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src/sas/perspectives/invariant/media/invariant_help.rst
rec392464 r0721c3d 3 3 .. This is a port of the original SasView html help file to ReSTructured text 4 4 .. by S King, ISIS, during SasView CodeCamp-III in Feb 2015. 5 6 .. |Ang| unicode:: U+212B 7 .. |pi| unicode:: U+03C0 8 .. |bigdelta| unicode:: U+0394 9 .. |rho| unicode:: U+03C1 10 .. |phi| unicode:: U+03C6 5 11 6 12 Invariant Calculation Perspective … … 9 15 Scattering_Invariant_ 10 16 17 How_to_Use_ 18 11 19 Volume_Fraction_ 12 20 13 21 Specific_Surface_Area_ 14 22 15 Definitions_16 17 23 Reference_ 18 19 How_to_Use_20 24 21 25 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ … … 23 27 .. _Scattering_Invariant: 24 28 25 Scattering Invariant26 -------------------- 29 Scattering (Porod) Invariant 30 ---------------------------- 27 31 28 The scattering invariant (Q*) is a model-independent quantity that can be29 easily calculated from scattering data.32 The scattering, or Porod, invariant (Q*\) is a model-independent quantity that 33 can be easily calculated from scattering data. 30 34 31 For two phase systems, the scattering invariant, Q*, is defined as the 32 integral of the square of the wave transfer (q) multiplied by the scattering 33 cross section over the full range of q. 34 35 Q* is given by the following equation 35 For two phase systems, the scattering invariant is defined as the integral of 36 the square of the wave transfer (Q) multiplied by the scattering cross section 37 over the full range of Q from zero to infinity, that is 36 38 37 39 .. image:: image001.gif 38 40 39 This model independent quantity (Q*) is calculated from the scattering data 40 that can be used to determine the volume fraction and the specific area of the 41 sample under consideration. 41 where *g = Q* for pinhole geometry (SAS) and *g = Qv* (the slit height) for 42 slit geometry (USAS). 42 43 43 These quantities are useful in their own right and can be used in further 44 analysis. With this scattering invariant module users will also be able to 45 determine the consistency of those properties between data. There is no real 46 data defined from zero to infinity, there usually have limited range. 44 The worth of Q*\ is that it can be used to determine the volume fraction and 45 the specific area of a sample. Whilst these quantities are useful in their own 46 right they can also be used in further analysis. 47 47 48 Q* is not really computed from zero to infinity. Our maximum q range is 49 1e-5 ~ 10 (1/Angstrom). The lower and/or higher q range than data given can be 50 extrapolated by fitting some data nearby. 48 The difficulty with using Q*\ arises from the fact that experimental data is 49 never measured over the range 0 =< *Q* =< infinity. At best, combining USAS and 50 WAS data might cover the range 1e-5 =< *Q* =< 10 1/\ |Ang| . Thus it is usually 51 necessary to extrapolate the experimental data to low and high *Q*. For this 51 52 52 The scattering invariant is computed as follows 53 High-*Q* region (>= *Qmax* in data) 53 54 54 *I(q)* = *I(q)* w/o background : If the data includes a background, user sets 55 the value to subtract the background for the Q* computation. 55 * The power law function *C*/*Q*\ :sup:`4` is used where the constant 56 *C* (= 2.\ |pi|\ .(\ |bigdelta|\ |rho|\ ).\ *Sv*\ ) is to be found by fitting part of data 57 within the range *Q*\ :sub:`N-m` to *Q*\ :sub:`N` (where m < N). 56 58 57 Reset *I(q)* = *I(q)* scaling factor* , delta *I(q) =* delta *I(q)*scaling 58 factor* : If non-zero scaling factor is given, it will be considered. 59 Low-*Q* region (<= *Qmin* in data) 59 60 60 Invariant 61 * The Guinier function *I0.exp(-Rg*\ :sup:`2`\ *Q*\ :sup:`2`\ */3)* where *I0* 62 and *Rg* are obtained by fitting as for the high-*Q* region above. 63 Alternatively a power law can be used. 61 64 62 .. image:: image001.gif65 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 63 66 64 where *g =q* for the pinhole geometry and *g =qv* (the slit height) for the 65 slit geometry which can be given in data or as a value. 67 .. _How_to_Use: 66 68 67 Higher q-region (\>= qmax in data) 69 How to Use 70 ---------- 68 71 69 Power law (w/o background term) function = C/q4will be used 72 1) Select *Invariant* from the *Analysis* menu on the SasView toolbar. 70 73 71 where the constant C(=2pi(delta(rho))Sv) is to be found by fitting part of 72 data with the range of qN-mto qN(m\<N). 74 2) Load some data with the *Data Explorer*. 73 75 74 Lower q-region (\<= qmin in data): 76 3) Select a dataset and use the *Send To* button on the *Data Explorer* to load 77 the dataset into the *Invariant* perspective. 