Symmetry Line Files

Purpose


This document provides a semi-automatic way to generate symmetry lines to generate energy bands in the Brillouin zone for any crystal structure.

Crystal lattices, symmetry points and labels are taken from Computational Materials Science 49, 299 (2010).

Cut and paste the contents of appropriate file to a temporary file, e.g. tmp.txt.
To create a symmetry lines file, invoke rdfile with variables defining the shape of your unit cell, e.g.

rdfile -va=#1 -vb=#2 -vc=#3 tmp.txt > qp.ext

and edit qp.txt to taste. rdfile is documented here.

To create energy bands, run a band program such as lmf with switch --band~mq~... .

Table of Contents

Cubic (CUB) Lattice

# The simple cubic lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires no special variables:
# rdfile tmp.txt > qp.ext
#
% vec G[3] 0   0   0                # G
% vec M[3] 1/2   1/2 0              # M
% vec R[3] 1/2 1/2 1/2              # R
% vec X[3] 0   1/2  0               # X

# Sequence G-X-M-G-R-X-R
11 {G}  {X}      G to X
11 {X}  {M}      X to M
11 {M}  {G}      M to G
11 {G}  {R}      G to R
11 {R}  {X}      R to X
11 {X}  {R}      X to R

Face-centered Cubic (FCC) Lattice

# The fcc lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires no special variables:
# rdfile tmp.txt > qp.ext
#
% vec G[3] 0   0   0                # G
% vec M[3] 1/2   1/2 0              # M
% vec R[3] 1/2 1/2 1/2              # R
% vec X[3] 0   1/2  0               # X

# Sequence G-X-M-G-R-X-R
11 {G}  {X}      G to X
11 {X}  {M}      X to M
11 {M}  {G}      M to G
11 {G}  {R}      G to R
11 {R}  {X}      R to X
11 {X}  {R}      X to R

Body-centered Cubic (BCC) Lattice

# The bcc lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires no special variables:
# rdfile tmp.txt > qp.ext
#
% vec G[3] 0   0   0               # G
% vec H[3] 1/2 -1/2 1/2            # H
% vec P[3] 1/4 1/4 1/4             # P
% vec N[3] 0   0  1/2              # N

# Sequence G-H-N-G-P-H-N
11 {G}  {H}      G to H
11 {H}  {N}      H to N
11 {N}  {G}      N to G
11 {G}  {P}      G to P
11 {P}  {H}      P to H
11 {H}  {N}      H to N

Tetragonal (TET) Lattice

# The tetragonal lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires no special variables:
# rdfile tmp.txt > qp.ext
#
% vec G[3] 0   0   0               # G
% vec A[3] 1/2 1/2 1/2             # A
% vec M[3] 1/2 1/2 0               # M
% vec R[3] 0   1/2  1/2            # R
% vec X[3] 0   1/2 0               # X
% vec Z[3] 0   0  1/2              # Z

# Sequence G-X-M-G-Z-R-A-X-R-A
11 {G}  {X}      G to X
11 {X}  {M}      X to M
11 {M}  {G}      M to G
11 {G}  {Z}      G to Z
11 {Z}  {R}      Z to R
11 {R}  {A}      R to A
11 {A}  {X}      A to X
11 {X}  {R}      X to R
11 {R}  {A}      R to A

Body-centered Tetragonal 1 (BCT1) Lattice

# The bct2 lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires one special variables, c/a:
# rdfile -vcbya=# tmp.txt > qp.ext
#
# R.S. Lattice vectors are: (units of a)
# -1/2  1/2   0               P1
#  1/2 -1/2   0               P2
#  1/2  1/2  1/2*cbya         P3
% const eta=(1+cbya*cbya)/4
% vec G[3] 0   0   0               # G
% vec M[3] -1/2 1/2 1/2            # M
% vec N[3] 0   1/2   0             # N
% vec P[3] 1/4   1/4   1/4         # P
% vec X[3] 0   0  1/2              # X
% vec Z[3] {eta} {eta} -{eta}      # Z
% vec Z1[3] -{eta} 1-{eta} {eta}   # Z1

