Face-centered cubic structur

Krypton is present in the air to the extent of about 1 ppm. The atmosphere of Mars has been found to contain 0.3 ppm of krypton. Solid krypton is a white crystalline substance with a face-centered cubic structure which is common to all the "rare gases."... 

At 31OC, lanthanum changes from a hexagonal to a face-centered cubic structure, and at 865C it again transforms into a body-centered cubic structure. 

Let us first consider, as an example, the copper-zinc system of alloys.1 The ordinary yellow brass of commerce is restricted in composition to the first (copper-rich) phase of the system. This phase, which has the face-centered cubic structure characteristic of copper, is followed successively, as the zinc content is increased, by the /3-phase (body-centered cubic),... 

Yet another common crystal lattice based on the simple cubic arrangement is known as the face-centered cubic structure. When four atoms form a square, there is open space at the center of the square. A fifth atom can fit into this space by moving the other four atoms away from one another. Stacking together two of these five-atom sets creates a cube. When we do this, additional atoms can be placed in the centers of the four faces along the sides of the cube, as Figure 11-28 shows. 

The ruthenium-copper and osmium-copper systems represent extreme cases in view of the very limited miscibility of either ruthenium or osmium with copper. It may also be noted that the crystal structure of ruthenium or osmium is different from that of copper, the former metals possessing the hep structure and the latter the fee structure. A system which is less extreme in these respects is the rhodium-copper system, since the components both possess the face centered cubic structure and also exhibit at least some miscibility at conditions of interest in catalysis. Recent EXAFS results from our group on rhodium-copper clusters (14) are similar to the earlier results on ruthenium-copper ( ) and osmium-copper (12) clusters, in that the rhodium atoms are coordinated predominantly to other rhodium atoms while the copper atoms are coordinated extensively to both copper and rhodium atoms. Also, we conclude that the copper concentrates in the surface of rhodium-copper clusters, as in the case of the ruthenium-copper and osmium-copper clusters. 

Only large clusters usually adopt the face-centered cubic structure of metallic platinum. A novel cuboctahedral cluster [Pt15Hx(CO)8(PBut3)6] has been reported by Spencer et al.512 and the first octahedral cluster [Pt6(CO)6(/i-dppm)3]2+ was only reported recently.573... 

The overlap between 5- and p-bands also occurs for the alkali metals and for the monovalent noble metals copper, silver, and gold, which have face-centered cubic structures. The noble metals differ from the alkalis because of the filled d-shell just below the 5-shell in energy the d-band and the 5-band overlap in the solid. 

Consider the NaCl face-centered cubic structure with a unit cell edge represented as a, shown here. 

Figure 3.10 Unit cell of face-centered cubic structure of copper. The vector shown represents the Burgers vector of a unit dislocation in this structure.

Figure 3.15 Change of stacking across a dislocation loop in a face-centered cubic structure. The structure is that of a Frank sessile dislocation loop.

There are many metal alloys that contain interstitial atoms embedded in the metal structure. Traditionally, the interstitial alloys most studied are those of the transition metals with carbon and nitrogen, as the addition of these atoms to the crystal structure increases the hardness of the metal considerably. Steel remains the most important traditional interstitial alloy from a world perspective. It consists of carbon atoms distributed at random in interstitial sites within the face-centered cubic structure of iron to form the phase austenite, which exists over the composition range from pure iron to approximately 7 at % carbon. 

The path that the diffusing atom takes will depend upon the structure of the crystal. For example, the 100 planes of the face-centered cubic structure of elements such as copper are identical to that drawn in Figure 5.7. Direct diffusion of a tracer atom along the cubic axes by vacancy diffusion will require that the moving atom must squeeze between two other atoms. It is more likely that the actual path will be a dog-leg, in <110> directions, shown as a dashed line on Figure 5.7. 

Inert Gases. The calculation of 7 should be relatively straightforward for crystals of inert gases, in which only one kind of interaction may be expected. These crystals have a face-centered cubic structure. If each atom is treated as a point source of attractive and repulsive forces, only the forces between the nearest pairs of atoms are considered, the zero point energy is neglected, and no re-arrangement of atoms in the surface region is permitted, then the calculated 7 still depends on the equation selected to represent the interatomic potential U. 

The number of independent elements of 4> may be restricted by symmetry. In the face-centered cubic structure, for example, the force constant matrix for two atoms 1/2 1/2 0 apart is given by (Willis and Pryor 1975)... 

In the face-centered cubic structure of silicon, atoms are located at 1/8 1/8 1/8 and at the center-of-symmetry related position of —1/8 —1/8 —1/8. The static structure factor can therefore be expressed simply as... 

Colorless, odorless, and tasteless gas density 3.733 g/L at 0°C liquefies at -153.22°C sohdifies at -157.36°C to a white crystalline substance that has a face-centered cubic structure critical temperature -63.6°C critical pressure... 

Silvery-white metal when freshly cut rapidly turns yellow on exposure to air forming a thin oxide coating face-centered cubic structure malleable, ductile, and somewhat softer than calcium density 2.64 g/cm melts at 777°C vaporizes at 1,382°C vapor pressure 5 torr at 847°C and 20 torr at 953°C electrical resistivity 23 microhm-cm at 20°C thermal neutron absorption cross section 1.21 barns reacts with water soluble in ethanol. Thermochemical Properties... 

Silvery lustrous metal soft, malleahle and ductile the metal exists in two allotropic forms an alpha form, which has a face-centered cubic structure and is stable at room temperature, and a beta form, a body-centered cubic modification that forms when the alpha form is heated to 798°C. Density of the alpha modification is 6.98 g/cm and that of beta form is 6.54 g/cm. Alpha phase exhibits metallic-type conductivity at ordinary temperatures and pressures, but becomes semi-conductive above 16,000 atm. At about 40,000 atm it again becomes metallic-type conductor. (In some texts, the term beta form refers to the alpha phase). 

Although the correlation between ionic porosity and diffusivity is imperfect, there is a rough trend that oxygen diffusivity in the minerals increases with increasing IP. The trend is useful in qualitative estimation of closure temperature (among other applications). Extending the relation to metallic systems, one prediction is that diffusion in face-centered cubic structure (25.95% free space) is slower that that in body-centered structure (31.98% free space) of the same metal composition. To avoid the issue of anisotropy, it would be worthwhile to reexamine the relations between diffusivity and ionic porosity using only isometric minerals. 

Beside dislocation density, dislocation orientation is the primary factor in determining the critical shear stress required for plastic deformation. Dislocations do not move with the same degree of ease in all crystallographic directions or in all crystallographic planes. There is usually a preferred direction for slip dislocation movement. The combination of slip direction and slip plane is called the slip system, and it depends on the crystal structure of the metal. The slip plane is usually that plane having the most dense atomic packing (cf. Section 1.1.1.2). In face-centered cubic structures, this plane is the (111) plane, and the slip direction is the [110] direction. Each slip plane may contain more than one possible slip direction, so several slip systems may exist for a particular crystal structure. Eor FCC, there are a total of 12 possible slip systems four different (111) planes and three independent [110] directions for each plane. The... 

Similarly, charged solid particles (such as latex spheres) —kinetically stable lyophobic colloids —may exist in colloidal crystalline phases (with body-centered or face-centered cubic structures) as a consequence of thermodynamically favored reduction in free energies (see Chapter 13). Even neutrally charged spherical particles ( hard spheres ) undergo a phase transition from a liquidlike isotropic structure to face-centered cubic crystalline structures due to entropic reasons. In this sense, the stability or instability is of thermodynamic origin. 

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