Accurate and time-saving quantification of a component present in a very small amount in a mixture by the direct derivation method

2020 ◽  
Vol 53 (5) ◽  
pp. 1225-1235
Author(s):  
Hideo Toraya
Keyword(s):  
Individual Component ◽  
Unit Area ◽  
Inorganic Materials ◽  
Quantitative Phase Analysis ◽  
High Angle ◽  
Time Saving ◽  
Direct Derivation ◽  
Scale Parameters ◽  
Present Procedure ◽  
Derivation Method

In quantitative phase analysis (QPA) using the direct derivation (DD) method, total sums of diffracted/scattered intensities for individual components are used as observed quantities. Fluctuation in their relative intensity ratios induces errors in derived weight fractions, and it ought to be suppressed for improving the accuracy in QPA, in particular, of a component that is present in a small amount. The fluctuation is primarily caused by the termination in summing/integrating diffracted/scattered intensities on the high-angle side. It is usually associated with changing the 2θ range in whole-powder-pattern fitting (WPPF) used to decompose the mixture pattern into individual component patterns. In this study, calculated patterns for individual components, fitted in WPPF, are normalized so as to give the unit area when they are separately integrated over their definition ranges in 2θ. The termination effect could effectively be reduced by extending the definition range to a certain high-angle limit. Scale parameters for adjusting the calculated patterns become non-fluctuating against the change of the 2θ range in WPPF. Thus, the time spent for intensity data collection of mixture patterns can be reduced by shortening the scan range. The present procedure has been tested with binary mixtures containing small amounts of crystalline phases of 0.02–0.4 wt%. QPA could be conducted with errors of 0.01–0.03 wt% for both inorganic materials chosen as ideal samples and pharmaceutical materials as practical ones. QPA of an amorphous component present in a small amount is also discussed.

X-Ray Diffraction Intensity of Oxife Soild Soultions: Application to Qualitative and Quantitative Phase Analysis

1982 ◽  
Vol 26 ◽  
pp. 119-128 ◽  
Author(s):  
Ronald C. Gehringer ◽  
Gregory J. McCarthy ◽  
R.G. Garvey ◽  
Deane K. Smith
Keyword(s):  
Phase Analysis ◽  
Solid Solutions ◽  
Inorganic Materials ◽  
Quantitative Phase Analysis ◽  
X Ray Diffraction ◽  
X Ray ◽  
Cell Parameters ◽  
Qualitative And Quantitative ◽  
Quantitative Analyses ◽  
End Members

Solid solutions are pervasive in minerals and in industrial inorganic materials. The analyst is often called upon to provide qualitative and quantitative X-ray phase analysis for specimens containing solid solutions when all that is available are Powder Diffraction File (PDF) data or commercial standards for the end members. In an earlier paper (1) we presented several examples of substantial errors in accuracy of quantitative analysis that can arise when the crystallinity and composition of the analyte standard do not match those of the analyte in the sample of interest. We recommended that to obtain more accurate quantitative analyses, one should determine the analyte composition (e.g., from XRF on grains seen in a SEM or from comparison of cell parameters with those of the end members) and synthesize an analyte standard with this composition and with a crystallinity approximating that of the analyte (e.g., as determined from peak breadth or α1/ α2 splitting).

Quantitative phase analysis of amorphous components in mixtures by using the direct-derivation method

2019 ◽  
Vol 52 (1) ◽  
pp. 13-22 ◽  
Author(s):  
Hideo Toraya ◽  
Kazuhiko Omote
Keyword(s):  
Phase Analysis ◽  
Periodic Structures ◽  
Amorphous Material ◽  
Peak Height ◽  
Quantitative Phase Analysis ◽  
Chemical Formula ◽  
Direct Derivation ◽  
Patterson Function ◽  
Formula One ◽  
Quantitative Phase