# Sequence G-X-M-G-Z-P-N-Z1-X-P
11 {Z}  {G}      Z to G
11 {G}  {X}      G to X
11 {X}  {M}      X to M
11 {M}  {G}      M to G
11 {G}  {Z}      G to Z
11 {Z}  {P}      Z to P
11 {P}  {N}      P to N
11 {N}  {Z1}     N to Z1
11 {Z1}  {X}     Z1 to X
11 {X}  {P}      X to P

Body-centered Tetragonal 2 (BCT2) Lattice

# The bct2 lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires one special variables, c/a:
# rdfile -vcbya=# tmp.txt > qp.ext
#
# R.S. Lattice vectors are: (units of a)
# -1/2  1/2   0               P1
#  1/2 -1/2   0               P2
#  1/2  1/2  1/2*cbya         P3
% const eta=(1+1/cbya/cbya)/4 zeta=1/2/cbya/cbya
% vec G[3] 0   0   0               # G
% vec N[3] 0   1/2 0               # N
% vec P[3] 1/4 1/4 1/4             # P
% vec X[3] 0   0   1/2             # X
% vec S[3] -{eta} {eta} {eta}      # Sigma
% vec Y[3] -{zeta} {zeta} 1/2      # Y
% vec Z[3] 1/2 1/2 -1/2            # Z

# Sequence Z-G-X-N
11 {Z}  {G}      Z to G
11 {G}  {X}      G to X
11 {X}  {N}      X to N

Orthorhombic (ORC) Lattice

# The orc lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires no special variables
# rdfile tmp.txt > qp.ext
#
% vec G[3] 0   0   0               # G
% vec R[3] 1/2 1/2 1/2             # R
% vec S[3] 1/2 1/2   0             # S
% vec T[3] 0  1/2   1/2            # T
% vec U[3] 1/2   0  1/2            # U
% vec X[3] 1/2   0  0              # X
% vec Y[3] 0   1/2  0              # Y
% vec Z[3] 0   0    1/2            # Z

# Sequence G-X-S-Y-G-Z-U-R-T-Y-U-S-R
11 {G}  {X}      G to X
11 {X}  {S}      X to S
11 {S}  {Y}      S to Y
11 {Y}  {G}      Y to G
11 {G}  {Z}      G to Z
11 {Z}  {U}      Z to U
11 {U}  {R}      U to R
11 {R}  {T}      R to T
11 {T}  {Y}      T to Y
11 {Y}  {U}      Y to U
11 {U}  {S}      U to S
11 {S}  {R}      S to R

Face-centered Orthorhombic 1 (ORCF1) Lattice

# The orcf1 lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires two special variables, b/a and c/a:
# rdfile -vbbya=# -vcbya=# tmp.txt > qp.ext
#
% const eta=(1+1/cbya/cbya+1/bbya/bbya)/4 zeta=(1+1/bbya/bbya-1/cbya/cbya)/4
% vec G[3] 0   0   0               # G
% vec A[3] 1/2 1/2+zeta zeta       # A
% vec A1[3] 1/2 1/2-zeta 1-zeta    # A1
% vec L[3] 1/2  1/2   1/2          # L
% vec T[3] 1    1/2   1/2          # T
% vec X[3] 0    eta   eta          # X
% vec X1[3] 1   1-eta  1-eta       # X1
% vec Y[3] 1/2   0    1/2          # Y
% vec Z[3] 1/2   1/2    0          # Z

# Sequence G-Y-T-Z-G-X-A1-T-X-A-L-G
11 {G}  {Y}      G to Y
11 {Y}  {T}      Y to T
11 {T}  {Z}      T to Z
11 {Z}  {G}      Z to G
11 {G}  {X}      G to X
11 {X}  {A1}     X to A1
11 {A1}  {T}     A1 to T
11 {T}  {X}      T to X
11 {X}  {A}      X to A
11 {A}  {L}      A to L
11 {L}  {G}      L to G

