Calculation of d -spacing and lattice parameters:

In the hexagonal system as displayed in Figure 4.07, the spacing involves both a and c as they are not generally equal.

Figure 4.07: Schematic of hexagonal system.

Hence, the value of d_hkl takes different form,

Similarly, in the orthorhombic lattice system as shown in Figure 4.08, the spacing involves all lengths (a, b and c) as they are not equal.

Figure 4.08: Schematic of orthorhombic system.

Hence, the value of d_hkl turns out to be,

The plane spacings of other lattice geometries are provided in the Appendix I of reference [1].

Ref.: [1]. B. D. Cullity, Elements of X-ray diffraction Addison-Wesley Publishing company, Inc., USA (1956)