The direct-derivation (DD) method is a new technique for quantitative phase analysis (QPA) [Toraya (2016). J. Appl. Cryst. 49, 1508–1516]. A simple equation, called the intensity–composition (IC) formula, is used to derive weight fractions of individual components (w k ; k = 1–K) in a mixture. Two kinds of parameters are required as input data of the formula. One is the parameter S k , which is the sum of observed powder diffraction intensities for each component, measured in a wide 2θ range and corrected for the Lorentz–polarization factor. The other is the parameter a k −1, defined by a k −1 = M k −1∑nik 2, where M k is the chemical formula weight and n ik is the number of electrons belonging to the ith atom in the chemical formula unit. The parameter a k −1 was originally derived by using the relationship between the peak height and the integrated value of the peak at the origin of the Patterson function, implicitly assuming the presence of periodic structures like crystals. In this study, the formula has been derived theoretically from a general assemblage of atoms resembling amorphous material, and the same expression as the original formula has been obtained. The physical meaning of a k −1, which represents `the total scattering power per chemical formula weight', has been reconfirmed in the present formulation. The IC formula has been tested experimentally by using two-, three- and four-component mixtures containing SiO2 or GeO2 glass powder. In the whole-powder-pattern fitting (WPPF) procedure, incorporated into the DD method, a background-subtracted halo pattern is directly fitted as one of the components in the mixture, together with profile models for crystalline components. In the WPPF, an interaction was observed between the parameters of the background function (BGF) and the parameter for scaling the halo pattern, and this resulted in systematic deviations of w k from weighed values. The deviations were ≤0.7% in the case of binary mixtures when the BGF was fixed at the correct background height, supporting the hypothesis that the DD method is applicable to the QPA of amorphous components.

scholarly journals Review of the direct derivation method: quantitative phase analysis with observed intensities and chemical composition data

2021 ◽  
pp. 1-10
Author(s):  
Hideo Toraya
Keyword(s):  
Chemical Composition ◽  
Phase Analysis ◽  
Technical Problem ◽  
Theoretical Background ◽  
Unit Weight ◽  
Quantitative Phase Analysis ◽  
Scattered Intensity ◽  
Direct Derivation ◽  
Quantitative Phase ◽  
Composition Data

The direct derivation (DD) method is a technique for quantitative phase analysis (QPA). It can be characterized by the use of the total sums of scattered/diffracted intensities from individual components as the observed data. The crystal structure parameters are required when we calculate the intensities of reflections or diffraction patterns. Intensity can, however, be calculated only with the chemical composition data if it is not of individual reflections but of a total sum of diffracted/scattered intensities for that material. Furthermore, it can be given in a form of the scattered intensity per unit weight. Therefore, we can calculate the weight proportion of a component material by dividing the total sum of observed scattered/diffracted intensities by the scattered intensity per unit weight. The chemical composition data of samples under investigation are known in almost all cases at the stage of QPA. Thus, a technical problem is how to separate the observed diffraction pattern of a mixture into individual component patterns. Various pattern decomposition techniques currently available can be used for separating the pattern of a mixture. In this report, the theoretical background of the DD method and various techniques for pattern decompositions are reviewed along with the examples of applications.

Effective Pre-Stress Identification for a Simply-Supported PRC Bridge Based on the Dynamic Response Induced by the Passing Vehicle

2012 ◽  
Vol 430-432 ◽  
pp. 1320-1325
Author(s):  
Jian Qing Bu ◽  
Hai Yun Wang
Keyword(s):  
Dynamic Responses ◽  
Simulation Studies ◽  
Euler Beam ◽  
Direct Derivation ◽  
Moving Vehicle ◽  
Simply Supported ◽  
Beam Elements ◽  
Road Surface Roughness ◽  
Derivation Method ◽  
Beam Bridge

A new method is proposed to identify the bridge effective pre-stress from the dynamic responses induced by the vehicle moving on a simply-supported beam bridge with eccentric straight pre-stress, based on the sensitivity analysis. The bridge is modeled as Euler beam elements and the moving vehicle is modeled as a two-degree freedom system with five parameters. After calculating dynamic responses of the bridge by vehicle-bridge coupled vibration analysis, the dynamic responses sensitivity can be obtained by using the direct derivation method, and the regularization method is adopted to identify the effective pre-stress. The effects on the identified results from different responses, different measuring locations and different road surface roughness are considered in the numerical simulations. The simulation studies indicate that the proposed method can be used to identify the effective pre-stress accurately and effectively for a simply-supported PRC beam bridges.

