Fitting Full X-Ray Diffraction Patterns for Quantitative Analysis: A Method for Readily Quantifying Crystalline and Disordered Phases

Fitting of full X-ray diffraction patterns is an effective method for quantifying abundances during X-ray diffraction (XRD) analyses. The method is based on the principal that the observed diffraction pattern is the sum of the individual phases that compose the sample. By adding an internal standard (usually corundum) to both the observed patterns and to those for individual pure phases (standards), all patterns can all be normalized to an equivalent intensity based on the internal standard intensity. Using least-squares refinement, the individual phase proportions are varied until an optimal match is reached. As the fitting of full patterns uses the entire pattern, including background, disordered and amorphous phases are explicitly considered as individual phases, with their individual intensity profiles or “amorphous humps” included in the refinement. The method can be applied not only to samples that contain well-ordered materials, but it is particularly well suited for samples containing amorphous and/or disordered materials. In cases with extremely disordered materials where no crystal structure is available for Rietveld refinement or there is no unique intensity area that can be measured for a traditional RIR analysis, full-pattern fitting may be the best or only way to readily obtain quantitative results. This approach is also applicable in cases where there are several coexisting highly disordered phases. As all phases are considered as discrete individual components, abundances are not constrained to sum to 100%.

Microstructures and micromechanical behaviors of high -entropy alloys investigated by synchrotron X-ray and neutron diffraction techniques: A review

High-entropy alloys(HEAs)possess outstanding features such as corrosion resistance,irradiation resistance,and good mechan-ical properties.A few HEAs have found applications in the fields of aerospace and defense.Extensive studies on the deformation mech-anisms of HEAs can guide microstructure control and toughness design,which is vital for understanding and studying state-of-the-art structural materials.Synchrotron X-ray and neutron diffraction are necessary techniques for materials science research,especially for in situ coupling of physical/chemical fields and for resolving macro/microcrystallographic information on materials.Recently,several re-searchers have applied synchrotron X-ray and neutron diffraction methods to study the deformation mechanisms,phase transformations,stress behaviors,and in situ processes of HEAs,such as variable-temperature,high-pressure,and hydrogenation processes.In this review,the principles and development of synchrotron X-ray and neutron diffraction are presented,and their applications in the deformation mechanisms of HEAs are discussed.The factors that influence the deformation mechanisms of HEAs are also outlined.This review fo-cuses on the microstructures and micromechanical behaviors during tension/compression or creep/fatigue deformation and the application of synchrotron X-ray and neutron diffraction methods to the characterization of dislocations,stacking faults,twins,phases,and intergrain/interphase stress changes.Perspectives on future developments of synchrotron X-ray and neutron diffraction and on research directions on the deformation mechanisms of novel metals are discussed.

Intensity correlation properties of x-ray beams split with Laue diffraction

Beam splitting is one of the main approaches to achieving x-ray ghost imaging, and the intensity correlation between diffraction beam and transmission beam will directly affect the imaging quality. In this paper, we investigate the intensity correlation between the split x-ray beams by Laue diffraction of stress-free crystal. The analysis based on the dynamical theory of x-ray diffraction indicates that the spatial resolution of diffraction image and transmission image are reduced due to the position shift of the exit beam. In the experimental setup, a stress-free crystal with a thickness of hundredmicrometers-level is used for beam splitting. The crystal is in a non-dispersive configuration equipped with a double-crystal monochromator to ensure that the dimension of the diffraction beam and transmission beam are consistent. A correlation coefficient of 0.92 is achieved experimentally and the high signal-to-noise ratio of the x-ray ghost imaging is anticipated.Results of this paper demonstrate that the developed beam splitter of Laue crystal has the potential in the efficient data acquisition of x-ray ghost imaging.

Direct observation of shock-induced phase transformation in polycrystalline iron via in situ x-ray diffraction

Phase transition of polycrystalline iron compressed along the Hugoniot is studied by combining laser-driven shock with in situ x-ray diffraction technique.It is suggested that polycrystalline iron changes from an initial body-centered cubic structure to a hexagonal close-packed structure with increasing pressure(i.e.,a phase transition fromαtoε).The relationship between density and pressure for polycrystalline iron obtained from the present experiments is found to be in good agreement with the gas-gun Hugoniot data.Our results show that experiments with samples at lower temperatures under static loading,such as in a diamond anvil cell,lead to higher densities measured than those found under dynamic loading.This means that extrapolating results of static experiments may not predict the dynamic responses of materials accurately.In addition,neither the face-centered cubic structure seen in previous molecular-dynamics simulations or twophase coexistence are found within our experimental pressure range.

