### Abstract

Large-angle rotational motion (libration) characteristic of molecular solids has not been properly included in many scattering calculations because of the need to develop scattering theory through small-angle approximations. A simple but effective approach to calculating the influence of large-angle librations on the thermal disorder scattering given by molecular solids is to treat the molecules as independent librators, each in a harmonic potential well, using the mathematics appropriate for large-angle rotations. The resulting probability distribution for angular misorientations is Gaussian and this distribution can be used to smear the molecular form factor, enabling the librational influence on the scattering to be calculated. It is shown how to apply this direct approach quite generally and by way of examples the technique is used with the molecular solids sulfur hexafluoride (SF6), adamantane (C10H16) and buckminsterfullerene (C-60). For these materials, the molecular Fourier transform (i.e. the molecular form factor) have been calculated in selected planes in reciprocal space, followed by the separate effects of librational and translational smearing. It is found that the librational smearing produces a large effect on the form factor, particularly at larger scattering vectors, that is not sensitive to approximations in the argument. Additionally, the Debye-Waller effect of vibrational motion is included in the calculations, showing quantitatively the decreasing influence of vibrations on the scattering with increasing scattering vector. Both effects illustrate with pedagogic clarity how different processes modify the basic molecular scattering.

Original language | English |
---|---|

Pages (from-to) | 380-386 |

Number of pages | 7 |

Journal | Acta Crystallographica. Section A, Foundations of Crystallography |

Volume | 63 |

Issue number | 5 |

DOIs | |

Publication status | Published - Sep 2007 |

### Keywords

- adamantane
- order
- diffraction
- transition
- phase
- C-60

### Cite this

*Acta Crystallographica. Section A, Foundations of Crystallography*,

*63*(5), 380-386. https://doi.org/10.1107/S0108767307032187

**Diffuse scattering from large-angle, thermally induced, orientational disorder in molecular crystals.** / Reid, John; Moore, Moreton; MacNay, Lucy Emma.

Research output: Contribution to journal › Article

*Acta Crystallographica. Section A, Foundations of Crystallography*, vol. 63, no. 5, pp. 380-386. https://doi.org/10.1107/S0108767307032187

}

TY - JOUR

T1 - Diffuse scattering from large-angle, thermally induced, orientational disorder in molecular crystals

AU - Reid, John

AU - Moore, Moreton

AU - MacNay, Lucy Emma

PY - 2007/9

Y1 - 2007/9

N2 - Large-angle rotational motion (libration) characteristic of molecular solids has not been properly included in many scattering calculations because of the need to develop scattering theory through small-angle approximations. A simple but effective approach to calculating the influence of large-angle librations on the thermal disorder scattering given by molecular solids is to treat the molecules as independent librators, each in a harmonic potential well, using the mathematics appropriate for large-angle rotations. The resulting probability distribution for angular misorientations is Gaussian and this distribution can be used to smear the molecular form factor, enabling the librational influence on the scattering to be calculated. It is shown how to apply this direct approach quite generally and by way of examples the technique is used with the molecular solids sulfur hexafluoride (SF6), adamantane (C10H16) and buckminsterfullerene (C-60). For these materials, the molecular Fourier transform (i.e. the molecular form factor) have been calculated in selected planes in reciprocal space, followed by the separate effects of librational and translational smearing. It is found that the librational smearing produces a large effect on the form factor, particularly at larger scattering vectors, that is not sensitive to approximations in the argument. Additionally, the Debye-Waller effect of vibrational motion is included in the calculations, showing quantitatively the decreasing influence of vibrations on the scattering with increasing scattering vector. Both effects illustrate with pedagogic clarity how different processes modify the basic molecular scattering.

AB - Large-angle rotational motion (libration) characteristic of molecular solids has not been properly included in many scattering calculations because of the need to develop scattering theory through small-angle approximations. A simple but effective approach to calculating the influence of large-angle librations on the thermal disorder scattering given by molecular solids is to treat the molecules as independent librators, each in a harmonic potential well, using the mathematics appropriate for large-angle rotations. The resulting probability distribution for angular misorientations is Gaussian and this distribution can be used to smear the molecular form factor, enabling the librational influence on the scattering to be calculated. It is shown how to apply this direct approach quite generally and by way of examples the technique is used with the molecular solids sulfur hexafluoride (SF6), adamantane (C10H16) and buckminsterfullerene (C-60). For these materials, the molecular Fourier transform (i.e. the molecular form factor) have been calculated in selected planes in reciprocal space, followed by the separate effects of librational and translational smearing. It is found that the librational smearing produces a large effect on the form factor, particularly at larger scattering vectors, that is not sensitive to approximations in the argument. Additionally, the Debye-Waller effect of vibrational motion is included in the calculations, showing quantitatively the decreasing influence of vibrations on the scattering with increasing scattering vector. Both effects illustrate with pedagogic clarity how different processes modify the basic molecular scattering.

KW - adamantane

KW - order

KW - diffraction

KW - transition

KW - phase

KW - C-60

U2 - 10.1107/S0108767307032187

DO - 10.1107/S0108767307032187

M3 - Article

VL - 63

SP - 380

EP - 386

JO - Acta Crystallographica. Section A, Foundations of Crystallography

JF - Acta Crystallographica. Section A, Foundations of Crystallography

SN - 0108-7673

IS - 5

ER -