[8007311] | 1 | r""" |
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| 2 | Definition |
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| 3 | ---------- |
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[40a87fa] | 4 | This model provides the form factor for a circular cylinder with a |
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| 5 | core-shell scattering length density profile. Thus this is a variation |
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| 6 | of a core-shell cylinder or disc where the shell on the walls and ends |
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| 7 | may be of different thicknesses and scattering length densities. The form |
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| 8 | factor is normalized by the particle volume. |
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[8007311] | 9 | |
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[fa8011eb] | 10 | .. _core-shell-bicelle-geometry: |
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[8007311] | 11 | |
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| 12 | .. figure:: img/core_shell_bicelle_geometry.png |
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| 13 | |
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[b0c4271] | 14 | Core shell geometry (Graphic from ref [#Matusmori]_). |
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| 15 | Note however that the model here calculates for rectangular, not curved, rims. |
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[8007311] | 16 | |
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| 17 | The output of the 1D scattering intensity function for randomly oriented |
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| 18 | cylinders is then given by the equation above. |
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| 19 | |
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| 20 | The *theta* and *phi* parameters are not used for the 1D output. |
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| 21 | Our implementation of the scattering kernel and the 1D scattering intensity |
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| 22 | use the c-library from NIST. |
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| 23 | |
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[2f0c07d] | 24 | .. figure:: img/cylinder_angle_definition.jpg |
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[8007311] | 25 | |
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[2f0c07d] | 26 | Definition of the angles for the oriented core shell bicelle tmodel. |
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[8007311] | 27 | |
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[2f0c07d] | 28 | .. figure:: img/cylinder_angle_projection.jpg |
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[b0c4271] | 29 | :width: 600px |
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[8007311] | 30 | |
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| 31 | Examples of the angles for oriented pp against the detector plane. |
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| 32 | |
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| 33 | References |
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| 34 | ---------- |
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| 35 | |
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[b0c4271] | 36 | .. [#Matusmori] `N Matsumori and M Murata <http://dx.doi.org/10.1039/C0NP0000 |
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| 37 | 2G>`_, *Nat. Prod. Rep.* 27 (2010) 1480-1492 |
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| 38 | .. [#] L A Feigin and D I Svergun, *Structure Analysis by Small-Angle X-Ray and |
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| 39 | Neutron Scattering,* Plenum Press, New York, (1987) |
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| 40 | |
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| 41 | Authorship and Verification |
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| 42 | ---------------------------- |
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| 43 | |
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| 44 | * **Author:** NIST IGOR/DANSE **Date:** pre 2010 |
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| 45 | * **Last Modified by:** Paul Butler **Date:** Septmber 30, 2016 |
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| 46 | * **Last Reviewed by:** Under Review **Date:** October 5, 2016 |
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[8007311] | 47 | |
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| 48 | """ |
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| 49 | |
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| 50 | from numpy import inf, sin, cos |
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| 51 | |
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| 52 | name = "core_shell_bicelle" |
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| 53 | title = "Circular cylinder with a core-shell scattering length density profile.." |
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| 54 | description = """ |
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[aad336c] | 55 | P(q,alpha)= scale/Vs*f(q)^(2) + bkg, where: f(q)= 2(sld_core |
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[8007311] | 56 | - solvant_sld)* Vc*sin[qLcos(alpha/2)] |
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| 57 | /[qLcos(alpha/2)]*J1(qRsin(alpha)) |
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[aad336c] | 58 | /[qRsin(alpha)]+2(shell_sld-sld_solvent) |
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[8007311] | 59 | *Vs*sin[q(L+T)cos(alpha/2)][[q(L+T) |
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| 60 | *cos(alpha/2)]*J1(q(R+T)sin(alpha)) |
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| 61 | /q(R+T)sin(alpha)] |
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| 62 | |
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| 63 | alpha:is the angle between the axis of |
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| 64 | the cylinder and the q-vector |
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| 65 | Vs: the volume of the outer shell |
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| 66 | Vc: the volume of the core |
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| 67 | L: the length of the core |
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| 68 | shell_sld: the scattering length density |
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| 69 | of the shell |
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[aad336c] | 70 | sld_solvent: the scattering length density |
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[8007311] | 71 | of the solvent |
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| 72 | bkg: the background |
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| 73 | T: the thickness |
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| 74 | R+T: is the outer radius |
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| 75 | L+2T: The total length of the outershell |