Face-centered Orthorhombic 2 (ORCF2) Lattice

# The orcf2 lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires two special variables, b/a and c/a:
# rdfile -vbbya=# -vcbya=# tmp.txt > qp.ext
#
% const cbyb=cbya/bbya
% const eta=(1+1/bbya/bbya-1/cbya/cbya)/4 delta=(1+bbya*bbya-1/cbyb/cbyb)/4 theta=(1+cbyb*cbyb-cbya*cbya)/4
% vec G[3] 0   0   0                   # G
% vec C[3] 1/2 1/2-eta 1-eta           # C
% vec C1[3] 1/2 1/2+eta eta            # C1
% vec D[3] 1/2-delta  1/2   1-delta    # D
% vec D1[3] 1/2+delta    1/2   delta   # D1
% vec L[3] 1/2    1/2   1/2            # L
% vec H[3] 1-theta   1/2-theta  1/2    # H
% vec H1[3] theta   1/2+theta  1/2     # H1
% vec X[3] 0   1/2    1/2              # X
% vec Y[3] 1/2   0    1/2              # Y
% vec Z[3] 1/2   1/2    0              # Z

# Sequence G-Y-C-D-X-G-Z-D1-H-C1-X-H-L-G
11 {G}  {Y}      G to Y
11 {Y}  {C}      Y to C
11 {C}  {D}      T to D
11 {D}  {X}      Z to X
11 {X}  {G}      G to G
11 {G}  {Z}     X to Z
11 {Z}  {D1}     A1 to D1
11 {D1}  {H}      T to H
11 {H}  {C1}      X to C1
11 {C1}  {X}      A to X
11 {X}  {H}      L to H
11 {H}  {L}      A to L
11 {L}  {G}      L to G

Face-centered Orthorhombic 3 (ORCF3) Lattice

# The orcf3 lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires two special variables, b/a and c/a:
# rdfile -vbbya=# -vcbya=# tmp.txt > qp.ext
#
% const eta=(1+1/cbya/cbya+1/bbya/bbya)/4 zeta=(1+1/bbya/bbya-1/cbya/cbya)/4
% vec G[3] 0   0   0                   # G
% vec A[3] 1/2 1/2+zeta zeta           # A
% vec A1[3] 1/2 1/2-zeta 1-zeta        # A1
% vec L[3] 1/2  1/2   1/2              # L
% vec T[3] 1    1/2   1/2              # T
% vec X[3] 0    eta   eta              # X
% vec X1[3] 1   1-eta  1-eta           # X1
% vec Y[3] 1/2   0    1/2              # Y
% vec Z[3] 1/2   1/2    0              # Z

# Sequence G-Y-T-Z-G-X-A1-X-A-L-G
11 {G}  {Y}      G to Y
11 {Y}  {T}      Y to T
11 {T}  {Z}      T to Z
11 {Z}  {G}      Z to G
11 {G}  {X}      G to X
11 {X}  {A1}     X to A1
11 {A1}  {X}     A1 to X
11 {X}  {A}      X to A
11 {A}  {L}      A to L
11 {L}  {G}      L to G

Body-centered Orthorhombic (ORCI) Lattice

# The orci lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires three special variables, b/a and c/a:
# rdfile -va=# -vb=# -vc=# > qp.ext
#
% const abyc=a/c bbyc=b/c
% const eta=(1+abyc*abyc)/4 zeta=(1+bbyc*bbyc)/4 delta=(b*b-a*a)/(c*c)/4 mu=(a*a+b*b)/(c*c)/4
% vec G[3] 0   0   0                    # G
% vec L[3] -mu  mu  1/2-delta           # L
% vec L1[3] mu  -mu  1/2+delta          # L1
% vec L2[3] 1/2-delta 1/2+delta -mu     # L2
% vec R[3] 0     1/2   0                # R
% vec S[3] 1/2   0    0                 # S
% vec T[3] 0     0   1/2                # T
% vec W[3] 1/4  1/4  1/4                # W
% vec X[3] -zeta  zeta  zeta            # X
% vec X1[3] zeta  1-zeta  -zeta         # X1
% vec Y[3] eta  -eta  eta               # Y
% vec Y1[3] 1-eta  eta  -eta            # Y1
% vec Z[3] 1/2  1/2  -1/2               # Z

