Identification of an unknown sample starts with making its diffraction pattern.

Transcription

1 Qualitative and Quantitative Analysis by X-Ray Diffraction A given substance always produces a characteristic diffraction pattern Whether that substance is present in the pure state or as one constituent of a mixture of substances. This fact is the basis for the diffraction method of chemical analysis. Qualitative analyses -- the goal is to determine what phases are present Quantitative analyses -- the goal is to determine how much of each phase is present Note that diffraction methods determine phases, not elements Diffraction methods have the advantage that the sample does not have to be dissociated, dissolved, or otherwise changed The advantage of diffraction analysis is that it identifies the presence of a substance as that substance exists in the sample. It does not identify the substance (sample) in terms of its constituent chemical elements. For example, if a sample contains the compounds A x B y, the diffraction methods will identify the presence of A x B y as such and not A and B. 1

2 The diffraction pattern is characteristic of the substance (being analysed) and forms a sort of fingerprint by which the substance can be identified. Experience has shown that the ensemble of d-spacings ( d s) and intensities ( I s) is sufficiently distinctive in order to identify phases Phase determination can be performed by a comparison of a set of experimental d s and I s (unknown pattern) with a database of d-i files of known patterns d-spacings are independent of wavelength Intensities are relative (most intense = 100) What is needed is a system of classifying the known patterns so that the one that matches the unknown can be located. Such system was devised by Hanawalt in Any one diffraction pattern is characterised by a set of line positions 2θ and a set of relative intensities. Exact matching of the interplanar spacings (d values) and intensities of all peaks (or lines in the case of powder camera) between the standard and observed diffraction patterns confirms the identity of the unknown as the same as the standard material 2

3 Hanawalt decided to use the d-values of the three strongest lines in the diffraction pattern (d 1, d 2, d 3 ) along with their respective intensities (I 1,I 2, I 3 ) to search the powder diffraction file (PDF) database. The PDF files list the following: Interplanar spacings (d values) and not the 2θ (because 2θ depend on the wavelength of the x-ray used). d is independent of the wavelength. Miller indices (hkl) of the planes having these spacings Relative intensities (I/I 1 ) of all the reflections observed Additional crystallographic data. An example of such file is shown in the Figure below 3

4 Identification of an unknown sample starts with making its diffraction pattern. The pattern may be recorded with a Debye-Scherrer camera or a diffractometer. Most of the patterns use CuK α radiation. After the pattern of the unknown is prepared, the plane spacings d corresponding to each line on the pattern is calculated, or obtained from tables which give d as a function of 2θ for various wavelengths. Identifying the unknown material involves the following steps: 1. Identify the 3 most intense reflections in the recorded pattern. Designate these spacings corresponding to the most intense peak by d 1, that for the next most intense by d 2, and the next one by d Locate the proper d 1 group in the Hanawalt search manual. 3. Once you have found a reasonable match for d 1, look for the closest match to d 2 4. Repeat the procedure for d 3 5. After the closest match has been found for d 1 d 2,and d 3, compare their relative intensities with the tabulated values 6. When the d values and the intensities for the 3 most intense reflections from the observed pattern match well with any of those listed in the manual, locate the proper card and compare the d and intensity values I/I 1 for all the reflections 7. When full agreement is obtained, identification is complete. 4

5 In practice, the unknown material may contain one or more phases. The procedure for identification, however, is the same in both cases except that if the material contains only phase the identification is easy. EXMAPLE 1: Single phase material The experimental 2θ, d and I/I 1 (I is the intensity of any peak and I/I 1 is the ratio of any given peak divided by the most intense peak, which is taken as 100%) values from the x-ray diffraction pattern (Figure A) of the unknown specimen recorded with CuK α radiation are listed in Table 8.1 Figure A: X-ray diffraction pattern of the unknown single-phase material 5

6 From the data in Table 8.1, the 3 most intense peaks in the pattern have d spacings 2.16, 2.50, and 1.53 A o with intensities 100, 85 and 55, respectively. In the Hanawalt Search Manual, you will find that the d spacings corresponding to the most intense peak is to 2.16 (± A o ) The d spacings corresponding to the second most intense peak has many entries. Table 8.2 reproduces some of the entries, with the most intense peak having a d spacing of 2.16 A o and the second most intense peak 2.50 A o Table 8.1: Experimental data for identifying an unknown specimen Peak number 2θ ( o ) d (A o ) I/I

7 In the Hanawalt Search Manual the d values of the 3 most intense peaks are shown in bold font (Table 8.2) In this table, notice that only 3 phases (NaFe 2 O 3, TaN and TiC) have d spacing of 1.53 A o for the third strongest reflection. Therefore, we now have to decide which of these materials is our unknown specimen. To do this, compare the list of d spacing obtained from the x-ray diffraction pattern of the unknown specimen and intensities of the other reflections with those of the possible materials in Table 8.2 7

