1 | .. invariant_help.rst |
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2 | |
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3 | .. This is a port of the original SasView html help file to ReSTructured text |
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4 | .. by S King, ISIS, during SasView CodeCamp-III in Feb 2015. |
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5 | |
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6 | .. |Ang| unicode:: U+212B |
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7 | .. |pi| unicode:: U+03C0 |
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8 | .. |bigdelta| unicode:: U+0394 |
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9 | .. |rho| unicode:: U+03C1 |
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10 | .. |phi| unicode:: U+03C6 |
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11 | |
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12 | Invariant Calculation Perspective |
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13 | ================================= |
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14 | |
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15 | Description |
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16 | ----------- |
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17 | |
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18 | The scattering, or Porod, invariant (Q*\) is a model-independent quantity that |
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19 | can be easily calculated from scattering data. |
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20 | |
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21 | For two phase systems, the scattering invariant is defined as the integral of |
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22 | the square of the wave transfer (Q) multiplied by the scattering cross section |
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23 | over the full range of Q from zero to infinity, that is |
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24 | |
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25 | .. image:: image001.gif |
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26 | |
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27 | where *g = Q* for pinhole geometry (SAS) and *g = Qv* (the slit height) for |
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28 | slit geometry (USAS). |
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29 | |
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30 | The worth of Q*\ is that it can be used to determine the volume fraction and |
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31 | the specific area of a sample. Whilst these quantities are useful in their own |
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32 | right they can also be used in further analysis. |
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33 | |
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34 | The difficulty with using Q*\ arises from the fact that experimental data is |
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35 | never measured over the range 0 =< *Q* =< infinity. At best, combining USAS and |
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36 | WAS data might cover the range 1e-5 =< *Q* =< 10 1/\ |Ang| . Thus it is usually |
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37 | necessary to extrapolate the experimental data to low and high *Q*. For this |
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38 | |
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39 | High-*Q* region (>= *Qmax* in data) |
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40 | |
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41 | * The power law function *C*/*Q*\ :sup:`4` is used where the constant |
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42 | *C* (= 2.\ |pi|\ .(\ |bigdelta|\ |rho|\ ).\ *Sv*\ ) is to be found by fitting part of data |
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43 | within the range *Q*\ :sub:`N-m` to *Q*\ :sub:`N` (where m < N). |
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44 | |
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45 | Low-*Q* region (<= *Qmin* in data) |
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46 | |
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47 | * The Guinier function *I0.exp(-Rg*\ :sup:`2`\ *Q*\ :sup:`2`\ */3)* where *I0* |
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48 | and *Rg* are obtained by fitting as for the high-*Q* region above. |
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49 | Alternatively a power law can be used. |
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50 | |
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51 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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52 | |
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53 | Using the perspective |
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54 | --------------------- |
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55 | |
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56 | 1) Select *Invariant* from the *Analysis* menu on the SasView toolbar. |
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57 | |
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58 | 2) Load some data with the *Data Explorer*. |
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59 | |
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60 | 3) Select a dataset and use the *Send To* button on the *Data Explorer* to load |
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61 | the dataset into the *Invariant* perspective. |
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62 | |
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63 | 4) Use the *Customised Input* boxes on the *Invariant* perspective to subtract |
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64 | any background, specify the contrast (i.e. difference in SLDs - this must be |
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65 | specified for the eventual value of Q*\ to be on an absolute scale), or to |
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66 | rescale the data. |
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67 | |
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68 | 5) Adjust the extrapolation range as necessary. In most cases the default |
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69 | values will suffice. |
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70 | |
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71 | 6) Click the *Compute* button. |
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72 | |
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73 | 7) To include a lower and/or higher Q range, check the relevant *Enable |
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74 | Extrapolate* check boxes. |
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75 | |
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76 | If power law extrapolations are chosen, the exponent can be either held |
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77 | fixed or fitted. The number of points, Npts, to be used for the basis of the |
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78 | extrapolation can also be specified. |
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79 | |
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80 | 8) If the value of Q*\ calculated with the extrapolated regions is invalid, a |
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81 | red warning will appear at the top of the *Invariant* perspective panel. |
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82 | |
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83 | The details of the calculation are available by clicking the *Details* |
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84 | button in the middle of the panel. |
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85 | |
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86 | .. image:: image005.gif |
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87 | |
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88 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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89 | |
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90 | Parameters |
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91 | ---------- |
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92 | |
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93 | Volume Fraction |
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94 | ^^^^^^^^^^^^^^^ |
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95 | |
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96 | The volume fraction |phi| is related to Q*\ by |
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97 | |
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98 | .. image:: image002.gif |
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99 | |
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100 | where |bigdelta|\ |rho| is the SLD contrast. |
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101 | |
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102 | .. image:: image003.gif |
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103 | |
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104 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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105 | |
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106 | Specific Surface Area |
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107 | ^^^^^^^^^^^^^^^^^^^^^ |
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108 | |
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109 | The specific surface area *Sv* is related to Q*\ by |
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110 | |
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111 | .. image:: image004.gif |
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112 | |
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113 | where *Cp* is the Porod constant. |
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114 | |
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115 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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116 | |
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117 | Reference |
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118 | --------- |
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119 | |
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120 | O. Glatter and O. Kratky |
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121 | Chapter 2 in *Small Angle X-Ray Scattering* |
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122 | Academic Press, New York, 1982 |
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123 | |
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124 | http://physchem.kfunigraz.ac.at/sm/ |
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125 | |
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126 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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127 | |
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128 | .. note:: This help document was last changed by Steve King, 01May2015 |
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