# Sequence G-X-L-T-W-R-X1-Z-G-Y-S-L1-Y1-Z
11 {G}  {X}      G to X
11 {X}  {L}      X to L
11 {L}  {T}      L to T
11 {T}  {W}      T to W
11 {W}  {R}      W to R
11 {R}  {X1}     R to X1
11 {X1}  {Z}     X1 to Z
11 {Z}  {G}      Z to G
11 {G}  {Y}      G to Y
11 {Y}  {S}      Y to S
11 {S}  {L1}     S to L1
11 {L1}  {Y1}    L1 to Y1
11 {Y1}  {Z}     YL to Z

C-centered Orthorhombic (ORCC) Lattice

# The orcc lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires one special variables, b/a
# rdfile -vbbya=# tmp.txt > qp.ext
#
% const abyb=1/bbya zeta=(1+abyb*abyb)/4
% vec G[3] 0   0   0                  # G
% vec A[3] zeta  zeta  1/2            # A
% vec A1[3] -zeta  1-zeta  1/2        # A1
% vec R[3] 0  1/2  1/2                # R
% vec S[3] 0  1/2  0                  # S
% vec T[3] -1/2  1/2  1/2             # T
% vec X[3] zeta  zeta  0              # X
% vec X1[3] -zeta  1-zeta  0          # X1
% vec Y[3] -1/2   1/2    0            # Y
% vec Z[3] 0   0   1/2                # Z

# Sequence G-X-S-R-A-Z-G-Y-X1-A1-T-Z-T
11 {G}  {X}      G to X
11 {X}  {S}      X to S
11 {S}  {R}      S to R
11 {R}  {A}      R to A
11 {A}  {Z}      A to Z
11 {Z}  {G}      Z to G
11 {G}  {Y}      G to Y
11 {Y}  {X1}     Y to X1
11 {X1}  {A1}    X1 to A1
11 {A1}  {T}     A1 to T
11 {T}  {Z}      T to Z
11 {Z}  {T}      Z to G

Hexagonal (HEX) Lattice

# The hex lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires no special variables
# rdfile tmp.txt > qp.ext
#
% vec G[3] 0   0   0               # G
% vec A[3] 0   0   1/2             # A
% vec H[3] 1/3  1/3  1/2           # H
% vec K[3] 1/3  1/3  0             # K
% vec L[3] 1/2  0    1/2           # L
% vec M[3] 1/2  0    0             # M

# Sequence G-M-K-G-A-L-H-L-K-H
11 {G}  {M}      G to M
11 {M}  {K}      X to S
11 {K}  {G}      S to R
11 {G}  {A}      R to A
11 {A}  {L}      A to Z
11 {L}  {H}      Z to G
11 {H}  {L}      G to Y
11 {L}  {K}      Y to X1
11 {K}  {H}      X1 to A1

Rhombohedral 1 (RHL1) Lattice

# The rhl1 lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires one special variables, angle alpha
# rdfile -valpha=# tmp.txt > qp.ext
#
% const eta=(1+4*cos(alpha))/(2+4*cos(alpha))
% const nu=(3/4-eta/2)
% vec G[3] 0   0   0               # G
% vec B[3] eta    1/2    1-eta     # B
% vec B1[3] 1/2   1-eta   eta-1    # B1
% vec F[3] 1/2   1/2   0           # F
% vec L[3] 1/2  0    0             # L
% vec L1[3] 0   0   -1/2           # L1
% vec P[3] eta   nu   nu           # P
% vec P1[3] 1-nu   1-nu   1-eta    # P1
% vec P2[3] nu   nu   eta-1        # P2
% vec Q[3] 1-nu   nu   0           # Q
% vec X[3] nu   0   -nu            # X
% vec Z[3] 1/2   1/2   1/2         # Z