Cam Profile Generation for Cam-Spring Mechanism With Desired Torque

2018 ◽  
Vol 10 (4) ◽  
Author(s):  
Fei Gao ◽  
Yannan Liu ◽  
Wei-Hsin Liao
Keyword(s):  
Friction Coefficient ◽  
Analytical Solution ◽  
Friction Force ◽  
Design Method ◽  
Nonlinear Behavior ◽  
Direct Derivation ◽  
Cam Profile ◽  
Derivation Method ◽  
Spring Mechanism ◽  
Pitch Curve

Commercial springs have linear characteristics. Nevertheless, in some cases, nonlinear behavior (e.g., nonlinear torque) is desired. To handle that, a cam-spring mechanism with a specified cam profile was proposed in our previous work. In this paper, to further study the cam profile generation, a new convenient design method is proposed. First, the model of cam-spring mechanism considering the friction force is analyzed. Based on this model, sorts of derivation processes are conducted for obtaining the expression of spring torque. When the friction coefficient is zero, the analytical solution of the equation (spring deformation) is derived. However, in practice, where the friction coefficient is not zero, an analytical solution is not available. Therefore, a numerical solution is sought. Then, with the obtained spring deformation, the cam profile and pitch curve are generated. Results of an experiment conducted to verify the new method show that the cam profile generated by the direct derivation method can precisely mimic the desired torque characteristics. In addition, the hysteresis induced by the friction force in the cam-spring mechanism is also studied. By increasing the spring stiffness, spring free length, and the cam eccentricity, the hysteresis in the cam-spring mechanism can be decreased.

Radiation Damage, Contrast and Statistics in High Resolution Biological Electron Microscopy

1970 ◽  
Vol 28 ◽  
pp. 260-261
Author(s):  
Robert M. Glaeser
Keyword(s):  
High Resolution ◽  
Particle Flux ◽  
Unit Area ◽  
Signal To Noise ◽  
Resolution Image ◽  
High Resolution Image ◽  
Pass Through ◽  
Counting Statistics ◽  
The Relationship ◽  
Picture Element

It is well known that a large flux of electrons must pass through a specimen in order to obtain a high resolution image while a smaller particle flux is satisfactory for a low resolution image. The minimum particle flux that is required depends upon the contrast in the image and the signal-to-noise (S/N) ratio at which the data are considered acceptable. For a given S/N associated with statistical fluxtuations, the relationship between contrast and “counting statistics” is s131_eqn1, where C = contrast; r2 is the area of a picture element corresponding to the resolution, r; N is the number of electrons incident per unit area of the specimen; f is the fraction of electrons that contribute to formation of the image, relative to the total number of electrons incident upon the object.

Measurement of the Displacement Across a Coincidence Grain Boundary

1977 ◽  
Vol 35 ◽  
pp. 124-125
Author(s):  
J. W. Matthews ◽  
W. M. Stobbs
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Stacking Fault ◽  
The Other ◽  
Measuring Technique ◽  
High Angle ◽  
Twin Boundaries ◽  
Rigid Displacement ◽  
Cubic Crystals ◽  
Lattice Displacement

Many high-angle grain boundaries in cubic crystals are thought to be either coincidence boundaries (1) or coincidence boundaries to which grain boundary dislocations have been added (1,2). Calculations of the arrangement of atoms inside coincidence boundaries suggest that the coincidence lattice will usually not be continuous across a coincidence boundary (3). There will usually be a rigid displacement of the lattice on one side of the boundary relative to that on the other. This displacement gives rise to a stacking fault in the coincidence lattice.Recently, Pond (4) and Smith (5) have measured the lattice displacement at coincidence boundaries in aluminum. We have developed (6) an alternative to the measuring technique used by them, and have used it to find two of the three components of the displacement at {112} lateral twin boundaries in gold. This paper describes our method and presents a brief account of the results we have obtained.

A High Angle, Double Tilting Cold Stage for the AEI EM7

1974 ◽  
Vol 32 ◽  
pp. 450-451
Author(s):  
P.R. Swann ◽  
A.E. Lloyd
Keyword(s):  
Habit Plane ◽  
Temperature Control ◽  
Tilt Angle ◽  
Cooling System ◽  
Thermal Drift ◽  
High Angle ◽  
Cold Stage ◽  
High Degree ◽  
Better Than

Figure 1 shows the design of a specimen stage used for the in situ observation of phase transformations in the temperature range between ambient and −160°C. The design has the following features a high degree of specimen stability during tilting linear tilt actuation about two orthogonal axes for accurate control of tilt angle read-out high angle tilt range for stereo work and habit plane determination simple, robust construction temperature control of better than ±0.5°C minimum thermal drift and transmission of vibration from the cooling system.

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