A Novel High Temperature Apparatus for in situ Synchrotron X-ray Diffraction Studies of Molten Salt

This study demonstrates the design and application of a novel high temperature rotatory apparatus for insitu synchrotron X-ray diffraction studies of molten salts,facilitating investigation into the interaction between various structural materials and molten salts.The apparatus enables accurate detection of every phase change during hightemperature experiments,including strong reaction processes like corrosion.Molten salts,such as chlorides or fluo⁃rides,together with the structure materials,are inserted into either quartz or boron nitride capillaries,where X-ray diffraction pattern can be continuously collected,as the samples are heated to high temperature.The replacement re⁃action,when molten ZnCl2 are etching Ti3AlC2,can be clearly observed through changes in diffraction peak intensity as well as expansion in c-axis lattice parameter of the hexagonal matrix,due to the larger atomic number and ionic ra⁃dius of Zn2+.Furthermore,we investigated the high-temperature corrosion process when GH3535 alloy is in FLiNaK molten salt,and can help to optimize its stability for potential applications in molten salt reactor.Additionally,this high temperature apparatus is fully compatible with the combined usage of X-ray diffraction and Raman technique,providing both bulk and surface structural information.This high temperature apparatus has been open to users and is extensively used at BL14B1 beamline of the Shanghai Synchrotron Radiation Facility.

X-ray Powder Diffraction Pattern of Bi_4(SiO_4)_3

In cooperation with figure-of-merits the Rietveld analysis can appraise both angular and intensity data of powder diffraction. In this work, X-ray diffraction pattern of Bi4(SiO4)3 was redetermined with intensity figure-of-merits, which qualify agreement between observed and calculated relative intensities. F30 is 158.90 (0.0059, 32), intensity figure of merit Rint is 8.7, I20(17), 8.0. The values of figure-of-merits show that the data of JCPDS cards are distorted. Both the experimental and calculated peak positions and heights are listed in detail.

CRYSTAL STRUCTURE OF A LONG－PERIOD ORDERED PHASE IN Fe－C MARTENSITE AND COMPUTER SIMULATION OF ITS ELECTRON DIFFRACTION PATTERNS

Different structure models of a long-period ordered phase in Fe-C martenstie formed during aging have been checked by computer simulation of electron diffraction(ED) patterns based on these models.The results showed that the simulated ED pattern of γ'-FexC(Ⅱ) model proposed by the present authors is in good agreement with experimentally observed ED pattern.It was also confirmed that the incommensurate superperiod stems from the coexistence of several γ'-Fe_xC(H) phases with different superperiods.The Fe(144)C(24)(Fe6C) model proposed by Uwakweh et al.generated ED patterns remarkably different from the experimental ones.

IDENTIFICATION AND SIMULATION OF X-RAY POWDER DIFFRACTION PATTERN

A new method for pattern identification and simulation of X-ray powder diffraction data is described, which can give definite phase composition of the unknown rapidly and correctly. The method is implemented in Microsoft Fortran 77 for the IBM PC/XT/AT personal computer or their compatibles.

ELECTRON DIFFRACTION PATTERNS ANALYSIS OF PRECIPITATES IN LD_(10) ALLOY

ＥＬＥＣＴＲＯＮＤＩＦＦＲＡＣＴＩＯＮＰＡＴＴＥＲＮＳＡＮＡＬＹＳＩＳＯＦＰＲＥＣＩＰＩＴＡＴＥＳＩＮＬＤ_（１０）ＡＬＬＯＹ￥Ｊｉｎ，Ｔｏｕｎａｎ；Ｙｉｎ，Ｚｈｉｍｉｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｅｒｉａｌｓＳｃｉｅｎｃｅａｎｄＥｎｇｉｎｅｅｒ?..

Phase Identification Using Series of Selected Area Diffraction Patterns and Energy Dispersive Spectrometry within TEM

Transmission electron microscopy (TEM) is a very powerful technique for materials characteriza-tion, providing information relating to morphology, composition, and crystal structure. Selected area diffraction patterns (SADPs) are crystallographic data that can be obtained using a TEM in-strument. Conventional identification through SADP/TEM is tricky and tedious, thereby increasing the difficulty of phase identification. To establish a procedure for phase identification of known and unknown phases, in this study we examined two samples: one, a known phase, was Si with alignment;the other, unknown, was the TixOy phase at the 96.4Au-3Ni-0.6Ti interlayer/ yttria-stabilized zirconia (YSZ) interface of a steel/96.4Au-3Ni-0.6Ti interlayer/YSZ joint. The procedures for phase identification of the known and unknown phases are described herein using a series of SADPs and energy dispersive spectrometry within TEM that would be useful for general researchers.

