所有布里渊区高对称点坐标

Triclinic(primitive) Basic vectors: arbitrary Volume:[a1a2a3] Kpoints: gamma(0 0 0) B(1/2 0 0) F(0 ½ 0) G(0 0 1/2) Monoclinic(primitive) Basic vectors: (0 -b 0) (a sinr -a cosr 0) (0 0 c) Volume:abc sinr Kpoints: gamma(0 0 0) B(-1/2 0 0) Y(0 ½ 0) Z(0 0 ½) C(0 ½ ½) D(-1/2 0 ½) A(-1/2 ½ 0) (-1/2 -1/2 0) or(½ ½ 0) E(-1/2 ½ ½) (-1/2 -1/2 ½) or(1/2 ½ ½) Monoclinic(Base centered) Basic vectors: (0 -b 0) 1/2(a sinr a cosr -c) 1/2(a sinr -a cosr c) Volume:1/2abc sinr Kpoints: gamma(0 0 0) A(-1/2 0 0) Z(0 -1/2 ½) M(-1/2 -1/2 ½) L(1/2 0 ½) V(0 0 ½) Othorhombic(Primitive) Basic vectors:(0 -b 0) (a 0 0) (0 0 c) Volume: abc Kpoints: gamma(0 0 0) Y(-1/2 0 0) X(0 ½ 0) Z(0 0 ½) U(0 ½ ½) T(-1/2 0 ½) S(-1/2 ½ 0) R( -1/2 ½ ½ ) Othorhombic(Base centered) Basic vectors: 1/2(a -b 0) 1/2(a b 0) (0 0 c) Volume: 1/2abc Kpoints: a>b: gamma (0 0 0) Y(1/2 ½ 0) Z(0 0 ½) T(1/2 ½ ½) S(0 ½ 0) R(0 ½ ½) ab and a>c: gamma(0 0 0) X(1/2 -1/2 ½) R(1/2 0 0) S(1/2 0 -1/2) T(1/2 ½ 0) W(3/4 -1/4 -1/4) b>a and b>c: gamma(0 0 0) X(1/2 -1/2 -½) R(1/2 0 0) S(1/2 0 -1/2) T(1/2 -½ 0) W(3/4 -1/4 -1/4) c>a and c>b: gamma(0 0 0) X(1/2 1/2 -½) R(1/2 0 0) S(1/2 0 -1/2) T(1/2 -½ 0) W(3/4 -1/4 -1/4) Othorhombic(Face centered) Basic vectors: ½(a 0 c) 1/2(0 -b c) 1/2(a -b 0) Volume: 1/4abc Kpoints: 1/a^2<1/b^2+1/c^2 1/b^2<1/c^2+1/a^2 and 1/c^2<1/a^2+1/b^2: gamma(0 0 0) Y(0 -1/2 -1/2) X(1/2 0 ½) Z(1/2 ½ 0) L(1/2 0 0) 1/c^2>1/a^2+1/b^2: gamma(0 0 0) Y(0 -1/2 -1/2) X(1/2 0 ½) Z(1/2 -½ 0) L(1/2 0 0) 1/b^2>1/c^2+1/a^2 gamma(0 0 0) Y(1 ½ 1/2) X(1/2 0 ½) Z(1/2 ½ 0) L(1/2 0 0) 1/a^2>1/b^2+1/c^2: gamma(0 0 0) Y(0 -½ -1/2) X(1/2 0 -½) Z(1/2 ½ 0) L(1/2 0 0) Tetragonal(primitive) Basic vectors: (a 0 0) (0 a 0) (0 0 c) Volume: a^2*c Kpoints: gamma(0 0 0) M(1/2 ½ 0) Z(0 0 ½) A(1/2 ½ ½) R(0 ½ ½) X(0 ½ 0) Tetragonal(body-centerd) Basic vectors: 1/2(-a a c) 1/2(a -a c) 1/2(a a -c) Volume: 1/2a^2*c Kpoints: a>c: gamma(0 0 0) N(0 ½ 0) X(0 0 ½) Z(-1/2 ½ ½) P(1/4 ¼ ¼) c>a: gamma(0 0 0) N(0 ½ 0) X(0 0 ½) Z(1/2 ½ -½) P(1/4 ¼ ¼) Trigonal(primitive) Basic vectors: (0 -a c) 1/2(sqrt(3)a a 2c) 1/2(-sqrt(3)a a 2c) Volume: 3/2sqrt(3)a^2*c Kpoints: a>sqrt(2)c gamma(0 0 0) Z(1/2 ½ ½) L(0 ½ 0) F(0 ½ ½) a