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Quantitative Analysis

Quantitative Analysis. Intuitive - in a mixture, higher intensities mean higher concentrations. Quantitative Analysis. Intuitive - in a mixture, higher intensities mean higher concentrations ….. but …. Quantitative Analysis. So, use measured intensities ….. but not straightforward.

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Quantitative Analysis

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  1. Quantitative Analysis Intuitive - in a mixture, higher intensities mean higher concentrations

  2. Quantitative Analysis Intuitive - in a mixture, higher intensities mean higher concentrations ….. but …..

  3. Quantitative Analysis So, use measured intensities ….. but not straightforward

  4. Quantitative Analysis KiaXa Iia= a  So, use measured intensities ….. but not straightforward Main equation for quantitative analysis

  5. Quantitative Analysis Iia = intensity of reflection i of phase a KiaXa Iia= a  So, use measured intensities ….. but not straightforward Main equation for quantitative analysis

  6. Quantitative Analysis KiaXa Iia= a  ais density of phase a So, use measured intensities ….. but not straightforward Main equation for quantitative analysis

  7. Quantitative Analysis Kia contains structure factor, multiplicity, Lorentz-polarization factor, temperature factor + scale factor for reflection i of phase a KiaXa Iia= a  So, use measured intensities ….. but not straightforward Main equation for quantitative analysis

  8. Quantitative Analysis Xa = wt fraction of phase a (want this!!) KiaXa Iia= a  So, use measured intensities ….. but not straightforward Main equation for quantitative analysis

  9. Quantitative Analysis Xa = wt fraction of phase a (want this!!) KiaXa Iia= a  So, use measured intensities ….. but not straightforward Main equation for quantitative analysis measure this!! But what do we do with ?

  10. Quantitative Analysis Xa = wt fraction of phase a (Want this!!) KiaXa Iia= a  So, use measured intensities ….. but not straightforward Main equation for quantitative analysis Measure this!! But what do we do with ?  is mass attenuation coefficient for mixture…. unknown, unless we know

  11. Quantitative Analysis If sample contains >one phase, then  unknown if wt fractions unknown KiaXa Iia= a   for each phase may be calculated from the chemical composition of each phase compd = X11 + X22 + X33 + ……… mix = X1phase1 + X2phase 2 + X3phase 3 + ………

  12. Quantitative Analysis KiaXa Iia= a  So, use measured intensities ….. but not straightforward Main equation for quantitative analysis also be nice not to calc Kia or get a

  13. 1. Special case - mixture of 2 polymorphs Since polymorphs have same composition mix = a = b

  14. 1. Special case - mixture of 2 polymorphs Suppose we measure Iia of pure a can eliminate mix (& other stuff) KiaXa Iia= a Kia Iia= aa Since polymorphs have same composition mix = a = b = Xa

  15. 1. Special case - mixture of 2 polymorphs Iia = Xa Iia Measure reflection intensities for pure mat’l & same phase in mixture

  16. 1. Special case - rutile/anatase mixture Pure rutile Reflection Intensity Background Net 1 102309 1508 100801 2 47564 1453 46111 Rutile-anatase mixture Reflection Intensity Background Net 1 36987 1486 35501 2 17408 1439 15969 1: 35501/100801=0.352 2: 15969/46111=0.346 wt. fract. anatase: 1-wt. fract. rutile=1-0.349=0.651

  17. 2. Quantitative Analysis KiaXa Iia= a  Main equation for quantitative analysis Determine reflection intensities for unknown & compare to those of standard Mix known amount of standard with unknown Measure reflection intensities for: 1) pure standard 2) pure analyte 3) analyte in unknown 4) standard in unknown

  18. 2. Quantitative Analysis Is KiaXa Xs s KsXs KsXs Ks Ks = Is = Is = Iia= Is= Is=  s s ss ss Is a  Ka KaXa Ia= Ia= aa a

  19. 2. Quantitative Analysis Ia KiaXa Xa a KsXs KaXa Ka Ks = Is = Ia = Iia= Ia= Is=  s a aa ss Ia a  Ka KaXa Ia= Ia= aa a

  20. 2. Quantitative Analysis Xs s Xs s Is Is Xa a Xa a Ia Ia = = = =     Is Is Ia Ia Xs s Is Ia = Is Ia Xa a

  21. Robs t = 1.0 sec Rtrue = 1 – t * Robs 2. Quantitative Analysis - intensity ratio method Now for the problem…. Determine amount of quartz in a rock Add known amount of KCl to rock sample Correct for deadtime and subtract background

