International Tables for Crystallography (2019). Vol. H. ch. 3.9, pp. 344-373
https://doi.org/10.1107/97809553602060000954

Chapter 3.9. Quantitative phase analysis

Contents

  • 3.9. Quantitative phase analysis  (pp. 344-373) | html | pdf | chapter contents |
    I. C. Madsen, N. V. Y. Scarlett, R. Kleeberg and K. Knorr
    • 3.9.1. Introduction  (p. 344) | html | pdf |
    • 3.9.2. Phase analysis  (pp. 344-345) | html | pdf |
    • 3.9.3. QPA methodology  (pp. 345-350) | html | pdf |
      • 3.9.3.1. Absorption–diffraction method  (pp. 345-346) | html | pdf |
      • 3.9.3.2. Internal standard method  (pp. 346-347) | html | pdf |
        • 3.9.3.2.1. Selection of an internal standard  (pp. 346-347) | html | pdf |
      • 3.9.3.3. Reference intensity ratio methods  (p. 347) | html | pdf |
      • 3.9.3.4. Matrix-flushing method  (pp. 347-348) | html | pdf |
      • 3.9.3.5. Full-pattern fitting methods  (p. 348) | html | pdf |
      • 3.9.3.6. Rietveld-based QPA  (pp. 348-350) | html | pdf |
    • 3.9.4. Demonstration of methods  (pp. 350-353) | html | pdf |
      • 3.9.4.1. Absorption–diffraction method  (p. 350) | html | pdf |
      • 3.9.4.2. Internal standard method  (pp. 350-351) | html | pdf |
      • 3.9.4.3. Reference intensity ratio  (p. 351) | html | pdf |
      • 3.9.4.4. Matrix flushing  (pp. 351-352) | html | pdf |
      • 3.9.4.5. Rietveld-based methods  (pp. 352-353) | html | pdf |
    • 3.9.5. Alternative methods for determination of calibration constants  (pp. 353-356) | html | pdf |
      • 3.9.5.1. Standardless determination of the phase constant C  (pp. 353-354) | html | pdf |
      • 3.9.5.2. Demonstration of the Zevin approach  (pp. 354-355) | html | pdf |
      • 3.9.5.3. Experiment constant – a whole-sample approach  (pp. 355-356) | html | pdf |
    • 3.9.6. Quantification of phases with partial or no known crystal structures  (pp. 356-360) | html | pdf |
      • 3.9.6.1. Use of calibrated models  (pp. 356-358) | html | pdf |
        • 3.9.6.1.1. Generation of calibrated PONKCS models  (p. 357) | html | pdf |
        • 3.9.6.1.2. Application of the model  (pp. 357-358) | html | pdf |
      • 3.9.6.2. Modelling of structural disorder  (pp. 358-359) | html | pdf |
      • 3.9.6.3. Quantitative determination of amorphous material  (pp. 360-361) | html | pdf |
    • 3.9.7. QPA from in situ experimentation  (pp. 361-362) | html | pdf |
      • 3.9.7.1. Data analysis  (pp. 361-362) | html | pdf |
    • 3.9.8. QPA using neutron diffraction data  (p. 362) | html | pdf |
    • 3.9.9. QPA using energy-dispersive diffraction data  (pp. 362-364) | html | pdf |
    • 3.9.10. Improving accuracy  (pp. 364-370) | html | pdf |
      • 3.9.10.1. Standard deviations and error estimates  (p. 364) | html | pdf |
      • 3.9.10.2. Minimizing systematic errors  (pp. 364-365) | html | pdf |
      • 3.9.10.3. Minimizing sample-related errors  (pp. 365-370) | html | pdf |
        • 3.9.10.3.1. Crystallite-size issues  (p. 365) | html | pdf |
        • 3.9.10.3.2. Preferred orientation  (pp. 365-366) | html | pdf |
        • 3.9.10.3.3. Microabsorption  (pp. 366-368) | html | pdf |
        • 3.9.10.3.4. Whole-pattern-refinement effects  (p. 368) | html | pdf |
        • 3.9.10.3.5. Element analytical standards  (pp. 368-369) | html | pdf |
        • 3.9.10.3.6. Phase-specific methods: diffraction SRMs, round-robin samples and synthetic mixtures  (pp. 369-370) | html | pdf |
    • 3.9.11. Summary  (p. 370) | html | pdf |
    • References | html | pdf |
    • Figures
      • Fig. 3.9.1. Plot of the analysed concentration (black diamonds – left axis) and the bias (open triangles – right axis) expressed as wt% for fluorite using the absorption–diffraction method  (p. 351) | html | pdf |
      • Fig. 3.9.2. Plot of the analysed concentration (black diamonds – left axis) and the bias (open triangles – right axis) expressed as wt% for fluorite using the internal standard method with zincite designated as the internal standard  (p. 351) | html | pdf |
      • Fig. 3.9.3. Plot of the 24 determined RIR values for fluorite (black diamonds) and zincite (open triangles) as a function of corundum concentration  (p. 351) | html | pdf |
      • Fig. 3.9.4. Plot of the analysed concentration (black diamonds – left axis) and the bias (open triangles – right axis) expressed as wt% for fluorite using the matrix-flushing method with RIRs of 1.0, 3.617 and 4.856 for corundum, fluorite and zincite, respectively  (p. 352) | html | pdf |
