## Crystal Structure DeterminationTo solve a crystal structure means to determine the precise spatial arrangements of all of the atoms in a chemical compound in the crystalline state. This knowledge gives a chemist access to a large range of information, including connectivity, conformation, and accurate bond lengths and angles. In addition, it implies the stoichiometry, the density, the symmetry and the three dimensional packing of the atoms in the solid. Since interatomic distances are in the region of100-300 pm or 1-3 A, 1 microscopy using visible light (wavelength Ä ca. 300-700 nm) is not applicable (Fig. l. l). In 1912, Max von Laue showed that crystals are based on a three dimensionallattice which scatters radiation with a wavelength in the vicinity of interatomic distances, i. e. X -rays with Ä = 50-300 pm. The process bywhich this radiation, without changing its wave length, is converted through interference by the lattice to a vast number of observable "reflections" with characteristic directions in space is called X-ray diffraction. The method by which the directions and the intensities of these reflections are measured, and the ordering of the atoms in the crystal deduced from them, is called X-ray struc ture analysis. The following chapter deals with the lattice properties of crystals, the starting point for the explanation of these interference phenomena. Interatomic distances Crystals . . . . . . . . . . |

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### Contents

I | 1 |

II | 3 |

III | 4 |

IV | 5 |

V | 6 |

VI | 7 |

VII | 8 |

VIII | 9 |

XLVIII | 101 |

XLIX | 102 |

L | 103 |

LI | 105 |

LII | 106 |

LIII | 111 |

LIV | 115 |

LV | 116 |

IX | 13 |

X | 16 |

XI | 18 |

XII | 20 |

XIII | 22 |

XIV | 23 |

XV | 27 |

XVI | 30 |

XVII | 33 |

XVIII | 35 |

XIX | 37 |

XX | 41 |

XXI | 42 |

XXII | 44 |

XXIII | 46 |

XXIV | 52 |

XXV | 55 |

XXVI | 56 |

XXVII | 57 |

XXVIII | 58 |

XXIX | 59 |

XXX | 61 |

XXXI | 62 |

XXXII | 65 |

XXXIII | 67 |

XXXIV | 71 |

XXXV | 74 |

XXXVI | 78 |

XXXVII | 81 |

XXXVIII | 86 |

XXXIX | 87 |

XL | 89 |

XLI | 91 |

XLII | 92 |

XLIII | 93 |

XLIV | 95 |

XLV | 97 |

XLVI | 99 |

XLVII | 100 |

LVI | 118 |

LVII | 119 |

LVIII | 120 |

LIX | 121 |

LX | 122 |

LXII | 123 |

LXIII | 124 |

LXIV | 127 |

LXV | 128 |

LXVI | 130 |

LXVII | 131 |

LXVIII | 132 |

LXIX | 137 |

LXX | 139 |

LXXI | 141 |

LXXII | 142 |

LXXIII | 143 |

LXXIV | 145 |

LXXV | 146 |

LXXVI | 147 |

LXXVII | 148 |

LXXVIII | 149 |

LXXIX | 155 |

LXXX | 156 |

LXXXI | 158 |

LXXXII | 159 |

LXXXIII | 161 |

LXXXIV | 162 |

LXXXV | 163 |

LXXXVI | 165 |

LXXXVII | 169 |

LXXXVIII | 171 |

LXXXIX | 175 |

XC | 176 |

XCI | 177 |

XCII | 181 |

199 | |

205 | |

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### Common terms and phrases

absorption Acta Crystallogr anisotropic anomalous scattering asymmetric unit atom positions atoms axes bond lengths Bragg equation Bravais lattice calculated centrosymmetric components correct crystal class crystal structure crystal system crystallographic CUHABS IN I2/A cycle data set described difference Fourier diffraction pattern diffractometer direct methods disorder displacement factor effect electron density errors example film Fourier synthesis geometry give given glide plane goniometer GooF H-atoms heavy atoms hexagonal indices intensity International Tables inversion center lattice constants lattice planes Laue group measured mirror plane molecule monoclinic non-centrosymmetric normal orientation matrix origin orthorhombic path difference Patterson Patterson function peaks planes hkl possible R-factor R-value radiation reciprocal lattice refinement reflection hkl relationship result rotation scattering angle scattering vector set of planes solution space group structure determination structure factor structure model symbol symmetry elements symmetry operations systematic absences translation triclinic trigonal twinning unit cell usually vibrations wavelength weighted X-ray beam