A Numerical Fourier-analysis Method for the Correction of Widths and Shapes of Lines on X-ray Powder Photographs

Stokes, A. R.

doi:10.1088/0959-5309/61/4/311

Cited by 757 publications

(219 citation statements)

References 9 publications

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“…furnace cooled over a period of 4 hrs. Appropriate instrument lineshapes were then deconvolved [32] from each peak with a fast Fourier transform method. The statistical scatter in'the experimental data contributed excessive amplitude to the higher order Fourier coefficients.…”

Section: Table 1 Chemical Compostion Of 9ni Steel (Wt%) -----------mentioning

confidence: 99%

The stability of precipitated austenite and the toughness of 9Ni steel

Fultz

Kim

et al. 1985

Metall Trans A

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Section: Table 1 Chemical Compostion Of 9ni Steel (Wt%) -----------mentioning

confidence: 99%

The stability of precipitated austenite and the toughness of 9Ni steel

Fultz

Kim

et al. 1985

Metall Trans A

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“…Similarly, the second term in (12) represents the amplification of the misfitting error in the background estimation. A similar argument can be made for the Stokes (1948) deconvolution method.…”

Section: = [~-')~;Zt(viln)4-(-1)(vilei H)lz[ '/Z (10)mentioning

confidence: 58%

“…The second involves the deconvolution of the observed profile using a reference profile, with several implementations available. These can be grouped into four broad categories: unconstrained deconvolution (Stokes, 1948) and matrix inversion; iterative deconvolution (Ergun, 1968); constrained deconvolution (Lou6r et al, 1969;Lou6r & t The calculated profile is the convolution between the trial specimen and instrument profiles.…”

Section: Introductionmentioning

confidence: 99%

Eigen-System Analysis of X-ray Diffraction Profile Deconvolution Methods Explains Ill-Conditioning

Armstrong¹,

Kalceff²

1998

J Appl Cryst

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Several deconvolution methods common in X-ray diffraction profile studies have been examined using an eigen-system analysis in which an error-bound function is used to represent the maximum difference between the solution and true specimen profiles. This approach quantifies the sources of misfitting and illconditioning that appear in the solution profile and expresses them as a function of the control parameter for a particular method. A simulation of an instrumentbroadened profile overlaid with random noise and background signals was used to evaluate the errorbound function for the iterative and constrained deconvolution methods, and the properties of the error-bound function were related to the features of the solution profile for each method. This analysis quantifies the terms that contribute to the ill-conditioning of the solution profile. It shows that, even for optimum values of the control parameters, positivity is not preserved and spurious oscillations are present in the solution profile.

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“…These effects can be removed by the Stokes correction [19], which is based on a Fourier analysis. In addition, a single MgO crystal was measured to resolve the instrument properties.…”

Section: Xrd Peak Analysismentioning

confidence: 99%

Microstructure of TiN coatings synthesized by direct pulsed Nd:YAG laser nitriding of titanium: Development of grain size, microstrain, and grain orientation

et al. 2008

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Pure titanium was irradiated by pulsed Nd:YAG laser irradiation in nitrogen atmosphere. As a result, nitrogen uptake and diffusion occurred and a TiN layer was synthesized at the titanium surface. These TiN coatings were analyzed by X-ray diffraction and the diffraction patterns were investigated in detail, in order to obtain more information about the physical processes during the coating formation. The diffraction peaks were fitted by Pearson VII profiles and the grain size and the microstrain were determined by the analysis of line broadening and peak shifts, using the Williamson-Hall and the Warren-Averbach formalisms. Additional single-line analyses were performed by means of the method of Langford and Keijser to obtain information about the preferred grain orientation and the texture development. The maximum grain size was about 100 nm and a corresponding average lattice strain of 0.002 was found. A relation between the treatment parameters and the coating properties, such as grain size and microstrain, can be shown. Thus, it was possible to determine optimal scan parameters for material processing and to establish the physical limits of the coating properties.PACS 81.65.Lp; 81.15.Fg; 61.10.Nz; 68.55.Jk IntroductionNitriding and carburizing of metals are well known techniques to improve the tribological properties like hardness and wear resistance of technical surfaces [1]. As an example, plasma-and gas nitriding are established methods for surface treatment [2,3]. Alternatively, it is possible to treat the surface with laser radiation and to directly synthesize hard coatings [4][5][6][7][8]. Previous works have shown the successful synthesis of titanium nitride with laser irradiation [9][10][11]. Here, a Q-switched Nd:YAG laser was used for the nitriding treatment. The main advantages of this method are a reduction of the processing time and the negligible heat load for the workpiece. Stress, microstrain and inhomogeneity remain the main problems. Also the texture of cubic titanium nitride is a decisive factor for the technical quality of the coatings, as the u Fax: +49-551-39-4493, E-mail: pschaaf@uni-goettingen.de texture influences strain development and finally crack formation and propagation. Some investigations on texture and strain development in relation to the process parameters have been reported in the literature [12][13][14].This work resolves the resulting grain size and strain development and relates them to laser treatment parameters like scan parameters. In this way, one can try to predict optimum treatment parameters for optimum coating properties, i.e. find parameters that minimize the lattice strain in order to reduce crack formation and propagation. Experiments 2.1 Sample treatmentConventional α-titanium (purity > 99.98%) was used for the treatments. Titanium sheets of 1 mm thickness were cut into pieces of 15 × 15 mm 2 and used in the asreceived state without any further treatment.For laser nitriding, the samples were placed in a chamber which was first evacuated and then fil...

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A Numerical Fourier-analysis Method for the Correction of Widths and Shapes of Lines on X-ray Powder Photographs

Cited by 757 publications

References 9 publications

The stability of precipitated austenite and the toughness of 9Ni steel

The stability of precipitated austenite and the toughness of 9Ni steel

Eigen-System Analysis of X-ray Diffraction Profile Deconvolution Methods Explains Ill-Conditioning

Microstructure of TiN coatings synthesized by direct pulsed Nd:YAG laser nitriding of titanium: Development of grain size, microstrain, and grain orientation

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