Crystallographic orientations

By using these principles the electrochemist has only to find out the CO of a piece of metal which was recognized as being an 

Symmetries and Angular Specifications of Principal Index Faces of Single Crystals 

Symmetry of the spots around this face Fourfold Threefold Twofol  

The most convenient method for determining the co of an individual crystal is the back-reflection Laiie method. This method requires only simple equipment the crystal is positioned in a goniometer head (or any instrument which provides adjustable orientation) and a flat X-ray film in a lightproof holder is mounted normal to the X-ray beam. The film must be at a precise distance R from the crystal (3, 6, or 12 cm) (Fig. 6).t 

The interpretation of the photograph obtained after about 20 min, is carried out by making use of a chart developed by Greninger (Fig. 7), a standard projection of the crystal system (Fig. 5 for the cubic system), and a table of the angles between the different faces (Table 1 for the cubic system). 

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Figure Bl.20.6. Short-range adliesion of a mica-mica contact as a fiinction of the relative crystallographic orientation of the mica surfaces, measured in a dry nitrogen atmosphere. With penuission from [94].

Single-crystal surfaces are characterized by a set of Miller indices that indicate tlie particular crystallographic orientation of the surface plane relative to the bulk lattice [5]. Thus, surfaces are labelled in the same way that atomic planes are labelled in bulk x-ray crystallography. For example, a Ni (111) surface has a surface plane... 

Fig. 2. The shape-memory process, where Tis temperature, (a) The cycle where the parent phase undergoes a self-accommodating martensite transformation on cooling to the 24 variants of martensite. No macroscopic shape change occurs. The variants coalesce under stress to a single martensite variant, resulting in deformation. Then, upon heating, they revert back to the original austenite crystallographic orientation, and reverse transformation, undergoing complete recovery to complete the cycle, (b) Shape deformation. Strain recovery is typically ca 7%.

Here N is the number of bonds or molecules of a given type in the crystal, and is a geometric tensor associated with a particular microscopic polarizabiHty P this tensor is related to the crystallographic orientation of the bond. In extended systems such as covalent soHds it becomes difficult to define a species to which one can assign a unique value of P, and thus the value of P for a given group can only be an approximate representation. In... 

A problem arises in using platelet reinforcements if their naturally mechanically weak crystallographic direction is aligned perpendicular to the crack front. The platelets easily fracture in this orientation. Further research is needed to grow platelets with favorable crystallographic orientations. 

SFA has been traditionally used to measure the forces between modified mica surfaces. Before the JKR theory was developed, Israelachvili and Tabor [57] measured the force versus distance (F vs. d) profile and pull-off force (Pf) between steric acid monolayers assembled on mica surfaces. The authors calculated the surface energy of these monolayers from the Hamaker constant determined from the F versus d data. In a later paper on the measurement of forces between surfaces immersed in a variety of electrolytic solutions, Israelachvili [93] reported that the interfacial energies in aqueous electrolytes varies over a wide range (0.01-10 mJ/m-). In this work Israelachvili found that the adhesion energies depended on pH, type of cation, and the crystallographic orientation of mica. 

Fig. 4.7. The dielectric permittivity of impact-loaded dielectrics can be determined from current pulse measurements on disks biased with a voltage V. The magnitudes of the normalized current pulse values shown for two crystallographic orientations of sapphire are linear change with applied strain (after Graham and Ingram [68G05]).

Numerous observations of the effect in ionic crystals were carried out by Mineev and Ivanov in the Soviet Union [76M01]. This is a class of crystals in which a number of materials factors can be confidently varied. By choice of crystallographic orientation, various slip directions can be invoked. By choice of various crystals other physical factors such as dielectric constant, ionic radius, and an electronic factor thought to be representative of dielec-... 

Figure 2. Segregation energy in layer Sp (p = 0 surface layer...) of a transition metal impurity of atomic number Z + 1 (d band-filling (Nj + l.l)e /atom, full curves (Nj + l)e /atom, dashed curve) in a BCC transition metal matrix of atomic number Z (d band-filling Nje" /atom) for various crystallographic orientations of the surface...

Using single crystals it has been shown that different low-index crystal faces see Section 20) exhibit different corrosion rates. However, the relative corrosion rate of the different faces varies with the environment and these structural effects are of little practical significance. On the other hand, the fact that polycrystal grains of different crystallographic orientation may corrode at different rates, is of some importance. 

It is well known that the 0 of a metal depends on the surface crystallographic orientation.6,65,66 In particular, it is well established that 0 increases with the surface atomic density as a consequence of an increase in the surface potential M. More specifically, for metals crystallizing in the face-centered cubic (fee) system, 0 increases in the sequence (110) <(100) <(111) for those crystallizing in the body-centered cubic (bcc) system, in the sequence (111) < (100) <(110) and for the hexagonal close-packed (hep) system, (1120) < (1010) < (0001). 

It is clear from Eq. (27) that owing to the crystal face specificity of 0, Eaao is expected to vary with the crystallographic orientation as well. Moreover, since the interfacial term X results from interfacial molecular interactions, it must be face-specific also. For a well-defined metal surface, Eq. (27) becomes... 

Equation (32) suffers from the same shortcomings as Eq. (27). In particular, d/dT must be known independently for the same metal sample as the one used as an electrode. Moreover, in view of the crystal-face specificity of ff=o, its temperature coefficient is also expected to depend on the crystallographic orientation. Being a differential quantity, dEa=JdT is an even more delicate experimental quantity than Eaa0 itself. 

Eas,o is found to depend on the crystallographic orientation of Ag faces, increasing with the atomic density of the faces. The dependence of Eas0 on the density of broken bonds on the surface of fee metals has been discussed by De Levie426 and Trasatti and Doubova.32 They found that... 

Figure 12(a) shows graphically the dependence of the pzc on the crystallographic orientation of the surface for Ag, Au, and (tentatively) Cu, all three crystallizing in the same fee system. The plots exhibit a typical pattern, with minima and maxima that fall at the same angle for all three metals, and that are correlated with the density of atoms on the given surface. In particular, the pzc is more positive for dense surfaces and more negative for open surfaces. 

The correct pzc of single-crystal faces of Cu was obtained576,578,587 only after a really oxide-free surface was produced, although unsuccessful attempts are still reported.597 The pzc values for the three main faces of Cu show the correct sequence with the crystallographic orientation, i.e., (Ill) >(100) >(110). These three values are still insufficient, however, to give definite evidence in a plot such as Fig. 12 of the characteristic pattern of the dependence on the crystallographic orientation. 

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