Study on the Diffraction Patterns of α"-Fe_(16)N_2 with Jack-1 and Jack-2 Structural Parameters

Two body centered tetragonal (bet) crystal structures of α'-Fe_(16)N_2 with x=0.25, z=0.3125 (Jack-1) and x=0.222, z=0.306 (Jack-2) respectively, were analyzed theoretically with EMS software package. The simulation of diffraction patterns indicates that both diffraction patterns of the same axis in these two structures obey bcc extinction rule. The conclusion is also obtained from the analyses of the diffracted waves. α'-Fe_(16)N_2 precipitates in the diffusion layer of ion-nitrided α-iron have been studied with transmission electron microscope (TEM). We have distinctly observed the electron diffraction patterns of α'-Fe_(16)N_2 in [100], [111], [110], [011], [210], [021], [311], [113], [331] and [133] zone axes with perfect symmetry, which indicate the parallel orientation relationship with α matrix:<001>α'//<001>α'// {100}.α'// {100}ｔα. The analyses of diffraction patterns, which obey bcc extinction rule, verify the bct structure of α'-Fe_(16)N_2 discovered by X-ray diffraction.

Method for Signals Detection in Single Crystal Diffraction Patterns through a Diffraction Pattern Indexing Software

The correct use of information in science and technology is very important for its progress. Nowadays, the equipment used for the scientific and technological development provides results that are later interpreted by the researchers, in most of the above mentioned equipment the results are images full of information which has to be analyzed. A powerful stage with multiple benefits in this field is the image pre-processing by means of intelligent systems, which are capable to do image analysis throwing very useful results that enhance the scientific and technological information. There are currently more than 500 functions in the computational vision specialized open source library OpenCV, which associated with the C＋＋ programming language. These functions are used for application development in many areas of computer vision such as products inspection, medical images, safety, user＇s interfaces, camera calibration, stereoscopic vision and robotics. In this development and research work, by using the available functions and modifying the exposed methods, we present a proposal for signal detection in images originated in the transmission electron microscope （known as diffraction patterns）, which are attached to the detailed analysis of crystalline structures used in the study of the materials science, the results show a profit of at least 18% in the detection of signs by means of the method proposed in this work.

Evaluation on residual stresses of silicon-doped CVD diamond films using X-ray diffraction and Raman spectroscopy

The effect of silicon doping on the residual stress of CVD diamond films is examined using both X-ray diffraction (XRD) analysis and Raman spectroscopy measurements. The examined Si-doped diamond films are deposited on WC-Co substrates in a home-made bias-enhanced HFCVD apparatus. Ethyl silicate (Si(OC2H5)4) is dissolved in acetone to obtain various Si/C mole ratio ranging from 0.1% to 1.4% in the reaction gas. Characterizations with SEM and XRD indicate increasing silicon concentration may result in grain size decreasing and diamond [110] texture becoming dominant. The residual stress values of as-deposited Si-doped diamond films are evaluated by both sin2ψ method, which measures the (220) diamond Bragg diffraction peaks using XRD, with ψ-values ranging from 0° to 45°, and Raman spectroscopy, which detects the diamond Raman peak shift from the natural diamond line at 1332 cm-1. The residual stress evolution on the silicon doping level estimated from the above two methods presents rather good agreements, exhibiting that all deposited Si-doped diamond films present compressive stress and the sample with Si/C mole ratio of 0.1% possesses the largest residual stress of ~1.75 GPa (Raman) or ~2.3 GPa (XRD). As the silicon doping level is up further, the residual stress reduces to a relative stable value around 1.3 GPa.

Thermal expansion of kyanite at ambient pressure:An X-ray powder diffraction study up to 1000℃

The thermal expansion coefficients of kyanite at ambient pressure have been investigated by an X-ray powder diffraction technique with temperatures up to 1000 ℃. No phase transition was observed in the experimental temperature range. Data for the unit-cell parameters and temperatures were fitted empirically resulting in the following thermal expansion coefficients： αa = 5.8（3） × 10^-5, αb = 5.8 （1）× 10^-5, αc = 5.2（1）× 10^-5, and αv = 7.4（1） × 10^-3 ℃ 1 in good agreement with a recent neutron powder diffraction study. On the other hand, the variation of the unit-cell angles α, β and γ of kyanite with increase in temperature is very complicated, and the agreement among all studies is poor. The thermal expansion data at ambient pressure reported here and the compression data at ambient temperature from the literature suggest that, for the kyanite lattice, the most and least thermally expandable directions correspond to the most and least compressible directions, respectively.

