CHECKING AND ESTIMATING RIR VALUES

Transcription

1 Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol CHECKING AND ESTIMATING RIR VALUES Q. Johnson and R.S. Zhou Materials Data, Inc Concannon Blvd. Livermore, CA ABSTRACT With the publication of nearly 38,000 calculated x-ray diffraction patterns in its new CD-ROM, the ICDD has provided users with a wealth of RIR values (i.e., reference intensity ratio values, also signified by Ill,, where c refers to corundum, the standard used currently). Compared to previous CDs, this new one will provide nearly ten times as many RIR values. In the past, quantitative calculations using RIRs were often frustrated by one or more missing values among the several phases in a mixture subjected to x-ray diffraction analysis. That is no longer much of an issue. But some new problems emerge. Do I believe these new RIR numbereall of them? Can I use calculated values to represent my real materials, especially when I know I may be dealing with possible solid solutions? What value among the several in the new database should I use? What should I do when I m still missing an RIR for a phase? How good are quantitative calculations using these RIRs anyway? Should the RIR definition, based primarily on experimental considerations, be fine-tuned now that calculated RIR values dominate? Here we present simple expressions to enable checking or estimating RIR values without need for structures. INTRODUCTION Suppose an XRD analyst, after conclusion of a qualitative phase identification analysis involving two unknowns, is asked to provide quantitative results as well. While there are many methods to choose from, one of the quickest ways to do this would be to measure the integrated intensity of the strongest peak in each phase and then, using the reference intensity ratio (RIR), basically a scaling factor, convert these intensity values to weight percent2-4. With the publication this year of nearly 38,000 calculated XRD powder patterns based on the ICSD structure database5, the ICDD will be placing a powerful new tool into the hands of the XRD analyst. Previous pattern files for Inorganic Level-II (sets l-47) contained less than 10% RIR scaling values. Furthermore, many of these RIR values were measured and there exists no method whereby editors could easily check the correctness of these values. If an analyst wished to perform an RIR-based quantitative analysis using RIR data from sets l-47, there exists only a

2 This document was presented at the Denver X-ray Conference (DXC) on Applications of X-ray Analysis. Sponsored by the International Centre for Diffraction Data (ICDD). This document is provided by ICDD in cooperation with the authors and presenters of the DXC for the express purpose of educating the scientific community. All copyrights for the document are retained by ICDD. Usage is restricted for the purposes of education and scientific research. DXC Website ICDD Website -

3 Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol % chance both RIR values would be available for a two-phase mixture. By contrast, for phases of the new calculated patterns, the likelihood of finding all RIR values for a five-phase mixture is better than 99%. Table 1 presents a comparison of some typical RIR values from the original (sets l-47) and new (sets 70-85) pattern databases for three minerals. Table 1. Comparison of RIR values from older versus new ICDD databases. Older patterns RIR New patterns RIR Rutile Hematite Anatase These are not especially complicated or troublesome materials. Yet, except for t-utile, there is great disagreement in RIR values that would lead to considerably different quantitative results. So what advice can be given, what tools are available to assist the analyst? First, like the stock market, things are neither as good or as bad as they seem. For example, Figure 1 shows an experimental pattern that is a mixture of the three phases of Table 1. moo IOOD~ 3503~ H,. 6 % P 2500~ B C mm.,503.,m- Figure 1. Experimental pattern containing a mixture of r-utile, hematite, and anatase.

4 Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol There is a resolved peak for each phase in the first three peaks. We can use these three lines in a quantitative analysis if we believe the intensity relationship these have to the strongest line in each phase and have confidence in the RIR values. Table 2 presents this one-line quantitative analysis using ICDD original RIR values together with intensity characterization by profile fitting, a more complete multi-line profile-based RIR quantitative analysis using Jade 5 (Ref. 6) with the original pattern database (l-47), one using Jade 5 with the new pattern database (70-85), and a Rietveld quantitative analysis using the Riqas program7. The latter values should be considered the best or most likely values. Table 2. Quantitative analysis results for the three-phase mixture pattern of Figure 1. One-line Jade 5 (l-47) Jade 5 (70-85) Riqas Rutile Hematite Anatase 50% 46% 54% 55.7% This single example does not, of course, prove much but it is encouraging and provides hope that the new patterns and their RIR values might be very useful, especially if combined with profile fitting. POSSIBILITY OF ERRORS One trouble that confronts us immediately, however, is the possibility that there may be errors in the new calculated patterns and their RIR values. It isn t reasonable to expect such a great undertaking could be accomplished without errors. Unfortunately, there is no way that the ICDD editors can exhaustively check all these patterns immediately even with the excellent help of the AIDS program. If some systematic error can be uncovered for certain phases, these patterns can easily be corrected with future updates. Simple tests have already led to a short exclusion list of patterns that should be avoided for now. These tests include such things as looking for excessively high or low calculated densities or RIR values, missing cell constants, or inconsistent combinations of formula, space group, Z, density, and molecular weight. Another area for potential trouble is that this new data set contains many materials that appear multiple times as a consequence of measurements made at non-ambient conditions of temperature or pressure as well as slight formula variations. For example, there are now 40 entries for corundum, all with space group R-3c, cell constants approximately a = 4.8 and c = 13, and density = 4. Of these 40 entries, no RIR value is provided for one pattern, another pattern lists RIR = 0.12,29 pattern RIRs vary between 0.89 and 1.04, and 9 pattern RIRs range from 1.96 to If you can t trust corundum, which is the standard for RIR and is defined as 1.O, what pattern can you trust?

