Rectangular point lattice, planes

If the crystal is rotated round its b axis (Fig. 89) the equatorial spots are reflections from hOl planes. The values for these spots are found as before by measuring the distance from the origin to each point of the (non-rectangular) hOl net plane (Fig. 88). Note that the indexing of equatorial reflections in this case cannot be done by a log d chart, since there are three variables, a, c, and / the reciprocal lattice method is essential. Once the indices for the equatorial reflections have been found, those of the reflections on upper and lower layer lines follow at once, since all reciprocal lattice points having the same h and l indices (such a set as 201, 211, 221, 231, and so on) are at the same distance from the axis of rotation and thus form row lines. 

In a crystal, the spacing of the lattice points is an important parameter to define its stmcture. In crystal stracture theory one normally uses the so-called Miller indices hkt) to characterize the lattice plane. These indices are the reciprocal of intersection distances (any resulting fractions are removed by multiplying with an appropriate factor). For example, in a 2D rectangular lattice, such as the one shown in Figure 26.1, the planes passing through the lattice points are represented by the smallest intersection... 

In some Hquid crystal phases with the positional order just described, there is additional positional order in the two directions parallel to the planes. A snapshot of the molecules at any one time reveals that the molecular centers have a higher density around points which form a two-dimensional lattice, and that these positions are the same from layer to layer. The symmetry of this lattice can be either triangular or rectangular, and again a positional distribution function, can be defined. This function can be expanded in a two-dimensional Fourier series, with the coefficients in front of the two... 

A flat board into which nails have been driven in a regular rectangular pattern. These nails represent the lattice points in the plane, geodesic... 

A primitive unit cell is a lattice unit cell that contains only one lattice point. The four primitive plane lattice unit cells are labelled p oblique, imp), rectangular, op), square, (tp) and hexagonal, (hp). They are normally drawn with a lattice... 

A rectangular lattice is a family of vertical and horizontal lines in the xy plane. The point of intersection of lines is often called a node. Each rectangle formed by two adjacent vertical lines and two horizontal lines in the lattice is called a mesh. Each side of the mesh is called a link. A rectangular lattice is said to be uniform if all of the horizontal links are equal to a constant b.lia = h, then we have a square lattice however, the condition a = b is not essential and... 

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