Experimental estimation of uncertainties in powder diffraction intensities with a two-dimensional X-ray detector

2016 ◽  
Vol 31 (3) ◽  
pp. 216-222 ◽  
Author(s):  
Takashi Ida
Keyword(s):  
Powder Diffraction ◽  
Rietveld Method ◽  
Two Dimensional ◽  
X Ray ◽  
Lattice Constants ◽  
Cell Dimensions ◽  
Fine Quartz ◽  
Experimental Errors ◽  
Estimation Of Uncertainties ◽  
Unit Cell Dimensions

A method to obtain both one-dimensional powder diffraction intensities I(2θ) and statistical uncertainties σ(2θ) from the data collected with a flat two-dimensional X-ray detector is proposed. The method has been applied to analysis of the diffraction data of fine quartz powder recorded with synchrotron X-ray. The profile and magnitude of the estimated uncertainties σ(2θ) have shown that the effects of propagation of the errors in 2θ are dominant as the uncertainties about the observed intensity values I(2θ). The powder diffraction intensity data I(2θ), including nine reflection peaks have been analyzed by the Rietveld method incorporating the experimentally estimated uncertainties σ(2θ). The observed I(2θ) data have been reproduced with a symmetric peak profile function (Rwp = 0.84 %), and no significant peak shifts from calculated locations have been detected as compared with the experimental errors. The optimized values of the lattice constants of the quartz sample have nominally been estimated at a = 4.9131(4) Å and c = 5.4043(2) Å, where the uncertainties in parentheses are evaluated by the Rietveld optimization based on the estimated uncertainties σ(2θ) for intensities I(2θ). It is likely that reliability of error estimation about unit-cell dimensions has been improved by this analytical method.

An X-ray powder diffraction study of amine zinc hydroxide nitrate

1995 ◽  
Vol 10 (1) ◽  
pp. 20-24 ◽  
Author(s):  
Patricia Bénard ◽  
Jean Paul Auffrédic ◽  
Daniel Louër
Keyword(s):  
Powder Diffraction ◽  
Rietveld Method ◽  
Zinc Hydroxide ◽  
X Ray ◽  
Metal Atoms ◽  
Type Layer ◽  
Cell Dimensions ◽  
Unit Cell Dimensions ◽  
Starting Model ◽  
Zinc Hydroxide Nitrate

A new amine zinc hydroxide nitrate has been synthesized and investigated by means of X-ray powder diffraction. The monoclinic unit cell dimensions are a = 20.781(3) Å, b = 6.2151(9) Å, c = 5.4952(6) Å, β = 92.24(1)° (space group C2/m with Z = 2). The crystal structure has been refined by the Rietveld method using the structure of the related dihydrated phase as a starting model (Rp = 0.092 and RF = 0.068 for 372 reflections). The structure is characterized by octahedra [Zn(OH)6] describing a brucite-type layer, with one-quarter of the metal atoms missing, and by tetrahedra [Zn(OH)3(NH3)] located above and below the empty octahedra. The complex positive sheet has the formula [Zn3octa(OH)8Zn2tetra(NH3)2]2+ and the cohesion of the structure is realized through hydrogen bonding.

Powder diffraction data for new bismuth yttrium ytterbium oxides by XRD

2009 ◽  
Vol 24 (1) ◽  
pp. 53-55
Author(s):  
M. Alizadeh ◽  
K. Ahmadi ◽  
A. Maghsoudipour
Keyword(s):  
Powder Diffraction ◽  
Diffraction Data ◽  
Diffraction Method ◽  
Solid State Reaction Method ◽  
Powder Diffraction Data ◽  
X Ray Diffraction ◽  
X Ray ◽  
Lattice Constants ◽  
Cell Dimensions ◽  
Unit Cell Dimensions

X-ray powder diffraction data for three new bismuth yttrium ytterbium oxide compounds synthesized by solid-state reaction method are reported. The unit-cell dimensions were determined from X-ray diffraction method using Cu Kα radiation and evaluated by indexing programs. The cubic δ-Bi2O3 phase was identified to be the sole crystalline phase in Bi0.82Y0.09Yb0.09O1.5, Bi0.82Y0.12Yb0.06O1.5, and Bi0.82Y0.06Yb0.12O1.5 with lattice constants of a=5.5110(3), 5.5154(2), and 5.5113(2) Å, respectively.