  22. 2. Quantitative Analysis - intensity ratio method corr corr Phase  I pure Ipure Imix Imix Quartz 35.0 48360 2648 KCl 124.0 19072 6160

  23. 2. Quantitative Analysis - intensity ratio method corr corr Phase  I pure Ipure Imix Imix Quartz 35.0 48360 50578 2648 2415 KCl 124.0 19072 19203 6160 5958

  24. 2. Quantitative Analysis - intensity ratio method

  25. 2. Quantitative Analysis - intensity ratio method

  26. 2. Quantitative Analysis - intensity ratio method

  27. 2. Quantitative Analysis - intensity ratio method

  28. 2. Quantitative Analysis - intensity ratio method

  29. KiaXa Iia= a  3. Quantitative Analysis - internal standard method Mix known amount of standard with unknown Make calibration sample containing known amounts of standard & analyte Measure reflections for standard & analyte in: 1) calibration sample 2) unknown mixture

  30. Ks Xs Ka Xa Is= Ia= s a Ka Xa Ia= Ia a Ka Xas = a Ks Xs Ks Xs Is Is= s Ia Kas Xa Xa = = C Xs Ksa Xs Is 3. Quantitative Analysis - internal standard method Measure reflections for standard & analyte in: 1) calibration sample 2) unknown mixture

  31. Ia Xs C = Is Xa Ia Kas Xa Xa = = C Xs Ksa Xs Is 3. Quantitative Analysis - internal standard method Measure reflections for standard & analyte in: 1) calibration sample 2) unknown mixture Get C from calibration sample (Xs & Xa known)

  32. Ia Xs C = Is Xa Iq XKCl (8041) (0.5) = 0.7064 = C = IKCl Xq (11383) (0.5) 3. Quantitative Analysis - internal standard method From calibration sample: Phase Robs Rtrue Inet Quartz 8105 8171 8041 KCl 11382 11513 11383

  33. Iq Xq = C IKCl XKCl Iq XKCl (2415) (0.1667) Xq = = IKCl C (5958) (0.7064) = 0.096 1200 Xqrock = 0.096 = 0.115 1000 3. Quantitative Analysis - internal standard method Now everything known to get wt. fract. of quartz in rock

  34. KiaXa Iia= a  4. Quantitative Analysis - reference intensity ratios Problem, as always, is what to do with 

  35. For corundum For analyte KaXa KcXc Ia= Ic= c a KaXa Ia KaXac Xa Ia= = = K a Ic KcXca Xc KcXc Ic= c For 50-50 mixture of analyte with corundum Ia = K …..denoted (I/Ic)a Ic 4. Quantitative Analysis - reference intensity ratios

  36. 4. Quantitative Analysis - reference intensity ratios For 50-50 mixture of analyte with corundum Then, for any a + corundum mixture (I/Ic)a Ia Ia = = K …..denoted (I/Ic)a Ic Ic Xa Xc

  37. For any a + b mixture Ia KaXac Ia = = K = Ic KcXca Ib Ka c Xa Xa Kc a (I/Ic)a Xb Xc = (I/Ic)b Kb c Ka Kc b a Kb = b 4. Quantitative Analysis - reference intensity ratios

  38. 4. Quantitative Analysis - reference intensity ratios Problem: rutile/anatase

  39. 4. Quantitative Analysis - reference intensity ratios Problem: rutile/anatase

  40. 4. Quantitative Analysis - reference intensity ratios Problem: quartz in rock

  41. 4. Quantitative Analysis - reference intensity ratios Problem: quartz in rock

  42. 4. Quantitative Analysis - reference intensity ratios Problem: quartz in rock

  43. 4. Quantitative Analysis - reference intensity ratios Problem: quartz in rock Fast….no calibration req’d I/Ics not accurate……instrument conditions change

  44. Quantitative Analysis: RIR - procedure • Use intensities from workshop 1. Will use multiple reflections with different relative intensities. Must normalize: divide intensities for Al2O3 and ZnO by relative intensities given in PDF • Calculate average Imeas/IPDF for Al2O3 and ZnO • Divide average for ZnO by average for Al2O3 to determine I/Ic for ZnO • Do same for CaF2 & Al2O3

  45. Quantitative Analysis: RIR Procedure • Follow similar procedure for unknown #1 to calculate average Imeas/IPDFs for ZnO and CaF2 • Get IZnO/ICaF2 • Using IZnO/ICaF2 & K (= I/Ic)s previously determined, solve for XCaF2 • Get XZnO from XZnO = 1 – XCaF2 • Repeat for unknowns #2 and #3

  46. RIR 5C5C

  47. RIR

  48. RIR

  49. RIR 5C5Z

  50. RIR

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