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| 76 | J1: the first order Bessel function |
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| 77 | theta: axis_theta of the cylinder |
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| 78 | phi: the axis_phi of the cylinder... |
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| 79 | """ |
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| 80 | category = "shape:cylinder" |
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| 81 | |
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| 82 | # pylint: disable=bad-whitespace, line-too-long |
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| 83 | # ["name", "units", default, [lower, upper], "type", "description"], |
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| 84 | parameters = [ |
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| 85 | ["radius", "Ang", 20, [0, inf], "volume", "Cylinder core radius"], |
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[2222134] | 86 | ["thick_rim", "Ang", 10, [0, inf], "volume", "Rim shell thickness"], |
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| 87 | ["thick_face", "Ang", 10, [0, inf], "volume", "Cylinder face thickness"], |
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[8007311] | 88 | ["length", "Ang", 400, [0, inf], "volume", "Cylinder length"], |
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[42356c8] | 89 | ["sld_core", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Cylinder core scattering length density"], |
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| 90 | ["sld_face", "1e-6/Ang^2", 4, [-inf, inf], "sld", "Cylinder face scattering length density"], |
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| 91 | ["sld_rim", "1e-6/Ang^2", 4, [-inf, inf], "sld", "Cylinder rim scattering length density"], |
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| 92 | ["sld_solvent", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Solvent scattering length density"], |
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[8007311] | 93 | ["theta", "degrees", 90, [-inf, inf], "orientation", "In plane angle"], |
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| 94 | ["phi", "degrees", 0, [-inf, inf], "orientation", "Out of plane angle"], |
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| 95 | ] |
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| 96 | |
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| 97 | # pylint: enable=bad-whitespace, line-too-long |
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| 98 | |
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[40a87fa] | 99 | source = ["lib/Si.c", "lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c", |
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| 100 | "core_shell_bicelle.c"] |
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[8007311] | 101 | |
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| 102 | demo = dict(scale=1, background=0, |
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| 103 | radius=20.0, |
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[2222134] | 104 | thick_rim=10.0, |
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| 105 | thick_face=10.0, |
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[8007311] | 106 | length=400.0, |
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[aad336c] | 107 | sld_core=1.0, |
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| 108 | sld_face=4.0, |
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| 109 | sld_rim=4.0, |
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| 110 | sld_solvent=1.0, |
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[8007311] | 111 | theta=90, |
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| 112 | phi=0) |
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| 113 | |
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| 114 | qx, qy = 0.4 * cos(90), 0.5 * sin(0) |
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| 115 | tests = [ |
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| 116 | # Accuracy tests based on content in test/utest_other_models.py |
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| 117 | [{'radius': 20.0, |
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[2222134] | 118 | 'thick_rim': 10.0, |
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| 119 | 'thick_face': 10.0, |
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[8007311] | 120 | 'length': 400.0, |
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[aad336c] | 121 | 'sld_core': 1.0, |
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| 122 | 'sld_face': 4.0, |
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| 123 | 'sld_rim': 4.0, |
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| 124 | 'sld_solvent': 1.0, |
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[8007311] | 125 | 'background': 0.0, |
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| 126 | }, 0.001, 353.550], |
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| 127 | |
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| 128 | [{'radius': 20.0, |
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[2222134] | 129 | 'thick_rim': 10.0, |
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| 130 | 'thick_face': 10.0, |
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[8007311] | 131 | 'length': 400.0, |
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[aad336c] | 132 | 'sld_core': 1.0, |
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| 133 | 'sld_face': 4.0, |
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| 134 | 'sld_rim': 4.0, |
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| 135 | 'sld_solvent': 1.0, |
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[8007311] | 136 | 'theta': 90.0, |
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| 137 | 'phi': 0.0, |
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| 138 | 'background': 0.00, |
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| 139 | }, (qx, qy), 24.9167], |
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| 140 | |
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| 141 | # Additional tests with larger range of parameters |
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| 142 | [{'radius': 3.0, |
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[2222134] | 143 | 'thick_rim': 100.0, |
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| 144 | 'thick_face': 100.0, |
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[8007311] | 145 | 'length': 1200.0, |
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[aad336c] | 146 | 'sld_core': 5.0, |
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| 147 | 'sld_face': 41.0, |
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| 148 | 'sld_rim': 42.0, |
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| 149 | 'sld_solvent': 21.0, |
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[8007311] | 150 | }, 0.05, 1670.1828], |
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| 151 | ] |
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