Method to generate all the geometrical ambiguities of powder indexing solutions

Abstract

A new algorithm is reported that returns all the lattices with the same set of d spacings as that of a given lattice. The algorithm is useful for quickly checking lattice parameters obtained for a considered powder diffraction pattern and assessing the reliability of the results of powder indexing. The proposed algorithm was implemented as a new function in the powder indexing software Conograph (http://sourceforge.jp/projects/conograph/; http://research.kek.jp/people/rtomi/ConographGUI/web_page.html). Examples of real cases are reported to explain how the algorithm can be used.

GAM-7: an organic–inorganic hybrid layered aluminophosphate crystal formed by zeolite transformation

“…† The clarified layered framework consists of three P sites (tetrahedral), four Al sites, and sixteen O sites, in which the four Al sites were further enabled to divide into two tetrahedral Al sites (Al1 and Al2) and two octahedral Al sites (Al3 and Al4). These T sites correspond to three resonance peaks in 31 P and 27 Al NMR spectra. In the 27 Al DEMAS NMR and 27 Al 3QMAS NMR spectra, in which the octahedral Al atom was almost observed as the one resonance peak, there are two octahedral Al sites in the structural model due to their approximate local environments in the framework.…”

“…Lattice constants and a space group were estimated by the indexing analysis using the program Conograph. 31 The observed integral intensities ( I obs ) of each diffraction peak were extracted by the Le Bail method 32 and a framework structure was solved by direct methods using the I obs dataset, which were conducted using the program EXPO2014. 33 A molecular conformation of diisopropylamine in a nanospace of GAM-7 was estimated by the direct space method using the program FOX v2022.1.…”

“…Local structures around 1 H, 13 C, 27 Al, and 31 P nuclei in assynthesized GAM-7 were investigated by the solid-state magic angle spinning (MAS) nuclear magnetic resonance (NMR) using an AVANCE III 400 WB spectrometer (Bruker Biospin K.K., Japan). 31 P dipolar decoupling (DD) MAS NMR, { 1 H}-31 P crosspolarization (CP)/MAS NMR, 27 Al direct-excitation (DE) MAS NMR, { 1 H}- 27 Al CP/MAS NMR and 1 H DEMAS spectra were recorded using a 4.0 mm VT-MAS probe with a rotor spinning rate of 14 kHz. The { 1 H}- 13 C CP/MAS spectrum was obtained with a spinning rate of 6 kHz for 13 C. The 27 Al 3QMAS NMR spectrum with a z-filter was also obtained using a 3.2 mm triple channel VT-MAS probe with an { 1 H} decoupling and spinning rate of 24 kHz.…”

Application of convex optimization to identification of atomic species from diffraction patterns

“…In powder indexing, although the problem to be solved is different, the problem about the uniqueness of solutions known as geometrical ambiguities was rigorously studied in Mighell and Santoro (1975). Recently, much progress was also made in the author's two papers (Oishi-Tomiyasu, 2014, 2016). In particular, the developed method can be used to check results of powder indexing.…”

Koordinationspolymere aus 3d-Übergangsmetallhalogeniden mit Cyanopyridinen : Synthese, Analytik und Kristallstrukturbestimmung aus Röntgenpulverdaten

“…Anschließend werden die Gitterparameter a, b, c, α, β und γ (Metrik der Elementarzelle) bestimmt. Die Indizierung erfolgte mit den Programmen DASH (Dicvol-Algorithmus) [10,11,12] und/ oder Conograph [20,34,35]. Zur Überprüfung der Verlässlichkeit eines Indiziervorschlages wurden die Volumeninkremente nach Hofmann [24] herangezogen.…”