5 Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol Because the RIR values were calculated, the best answer to that question is to obtain the structure and calculate it again if you have any question. This approach is shown in Table 3 where two very different results were obtained for old and new AlF, patterns.

6 Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol Table 3. RIR values for AlF,. Pattern Comments (old) 7.08 Measured? 76-l 623 (new) 3.20 Calculated (new) 3.22 Calculated (new) 2.9 This work, calculated using Micro-Powd The final entry in Table 3 confirms the two calculated values by agreeing within 10% of their values. This small difference is no cause for concern because slightly different theoretical models were used. As good as this approach is, it isn t simple and it s not practical for every lab. Before moving on to some simpler methods, it should be stressed that the new database is an excellent first step by the ICDD. We shouldn t expect all entries to be absolutely correct at this early date (unfortunately that s what we want for quantitative analysis). A large percentage of these patterns will be correct, and new ideas and new tools in the future will bring greater confidence in all the data. For the present, the user should be cautious and verify RIR values before using them in quantitative analysis if there is any question. VERIFYING RIR VALUES So how do I verify an RIR value? To check an RIR value, you should either recalculate it from the structure or measure it. Either option may prove difficult. Some help may be found in an amazingly simple relationship that exists between RIR and density (p). Nearly 95% of the new patterns have an RIR/p ratio within the range of 0.2 to 3.0. You should be suspicious of values outside this range. This RIR-p relationship can be rationalized by substituting the approximate expression for F,!&l given in equation (1) below into the expression for RIR given later in equation (2). Fhkl = Fooo(B) z k z, Mol. Wt. * 2, (1) where Fooo(0) is Fooo adjusted for the fall-off of the scattering factor at 8, k is a constant, Mol. Wt. is the molecular weight, and 2 is the number of molecules or formula weights in the unit cell. There is a symmetry dependence that should be considered to make this RIR/p rule-of-thumb more valuable. First, consider the concept of average RIR for a symmetry type. To determine this, we take a symmetry system, for example, orthorhombic, remove a small number of excessively low and high RIR values (below 0.1 and greater than 25) and then compute the average RIR. These numbers are shown in Table 4.

7 Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol Table 4. Average RIR values for different symmetries. Symmetry Avg. RIR Symmetry factor Cubic Tetragonal Hexagonal Rhombohedral 5.O 0.42 Orthorhombic Monoclinic Triclinic The symmetry factor is a heuristically derived number approximately one-tenth of the average RIR value. It can be used to set the low end of a four-fold range of RIIUp values that will accommodate more than 70% of the observed values. For example, over 70% of the RIR/p values lie between 0.3 and 1.2 for orthorhombic symmetries and more than 80% lie between 0.5 and 2.0 for tetragonal symmetries. Another relationship may prove helpful. We will first need to consider the Maximum Derived Intensity for a phase. We define this as the intensity of the reflection having the highest value after corrections for geometrical, multiplicity, density, and unit cell volume considerations. Consider the following equation, which expresses the RIR, Ill,, without the assumption or need of corundum as a reference standard: where I/I, = U * Fh,$ * Lp(8) * mhkl / (p e p) (2) K = a constant depending on the standard used, F = structure factor, hkl = reflection indices, Lp = Lorentz-polarization factor, m = reflection multiplicity, V = cell volume, p = density. The problem with this relationship is that, without the structure, we have no way to determine the structure factor, Fhkl. On the other hand, if we assume the Maximum Derived Intensity can be represented by F,,,(8), we can easily calculate a maximum value for RIR, I/I,. We know this value will be the maximum possible RIR value because no structure factor can be larger than Fooo(0). For relatively uncomplicated materials, this maximum value will be a good approximation. For example, some estimates for MgO (periclase) are provided in Table 5.

