Index

Core dictionary version 3.3.0

_atom_site_aniso.matrix_beta

Definition:

   
    The symmetric anisotropic atomic displacement parameter (ADP) matrix, β,
    which appears in a structure-factor expression.

    The contribution of the ADPs to the calculation of the structure factor is
    given as

    T = exp{-1 * Sum[Sum(β^ij^ * h~i~ * h~j~, j=1:3), i=1:3]}

    where β^ij^ are the matrix elements and h~m~ are the Miller indices.

    The ADP matrix β is related to the ADP matrices U and B as follows:

            |a~1~*   0     0  |   |t^11^ t^12^ t^13^|   |a~1~*   0     0  |
    β = C * |  0   a~2~*   0  | * |t^12^ t^22^ t^23^| * |  0   a~2~*   0  |
            |  0     0   a~3~*|   |t^13^ t^23^ t^33^|   |  0     0   a~3~*|

    where C is a constant (2 * π^2^ for U and 0.25 for B), a~i~* is the
    length of the respective reciprocal unit-cell vector, and t represents
    the individual anisotropic values, U^ij^ or B^ij^.

Type: Real

Values appear in Matrix context.

Dimension: [3,3]

Units: none

Evaluation method:

    With a as atom_site_aniso

        label = a.label

        If (a.ADP_type == 'betaani')
        {
            a.matrix_beta =  [[ a.beta_11, a.beta_12, a.beta_13 ],
                              [ a.beta_12, a.beta_22, a.beta_23 ],
                              [ a.beta_13, a.beta_23, a.beta_33 ]]
        }
        Else
        {
            If (a.ADP_type == 'Uani')
            {
                UIJ = a.matrix_U
            }
            Else If (a.ADP_type == 'Bani')
            {
                UIJ = a.matrix_B / (8 * Pi**2)
            }
            Else {
                If (a.ADP_type == 'Uiso')
                {
                    Loop b as atom_site
                    {
                        If(label == b.label)
                        {
                            U  =  b.U_iso_or_equiv
                            Break
                        }
                    }
                }
                Else If (a.ADP_type == 'Biso')
                {
                    Loop b as atom_site
                    {
                        If(label == b.label)
                        {
                            U  = b.B_iso_or_equiv / (8 * Pi**2)
                            Break
                        }
                    }
                }
                UIJ = U * _cell.convert_Uiso_to_Uij
            }
            CUB = _cell.convert_Uij_to_betaij
            a.matrix_beta =  CUB * UIJ * CUB
        }

Category:
atom_site_aniso