# Sequence G-L-B-Z-G-Q-F-P1-L-P
11 {G}  {L}      G to L
11 {L}  {B}      L to B
11 {B}  {Z}      B to Z
11 {Z}  {G}      Z to G
11 {G}  {Q}      G to Q
11 {Q}  {F}      Q to F
11 {F}  {P1}     F to P1
11 {P1}  {L}     P1 to L
11 {L}  {P}      L to P

Rhombohedral 2 (RHL2) Lattice

# The rhl2 lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires one special variable, angle alpha
# rdfile -valpha=# tmp.txt > qp.ext
#
% const eta=1/(2*tan(alpha/2)*tan(alpha/2))
% const nu=(3/4-eta/2)
% vec G[3] 0   0   0               # G
% vec F[3] 1/2   -1/2   0          # F
% vec L[3] 1/2   0   0             # L
% vec P[3] 1-nu   -nu   1-nu       # P
% vec P1[3] nu   nu-1   nu-1       # P1
% vec Q[3] eta   eta   eta         # Q
% vec Q1[3] 1-eta   -eta   -eta    # Q1
% vec Z[3] 1/2   -1/2   1/2        # Z

# Sequence G-P-Z-Q-G-F-P1-Q1-L-Z
11 {G}  {P}      G to L
11 {P}  {Z}      P to Z
11 {Z}  {Q}      Z to Q
11 {Q}  {G}      Q to G
11 {G}  {F}      G to F
11 {F}  {P1}      F to P1
11 {P1}  {Q1}     P1 to Q1
11 {Q1}  {L}     Q1 to L
11 {L}  {Z}      L to Z

Monoclinic (MCL) Lattice

# The mcl lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires one special variable, angle alpha
# rdfile -valpha=# tmp.txt > qp.ext
# Note: this file is incorrect
#
% const eta=(1-b*cos(alphabyc))/(2*sin(alpha)*sin(alpha))
% const nu=(1/2-eta*c*cos(alphabyb))
% vec G[3] 0   0   0               # G
% vec A[3] 1/2   -1/2   0          # A
% vec C[3] 0  1/2  1/2             # C
% vec D[3] 1/2  0  1/2             # D
% vec D1[3] 1/2  0  -1/2           # D1
% vec E[3] 1/2  1/2  1/2           # E
% vec H[3] 0  eta  1-nu            # H
% vec H1[3] 0  1-eta  nu           # H1
% vec H2[3] 0  eta  -nu            # H2
% vec M[3] 1/2  eta  1-nu          # M
% vec M1[3] 1/2  1-eta  nu         # M1
% vec M2[3] 1/2  eta  -nu          # M2
% vec X[3] 0  1/2  0               # X
% vec Y[3] 0  0  1/2               # Y
% vec Y1[3] 0  0  -1/2             # Y1
% vec Z[3] 1/2  0  0               # Z

# Sequence G-Y-H-C-E-M1-A-X-M-D-Y-D
11 {G}  {Y}      G to Y
11 {Y}  {H}      Y to H
11 {H}  {C}      H to C
11 {C}  {E}      C to E
11 {E}  {M1}     E to M1
11 {M1}  {A}     M1 to A
11 {A}  {X}      A to X
11 {X}  {M}      X to M
11 {M}  {D}      M to D
11 {D}  {Y}      D to Y
11 {Y}  {D}      Y to D

C-centered Monoclinic 1 (MCLC1) Lattice

# The mcl lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires one special variable, angle alpha
# rdfile -valpha=# tmp.txt > qp.ext
# Note: this file is incorrect
#
% const zeta=(2-b*cos(alphabyc))/(4*sin(alpha)*sin(alpha))
% const eta=(1/2+2*zeta*c*cos(alphabyb))
% const psi=(3/4-(1/4)*abyb*abyb*(1/sin(alpha))*(1/sin(alpha)))
% const phi=(psi+(3/4-psi)*b*cos(alphabyc))
% vec G[3] 0   0   0                 # G
% vec N[3] 1/2   0   0               # N
% vec N1[3] 0  -1/2  0               # N1
% vec F[3] 1-zeta  1-zeta  1-eta     # F
% vec F1[3] zeta  zeta  eta          # F1
% vec F2[3] -zeta  -zeta  1-eta      # F2
% vec F3[3] 1-zeta  -zeta  1-eta     # F3
% vec I[3] phi  1-phi  1/2           # I
% vec I1[3] 1-phi  phi-1  1/2        # I1
% vec L[3] 1/2  1/2  1/2             # L
% vec M[3] 1/2  0  1/2               # M
% vec X[3] 1-psi  psi-1  0           # X
% vec X1[3] psi  1-psi  0            # X1
% vec X2[3] psi-1  -psi  0           # X2
% vec Y[3] 1/2  1/2  0               # Y
% vec Y1[3] -1/2  -1/2  0            # Y1
% vec Z[3] 0  0  1/2                 # Z