SnO_2-based solid solutions for CH_4 deep oxidation: Quantifying the lattice capacity of SnO_2 using an X-ray diffraction extrapolation method

A series of SnO2‐based catalysts modified by Mn, Zr, Ti and Pb oxides with a Sn/M （M=Mn, Zr, Ti and Pb） molar ratio of 9/1 were prepared by a co‐precipitation method and used for CH4 and CO oxidation. The Mn3＋, Zr4＋, Ti4＋and Pb4＋cations are incorporated into the lattice of tetragonal rutile SnO2 to form a solid solution structure. As a consequence, the surface area and thermal stability of the catalysts are improved. Moreover, the oxygen species of the modified catalysts become easier to be reduced. Therefore, the oxidation activity over the catalysts was improved, except for the one modified by Pb oxide. Manganese oxide demonstrates the best promotional effects for SnO2. Using an X‐ray diffraction extrapolation method, the lattice capacity of SnO2 for Mn2O3 was 0.135 g Mn2O3/g SnO2, which indicates that to form stable solid solution, only 21%Sn4＋cations in the lattice can be maximally replaced by Mn3＋. If the amount of Mn3＋cations is over the capacity, Mn2O3 will be formed, which is not favorable for the activity of the catalysts. The Sn rich samples with only Sn‐Mn solid solution phase show higher activity than the ones with excess Mn2O3 species.

X-ray Diffraction of Dust Particles in Spring Beijing

X-ray diffractometry was utilized to study the mineralogical characteristics of the inhalable particles （PM10） sampled during two dust storms in Beijing city on March 18th and May 21st, 2008. We confirm, for the first time, that there stably exists ammonium chloride in the atmosphere when temperature is low. The total sulfates particles were affected by relative humidity. Both species and concentration of sulfates decreased first and then grew back by the end of each dust storm. Koninckite, a phosphate mineral never reported as particulate aerosol before, was identified. Meanwhile, our result shows that a chemical modification on dust minerals occurs during long range transportation. PM10 samples collected during the period of dust storms were dominated by crustal minerals such as quartz, illite/smectite, illite, chlorite, feldspar and calcite, and were notably higher in concentration than that in normal periods of time. The amounts of total sulfates, calcite and feldspar altered in each dust storm. It is derived from 24-hour isentropic backward trajectories that two dust events in spring 2008 originated in different sources.

MULTI-PEAK MATCH INTENSITY RATIO METHOD OF QUANTI-TATIVE X-RAY DIFFRACTION PHASE ANALYSIS

A new method for quantitative phase analysis is proposed by using X-ray diffraction multi-peak match intensity ratio. This method can obtain the multi-peak match intensity ratio among each phase in the mixture sample by using all diffraction peak data in the mixture sample X-ray diffraction spectrum and combining the relative intensity distribution data of each phase standard peak in JCPDS card to carry on the least square method regression analysis. It is benefit to improve the precision of quantitative phase analysis that the given single line ratio which is usually adopted is taken the place of the multi-peak match intensity ratio and is used in X-ray diffraction quantitative phase analysis of the mixture sample. By analyzing four-group mixture sample, adopting multi-peak match intensity ratio and X-ray diffraction quantitative phase analysis principle of combining the adiabatic and matrix flushing method, it is tested that the experimental results are identical with theory.

Analysis of surface orange peel of aluminum-alloy automobile sheet by using of EBSD and X-ray diffraction

The formation cause of orange peel of aluminum-alloy automotive sheet after tensile deformation was analysed by using X-ray diffraction and electron back-scattered diffraction(EBSD).The test results showed that formation cause of surface orange peel after tensile deformation related to product texture and nonuniform deformation during the tensile process.The grain size has significant effect on deformation uniform and texture formation.Coarse grains were easy to produce nonuniform deformation and texture,which would produce surface orange peel after tensile deformation.

Investigation of Peak Separation for X-ray Diffraction Profiles of Spinodal Decomposition by a Kind of Optimized Voigt Function

The intensity and position of sidebands (satellites) on both sides of main diffraction peak in a great number of X-ray diffraction profiles of alloys always change with progress of aging. The sidebands position is determined by a newly optimized Voigt function in present investigation. Furthermore, for Cu-4 wt pet Ti alloy aged at 400℃ for 720 min and 1080 min, after introducing the weight factor of above two satellites intensity, the relative error between the fitting curves and X-ray diffraction profiles is less than 0.185%, which is more precise than the previously calculating result.