      • Fig. 3.9.5. The results of QPA of the in situ XRD data collected during the seeding experiments of Webster et al  (p. 354) | html | pdf |
      • Fig. 3.9.6. The results of QPA of the in situ XRD data collected during the seeding experiments of Webster et al  (p. 354) | html | pdf |
      • Fig. 3.9.7. The results of QPA of the in situ XRD data collected during the seeding experiments of Webster et al  (p. 354) | html | pdf |
      • Fig. 3.9.8. SEM image of Al(OH)3 (grey hexagon) which has crystallized on goethite seed (light grey needles) (Webster et al  (p. 355) | html | pdf |
      • Fig. 3.9.9. Plot of the bias (known − determined) in the analysed phase abundances using the Zevin & Kimmel (1995) approach for corundum (black diamonds), fluorite (open triangles) and zincite (crosses)  (p. 356) | html | pdf |
      • Fig. 3.9.10. Plot of the experiment constant K as a function of known phase concentration for corundum (closed diamonds), fluorite (open triangles) and zincite (crosses) using the phase-specific method  (p. 356) | html | pdf |
      • Fig. 3.9.11. Turbostratic disorder, illustrated by the stacking of two hexagonal layers rotated by 7°  (p. 358) | html | pdf |
      • Fig. 3.9.12. Section of the reciprocal lattice of a turbostratically disordered pseudo-hexagonal C-centred structure  (p. 359) | html | pdf |
      • Fig. 3.9.13. Output of Rietveld refinement of XRD data (Cu Kα radiation) for a synthetic sample containing a mixture crystalline and amorphous phases  (p. 360) | html | pdf |
      • Fig. 3.9.14. Raw in situ XRD data (Co Kα radiation) collected during the synthesis of the iron-ore sinter bonding phase SFCA-I (Webster et al  (p. 362) | html | pdf |
      • Fig. 3.9.15. Results of Rietveld-based QPA of the in situ data sequence shown in Fig  (p. 363) | html | pdf |
      • Fig. 3.9.16. Basic experimental arrangement for energy-dispersive diffraction  (p. 363) | html | pdf |
      • Fig. 3.9.17. Variation of the magnetite (filled diamonds) and quartz (open squares) concentration of an iron-ore sample with grinding time  (p. 365) | html | pdf |
      • Fig. 3.9.18. Increase of the March–Dollase (Dollase, 1986) parameter and related decrease of the degree of preferred orientation with grinding time for the two amphibole species actinolite (filled diamonds) and grunerite (open squares) in an iron ore  (p. 366) | html | pdf |
      • Fig. 3.9.19. Backscattered-electron SEM image of a mixture of approximately equal amounts of corundum (dark grey), magnetite and zircon (lighter grey)  (p. 367) | html | pdf |
      • Fig. 3.9.20. Bias as a function of phase concentration for industrial salt samples for (i) structure-based QPA (filled symbols) and (ii) calibrated hkl_phase (open symbols) for halite (circles) and sylvite (squares)  (p. 368) | html | pdf |
      • Fig. 3.9.21. Profile fit of anatase and rutile (a) without and (b) with a Kβ filter absorption-edge correction  (p. 369) | html | pdf |
      • Fig. 3.9.22. Output of Rietveld refinement and results of QPA for the iron-ore certified reference material SX 11–14 from Dillinger Hütte  (p. 370) | html | pdf |
    • Tables
      • Table 3.9.1. Weighed composition (weight fraction) of the eight mixtures comprising sample 1 in the IUCr CPD round robin on QPA (Madsen et al., 2001)  (p. 350) | html | pdf |
      • Table 3.9.2. Average values (n = 3) of net peak intensity derived using profile fitting for the strongest peaks of corundum (113), fluorite (022) and zincite (011)  (p. 350) | html | pdf |
      • Table 3.9.3. Phase calibration constants for corundum, fluorite and zincite determined using the Zevin (Zevin & Kimmel, 1995) and Knudsen (Knudsen, 1981) method  (p. 355) | html | pdf |
      • Table 3.9.4. Comparison of errors generated during the analysis of XRD data (Cu Kα radiation) from three sub-samples of sample 4 from the IUCr CPD round robin on QPA (Scarlett et al., 2002)  (p. 364) | html | pdf |
      • Table 3.9.5. Calculated values of μD (where μ is the linear absorption coefficient and D is the particle diameter) for Cu Kα X-rays for corundum, magnetite and zircon with a range of particle sizes  (p. 367) | html | pdf |
      • Table 3.9.6. Compositional analysis of the Dillinger Hütte iron-ore certified reference material SX 11–14, (i) derived from QPA results, taking into account the nominal stoichiometry of the phases (XRD) and (ii) the certified analyses (Cert) (Knorr & Bornefeld, 2013)  (p. 369) | html | pdf |