# Sequence G-Y-F-L-I1-Z-H-H1-Y1-X-G-M-G
11 {G}  {Y}      G to Y
11 {Y}  {F}      Y to F
11 {F}  {L}      F to L
11 {L}  {I1}      L to I1
11 {I1}  {Z}     I1 to Z
11 {Z}  {H}     Z to H
11 {H}  {H1}      H to H1
11 {H1}  {Y1}      H1 to Y1
11 {Y1}  {X}      Y1 to X
11 {X}  {G}      X to G
11 {G}  {M}      G to M
11 {M}  {G}      M to G

C-centered Monoclinic 2 (MCLC2) Lattice

# The mclc2 lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires one special variable, angle alpha
# rdfile -valpha=# tmp.txt > qp.ext
# Note: this file is incorrect
#
% const zeta=(2-b*cos(alphabyc))/(4*sin(alpha)*sin(alpha))
% const eta=(1/2+2*zeta*c*cos(alphabyb))
% const psi=(3/4-(1/4)*abyb*abyb*(1/sin(alpha))*(1/sin(alpha)))
% const phi=(psi+(3/4-psi)*b*cos(alphabyc))
% vec G[3] 0   0   0                 # G
% vec N[3] 1/2   0   0                # N
% vec N1[3] 0  -1/2  0                # N1
% vec F[3] 1-zeta  1-zeta  1-eta     # F
% vec F1[3] zeta  zeta  eta          # F1
% vec F2[3] -zeta  -zeta  1-eta      # F2
% vec F3[3] 1-zeta  -zeta  1-eta     # F3
% vec I[3] phi  1-phi  1/2           # I
% vec I1[3] 1-phi  phi-1  1/2        # I1
% vec L[3] 1/2  1/2  1/2             # L
% vec M[3] 1/2  0  1/2               # M
% vec X[3] 1-psi  psi-1  0           # X
% vec X1[3] psi  1-psi  0            # X1
% vec X2[3] psi-1  -psi  0           # X2
% vec Y[3] 1/2  1/2  0               # Y
% vec Y1[3] -1/2  -1/2  0            # Y1
% vec Z[3] 0  0  1/2                 # Z

# Sequence G-Y-F-L-I1-Z-N-G-M
11 {G}  {Y}      G to Y
11 {Y}  {F}      Y to F
11 {F}  {L}      F to L
11 {L}  {I1}      L to I1
11 {I1}  {Z}     I1 to Z
11 {Z}  {N}     Z to N
11 {N}  {G}      N to G
11 {G}  {M}      G to M

