Powder mixtures quantitative analyses

A digitized representation of powder data is quite compact and is especially convenient for comparison with other patterns, provided a suitable database is available. In addition to a digitized pattern, each entry in such a database may (and usually does) contain symmetry, imit cell dimensions, and other useful information phase name, chemical composition, references, basic physical and chemical properties, etc. Powder diffraction databases find substantial use in both simple identification of compounds (qualitative analysis) and in quantitative determination of the amounts of crystalline phases present in a mixture (quantitative analysis). 

The theoretical basis of the quantitative analysis of powder mixtures was developed by Alexander and Klug [1,45]. When an x-ray beam passes through any homogenous substance, the fractional decrease in the intensity, I, is proportional to the distance traveled, b. This relationship is given by... 

Although simple intensity correction techniques can be used to develop very adequate XRPD methods of quantitative analysis, the introduction of more sophisticated data acquisition and handling techniques can greatly improve the quality of the developed method. For instance, improvement of the powder pattern quality through the use of the Rietveld method has been used to evaluate mixtures of two anhydrous polymorphs of carbamazepine and the dihydrate solvatomorph [43]. The method of whole pattern analysis developed by Rietveld [44] has found widespread use in crystal structure refinement and in the quantitative analysis of complex mixtures. Using this approach, the detection of analyte species was possible even when their concentration was less than 1% in the sample matrix. It was reported that good quantitation of analytes could be obtained in complex mixtures even without the requirement of calibration curves. 

A.D. Patel, P.E. Luner and M.S. Kemper, Quantitative analysis of polymorphs in binary and multi-component powder mixtures by near-infrared reflectance spectroscopy, Int. J. Pharm. 206, 63-74. Erratum in Int. J. Pharm., 212, 295 (2000). 

Besides structure, X-ray diffraction gives a host of other valuable information. For example, powder diffraction, especially with counter diffractometers, has been widely used for phase identification, quantitative analysis of a mixture of phases, particle size analysis, characterization of physical imperfections (the last two being obtainable from line broadening) and in situ studies of reactions. In the case of amorphous solids, X-ray... 

Alexander LE, Klug HP. 1948. Basic aspects of X-ray absorption in quantitative diffraction analysis of powder mixtures. Anal. Chem. 20 886-894. 

Quantitative Analysis of Mixtures of Sugars by the Method of Partition Chromatography. Part IV. The Separation of the Sugars and Their Methylated Derivatives on Columns of Powdered Cellulose, L. Hough, J. K. N. Jones, and W. H. Wadman,/. Chem. Soc., (1949) 2511-2516. 

Many practical electrodes are prepared from powdered active mass and some conductive additive, such as carbonaceous materials, that are bonded to a metallic current collector with a polymeric binder such as PVDF (described in the previous section). Such electrodes can be measured directly. Is it very useful to measure such electrodes in their pristine from, before any electrochemical treatment, and then as a function of their electrochemical history. For quantitative analysis (phase composition, evaluation of concentration of constituents in mixtures, etc.) it is important to use internal standards in the sample. Fortunately, several components of composite electrodes, which are, in any event, contained in the sample measured, can be used as internal standards. These include the current collector (Cu, Al), the conductive additive, such as graphite, or the binder, such as Teflon. 

The central problem in carrying out quantitative analysis of a mixture of phases by X-ray powder diffractometry is that the intensity of the peaks is not linear with concentration. For quantitative analysis of binary solid solutions, see the section on solid solutions. Here we concern ourselves with mixtures of two or more phases. In such cases the intensity depends upon the absorption of the sample. We assume that the two phases have already been identified from prior knowledge or from the powder pattern. The expression for the intensity of a reflection from a set of parallel planes hkl, hu is a very complex equation. For our purpose we will use a simplified form. i... 

