X-ray diffraction method of the radial electron density distribution. Structure of nanophase supports and supported catalysts

2012 ◽  
Vol 53 (S1) ◽  
pp. 63-85
Author(s):  
É. M. Moroz
2019 ◽  
Vol 2019 (6) ◽  
pp. 875-884 ◽  
Author(s):  
Maxim G. Chegerev ◽  
Alexandr V. Piskunov ◽  
Kseniya V. Tsys ◽  
Andrey G. Starikov ◽  
Klaus Jurkschat ◽  
...  

1999 ◽  
Vol 55 (3) ◽  
pp. 273-284 ◽  
Author(s):  
Sandrine Kuntzinger ◽  
Nour Eddine Ghermani

The electron density distribution in α-spodumene, LiAl(SiO3)2, was derived from high-resolution X-ray diffraction experiments. The results obtained from both Mo Kα- and Ag Kα-wavelength data sets are reported. The features of the Si—O and Al—O bonds are related to the geometrical parameters of the Si—O—Al and Si—O—Si bridges on the one hand and to the O...Li+ interaction on the other. Kappa refinements against the two data sets yielded almost the same net charges for the Si (+1.8 e) and O (−1.0 e) atoms in spodumene. However, the Al net charge obtained from the Ag Kα data (+1.9 e) is larger than the net charge derived from the Mo Kα data (+1.5 e). This difference correlates with a more contracted Al valence shell revealed by the shorter X-ray wavelength (κ = 1.4 for the Ag Kα data set). The derived net charges were used to calculate the Madelung potential at the spodumene atomic sites. The electrostatic energy for the chemical formula LiAl(SiO3)2 was −8.60 e2 Å−1 (−123.84 eV) from the net charges derived from the Ag Kα data and −6.97 e2 Å−1 (−100.37 eV) from the net charges derived from the Mo Kα data.


2002 ◽  
Vol 14 (22) ◽  
pp. 5477-5484 ◽  
Author(s):  
Yasuhiko Takahashi ◽  
Xioali Ji ◽  
Taichiro Nishio ◽  
Hiromoto Uwe ◽  
Ken-ichi Ohshima

1997 ◽  
Vol 53 (6) ◽  
pp. 870-879 ◽  
Author(s):  
C. Le Hénaff ◽  
N. K. Hansen ◽  
J. Protas ◽  
G. Marnier

The electron density distribution in lithium triborate LiB3O5 has been studied at room temperature by X-ray diffraction using Ag K \alpha radiation up to 1.02 Å−1 [1439 unique reflections with I > 3\sigma(I)]. Conventional refinements with a free-atom model yield R(F) = 0.0223, wR(F) = 0.0299, S = 1.632. Atom charge refinements show that the lithium should be considered a monovalent ion. Multipolar refinements were undertaken up to fourth order, imposing local non-crystallographic symmetry constraints in order to avoid phase problems leading to meaningless multipole populations due to the non-centrosymmetry of the structure (space group: Pn a21). The residual indices decreased to: R(F) = 0.0147, wR(F) = 0.0193, S = 1.106. The net charges are in good agreement with what can be expected in borate chemistry. Deformation density maps are analysed in terms of \sigma and \pi bonding. The experimental electron distribution in the p z orbitals of triangular B atoms and surrounding O atoms has been analysed by introducing idealized hybridized states. In parallel, the electron density has been determined from ab initio Hartree–Fock calculations on fragments of the structure. Agreement with the X-ray determination is very good and confirms the nature of bonding in the crystal. The amount of transfer of \pi electrons from the oxygen to the triangular B atoms is estimated to be 0.22 electrons by theory.


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