75 78 76 Guinier function = *I0exp(-Rg2q2/3)* where I0and Rgare obtained by fitting, 79 4) Use the *Customised Input* boxes on the *Invariant* perspective to subtract 80 any background, specify the contrast (i.e. difference in SLDs - this must be 81 specified for the eventual value of Q*\ to be on an absolute scale), or to 82 rescale the data. 77 83 78 similarly to the high q region above. 84 5) Adjust the extrapolation range as necessary. In most cases the default 85 values will suffice. 79 86 80 Power law can also be used. 87 6) Click the *Compute* button. 88 89 7) To include a lower and/or higher Q range, check the relevant *Enable 90 Extrapolate* check boxes. 91 92 If power law extrapolations are chosen, the exponent can be either held 93 fixed or fitted. The number of points, Npts, to be used for the basis of the 94 extrapolation can also be specified. 95 96 8) If the value of Q*\ calculated with the extrapolated regions is invalid, a 97 red warning will appear at the top of the *Invariant* perspective panel. 98 99 The details of the calculation are available by clicking the *Details* 100 button in the middle of the panel. 101 102 .. image:: image005.gif 81 103 82 104 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ … … 87 109 --------------- 88 110 111 The volume fraction |phi| is related to Q*\ by 112 89 113 .. image:: image002.gif 90 114 91 where delta(rho) is the SLD contrast of which value is given by users.115 where |bigdelta|\ |rho| is the SLD contrast. 92 116 93 117 .. image:: image003.gif 94 95 Thus96 97 where 0 =\< *A* =\<1/4 in order for these values to be physically valid.98 118 99 119 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ … … 104 124 --------------------- 105 125 126 The specific surface area *Sv* is related to Q*\ by 127 106 128 .. image:: image004.gif 107 129 108 where *A* and *Q** are obtained from previous sections, and the Porod 109 constant *Cp* is given by users. 110 111 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 112 113 .. _Definitions: 114 115 Definitions 116 ----------- 117 118 Q: the magnitude of neutron (or X-ray) momentum transfer vector. 119 120 I(Q): the scattering intensity as a function of the momentum transfer Q. 121 122 Invariant total is the sum of the invariant calculated from datas q range and 123 the invariant resulting from extrapolation at low q range and at high q range 124 if considered. 130 where *Cp* is the Porod constant. 125 131 126 132 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ … … 131 137 ---------- 132 138 133 Chapter 2 in O. Glatter and O. Kratky, "Small Angle X-Ray Scattering", Academic 134 Press, New York, 1982 139 O. Glatter and O. Kratky 140 Chapter 2 in *Small Angle X-Ray Scattering* 141 Academic Press, New York, 1982 135 142 136 143 http://physchem.kfunigraz.ac.at/sm/ 137 144 138 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 145 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 139 146 140 .. _How_to_Use: 141 142 How to Use 143 ---------- 144 145 1. Loading data to the panel: Open the data file from File in the menu bar. 146 Select loaded data from a plot panel by highlighting that it until its color 147 turns yellow. Then right click on that the data and selects the option Compute 148 Invariant. The application automatically computes the invariant value if the 149 data loaded is valid. 150 151 2. To subtract a background or/and to rescale the data, type the values in 152 Customized Input box. 153 154 3. If you want to calculate the volume fraction and the specific surface 155 area, type the optional inputs in the customized input box, and then press 156 'Compute' button. 157 158 4. The invariant can also be calculated including the outside of the data Q 159 range: To include the lower Q and/or the higher Q range, check in the enable 160 extrapolation check box in 'Extrapolation' box. If the power low is chosen, 161 the power (exponent) can be either held or fitted by checking the 162 corresponding radio button. The Npts that is being used for the extrapolation 163 can be specified. 164 165 5. If the invariant calculated from the extrapolated region is too large, it 166 will be warn in red at the top of the panel, which means that your data is not 167 proper to calculate the invariant. 168 169 6. The details of the calculation is available by clicking the 'Details' 170 button in the middle of the panel. 171 172 .. image:: image005.gif 147 .. note:: This help document was last changed by Steve King, 19Feb2015
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