Because of the general similarities in the diffraction patterns, and the lack of clearly resolvable distinguishing peaks, they employed the Rietveld method (Young 1993). In the Rietveld method, the entire experimental diffraction pattern for each solid phase is used as a basis for comparison. For structure determination using powder diffraction, this comparison is made with a structural model used to generate a calculated pattern. In quantitative analysis of polymorphic phases, the known crystal stmctures are used to generate the standard diffraction patterns and these are then refined against the experimental powder pattern of the mixture to obtain the relative amounts of the polymorphs. 

In a mixture of crystalline materials, each species will be characterized by its distinctive series of scattering peaks, and the observed powder pattern will consist of a sum of the individual components. The intensities of the peaks associated with each component are proportional to its weight fraction in the mixture, so the performance of a quantitative analysis is based on the accurate and reproducible measurement of peak intensities. The analysis can be performed either with or without an international standard, and the theory associated with each approach has been set forth by Suryanarayanan12 and others.18-21... 

A Michelson interferometer with the facility for step and integrate, and rapid scan operation has been used for Fourier transform PAS. The merits of the two methods were considered. The versatility of this technique for the measurement of the infrared spectra of powdered samples has been demonstrated. Some possible reasons for the distortion of such measurements have been discussed. " FT-PAS has enabled discrimination between K N03 and K NOj and has shown the technique to be suitable for quantitative analysis of solid mixtures. ... 

When a nonequivalence in absorption bands is identified for a polymorphic or solvate system, the band intensities can be used for a quantitative analysis of mixtures containing the various phases. Such work requires the nontrivial preparation of homogeneous calibration samples containing known amounts of the phases in question, but most workers underestimate the difficulty associated with mixing powders of potentially different morphologies. For example, the monohydrate phase of cefepime dihydrochloride consists of rods, while the dihydrate phase consists of needles, and the mixing of these could only be prop-... 

Bish, D. L. S. J. Chipera, 1988. Problems and solutions in quantitative analysis of complex mixtures by x-ray powder diffraction. Adv. X-ray Anal. 31 295-308. 

For phase determination and phase proportions in a powder mixture XRD is useful, allowing quantitative phase analysis down to -1% in a powder sample. 

For a physical mixture, the powder diffraction pattern is the sum of the patterns of the individual materials. The diffraction pattern can therefore be used to identify the crystalline phases in a mixture. The concentrations of the crystalline phases can be determined by methods based on comparing the intensities of the diffraction peaks with standards (6-8). If the crystal structures of the phases are known, the concentration of each phase can be detamined by Rietveld analysis (20,21). In the Rietveld method, a theoretical diffraction pattern is computed and the difference between the theoretical and observed patterns is minimized. For quantitative analysis, some care should be taken with specimen preparation if accurate and reliable results are to be obtained. The effects of factors such as preferred orientation, texturing, and particle size broadening must be minimized. 

Jansen [190] has compared FT-NIR diffuse reflection and diffuse transmission measurements for quantitative analysis of powder mixtures. Diffuse transmission as a mode for powder measurements has been quite rarely considered in the past but appears to have some advantages, especially when it comes to low concentrations. 

The areas of application of quantiative X-ray powder diffraction are many and varied. Many hundreds of analysts are using this technique on a daily basis. Some of the more common applications would include ore and mineral analysis, quality control of rutile/anatase mixtures, retained austenite in steels, determination of phases in airborne particulates, various thin-film applications, study of catalysts, and analysis of cements. The current state of the art in the quantitative analysis of multiphase materials is that accuracies of the order of a percent or so can be obtained in those cases where the particle orientation effect either is nonexistent or has been adequately compensated for. 

Beef kidney samples were analyzed for atrazine by dispersing 0.5-g portions of kidney with 2-g portions of XAD-7 HP resin for matrix solid-phase dispersion. " By using a mortar and pestle, a powder-like mixture was prepared that was subjected to subcritical extraction using ethanol-modified water at 100 °C and 50 atm. The ethanol-water extract was sampled using a CW-DVB SPME fiber for direct analysis using ion-trap GC/MS, and the recoveries were quantitative for atrazine at the 0.2 mg kg fortification level. 

---