Rmatrix is the reciprocal axes matrix.
This matrix can be stored in an rmatfile, together
with other optional data.
Rmatrix, Dmatrix, Tmatrix and Cell Parameters
matrix indices
11 12 13
21 22 23
31 32 33
The rmatrix is build by the components of
the reciprocal axes (in the laboratory system) in columns with
all goniostat angles set to zero.
a*x b*x c*x
R = a*y b*y c*y
a*z b*z c*z
The dmatrix is build by the components of
the direct axes (in the laboratory system) in rows with
all goniostat angles set to zero.
ax ay az
D = bx by bz
cx cy cz
D = R-1
R = D-1
The tmatrix is a transformation matrix. It is applied on the
dmatrix.
D1 = R1-1
D2 = T·D1
R2 = D2-1
cell parameters
a = row 1 of dmatrix = ( d11,d12,d13 )
b = row 1 of dmatrix = ( d21,d22,d23 )
c = row 1 of dmatrix = ( d31,d32,d33 )
a = |a| = √( d11² + d12² + d13²)
b = |b| = √( d21² + d22² + d23²)
c = |c| = √( d31² + d32² + d33²)
alpha = acos( b·c/b*c )
beta = acos( c·a/c*a )
gamma = acos( a·b/a*b )
volume = determinant(D)
reciprocal cell parameters
a* = column 1 of rmatrix = ( r11,r21,r31 )
b* = column 1 of rmatrix = ( r12,r22,r32 )
c* = column 1 of rmatrix = ( r13,r23,r33 )
a* = |a*| = √( r11² + r21² + r31²)
b* = |b*| = √( r12² + r22² + r32²)
c* = |c*| = √( r13² + r23² + r33²)
alpha* = acos( b*·c*/b**c* )
beta* = acos( c*·a*/c**a* )
gamma* = acos( a*·b*/a**b* )
reciprocal volume = determinant(R)
Notes
- The definition of the RMAT corresponds to the definition
of a CAD4 orientation matrix.
- Users of the Nonius KappaCCD can generate an rmatfile with the
program xmatrix (from a denzo x-file).
- The DirAx output file is already in the correct format (but always
in a Primitive Bravais-centering, and without point group information).
Users of the Nonius KappaCCD Collect Software or EVAL Suite can add this information with the
program rmatrix.
- misc
- R*h = c
- |c| = 2sin(θ)/λ
- reso = sin(θ)/λ
- d = λ/2sin(θ)
- sin(θ) = λ/2d = λ*reso = |c|λ/2