Reference intensity ratio methods

The reference intensity ratio method is based on the experimentally established intensity ratio between the strongest Bragg peaks in the examined phase and in a standard reference material. The most typical reference material is corundum, and the corresponding peak is (113). The reference intensity ratio k) is quoted for a 50 50 (wt. %) mixture of the material with corundum, and it is known as the corundum number . The latter is commonly accepted and listed for many compounds in the ICDD s Powder Diffraction File. Even though this method is simple and relatively quick, careful account and/or experimental minimization of preferred orientation effects are necessary to obtain reliable quantitative results. 

Quantification of the relative abundance of crystalline phases in a multiphase mixture is an everyday problem in a wide range of applications. Common examples are evaluation of the yield in inorganic synthesis and catalytic processes, characterization of raw mineral materials for industrial processes, quality check of fired ceramic products, and many more. While in most cases the required accuracy level of the analysis is a few percent at best, in particular cases such as in the quantification of phase contaminants in technologically important materials, or of hazardous and toxic phases in environmentally dispersed aerosols, the required level of accuracy must be substantially lower than 1 wt% relative abundance. Accuracy levels of 2-3 wt% are commonly reached if standard procedures of quantitative phase analysis by diffraction data are properly performed. Generally employed analytical methods include the internal or external standard method, the matrix flushing method, and the reference intensity ratio method. Very recently, the availability of analysis techniques of powder diffraction data based on full-profile (Rietveld method), originally developed... 

Many of these difficulties can be monitored and overcome with the use of standards, either internal or external (Zevin and Kimmel 1995). For the internal standard method, a known quantity of standard material is added to an unknown mixture, and the ratio of the intensity of the standard component is compared to a previously determined calibration curve to determine the mass fraction of the unknown (e.g. one or more of the polymorphic components). In the external standard method, the entire composition of the unknown sample is determined simultaneously by comparing the measured intensities and respective calibration constants of reference intensity ratios (determined beforehand), which must all be with reference to the same reference standard. 

The evaluation of mixing properties of melts and solid solutions from measured ion intensities and temperatures are described in the reviews by Chatillon et al. [12], Sidorov and Korobov [115], as well as Raychaudhuri and Stafford [13] and the references quoted in these articles. The chemical activities, or activity coefficients, can be obtained from the partial pressures of the mixture components. The pressure calibration constant (see Sect. 2.4) has to be determined in this case. The pressure calibration can be avoided by the use of the ion intensity ratio method described by Lyubimov et al. [116]j Belton and Fruehan [117], as well as Neckel and Wagner [118, 119]. The Gibbs-Duhem relation is used to obtain the activity coefficient f of the component A in the mixture... 

HIL 00] HILLIER S., Accurate quantitative analysis of clay and other minerals in sandstones by XRD comparison of a Rietveld and a reference intensity ratio (RIR) method and the importance of sample preparation . Clay minerals, vol. 35, p. 291-302, 2000. 

This approach is commonly employed for bound zeolites. In this manner the relative amount of crystalline zeolite present can be determined. As usually implemented, the method provides a number that is the ratio of intensities for peaks in the diffraction pattern of the sample of interest to the intensity of the same peaks in the pattern of a reference zeolite. Since the intensity ratio is often expressed as a percentage, it is commonly referred to as percent zeolite crystallinity. The better terminology is relative amount of crystalline zeolite compared to a specific reference. 

There are several other chemometric approaches to calibration transfer that will only be mentioned in passing here. An approach based on finite impulse response (FIR) filters, which does not require the analysis of standardization samples on any of the analyzers, has been shown to provide good results in several different applications.81 Furthermore, the effectiveness of three-way chemometric modeling methods for calibration transfer has been recently discussed.82 Three-way methods refer to those methods that apply to A -data that must be expressed as a third-order data array, rather than a matrix. Such data include excitation/emission fluorescence data (where the three orders are excitation wavelength, emission wavelength, and fluorescence intensity) and GC/MS data (where the three orders are retention time, mass/charge ratio, and mass spectrum intensity). It is important to note, however, that a series of spectral data that are continuously obtained on a process can be constructed as a third-order array, where the three orders are wavelength, intensity, and time. 