C-centered Monoclinic 3 (MCLC3) Lattice

# The mclc3 lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires one special variable, angle alpha
# rdfile -valpha=# tmp.txt > qp.ext
# Note: this file is incorrect
#
% const mu=(1+bbya*bbya)/4
% const delta=(b*c*cos(alpha*(1/2)*(1/a)*(1/a)))
% const zeta=(mu-1/4+(1-b*cos(alphabyc))/(4*sin(alpha)*sin(alpha)))
% const eta=(1/2+2*zeta*c*cos(alphabyb))
% const phi=(1+zeta-2*mu)
% const psi=(eta-2*delta)
% vec G[3] 0   0   0                 # G
% vec F[3] 1-phi   1-phi  1-psi      # F
% vec F1[3] phi  phi-1  psi          # F1
% vec F2[3] 1-phi  -phi  1-psi       # F2
% vec H[3] zeta  zeta  eta           # H
% vec H1[3] 1-zeta  -zeta  1-eta     # H1
% vec H2[3] -zeta  -zeta  1-eta      # H2
% vec I[3] 1/2  -1/2  1/2            # I
% vec M[3] 1/2  0  1/2               # M
% vec N[3] 1/2  0  0                 # N
% vec N1[3] 0  -1/2  0               # N1
% vec X[3] 1/2  -1/2  0              # X
% vec Y[3] mu  mu  delta             # Y
% vec Y1[3] 1-mu  -mu  -delta        # Y1
% vec Y2[3] -mu  -mu  -deta          # Y2
% vec Y3[3] mu  mu-1  delta          # Y3
% vec Z[3] 0  0  1/2                 # Z

# Sequence G-Y-F-H-Z-I-H1-Y1-X-G-M-G
11 {G}  {Y}      G to Y
11 {Y}  {F}      Y to F
11 {F}  {H}      F to H
11 {H}  {Z}      H to Z
11 {Z}  {I}      Z to I
11 {I}  {H1}     I to H1
11 {H1}  {Y1}    H1 to Y1
11 {Y1}  {X}     Y1 to X
11 {X}  {G}      X to G
11 {G}  {M}      G to M
11 {M}  {G}      M to G

C-centered Monoclinic 4 (MCLC4) Lattice

# The mclc4 lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires one special variable, angle alpha
# rdfile -valpha=# tmp.txt > qp.ext
# Note: this file is incorrect
#
% const mu=(1+bbya*bbya)/4
% const delta=(b*c*cos(alpha*(1/2)*(1/a)*(1/a)))
% const zeta=(mu-1/4+(1-b*cos(alphabyc))/(4*sin(alpha)*sin(alpha)))
% const eta=(1/2+2*zeta*c*cos(alphabyb))
% const phi=(1+zeta-2*mu)
% const psi=(eta-2*delta)
% vec G[3] 0   0   0                 # G
% vec F[3] 1-phi   1-phi  1-psi      # F
% vec F1[3] phi  phi-1  psi          # F1
% vec F2[3] 1-phi  -phi  1-psi       # F2
% vec H[3] zeta  zeta  eta           # H
% vec H1[3] 1-zeta  -zeta  1-eta     # H1
% vec H2[3] -zeta  -zeta  1-eta      # H2
% vec I[3] 1/2  -1/2  1/2            # I
% vec M[3] 1/2  0  1/2               # M
% vec N[3] 1/2  0  0                 # N
% vec N1[3] 0  -1/2  0               # N1
% vec X[3] 1/2  -1/2  0              # X
% vec Y[3] mu  mu  delta             # Y
% vec Y1[3] 1-mu  -mu  -delta        # Y1
% vec Y2[3] -mu  -mu  -deta          # Y2
% vec Y3[3] mu  mu-1  delta          # Y3
% vec Z[3] 0  0  1/2                 # Z

# Sequence G-Y-F-H-Z-H1-Y1-X-G-M-G
11 {G}  {Y}      G to Y
11 {Y}  {F}      Y to F
11 {F}  {H}      F to H
11 {H}  {Z}      H to Z
11 {Z}  {H1}      Z to H1
11 {H1}  {Y1}    H1 to Y1
11 {Y1}  {X}     Y1 to X
11 {X}  {G}      X to G
11 {G}  {M}      G to M
11 {M}  {G}      M to G

