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

rmatrix

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

dmatrix

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

tmatrix

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