Changeset 094b9eb in sasview
 Timestamp:
 Apr 6, 2017 5:42:22 PM (3 years ago)
 Branches:
 master, ESS_GUI, ESS_GUI_Docs, ESS_GUI_batch_fitting, ESS_GUI_bumps_abstraction, ESS_GUI_iss1116, ESS_GUI_iss879, ESS_GUI_iss959, ESS_GUI_opencl, ESS_GUI_ordering, ESS_GUI_sync_sascalc, magnetic_scatt, release4.2.2, ticket1009, ticket1094headless, ticket12422dresolution, ticket1243, ticket1249, ticket885, unittestsaveload
 Children:
 727c05f
 Parents:
 6aad2e8
 Location:
 src/sas/sasgui/perspectives/invariant/media
 Files:

 4 deleted
 1 edited
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src/sas/sasgui/perspectives/invariant/media/invariant_help.rst
r6aad2e8 r094b9eb 10 10  11 11 12 The scattering, or Porod, invariant ( Q*\) is a modelindependent quantity that12 The scattering, or Porod, invariant ($Q^*$) is a modelindependent quantity that 13 13 can be easily calculated from scattering data. 14 14 15 For two phase systems, the scattering invariant is defined as the integral of 16 the square of the wave transfer (Q) multiplied by the scattering cross section17 over the full range of Qfrom zero to infinity, that is15 For two phase systems, the scattering invariant is defined as the integral of 16 the square of the wavevector transfer ($Q$) multiplied by the scattering cross section 17 over the full range of $Q$ from zero to infinity, that is 18 18 19 .. image:: image001.png19 .. math:: 20 20 21 where *g = q* for pinhole geometry (SAS) and *g = q*\ :sub:`v` (the slit height) for 22 slit geometry (USAS). 21 Q^* = \int_0^\infty q^2I(q)\,dq 23 22 24 The worth of Q*\ is that it can be used to determine the volume fraction and 25 the specific area of a sample. Whilst these quantities are useful in their own 23 in the case of pinhole geometry. For slit geometry the invariant is given by 24 25 .. math:: 26 27 Q^* = \Delta q_v \int_0^\infty qI(q)\,dq 28 29 where $\Delta q_v$ is the slit height. 30 31 The worth of $Q^*$ is that it can be used to determine the volume fraction and 32 the specific area of a sample. Whilst these quantities are useful in their own 26 33 right they can also be used in further analysis. 27 34 28 The difficulty with using Q*\ arises from the fact that experimental data is29 never measured over the range 0 =< *Q* =< infinity. At best, combining USAS and30 WAS data might cover the range 1e5 =< *Q* =< 10 1/\ Ang . Thus it is usually31 necessary to extrapolate the experimental data to low and high *Q*. For this35 The difficulty with using $Q^*$ arises from the fact that experimental data is 36 never measured over the range $0 \le Q \le \infty$. At best, combining USAS and 37 WAS data might cover the range $10^{5} \le Q \le 10$ 1/\ Ang . Thus it is usually 38 necessary to extrapolate the experimental data to low and high $Q$. For this 32 39 33 High *Q*region (>= *Qmax* in data)40 High\ $Q$ region (>= *Qmax* in data) 34 41 35 * The power law function *C*/*Q*\ :sup:`4` is used where the constant36 *C* (= 2.\ pi\ .(\ bigdelta\ rho\ ).\ *Sv*\ ) is to be found by fitting part of data37 within the range *Q*\ :sub:`Nm` to *Q*\ :sub:`N` (where m < N).42 * The power law function $C/Q^4$ is used where the constant 43 $C = 2 \pi \Delta\rho S_v$ is to be found by fitting part of data 44 within the range $Q_{Nm}$ to $Q_N$ (where $m < N$). 38 45 39 Low *Q*region (<= *Qmin* in data)46 Low\ $Q$ region (<= *Qmin* in data) 40 47 41 * The Guinier function *I0.exp(Rg*\ :sup:`2`\ *Q*\ :sup:`2`\ */3)* where *I0*42 and *Rg* are obtained by fitting as for the high*Q* region above.48 * The Guinier function $I_0 exp(R_g^2 Q^2/3)$ where $I_0$ 49 and $R_g$ are obtained by fitting as for the high\ $Q$ region above. 43 50 Alternatively a power law can be used. 44 51 … … 52 59 2) Load some data with the *Data Explorer*. 53 60 54 3) Select a dataset and use the *Send To* button on the *Data Explorer* to load 61 3) Select a dataset and use the *Send To* button on the *Data Explorer* to load 55 62 the dataset into the *Invariant* panel. 56 63 57 4) Use the *Customised Input* boxes on the *Invariant* panel to subtract 58 any background, specify the contrast (i.e. difference in SLDs  this must be 59 specified for the eventual value of Q*\ to be on an absolute scale), or to64 4) Use the *Customised Input* boxes on the *Invariant* panel to subtract 65 any background, specify the contrast (i.e. difference in SLDs  this must be 66 specified for the eventual value of $Q^*$ to be on an absolute scale), or to 60 67 rescale the data. 61 68 62 5) Adjust the extrapolation range as necessary. In most cases the default 69 5) Adjust the extrapolation range as necessary. In most cases the default 63 70 values will suffice. 64 71 65 72 6) Click the *Compute* button. 66 73 67 7) To include a lower and/or higher Q range, check the relevant *Enable74 7) To include a lower and/or higher $Q$ range, check the relevant *Enable 68 75 Extrapolate* check boxes. 69 70 If power law extrapolations are chosen, the exponent can be either held 71 fixed or fitted. The number of points, Npts, to be used for the basis of the 76 77 If power law extrapolations are chosen, the exponent can be either held 78 fixed or fitted. The number of points, Npts, to be used for the basis of the 72 79 extrapolation can also be specified. 73 80 74 8) If the value of Q*\ calculated with the extrapolated regions is invalid, a81 8) If the value of $Q^*$ calculated with the extrapolated regions is invalid, a 75 82 red warning will appear at the top of the *Invariant* panel. 76 83 77 The details of the calculation are available by clicking the *Details* 84 The details of the calculation are available by clicking the *Details* 78 85 button in the middle of the panel. 79 86 … … 88 95 ^^^^^^^^^^^^^^^ 89 96 90 The volume fraction phi is related to Q*\by97 The volume fraction $\phi$ is related to $Q^*$ by 91 98 92 .. image:: image002.png99 .. math:: 93 100 94 where bigdelta\ rho is the SLD contrast. 101 \phi(1  \phi) = \frac{Q^*}{2\pi^2(\Delta\rho)^2} \equiv A 95 102 96 .. image:: image003.png 103 where $\Delta\rho$ is the SLD contrast. 104 105 .. math:: 106 107 \phi = \frac{1 \pm \sqrt{1  4A}}{2} 97 108 98 109 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ … … 101 112 ^^^^^^^^^^^^^^^^^^^^^ 102 113 103 The specific surface area *Sv* is related to Q*\by114 The specific surface area $S_v$ is related to $Q^*$ by 104 115 105 .. image:: image004.png116 .. math:: 106 117 107 where *Cp* is the Porod constant. 118 S_v = \frac{2\pi\phi(1\phi)C_p}{Q^*} = \frac{2\pi A C_p}{Q^*} 119 120 where $C_p$ is the Porod constant. 108 121 109 122 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
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