Primitive surface

As the tangent plane rolls on the primitive surface, it may happen that the two branches of the connodal curve traced out by its motion ultimately coincide. The point of ultimate coincidence is called a plait point, and the corresponding homogeneous state, the critical state. 

If we imagine a line drawn on the primitive surface dividing all parts of the surface which are convex downwards in all directions from those which are concave downwards in one or both directions of principal curvature, this curve will have the equation (26), and is known as the spinodal carve. It divides the surface into two parts, which represent respectively states of stable and unstable equilibrium. For on one side A is positive, and on the other it is negative. If we assume that the tie-line of corresponding points on the connodal curve is ultimately tangent to that the direction of equations ... 

Let us suppose that T and p are always given by equation (3), even on parts of the primitive surface which represent essentially unstable states. Then for motion from one point on that surface to another point we have ... 

All the work we describe in this chapter was carried out in UHV on the rutile Ti02(l 1 0)1 x 1 surface. Exposures to vapors and gases are given in Langmuirs (L) where 1 L = 1.333 x 10 s mbar s. Coverages of defects or molecules adsorbed at the surface will be given in monolayers (ML), where 1 ML corresponds to the density of primitive surface unit cells. 

Hanoman, 1961 and Lander, Gobeli, and Morrison, 1963) this lowering of symmetry is called lecoiistniction. For the ideal unreconstructed crystal it is not difficult to construct primitive surface translations (sec Section 3-C for discussion of primitive translations), which are the smallest translations in the plane of the surface by which each atom is replaced by another atom. Let two of these translations be written and T2 Low-Energy Electron Diffraction (LHED) measurements tell what the actual translational symmetry of a surface is and frequently give a lower symmetry. For example, it may indicate primitive translations of 2T[ and T2 this is called a 2 x 1 reconstruction. Similarly, an observed translational symmetry of T, and mtj is called an n x m reconstruction. 

This conclusion appears to be true since a 2 x 1 reconstruction is. seen on freshly cleaved (111) surfaces of silicon (Lander, Gobeli, and Morri.son, 196.3). Alternate atoms arc distinguishable they form a primitive surface cell of two surface atoms. However, the conclusion is not nearly so persuasive as it seems. 

This adds 13 atoms in each primitive surface cell (80 percent-coverage), leaving 10 surface atoms uncovered. 

It is premature to speculate on the detailed 7x7 pattern, but an appealing pattern can be obtained by starting with a pattern of vacancies proposed by Lander and Morrison (1963). We do this by adding atoms to each vacant site to obtain the starting planar structure, and then add one atom outside the surface to correspond with each site that Lander and Morrison left vacant. This adds 13 atoms in each primitive surface cell (80 percent coverage), leaving 10 surface atoms uncovered. 

Fig. 17. Primitive surfaces recognized in Geomagic, (a) recognized regions, and (b) extracted primitive surfaces in SolidWorks...

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