Simple cubic crystal structure

A number of other thermodynamic properties of adamantane and diamantane in different phases are reported by Kabo et al. [5]. They include (1) standard molar thermodynamic functions for adamantane in the ideal gas state as calculated by statistical thermodynamics methods and (2) temperature dependence of the heat capacities of adamantane in the condensed state between 340 and 600 K as measured by a scanning calorimeter and reported here in Fig. 8. According to this figure, liquid adamantane converts to a solid plastic with simple cubic crystal structure upon freezing. After further cooling it moves into another solid state, an fee crystalline phase. 

Figure 4.1 Schematic dislocation line a simple cubic crystal structure. The line enters the crystal at the center of the left-front face. It emerges at the center of the right-front face. The shortest translation vector of the structure is the Burgers Vector, b. The line bounds the glided area of the glide plane (100) from the unglided area.

You now know how to define a supercell for a DFT calculation for a material with the simple cubic crystal structure. We also said at the outset that we assume for the purposes of this chapter that we have a DFT code that can give us the total energy of some collection of atoms. How can we use calculations of this type to determine the lattice constant of our simple cubic metal that would be observed in nature The sensible approach would be to calculate the total energy of our material as a function of the lattice constant, that is, tot(a). A typical result from doing this type of calculation is shown in Fig. 2.1. The details of how these calculations (and the other calculations described in the rest of the chapter) were done are listed in the Appendix at the end of the chapter. 

Figure 2.1 Total energy, L tot, of Cu in the simple cubic crystal structure as a function of the lattice parameter, a. The filled symbols show the results of DFT calculations, while the three curves show the fits of the DFT data described in the text.

The simple cubic crystal structure we discussed above is the simplest crystal structure to visualize, but it is of limited practical interest at least for elements in their bulk form because other than polonium no elements exist with this structure. A much more common crystal stmcture in the periodic table is the face-centered-cubic (fee) structure. We can form this structure by filling space with cubes of side length a that have atoms at the corners of each cube and also atoms in the center of each face of each cube. We can define a supercell for an fee material using the same cube of side length a that we used for the simple cubic material and placing atoms at (0,0,0), (0,g/2,g/2), (g/2,0,g/2), and (g/2,g/2,0). You should be able to check this statement for yourself by sketching the structure. 

Formation of the energy-band structure of KCl. We start with argon atoms, and then put them in a simple-cubic crystal structure. Protons arc then transferred between neighboring nuclei to form potassium and chlorine ions. 

Mn has a complicated (simple cubic) crystal structure with four inequivalent atomic positions and 58 atoms in the unit cell. See Table 25 3 of Ref. 191. "Extended x-ray absorption fine structure (EXAFS) in argon. 

Polonium is the only metal that forms a simple cubic crystal structure. Use the fact that the density of polonium is 9.32 g/cm to calculate its atomic radius. 

Figure 3.3 For the simple cubic crystal structure, (a) a hard-sphere unit cell, and (b) a reduced-sphere unit cell.

X-Ray Diffraction Reflection Rules and Reflection Indices for Body-Centered Cubic, Face-Centered Cubic, and Simple Cubic Crystal Structures... 

For a single crystal of some hypothetical metal that has the simple cubic crystal structure (Figure 3.3), would you expect the surface energy for a (100) plane to be greater, equal to, or less than a (110) plane. Why ... 

Concept Check 7.1 Which of the following is the slip system for the simple cubic crystal structure Why ... 

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