Lattice origin

By definition, a zone axis is normal to both g and h and other reciprocal lattice vectors in the plane defined by these two vectors. The reciprocal lattice plane passing through the reciprocal lattice origin is called the zero-order zone axis. A G-vector with z - G=n with n O is said to belong to a high order Laue zones, which separate to upper Laue zones (n>0) and lower Laue zones (n<0). 

Fig. 80. Formation of reciprocal lattice rotation diagram, set of planes is the corresponding reciprocal lattice point V, the distance of which from the reciprocal lattice origin X is inversely proportional to...

Here, (I, 12,13) denote three linearly independent vectors of R3, serving as a basis of A, whereas n1,n2>n3 = n> say, is a triad of integers. The symbol 0 = 0,0,0 will be arbitrarily chosen to designate the lattice origin. 

In this case, a given lattice site can be occupied at random by particle A with the probability q or by particle B with the probability 1 - q. Each edge is declared to be open if its end vertices are occupied by particles of different types (the idea is that dissimilar particles bind together, whereas similar ones repel each other). Of principal interest is the probability of the lattice origin to be an infinite cluster of open edges. 

Not all of these n points will cause a separate reflection some of them may have a zero structure factor, and some may be at equal distances from the reciprocal-lattice origin, i.e., correspond to planes of the same spacing. (The latter effect is taken care of by the multiplicity factor, since this gives the number of different planes in... 

The direction of these vectors is perpendicular to the end faces of the direct lattice unit cell. The lengths of the basis vectors of the reciprocal lattice are the inverse of the perpendicular distance from the lattice origin to the end faces of the direct lattice unit cell. For the square and rectan-... 

Fig. 6.9. Ewald s sphere of radius 1 /A, crystal may be stationed either at the center O or at C. The reciprocal lattice origin is also at C, 0 is the Bragg angle of reflection from the Miller plane hkl) in the crystal, CB is drawn normal on the hkl plane...

A factor-group operation consists of a rotation (a ) and a noninimitive translation (tj [see Slater (1965)]. For the orthorhombic polyethylene crystal of the space group Pnam, symmetry operations are listed in Table IV.l. The symmetry operation R (at the lattice origin) transforms the Cartesian coordinate vector X(g,) as... 

The rocksalt stmcture is illustrated in figure Al.3.5. This stmcture represents one of the simplest compound stmctures. Numerous ionic crystals fonn in the rocksalt stmcture, such as sodium chloride (NaCl). The conventional unit cell of the rocksalt stmcture is cubic. There are eight atoms in the conventional cell. For the primitive unit cell, the lattice vectors are the same as FCC. The basis consists of two atoms one at the origin and one displaced by one-half the body diagonal of the conventional cell. 

The linear dependence of C witii temperahire agrees well with experiment, but the pre-factor can differ by a factor of two or more from the free electron value. The origin of the difference is thought to arise from several factors the electrons are not tndy free, they interact with each other and with the crystal lattice, and the dynamical behaviour the electrons interacting witii the lattice results in an effective mass which differs from the free electron mass. For example, as the electron moves tlirough tiie lattice, the lattice can distort and exert a dragging force. 

The original Polacolot negative had water-coated intedayers of gelatin (60). The SX-70 and Polacolot 2 negatives use as intedayers a combination of a polymeric latex with a water-soluble polymer. A key development was the constmction of lattices that function as temporary batnets, reducing interimage problems. The water-soluble polymer functions as a permeator, so that the harder properties ate tunable (61). 

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