Least squares method for analyzing broadened x-ray line shapes

1980 ◽  
Vol 23 (5) ◽  
pp. 513-515
Author(s):  
R.H. Howell ◽  
D.L. Matthews
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
X Ray ◽  
Line Shapes

The crystal structure of kogarkoite, Na3SO4F

1980 ◽  
Vol 43 (330) ◽  
pp. 753-759 ◽  
Author(s):  
L. Fanfani ◽  
G. Giuseppetti ◽  
C. Tadini ◽  
P. F. Zanazzi
Keyword(s):  
Crystal Structure ◽  
Least Squares ◽  
Least Squares Method ◽  
Thermal Parameters ◽  
Cell Content ◽  
Space Group ◽  
X Ray ◽  
Structural Relationships ◽  
Automatic Diffractometer ◽  
Monoclinic Cell

SummaryThe crystal structure of synthetic kogarkoite has been determined from X-ray data collected on an automatic diffractometer. The refinement was performed by a least-squares method employing anisotropic thermal parameters. The 3157 reflections with I > 3σ(I) converged to a conventional R value of 0.033. The cell content is 12 Na3SO4F, the space-group P21/m, a = 18.074, b = 6.958, c = 11.443 Å, β = 107.71°.Kogarkoite presents a marked trigonal subcell with c′ corresponding to [102] of the monoclinic cell. The tridimensional framework can be considered built up by nine differently stacked layers of Na atoms approximately perpendicular to the c′ axis (five sheets are present in galeite, six in sulphohalite, and seven in schairerite). The very close structural relationships between these minerals are discussed.

Crystal and molecular structure of 3-ethyl-4-hydroxy-1,2,3(4H)-benzotriazine and 6-chloro-4-hydroxy-3-methyl-4-phenyl-1,2,3-benzotriazine

1985 ◽  
Vol 63 (3) ◽  
pp. 581-585 ◽  
Author(s):  
Kwong Khee Lai ◽  
Carl H. Schwalbe ◽  
Keith Vaughan ◽  
Ronald J. Lafrance ◽  
Clive D. Whiston
Keyword(s):  
Molecular Structure ◽  
Hydrogen Bonds ◽  
Least Squares ◽  
Least Squares Method ◽  
Crystal And Molecular Structure ◽  
Tetrahedral Geometry ◽  
Orthorhombic System ◽  
Full Matrix ◽  
X Ray ◽  
R Factor

The crystal structures of the title compounds have been determined from X-ray data collected on a four-circle diffractometer and refined by the full-matrix least-squares method. The former compound crystallizes in the orthorhombic system, space group Pbcn, with a = 14.346(8), b = 7.239(1), c = 17.276(2) Å, and has been refined to a conventional R factor of 0.043 for 890 observed reflections. Corresponding results for the latter compound are monoclinic, P21/n, a = 12.222(4), b = 7.482(2), c = 14.170(8) Å, β = 94.06(4)°, R = 0.060 for 2128 observed data. The triazine rings of both compounds exhibit short N(1)—N(2) bonds and tetrahedral geometry at C(4); however, the ring is puckered in the first compound but flat in the second. Molecules in both crystals are linked by [Formula: see text] hydrogen bonds.

The crystal structure of nickel(II) dimethyldithiocarbamate

1980 ◽  
Vol 45 (8) ◽  
pp. 2147-2151 ◽  
Author(s):  
Jan Lokaj ◽  
Ján Garaj ◽  
Viktor Kettmann ◽  
Viktor Vrábel
Keyword(s):  
Molecular Structure ◽  
Crystal Structure ◽  
Structural Analysis ◽  
Least Squares ◽  
Least Squares Method ◽  
Crystal And Molecular Structure ◽  
Unit Cell ◽  
Special Position ◽  
X Ray ◽  
Triclinic Unit Cell

Crystal and molecular structure of nickel(II) dimethyldithiocarbamate, Ni[S2CN(CH3)2]2 was solved by X-ray structural analysis and refined by the least squares method to R = 0.06 for 1065 reflections. The compound crystallizes in a space group P I and the triclinic unit cell has the dimensions: a = 6.521 (7), b = 6.798 (9), c = 7.633 (4), α = 67.21 (8)°, β = 67.34 (6)° γ =85.59 (9)°. The experimentally observed density is 1.75 g cm-3 and the calculated value for Z = 1 is 1.73 g cm-3. In the structure , the Ni atom occupies a special position in the centre of symmetry and is coordinated by four sulphur atoms in a plane: Ni-S 0.2218 (4) and 0.2198 nm S1-Ni-S2 angle 79.62 (8)°. The ligand S2CNC2 is nearly planar.