Thermal reaction mixtures in this work were analyzed by FTIR spectroscopy, tunable diode laser spectroscopy and vibrational circular dichroismA pair of representative VCD spectra are shown in Figure 1. The more intense spectrum is an optically pure reference sample of the (25, 35) isomer at 53.59 torr the other is a thermal reaction product mixture from this isomer after 360 min at 407 °C and gas chromatographic isolation, recorded at 81.30 torr . From the measured Ay4/A 4ref absorption intensity ratio and the pressures, one may calculate that the sample retains 51.65% of its original optical activity, which compares well with the value calculated from the value obtained from the least-squares fit of all five VCD experimental points (51.2%). These spectra, obtained in the gas phase with a few mg of chromatographically purified labeled cyclopropanes, demonstrate the promise of VCD for assessing enantiomeric excess in situations where classical polari-metric methods would be of limited utility. 

One of the shortcomings of LIBS, particularly in relation to quantitative elemental analysis, arises from the instability of the laser-induced plasma emission resulting from laser intensity fluctuations (1-5%) the amount of scattered light present depends on local matrix effects and on physical and chemical properties of the target material. The most common way of compensating for signal fluctuations in LIBS is by calculating the ratio of the spectral peak intensity to that of a reference intensity. However, this internal calibration method provides relative rather than absolute concentrations. 

Method of standard additions or spiking method consists of adding known amounts of pure component a to a mixture containing X and Xb of a and b phases. It requires the preparation of several samples and measurement of several diffraction patterns containing different yet known additions (7o) of phase a. Other phases in the mixture are not analyzed but at least one of them b) should have a reference Bragg peak hkl) which does not overlap any reflection from phase a. The intensity ratio for this method is given as ... 

As molecules become larger and more complex, the number of possible combinations that yield M + 1 and M+2 peaks grows. For a particular combination of atoms, the intensities of these peaks relative to the intensity of the molecular ion peak are unique. Thus, the isotope ratio method can be used to establish the molecular formula of a compound. Tables of possible combinations of carbon, hydrogen, oxygen, and nitrogen and intensity ratios for the M + 1 and M+2 peaks for each combination have been developed. Appendices 10 an 11 and the book by Beynon (in the reference hst at the end of this chapter) contain extensive tables of this sort. For a given molecular weight, you can examine the tables to find the molecular formula that corresponds to the isotope ratios observed. 

It is accepted that the features in the Raman spectra of amorphous solids resemble the vibrational densities of states (VDOS) of their crystalline counterparts [111]. The Raman spectrum of amorphous silicon is characterized by four broad bands around 160,300,390, and 470 cm [112,113]. They correspond to the features in the vibrational density of states of a-Si and are referred to as TA-, LA-, LO-, and TO-like bands, respectively [114]. In general, the TA/TO intensity ratio, their linewidths, and frequency positions depend on the method of preparation, deposition conditions, and the degree of structural disorder [115] (Fig. 16). 

A. Relative Peak Intensity Method Mix a given enantiopure chiral host with enantiopure guest and an achiral reference host record ESI mass spectrum of this sample and evaluate peak intensity ratio of both host-guest complexes repeat same experiment, but with a sample containing the same two hosts and the other guest enantiomer again, evaluate peak intensity ratio compare both ratios. 

Chemical identification of unknowns by XRD relies in the accurate determination of a set of ii-spacings for the various crystallographic orientations. The data are screened against database of reference materials which are typically powder data with no preferred orientation. Accuracy of XRD identification of unknown species depends on the careful preparation of the samples, if powder form is required. On the other hand, if samples are not in powder form, care must be taken to account for missing lines in the XRD pattern and for abnormal intensity ratio in the observed peaks due to preferred orientation (texture). Detection limits in this case are within 0.1-1 wt%, which is worse than the ppm or ppb levels provided by surface analysis methods such as XPS or SIMS (discussed in this book). Chemical determination by XRD is limited to crystalline phases rally, but compounds can be identified down to their polymorphic phases. 

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