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Documentation on crystal structure upated
git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@8031 c92efa57-630b-4861-b058-cf58834340f0
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@ -354,116 +354,94 @@ input_description -distribution {Quantum Espresso} -package PWscf -program pw.x
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var ibrav -type INTEGER {
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status { REQUIRED }
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info {
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Bravais-lattice index:
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ibrav structure celldm(2)-celldm(6)
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0 "free", see above not used
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1 cubic P (sc) not used
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2 cubic F (fcc) not used
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3 cubic I (bcc) not used
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4 Hexagonal and Trigonal P celldm(3)=c/a
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5 Trigonal R, 3fold axis c celldm(4)=cos(alpha)
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-5 Trigonal R, 3fold axis <111> celldm(4)=cos(alpha)
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6 Tetragonal P (st) celldm(3)=c/a
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7 Tetragonal I (bct) celldm(3)=c/a
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8 Orthorhombic P celldm(2)=b/a,celldm(3)=c/a
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9 Orthorhombic base-centered(bco) celldm(2)=b/a,celldm(3)=c/a
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10 Orthorhombic face-centered celldm(2)=b/a,celldm(3)=c/a
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11 Orthorhombic body-centered celldm(2)=b/a,celldm(3)=c/a
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12 Monoclinic P, unique axis c celldm(2)=b/a,celldm(3)=c/a,
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celldm(4)=cos(ab)
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-12 Monoclinic P, unique axis b celldm(2)=b/a,celldm(3)=c/a,
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celldm(5)=cos(ac)
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13 Monoclinic base-centered celldm(2)=b/a,celldm(3)=c/a,
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celldm(4)=cos(ab)
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14 Triclinic celldm(2)= b/a,
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celldm(3)= c/a,
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celldm(4)= cos(bc),
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celldm(5)= cos(ac),
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celldm(6)= cos(ab)
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For P lattices: the special (or unique) axis (c) is the z-axis, one basal-plane
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vector (a) is along x, the other basal-plane vector (b) is at angle
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gamma for monoclinic, at 120 degrees for trigonal and hexagonal
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lattices, at 90 degrees for cubic, tetragonal, orthorhombic lattices
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Alternate choice (more commonly used in crystallography) for monoclinic:
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axis b is unique (orthogonal to a); axis c forms angle beta with axis a.
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sc simple cubic
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====================
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v1 = a(1,0,0), v2 = a(0,1,0), v3 = a(0,0,1)
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fcc face centered cubic
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====================
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v1 = (a/2)(-1,0,1), v2 = (a/2)(0,1,1), v3 = (a/2)(-1,1,0).
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bcc body entered cubic
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====================
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v1 = (a/2)(1,1,1), v2 = (a/2)(-1,1,1), v3 = (a/2)(-1,-1,1).
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simple hexagonal and trigonal(p)
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====================
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v1 = a(1,0,0), v2 = a(-1/2,sqrt(3)/2,0), v3 = a(0,0,c/a).
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trigonal(r)
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===================
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ibrav=5: The z-axis is chosen as the 3-fold axis, the crystallographic
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vectors form a three-fold star around the z-axis, the primitive cell
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is a simple rhombohedron. The crystallographic vectors are:
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v1 = a(tx,-ty,tz), v2 = a(0,2ty,tz), v3 = a(-tx,-ty,tz).
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where c=cos(alpha) is the cosine of the angle alpha between any pair
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of crystallographic vectors, tc, ty, tz are defined as
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Bravais-lattice index. In all cases except ibrav=0,
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either [celldm(1)-celldm(6)] or [a,b,c,cosab,cosac,cosbc]
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must be specified: see their description. For ibrav=0
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you may specify the lattice parameter celldm(1) or a.
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ibrav structure celldm(2)-celldm(6)
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or: b,c,cosab,cosac,cosbc
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0 free
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crystal axis provided in input: see card CELL_PARAMETERS
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1 cubic P (sc)
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v1 = a(1,0,0), v2 = a(0,1,0), v3 = a(0,0,1)
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2 cubic F (fcc)
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v1 = (a/2)(-1,0,1), v2 = (a/2)(0,1,1), v3 = (a/2)(-1,1,0)
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3 cubic I (bcc)
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v1 = (a/2)(1,1,1), v2 = (a/2)(-1,1,1), v3 = (a/2)(-1,-1,1)
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4 Hexagonal and Trigonal P celldm(3)=c/a
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v1 = a(1,0,0), v2 = a(-1/2,sqrt(3)/2,0), v3 = a(0,0,c/a)
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5 Trigonal R, 3fold axis c celldm(4)=cos(alpha)
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The crystallographic vectors form a three-fold star around
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the z-axis, the primitive cell is a simple rhombohedron:
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v1 = a(tx,-ty,tz), v2 = a(0,2ty,tz), v3 = a(-tx,-ty,tz)
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where c=cos(alpha) is the cosine of the angle alpha between
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any pair of crystallographic vectors, tx, ty, tz are:
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tx=sqrt((1-c)/2), ty=sqrt((1-c)/6), tz=sqrt((1+2c)/3)
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ibrav=-5, alternate description: the crystallographic vectors are
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v1 = a/sqrt(3) (u,v,v), v2 = a/sqrt(3) (v,u,v), v3 = a/sqrt(3) (v,v,u)
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and form a three-fold star around <111>. u and v are defined as
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-5 Trigonal R, 3fold axis <111> celldm(4)=cos(alpha)
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The crystallographic vectors form a three-fold star around
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<111>. Defining a' = a/sqrt(3) :
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v1 = a' (u,v,v), v2 = a' (v,u,v), v3 = a' (v,v,u)
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where u and v are defined as
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u = tz - 2*sqrt(2)*ty, v = tz + sqrt(2)*ty
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and tx, ty, tz as for case ibrav=5
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simple tetragonal (p)
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====================
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v1 = a(1,0,0), v2 = a(0,1,0), v3 = a(0,0,c/a)
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body centered tetragonal (i)
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================================
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v1 = (a/2)(1,-1,c/a), v2 = (a/2)(1,1,c/a), v3 = (a/2)(-1,-1,c/a).