Crystal structure of silver metagermanate, Ag2GeO3

2010 ◽  
Vol 25 (1) ◽  
pp. 15-18 ◽  
Author(s):  
Hirokazu Kurachi ◽  
Tomoyuki Iwata ◽  
Shuxin Ouyang ◽  
Jinhua Ye ◽  
Koichiro Fukuda
Keyword(s):  
Crystal Structure ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Rietveld Method ◽  
Powder Diffraction Data ◽  
X Ray ◽  
Reliability Indices ◽  
Cell Dimensions ◽  
Unit Cell Dimensions ◽  
Identity Period

The crystal structure of Ag2GeO3 was determined from laboratory X-ray powder diffraction data (Cu Kα1) using the Rietveld method. The title compound is orthorhombic with space group P212121, Z=4, unit-cell dimensions a=0.463 09(1) nm, b=0.713 93(2) nm, and c=1.040 79(3) nm, and V=0.344 10(2) nm3 . The final reliability indices were Rwp=5.58%, S=1.26, Rp=4.20%, RB=0.67% , and RF=0.35% . The GeO4 tetrahedra form infinite chains of [Ge2O6] along the a axis, with two tetrahedra per identity period of 0.463 nm. Individual chains are connected by Ag atoms, one-half of which are almost linearly coordinated by two O atoms and the rest are coordinated by three O atoms. The relatively short Ag-Ag distances of 0.299 to 0.339 nm indicate Ag(I)-Ag(I) interaction. This compound is isostructural with Ag2SiO3.

X-Ray and Optical Data for a Rare Earth–Poor Eudialyte from the North–Central Alaska Range

1990 ◽  
Vol 5 (2) ◽  
pp. 89-92 ◽  
Author(s):  
Neil E. Johnson ◽  
Mickey E. Gunter ◽  
Diana N. Solie ◽  
Charles R. Knowles
Keyword(s):  
Rare Earth ◽  
Powder Diffraction ◽  
Weight Percent ◽  
Optical Data ◽  
Alaska Range ◽  
North Central ◽  
X Ray ◽  
The North ◽  
Cell Dimensions ◽  
Unit Cell Dimensions

AbstractPowder X-ray and optical data have been recorded for a sample of exceptionally rare earth-poor eudialyte (Na12(Ca, REE)6(Fe2+,Mn,Mg)3Zr3(Zr,Nb)x[Si9O27−y(OH)y]2[Si3O9]2(C1,F)z, with x = 0. 1–0.9, y = 1–3 and z = 0.7–1.4) from a pegmatitic vein associated with the peralkaline Windy Fork granite in the north–central Alaska range. The eudialyte is uniaxial positive with ω= 1.6062(2), ε= 1.6138 (3) and microprobe analyses indicate that the sum of REE + Yis less than 0.1 weight percent. Refined unit cell dimensions are: a = 14.2572(4), c = 30.1338(27), Dx= 2.67, F30= 128 (0.006, 42), M20= 76. An indexed powder diffraction pattern is given.

