.73r, where r is the radius of the comer atoms, will fit in the center of a primitive cubic structure. 

We therefore switch to the spin-polarized case but still stay with the primitive cubic structure. It turns out that the total energies are lowered by 0.243 eV (LMTO-ASA, LDA) and 0.393 eV (FLAPW, GGA), simply due to the different occupations of the a. and jS spin sublattices. The number of unpaired electrons is 1.94 (LMTO-ASA, LDA) and 1.85 (FLAPW, GGA), respectively, and the charge transfer between A1 and Mn is almost unchanged. The new DOS plot on the basis of the LMTO electronic structure can be found in Figure 3.36(a). 

What is the coordination number of each sphere in (a) a three-dimensional, close-packed array of equal-sized spheres (b) a primitive cubic structure (c) a body-centered cubic lattice ... 

The IRMOFs [Zn40(00C-(S)-C00)3] thus obtained all have the same primitive cubic structure sketched in Fig. 30.3, with three series of identical perpendicular channels whose free diameters are directly related to the dimensions of the spacers, provided that no interpenetration occurred [7]. This was certainly one of the best results in the designed synthesis of MOFs, evidencing the value of the researcher s imagination, pursued with the aim to obtain a series of derivatives having structural properties directly related to the dimensions of the spacers used. 

Polonium is a radioactive metal, the only one to have a primitive cubic structure. 

In a primitive cubic structure each polonium atom is surrounded by six others at the corners of an octahedron. 

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