lattice Three-index notation Four-index notation Meaning (002) (0002) Plane (102) (10-12) [002] [0002] Direction [102] [10-12] Table 3.1 Bracketing conversions to differ crystal planes and directions in XRD For a hexagonal lattice, any or direction can be defined by either three-index or notations. For a four-index notation, the first three digits are the reciprocal of three vectors in the hexagonal plane a1, a2 and a3, while the 4th digit is the reciprocal of the vector c. For convenience, 4 crystal planes are named after c-, a-, and m-planes in GaN crystal as shown in figure 3.5. Figure 3.5 crystal planes in a hexagonal lattice The miller index of c-, a-, m- and r-plane in a hexagonal lattice are listed in table 3.2. notation Three-index notation c-plane (0001) (001) a-plane (11-20) (110) m-plane (10-10) (100) r-plane (11-22), (10-15), (20-21) etc. (112), (105), (201) etc. Table 3.2 Miller index of c-, a, m- and r-plane Here, c-, a- and m-planes have one equivalent in the hexagonal lattice, while many r-planes can be found, since any crystal plane that is neither 0° nor 90° to the c-plane can be defined as an r-plane. Identification of parameters in XRD measurement Since the exit of the x-ray from the generating vacuum tube is a simple hole, the
lattice Three-index notation Four-index notation Meaning (002) (102) (0002) (10-12) Plane [002] [102] [0002] [10-12] Direction Table 3.1 Bracketing conversions to differ crystal planes and directions in XRD For a hexagonal lattice, any or direction can be defined by either three-index or notations. For a four-index notation, the first three digits are the reciprocal of three vectors in the hexagonal plane a1, a2 and a3, while the 4th digit is the reciprocal of the vector c. For convenience, 4 crystal planes are named after c-, a-, and m-planes in GaN crystal as shown in figure 3.5. Figure 3.5 crystal planes in a hexagonal lattice The miller index of c-, a-, m- and r-plane in a hexagonal lattice are listed in table 3.2. notation Three-index notation c-plane (0001) (001) a-plane (11-20) (110) m-plane (10-10) (100) r-plane (11-22), (10-15), (20-21) etc. (112), (105), (201) etc. Table 3.2 Miller index of c-, a, m- and r-plane Here, c-, a- and m-planes have one equivalent in the hexagonal lattice, while many r-planes can be found, since any crystal plane that is neither 0° nor 90° to the c-plane can be defined as an r-plane. Identification of parameters in XRD measurement Since the exit of the x-ray from the generating vacuum tube is a simple hole, the