X–Ray Powder Diffraction Data for Synthetic Varieties of Tetrahedrite

1991 ◽  
Vol 6 (1) ◽  
pp. 43-47 ◽  
Author(s):  
Neil E. Johnson
Keyword(s):  
Powder Diffraction ◽  
Experimental Unit ◽  
Regression Equations ◽  
Powder Diffraction Data ◽  
X Ray Diffraction ◽  
X Ray ◽  
Validation Test ◽  
Cell Dimensions ◽  
Synthetic Varieties ◽  
Unit Cell Dimensions

AbstractA series of five synthetic tetrahedrite-group minerals has been prepared and examined using powder X-ray diffraction in order to update current powder data and provide a validation test of cell dimension prediction equations. The tetrahedrites (nominally (Cu10X2)Sb4S13 with X = Zn, Cd, Mn, Hg and Fe) have the following properties: zincian tetrahedrite, a = 10.3833 (1) Å, Dx = 4.974 (1) g/cm3, F30 = 264 (0.004, 31), M20 = 279; cadmian tetrahedrite, a = 10.5066 (1) Å, Dx = 5.073 (1) g/cm3, F30 = 208 (0.004, 37), M20 = 249; manganoan tetrahedrite, a = 10.4384 (1) Å, Dx = 4.822 (1) g/cm3, F30 = 274 (0.003, 33), M20 = 302; mercurian tetrahedrite, a = 10.5071 (1) Å, Dx = 5.570 (1) g/cm3, F30 = 150 (0.006, 35), M20 = 156; ferroan tetrahedrite, a = 10.3630 (1) Å, Dx = 5.002 (1) g/cm3, F30 = 253 (0.004, 33), M20 = 281. The experimental unit cell dimensions obtained in this study are in excellent agreement with calculated values produced using regression equations developed previously.

Crystal data and X-ray powder diffraction data of 2,4-diiodo-4-nitrophenol (disophenol), C6H3I2NO3. More precise X-ray powder diffraction data of p-nitrophenol, C6H5NO3

1996 ◽  
Vol 11 (4) ◽  
pp. 301-304
Author(s):  
Héctor Novoa de Armas ◽  
Rolando González Hernández ◽  
José Antonio Henao Martínez ◽  
Ramón Poméz Hernández
Keyword(s):  
Powder Diffraction ◽  
Diffraction Data ◽  
Unit Cell ◽  
Crystal Data ◽  
Powder Diffraction Data ◽  
Space Group ◽  
X Ray ◽  
Cell Dimensions ◽  
Unit Cell Dimensions ◽  
Monoclinic Cell

p-nitrophenol, C6H5NO3, and disophenol, C6H3I2NO3, have been investigated by means of X-ray powder diffraction. The unit cell dimensions were determined from diffractometer methods, using monochromatic CuKα1 radiation, and evaluated by indexing programs. The monoclinic cell found for p-nitrophenol was a=6.159(2) Å, b=8.890(2) Å, c=11.770(2) Å, β=103.04(2)°, Z=4, space group P21 or P2l/m, Dx=1.469 Mg/m3. The monoclinic cell found for disophenol has the dimensions a=8.886(1) Å, b=14.088(2) Å, c=8.521(1) Å, β=91.11(1)°, Z=4, space group P2, P2, Pm or P2/m, Dx=2.438 Mg/m3.

Powder X-Ray Diffraction Data for Ca2Bi2O5and C4Bi6O13

1992 ◽  
Vol 7 (2) ◽  
pp. 109-111 ◽  
Author(s):  
C.J. Rawn ◽  
R.S. Roth ◽  
H.F. McMurdie
Keyword(s):  
Powder Diffraction ◽  
Diffraction Data ◽  
Neutron Powder Diffraction ◽  
X Ray Diffraction ◽  
Space Group ◽  
X Ray ◽  
Cell Dimensions ◽  
Powder Samples ◽  
Orthorhombic Cell ◽  
Unit Cell Dimensions

AbstractSingle crystals and powder samples of Ca2Bi5O5and Ca4Bi6O13have been synthesized and studied using single crystal X-ray diffraction as well as X-ray and neutron powder diffraction. Unit cell dimensions were calculated using a least squares analysis that refined to a δ2θof no more than 0.03°. A triclinic cell was found with space group , a = 10.1222(7), b = 10.1466(6), c = 10.4833(7) Å. α= 116.912(5), β= 107.135(6) and γ= 92.939(6)°, Z = 6 for the Ca2Bi2O5compound. An orthorhombic cell was found with space group C2mm, a = 17.3795(5), b = 5.9419(2) and c = 7.2306(2) Å, Z = 2 for the Ca4Bi6O13compound.