8 The unknown pattern has a d spacing of 1.30 A o for the fourth most intense reflection, so the specimen cannot be NaFe 2 O 3, which has a d spacing of 1.56 for the fourth most intense reflection. Now the fifth most intense reflection has a d spacing of 0.97 A o for the unknown specimen. Comparing TaN and TiC, we can see that only TiC has a d spacing of 0.97 A o and an intensity of 30%. NOTE: the small sub-number shown on each d value in Table 8.2 indicates the relative intensity. For example: 1 means that the 2 = 20%, 9 = 90% relative This matches very well with the values for the unknown specimen. intensity = 10%, A comparison of the d values and intensities in the unknown pattern and those of TiC (PDf file) confirms that the unknown specimen is TiC EXAMPLE 2: Two-phase material Identification of phases in a two-phase mixture is a little more complex, but follows exactly the same procedure. An x-ray diffraction pattern is recorded from the material, and the d and I/I 1 values are listed for all reflections in the pattern The d 1, d 2 and d 3 values of the 3 most intense reflections are noted and compared with the Hanwalt Search Manual and one of the phases is identified. A similar procedure is followed for identifying the second phase. 8

9 Figure B: X-ray diffraction pattern of the unknown two-phase material Table 8.3 lists the d, and I/I 1 and also the 2θ values (although the 2θ values are not required) for all observed reflections from the diffraction pattern of the two-phase materials recorded with CuK α radiation shown in Figure B From Table 8.3 the 3 strongest peaks have d spacings 2.09, 2.41 and 2.03 A o. In the Hanwalt Search Manual,, we find that 2.09 A o lies bewtween 2.15 and 2.09 A o. 10 Possible materials are found with d 1 and d 2 spacings given as 2.09 and 2.41 A o as shown in Table 8.4 9

10 10

11 However, none of these have a d spacing of 2.03 A o for d 3, which is observed in the unknown specimen. Since this diffraction pattern was obtained from a two-phase material, it is possible that d 3 is in fact the most intense (d 1 ) peak for the second phase and does not belong to the first phase. Assuming that this is the case, we need to decide which of these 10 materials forms the first phase. From Table 8.4 we notice that 6 materials have d spacings of 2.09 A o and 2.41 A o for d 1 and d 2. These are: Rh 2 Si, TmAg 3, NiO, NiO (Bunsenite), Co 17 Gd 2 and V 8 C 7. Both Rh 2 Si and Co 17 Gd 2 have d 3 values of 2.23A o and 2.92A o respectively. Their respective relative intensities I/I 1 = 100 and 30. In our diffraction pattern, we have neither a d spacing of 2.23 A o nor of 2.92A o Therefore, the first phase is not Rh 2 Si or Co 17 Gd 2 Consider the other 4 possibilities: TmAg 3, NiO, NiO (Bunsenite) and V 8 C 7. We note that they all have d 3 value of 1.48 A o. However, the corresponding relative intensity is = 100 for TmAg 3, whereas for NiO, NiO (Bunsenite) and V 8 C 7 it is 60. Since the reflection with 1.48 A o in our pattern has an intensity of 57, it is possible that the phase is either NiO, NiO (Bunsenite) or V 8 C 7. 11

12 The fourth most intense peak (d 4 ) for both NiO and V 8 C 7 has a d value of 1.26 A o and an intensity of 10 and 30 respectively, whereas for NiO (Bunsenite) these values are 0.93 A o and 20. When we compare our data with those of NiO, NiO (Bunsenite), and V 8 C 7 it can be seen that complete matching is obtained only for NiO (Bunsenite). Comparison between the patterns of the unknown pattern and that of the NiO (Bunsenite) shows good matching (Table 8.5) 12

13 Identification of the unknown specimen will not be complete without assigning all the remaining peaks and identify the other phase. These remaining peaks are listed in Table 8.6, with the intensities normalised so that the most intense peak of the remaining peaks has an intensity of 100%. From the Hanawalt Search Manual for 2.03, 1.76 and 1.25 A o as the d values of the three strongest peaks, there are 3 possibilities: FeNi 3, Ni, and Ni 3 Si (Table 8.7) Notice that even though the first four d spacings (d 1, d 2, d 3 and d 4 ) of the unknown specimen match those of FeNi 3, Ni, and Ni 3 Si, the intensities are slightly different. 13

14 The observed intensity for the second reflection in the unknown specimen is 47, and it is 60 for FeNi 3, 40 for Ni, and 70 forni 3 Si. The intensities of the other reflections for FeNi 3 and Ni 3 Si are consistently higher than those of the unknown specimen. Therefore, we can consider Ni as the second phase in the unknown specimen. The starting material is thus a mixture of Ni and NiO (Bunsenite). 14

15 Searching of the PDF requires high-quality data accurate line positions are a must! calibration of camera and diffractometer with known d- spacing standards careful measurement of line intensities Poor quality data will usually give a poor match Mixtures of two or more phases Errors in the database 15