8 Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol Table 5. Comparison of ICDD RIR values for periclase and estimates based on our Maximum Derived Intensity approximation. ICDD pattern ICDD RIR Our estimate (new) (new) (new) (old) 1.oo 3.28 Notice two things about these values. First, RIR for is strongly suspect. Second, the estimated RIR for is smaller than the calculated value, which we just pointed out above cannot happen. The reason for this discrepancy is that the calculation for the estimated value did not include anomalous scattering whereas the ICDD calculation included it, resulting in this slight difference. This simple calculation, made without reference to the structure but using only cell volume, density, Lp and reflection multiplicity, provides good guidance for RIR values. Nearly 80% of the new patterns have a ratio of RIR (estimated)/rir (ICDD) within the range of 1 to 4. If the estimated value is used in place of the true RIR, the result for that particular phase would be to place a lower bound on the amount present in a quantitative analysis. OBSERVATIONS AND RECOMMENDATIONS Listed below are some observations and recommendations that can be made based on this study: Previously, only about 4000 RIR values were known, many of them measured. The available RIR values have now been expanded in one year to over ten times as many as before, most of which have been calculated. The present method for defining RIR was based more on experimental considerations than calculational ones. With ubiquitous PCs and far more calculated than measured RIR values, a redefinition more in tune with calculational concerns should be considered. Present conventions don t specify the hkl values for a material s reference reflection. Present conventions don t specify whether the RIR value was calculated or measured. Compare this practice with what is done for density values. Certain classes of materials have very large RIR values that severely limit their use in such analyses (see below). Perhaps it is time to provide a simple Greek symbol for this important number, for example, the Greek letter iota (t), as one possibility, is far easier to verbalize than RIR. Item 6 above should be dealt with in more detail. Consider the standard Lp factor as shown in Fig. 2.

9 Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol Lorentz Polarization ~. 40 ~~ UT * 7 z t? 2 I Theta Figure 2. Lorentz-polarization must be made at small angles. correction as a function of Theta shows that very large corrections This theta-dependent value is extreme at low theta values, resulting in very intense reflections for some materials. For example, Figure 3 shows one pattern with and without Lp factors. Simulated I corrected for Lp Z-Theta(deg) Figure 3. Simulated pattern for with and without Lp factors.

10 Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol Using the present definition for RIR, we would select the reflection at 10 for our RIR measurement. Unfortunately, this reflection has a very small structure component for its intensity, deriving its dominance over a much better reflection at 44,. to the Lp factor. The problem this presents is that if the structure exhibits slight compositional variations such that the lattice constant changes slightly, the calculated RIR value can change significantly and affect your quantitative analysis adversely. The problem won t arise if the 44 reflection is used. Summarizing, the new database of the ICDD will be of enormous significance for XRD pattern analysis, but it is important to proceed carefully in using RIR-based quantitative analysis because some of the new RIR values may prove to be in error. Certain earlier practices and definitions with respect to RIR should be reviewed and perhaps changed by the community. Finally, we have presented two approximate methods useful for checking and estimating RIR values that don t require full knowledge of the structures. and 1.O < RIR (estimated)/rir (ICDD) < 4.0 (4) 0.2 -=c RIRlp -==c 3.0. (5) Expression (5) can be fine-tuned using symmetry considerations as discussed in this work. These approximations may save an analysis missing an RIR value so long as the limitations are understood. They also provide a tool for evaluating correctness of existing values or for estimating values where few exist (for example prior sets 1-47). REFERENCES 1. J. W. Visser and P. M. DeWolff, Absolute Intensities, Report , Technisch Physische Dienst, Delft, Netherlands (1964). 2. C. R. Hubbard, E. H. Evans, and D. K. Smith, The Reference Intensity Ratio, I/I,-, for Computer Simulated Powder Patterns, J. Appl. Cryst. 9, 169 (1976). 3. C. R. Hubbard and R.L. Snyder, RIR-Measurement and Use in Quantitative XRD, Powder Diffraction 3(2), 74 (1988). 4. Robert L. Snyder, The Use of Reference Intensity Ratios in X-Ray Quantitative Analysis, Powder Diffraction 7(4), 186 (1992). 5. Powder Diffraction File, PDF-2 Database Release 1998, announcement of new database release, International Centre for Diffraction Data (ICDD). 6. Jade program for analyzing x-ray diffraction pattern data, Materials Data Inc., 1224 Concannon Blvd., Livermore, CA Riqas program for analyzing x-ray diffraction pattern data, Materials Data Inc., 1224 Concannon Blvd., Liver-more, CA A manual describing the data format used in NBS AIDS83, Standard Reference Data, U.S. Dept. of Commerce, National Institute of Standards and Technology (1990).

11 Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol MD1 MicroPowd code, Materials Data Inc., 1224 Concannon Blvd., Livermore, CA