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simple orthorhombic (p)
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=============================
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v1 = (a,0,0), v2 = (0,b,0), v3 = (0,0,c)
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bco base centered orthorhombic
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=============================
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v1 = (a/2,b/2,0), v2 = (-a/2,b/2,0), v3 = (0,0,c)
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face centered orthorhombic
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=============================
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v1 = (a/2,0,c/2), v2 = (a/2,b/2,0), v3 = (0,b/2,c/2)
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body centered orthorhombic
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=============================
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v1 = (a/2,b/2,c/2), v2 = (-a/2,b/2,c/2), v3 = (-a/2,-b/2,c/2)
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monoclinic (p)
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=============================
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v1 = (a,0,0), v2= (b*cos(gamma), b*sin(gamma), 0), v3 = (0,0,c)
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(unique axis c) where gamma is the angle between axis a and b.
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Alternate choice (ibrav=-12) uses b as unique axis:
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v1 = (a,0,0), v2 = (0,b,0), v3 = (a*sin(beta),0,c*cos(beta))
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where beta is the angle between axis a and c
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base centered monoclinic
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=============================
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v1 = ( a/2, 0, -c/2),
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v2 = (b*cos(gamma), b*sin(gamma), 0),
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v3 = ( a/2, 0, c/2),
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where gamma is the angle between axis a and b
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triclinic
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=============================
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v1 = (a, 0, 0),
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v2 = (b*cos(gamma), b*sin(gamma), 0)
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v3 = (c*cos(beta), c*(cos(alpha)-cos(beta)cos(gamma))/sin(gamma),
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6 Tetragonal P (st) celldm(3)=c/a
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v1 = a(1,0,0), v2 = a(0,1,0), v3 = a(0,0,c/a)
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7 Tetragonal I (bct) celldm(3)=c/a
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v1=(a/2)(1,-1,c/a), v2=(a/2)(1,1,c/a), v3=(a/2)(-1,-1,c/a)
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8 Orthorhombic P celldm(2)=b/a
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celldm(3)=c/a
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v1 = (a,0,0), v2 = (0,b,0), v3 = (0,0,c)
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9 Orthorhombic base-centered(bco) celldm(2)=b/a
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celldm(3)=c/a
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v1 = (a/2, b/2,0), v2 = (-a/2,b/2,0), v3 = (0,0,c)
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-9 as 9, alternate description
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v1 = (a/2,-b/2,0), v2 = (a/2,-b/2,0), v3 = (0,0,c)
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10 Orthorhombic face-centered celldm(2)=b/a
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celldm(3)=c/a
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v1 = (a/2,0,c/2), v2 = (a/2,b/2,0), v3 = (0,b/2,c/2)
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11 Orthorhombic body-centered celldm(2)=b/a
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celldm(3)=c/a
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v1=(a/2,b/2,c/2), v2=(-a/2,b/2,c/2), v3=(-a/2,-b/2,c/2)
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12 Monoclinic P, unique axis c celldm(2)=b/a
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celldm(3)=c/a,
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celldm(4)=cos(ab)
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v1=(a,0,0), v2=(b*cos(gamma),b*sin(gamma),0), v3 = (0,0,c)
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where gamma is the angle between axis a and b.
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-12 Monoclinic P, unique axis b celldm(2)=b/a
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celldm(3)=c/a,
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celldm(5)=cos(ac)
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v1 = (a,0,0), v2 = (0,b,0), v3 = (a*sin(beta),0,c*cos(beta))
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where beta is the angle between axis a and c
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13 Monoclinic base-centered celldm(2)=b/a
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celldm(3)=c/a,
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celldm(4)=cos(ab)
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v1 = ( a/2, 0, -c/2),
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v2 = (b*cos(gamma), b*sin(gamma), 0),
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v3 = ( a/2, 0, c/2),
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where gamma is the angle between axis a and b
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14 Triclinic celldm(2)= b/a,
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celldm(3)= c/a,
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celldm(4)= cos(bc),
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celldm(5)= cos(ac),
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celldm(6)= cos(ab)
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v1 = (a, 0, 0),
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v2 = (b*cos(gamma), b*sin(gamma), 0)
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v3 = (c*cos(beta), c*(cos(alpha)-cos(beta)cos(gamma))/sin(gamma),
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c*sqrt( 1 + 2*cos(alpha)cos(beta)cos(gamma)
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- cos(alpha)^2-cos(beta)^2-cos(gamma)^2 )/sin(gamma) )
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where alpha is the angle between axis b and c
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