Ref. p. 4581 Appendix Fig. 8. First Brillouin zone of the fee lattice. Symmetry ) points and symmetry lines are indicated (BSW notation [36Bo]). The following coordinates refer to the Cartesian system k,, k,,, k,, (see Fig. 7) and are given in units of 2x/a. Coordinates of points: I-: (000); x: (010); L: (l/2; l/2; l/2); w: (l/2 10) K: (3/4 3/4 0); u: (l/4 1 l/4); along lines: A: [OOQ withO<[<l; C: [CYO] with 0<5<3/4 forT--%KandO<[<lforTAKAX’; A: [c[[] with 0<5<1/2; (The coordinates are those in the drawn BZ or in a neigh- bouring repeated zone, as commonly used in the literature). - Distances: l-X=2x/a; TKX =1/2 2x/a; TL=fix/a; 3 Hexagonal close packed (hcp, A3) metals : Be, (C), Cd, a-Co, Dy, Er, Gd, Hf, Ho, Lu, Mg, OS, Re, Ru, SC,Tb, Tc, Ti, Tl, Tm, Y, Zn, a-Zr Fig. 10. The primitive unit cell of the hexagonal lattice (full characterized by lattice parameters a and c*). The size of lines) with its basis vectors ti (i = 1,2,3, bold arrows) relative the atoms (circles) is drawn arbitrarily. Representative to the conventional (Bravais) unit cell (dashedwith full lines). positions of the first to eighth neighbours of atom “0.” are The basis consists of two atoms (hatched circles): one “0.” indicated (the order of succession may change if the ratio at (000) and a second one “1.” at ((a/l/j, 0 c/2) (see Fig. 9). of c/a is not ideal). Their Cartesian coordinates (xyz) are also given. t, = (fi a/Z -a/2, O), tz = (0, a, 01, *) (The ideal ratio of c/a = 1.633). 1, = (0, 0, c). (Components are given in the Cartesian system x, y. z). Volume of the conventional (Bravais) unit cell: 62,= (3/2) fi a2c. Volume of the primitive unit cell: Q= G&/3. Fig. 11. Reciprocal lattice (hexagonal, full lines), reciprocal ) basis vectors gj (j =l, 2,3, bold arrows) and first Brillouin zone (dashed lines) of the hcp lattice. k,, k,, k, indicate the Cartesian coordinate system in reciprocal space parallel to the x, y, z system in real space (see Fig. 10). The following components of the gj are referred to this system: gl=(4@a, 0, O),*) g,=(Wjba, Wa, O), g,=@, 0, 297/C). Volume of the reciprocal hexagonal unit cell: 0,=(6/~@(2x)~/a~c. Volume of the first Brillouin zone: 62,,=8,/3. *) Seecaption of Fig. 3. 449
Fig. 8. First Brillouin zone of the fee lattice. Symmetry )
points and symmetry lines are indicated (BSW notation [36Bo]). The
following coordinates refer to the Cartesian system k,, k,,, k,,
(see Fig. 7) and are given in units of 2x/a. Coordinates of points:
I-: (000); x: (010); L: (l/2; l/2; l/2); w: (l/2 10) K: (3/4 3/4
0); u: (l/4 1 l/4); along lines: A: [OOQ withO