C-centered Monoclinic 5 (MCLC5) Lattice

# The mclc5 lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires one special variable, angle alpha
# rdfile -valpha=# tmp.txt > qp.ext
# Note: this file is incorrect
#
% const zeta=(bbya*bbya+(1-b*cos(alphabyc))/(sin(alpha)*sin(alpha)))/4
% const eta=(1/2+2*zeta*c*cos(alphabyb))
% const mu=(eta/2+(1/4)*bbya*bbya-b*c*cos(alphabya*(1/2)*(1/a)))
% const nu=(2*mu-zeta)
% const rho=(1-zeta*abyb*abyb)
% const eta=(1/2+2*zeta*c*cos(alphabyb))
% const omega=((4*nu-1-b*b*sin(alphabya*(1/a))*sin(alphabya*(1/a)))*c/(2*b*cos(alpha)))
% const delta=(zeta*c*cos(alphabyb)+omega/2-1/4)
% vec G[3] 0   0   0                 # G
% vec F[3] nu  nu  omega             # F
% vec F1[3] 1-nu  1-nu  1-omega      # F1
% vec F2[3] nu  nu-1  omega          # F2
% vec H[3] zeta  zeta  eta           # H
% vec H1[3] 1-zeta  -zeta  1-eta     # H1
% vec H2[3] -zeta  -zeta  1-eta      # H2
% vec I[3] rho  1-rho  1/2           # I
% vec I1[3] 1-rho  rho-1  1/2        # I1
% vec L[3] 1/2  1/2  1/2             # L
% vec M[3] 1/2  0  1/2               # M
% vec N[3] 1/2  0  0                 # N
% vec N1[3] 0  -1/2  0               # N1
% vec X[3] 1/2  -1/2  0              # X
% vec Y[3] mu  mu  delta             # Y
% vec Y1[3] 1-mu  -mu  -delta        # Y1
% vec Y2[3] -mu  -mu  -deta          # Y2
% vec Y3[3] mu  mu-1  delta          # Y3
% vec Z[3] 0  0  1/2                 # Z

# Sequence G-Y-F-L-I1-Z-H-H1-Y1-X-G-M-G
11 {G}  {Y}      G to Y
11 {Y}  {F}      Y to F
11 {F}  {L}      F to L
11 {L}  {H}      L to H
11 {H}  {Z}      H to Z
11 {Z}  {H}    Z to H
11 {H}  {H1}     H to H1
11 {H1}  {Y1}      H1 to Y1
11 {Y1}  {X}      Y1 to X
11 {X}  {G}      X to G
11 {G}  {M}     G to M
11 {M}  {G}      M to G

Triclinic 1a(/2a) (TRI1a) Lattice

# The tri1a lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires no special variables
# rdfile tmp.txt > qp.ext
#
% vec G[3] 0   0   0               # G
% vec L[3] 1/2  1/2  0             # L
% vec M[3] 0  1/2  1/2             # M
% vec N[3] 1/2  0  1/2             # N
% vec R[3] 1/2  1/2  1/2           # R
% vec X[3] 1/2  0  0               # X
% vec Y[3] 0  1/2  0               # Y
% vec Z[3] 0  0  1/2               # Z

# Sequence X-G-L-G-N-G-R-G
11 {X}  {G}      X to G
11 {G}  {L}      G to L
11 {L}  {G}      L to G
11 {G}  {N}      G to N
11 {N}  {G}      N to G
11 {G}  {R}      G to R
11 {R}  {G}      R to G

Triclinic 1b(/2b) (TRI1b) Lattice

# The tri1b lattice is taken from Computational Materials Science 49, 299 (2010)
# Cut and paste the contents of this file to a temporary file, e.g. tmp.txt.
# This structure requires no special variables
# rdfile tmp.txt > qp.ext
#
% vec G[3] 0   0   0                 # G
% vec L[3] 1/2  -1/2  0              # L
% vec M[3] 0  0  1/2                 # M
% vec N[3] -1/2  -1/2  1/2           # N
% vec R[3] 0  -1/2  1/2              # R
% vec X[3] 0  -1/2  0                # X
% vec Y[3] 1/2  0  0                 # Y
% vec Z[3] -1/2  0  1/2              # Z

# Sequence X-G-L-G-N-G-R-G
11 {X}  {G}      X to G
11 {G}  {L}      G to L
11 {L}  {G}      L to G
11 {G}  {N}      G to N
11 {N}  {G}      N to G
11 {G}  {R}      G to R
11 {R}  {G}      R to G

References


The contents of this page are found in Computational Materials Science 49, 299 (2010).


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