Crystallographic planes

When plastic deformation occurs, crystallographic planes sHp past each other. SHp is fackitated by the unique atomic stmcture of metals, which consists of an electron cloud surrounding positive nuclei. This stmcture permits shifting of atomic position without separation of atomic planes and resultant fracture. The stress requked to sHp an atomic plane past an adjacent plane is extremely high if the entire plane moves at the same time. Therefore, the plane moves locally, which gives rise to line defects called dislocations. These dislocations explain strain hardening and many other phenomena. 

Both ultrasonic and radiographic techniques have shown appHcations which ate useful in determining residual stresses (27,28,33,34). Ultrasonic techniques use the acoustoelastic effect where the ultrasonic wave velocity changes with stress. The x-ray diffraction (xrd) method uses Bragg s law of diffraction of crystallographic planes to experimentally determine the strain in a material. The result is used to calculate the stress. As of this writing, whereas xrd equipment has been developed to where the technique may be conveniently appHed in the field, convenient ultrasonic stress measurement equipment has not. This latter technique has shown an abiHty to differentiate between stress reHeved and nonstress reHeved welds in laboratory experiments. 

Fig. 6. Unit cell for silver haUde where shaded areas represent crystallographic planes, (Q) haUde ions, and ( ) silver ions, (a) Complete cell (b) showing a...

FIG. 19 Scheme of a simple fluid confined by a chemically heterogeneous model pore. Fluid modecules (grey spheres) are spherically symmetric. Each substrate consists of a sequence of crystallographic planes separated by a distance 8 along the z axis. The surface planes of the two opposite substrates are separated by a distance s,. Periodic boundary conditions are imposed in the x and y directions (see text) (from Ref. 77). 

It is well known that the catalytic oxidation of CO on certain Pt surfaces exhibits oscillatory behavior, within a restricted range of pressures and temperatures, which are coupled with adsorbate-induced surface phase transitions [16,17]. In fact, in their clean states the reconstructed surfaces of some crystallographic planes, e.g. Pt(lOO) and Pt(llO), are... 

Draw ratio Degree of crystallinity Lattice disorder coefficient (k) Average crystallite size perpendicular to the crystallographic plane (hkl) Dhki (nm) ... 

The quantities jXe, pe >

bulk properties of the metal. The quantities O, and of course F, are surface properties which can vary on a metal surface from one crystallographic plane to the other. Such variations are typically on the order of 0.1 eV but can be as high as 0.5 V. The measured work function , of a polycrystalline metal is an average of the d> values on different crystallographic planes. 

It may be noted that the Brillouin polyhedron used in this calculation corresponds to the only strongly reflecting planes in the entire range 262/F 46. Thus the Brillouin polyhedron is, in effect, isolated from interference by any neighboring crystallographic planes. 

In some specific cases one would like to convert the chemisorption data into an averaged particle size. In that case, the number of surface atoms per unit surface area (density of surface atoms) is an essential parameter. Since this number depends on the type of the crystallographic plane, (see Table 3.7), one also needs information on the types of crystallographic planes exposed to the gas phase. This is also important for another reason the adsorption stoichiometry may depend on the crystallographic plane. 

The theoretical surface density of oxygen ions was evaluated by Madier el al. for different crystallographic planes of Ce02 and Ce Zr Oj oxides [14], For ceria, the theoretical O density would be of 13.7, 9.7 and 15.8at.Onm 2 for (100), (110) and (111) surfaces respectively, which gives a mean surface density of 13.1 at.O nm 2 if one assumes an equidistribution of the three crystallographic planes. This figure leads to a theoretical OSC of 5.4 p,mol O m-2. The hypothesis of equidistribution may be not valid in all cases, which can explain some difference in the reported results. Note that the (111) surface is thermodynamically the most stable [34,35],... 

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