X-Ray Powder Diffraction (XRPD)

2016 ◽  
pp. 326-341 ◽  
Author(s):  
Robert Heimann
Keyword(s):  
Powder Diffraction ◽  
X Rays ◽  
Powder Diffraction File ◽  
Thin Beam ◽  
Archaeological Ceramics ◽  
X Ray ◽  
Analytical Technique ◽  
Cell Dimensions ◽  
Unit Cell Dimensions

X-ray powder diffraction (XRPD) is an important tool to determine the phase composition of archaeological ceramics. In principle, a thin beam of X-rays incident to a lattice plane of crystalline matter is scattered in specific directions and angles depending on the distances of atoms. This allows determination of characteristic unit cell dimensions and serves to unambiguously identify crystalline phases in the ceramics. In this chapter, generation of X-rays and the theory of diffraction will be briefly discussed as well as equipment, focusing conditions, and sample preparation procedures of common XRPD methods. The X-ray pattern obtained will provide an analytical fingerprint that can be matched against the Powder Diffraction File of the International Centre for Diffraction Data. Examples will be given of application of this analytical technique to archaeological clays and ceramics.

ZrSiO4 mit monokliner Baddeleyitstruktur?.

1976 ◽  
Vol 31 (9) ◽  
pp. 1175-1178 ◽  
Author(s):  
Kurt Walenta
Keyword(s):  
Powder Diffraction ◽  
Diffraction Data ◽  
Unit Cell ◽  
Powder Diffraction Data ◽  
X Ray ◽  
Cell Dimensions ◽  
Unit Cell Dimensions ◽  
Limits Of Error ◽  
Zircon Particles

A new compound having the same composition as zircon, ZrSiO4, but differing from it in its structure has been obtained by heating zircon particles to a temperature of 5000 to 10000°K. According to X-ray powder diffraction data the structure and within limits of error also the unit-cell dimensions are identical with that of monoclinic baddeleyite, ZrO2. This suggests that the baddeleyite lattice can not only accommodate 10 molecular % SiO2 as is already known for some time, but substantially more, unless it is assumed that some kind of submicroscopic exsolution of amorphous SiO2 has taken place.

Powder X-ray diffraction data for Ba4ZnTi11O27 and Ba2ZnTi5O13

1994 ◽  
Vol 9 (1) ◽  
pp. 56-62 ◽  
Author(s):  
C. G. Lindsay ◽  
C. J. Rawn ◽  
R. S. Roth
Keyword(s):  
Single Crystal ◽  
Single Crystals ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Lattice Parameters ◽  
X Ray Diffraction ◽  
X Ray ◽  
Cell Dimensions ◽  
Powder Samples ◽  
Unit Cell Dimensions

Single crystals and powder samples of Ba4ZnTi11O27 and Ba2ZnTi5O13 have been synthesized and studied using single-crystal X-ray precession photographs and X-ray powder diffraction. Unit cell dimensions were calculated from a least-squares refinement with a final maximum Δ2θ of 0.05°. Both phases were found to have monoclinic cells, space group C2/m. The refined lattice parameters for the Ba4ZnTi11O27 compound are a= 19.8687(8) Å, b=11.4674(5) Å, c=9.9184(4) Å, β= 109.223(4)°, and Z=4. The refined lattice parameters for the Ba2ZnTi5O13 compound are a= 15.2822(7) Å, b=3.8977(1) Å, c=9.1398(3) Å, β=98.769(4)°, and Z=2.

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