The crystal and molecular structure of tris-butyl-tin(IV)-(1-pyrrolidinecarbodithioato)-3-propionate

1989 ◽  
Vol 54 (3) ◽  
pp. 684-690 ◽  
Author(s):  
Jan Lokaj ◽  
Viktor Vrábel ◽  
Eleonóra Kellö ◽  
Vladimír Ratay
Keyword(s):  
Molecular Structure ◽  
Structural Analysis ◽  
Least Squares ◽  
Least Squares Method ◽  
Crystal And Molecular Structure ◽  
Analysis Method ◽  
Monoclinic System ◽  
X Ray ◽  
Cell Dimensions ◽  
Unit Cell Dimensions

The crystal and molecular structure of Bu3Sn(pyrn-dtc-prop) was solved by the X-ray structural analysis method and refined by the block diagonal least squares method to R = 0.053 for 1 930 observed reflections. The compound crystallizes in the monoclinic system with a space group of P21/c, Z = 4, F(000) = 1 056, with unit cell dimensions of a = 1.4758(5), b = 0.9970(3), c = 1.9166(6) nm; β = 113.90(2)°. The measured and calculated crystal densities were Dm = 1.32 and Dc = 1.31.103 kg m-3. The tin atom is coordinated by three carbon atoms at distances of Sn-C 0.2117(8), 0.2133(8), 0.2158(11) nm and two oxygen atoms O(1) and O(2) at distances of Sn-O 0.2210(5) and 0.2399(5) nm. The coordination polyhedron is a deformed trigonal bipyramid. The S2CN ligand is approximately planar.

SOLVING MINERALOGY PROBLEMS WITH THE HELP OF THE “ORIGIN" PACKAGE

2020 ◽  
Vol 386 (4) ◽  
pp. 6-12
Author(s):  
R. T. Abdraimov ◽  
B. E. Vintaykin ◽  
P. A. Saidakhmetov ◽  
N. K. Madiyarov ◽  
M. A. Abdualiyeva
Keyword(s):  
Spectral Analysis ◽  
Fourier Analysis ◽  
Least Squares ◽  
Phase Analysis ◽  
Least Squares Method ◽  
Spectral Lines ◽  
X Rays ◽  
Cauchy Function ◽  
X Ray ◽  
Smoothing Functions

Algorithms for solving typical mineralogical problems associated with quantitative x-ray spectral analysis and quantitative x-ray phase analysis using the program “Origin” are developed. The calculation of the areas and midpoint of spectral lines using the tabular processor of the program “Origin” is considered. Various approaches to determining the parameters of spectral lines using the least squares method using the standard functions of the program “Origin” were tested. The creation of a user function for approximation of diffraction maxima by the Cauchy function taking into account the doublet character of Ka series of x-rays is also considered. Various built-in algorithms for smoothing functions (based on averaging, polynomial approximation and Fourier analysis – synthesis) were tested to find weak diffraction maxima against strong noise; optimal schemes for the application of these algorithms were found. The considered algorithms can be applied in universities when processing the results of laboratory works on the topics "Analysis of spectra of emission of atoms", "Quantitative x-ray spectral analysis" and "Quantitative x-ray phase analysis".

X-ray fluorescence spectra quantitative analysis based on characteristic spectra optimization of partial least-squares method

2014 ◽  
Vol 12 (s2) ◽  
pp. S23001-323005
Author(s):  
Wei Zhang Wei Zhang ◽  
Lianfei Duan Lianfei Duan ◽  
Luozheng Zhang Luozheng Zhang ◽  
Yujun Zhang Yujun Zhang ◽  
Liuyi Ling Liuyi Ling ◽  
...  
Keyword(s):  
Quantitative Analysis ◽  
Least Squares ◽  
Partial Least Squares ◽  
Fluorescence Spectra ◽  
Least Squares Method ◽  
X Ray ◽  
Partial Least Squares Method

The Application of Digital Filters to the Analysis of Ge and Si(Li) Detector X-Ray Spectra

1979 ◽  
Vol 23 ◽  
pp. 125-131
Author(s):  
L. A. Rayburn
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Digital Filter ◽  
Digital Filters ◽  
Least Squares Method ◽  
Linear Least Squares ◽  
Raw Data ◽  
X Ray ◽  
Peak Structure

AbstractOne of the uncertain aspects in the analysis of x-ray spectra is the determination of the proper background to subtract from the raw data. In those cases where the background is a smoothly varying funct ion of the x-ray energy, the application of a digital filter to the raw data will effectively remove the background leaving only the filtered peak information. These filtered peaks can then be fit by using a non-linear least squares method in conjunction with a suitably chosen mathematical model of the peak structure.

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