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src/sans/models/media/model_functions.rst (modified) (56 diffs)
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src/sans/models/media/model_functions.rst
r4ed2d0a1 r58eccf6 1 1 .. model_functions.rst 2 3 .. NB: This document does not have M Gonzalez's model descriptions in it. 2 4 3 5 .. This is a port of the original SasView model_functions.html to ReSTructured text … … 32 34 .. |psi| unicode:: U+03C8 33 35 .. |omega| unicode:: U+03C9 34 35 36 .. |bigdelta| unicode:: U+0394 36 37 .. |biggamma| unicode:: U+0393 37 38 .. |bigpsi| unicode:: U+03A8 38 39 39 .. |drho| replace:: |bigdelta|\ |rho| 40 41 40 .. |Ang| unicode:: U+212B 42 41 .. |Ang^-1| replace:: |Ang|\ :sup:`-1` … … 44 43 .. |Ang^-2| replace:: |Ang|\ :sup:`-2` 45 44 .. |Ang^3| replace:: |Ang|\ :sup:`3` 45 .. |Ang^-3| replace:: |Ang|\ :sup:`-3` 46 .. |Ang^-4| replace:: |Ang|\ :sup:`-4` 46 47 .. |cm^-1| replace:: cm\ :sup:`-1` 47 48 .. |cm^2| replace:: cm\ :sup:`2` … … 50 51 .. |cm^-3| replace:: cm\ :sup:`-3` 51 52 .. |sr^-1| replace:: sr\ :sup:`-1` 52 53 53 .. |P0| replace:: P\ :sub:`0`\ 54 54 .. |A2| replace:: A\ :sub:`2`\ … … 1217 1217 1218 1218 and |alpha| is the angle between the axis of the cylinder and the *q*-vector, *V* is the volume of the cylinder, 1219 *L* is the length of the cylinder, *r* is the radius of the cylinder, and | bigdelta|\ |rho| (contrast) is the1219 *L* is the length of the cylinder, *r* is the radius of the cylinder, and |drho| (contrast) is the 1220 1220 scattering length density difference between the scatterer and the solvent. *J1* is the first order Bessel function. 1221 1221 … … 2074 2074 |alpha| is the angle between the axis of the ellipsoid and the *q*\ -vector, *V* is the volume of the ellipsoid, *Ra* 2075 2075 is the radius along the rotational axis of the ellipsoid, *Rb* is the radius perpendicular to the rotational axis of 2076 the ellipsoid and | bigdelta|\ |rho| (contrast) is the scattering length density difference between the scatterer and2076 the ellipsoid and |drho| (contrast) is the scattering length density difference between the scatterer and 2077 2077 the solvent. 2078 2078 … … 2421 2421 2422 2422 where |delta|\ T = tail length (or *t_length*), |delta|\ H = head thickness (or *h_thickness*), 2423 | bigdelta|\ |rho|\ H = SLD(headgroup) - SLD(solvent), and |bigdelta|\ |rho|\ T = SLD(tail) - SLD(solvent).2423 |drho|\ H = SLD(headgroup) - SLD(solvent), and |drho|\ T = SLD(tail) - SLD(solvent). 2424 2424 2425 2425 The 2D scattering intensity is calculated in the same way as 1D, where the *q* vector is defined as … … 2484 2484 .. image:: img/image141.PNG 2485 2485 2486 Here *d* = (repeat) spacing, |delta| = bilayer thickness, the contrast | bigdelta|\ |rho| = SLD(headgroup) - SLD(solvent),2486 Here *d* = (repeat) spacing, |delta| = bilayer thickness, the contrast |drho| = SLD(headgroup) - SLD(solvent), 2487 2487 K = smectic bending elasticity, B = compression modulus, and N = number of lamellar plates (*n_plates*). 2488 2488 … … 2551 2551 2552 2552 where |delta|\ T = tail length (or *t_length*), |delta|\ H = head thickness (or *h_thickness*), 2553 | bigdelta|\ |rho|\ H = SLD(headgroup) - SLD(solvent), and |bigdelta|\ |rho|\ T = SLD(tail) - SLD(headgroup).2553 |drho|\ H = SLD(headgroup) - SLD(solvent), and |drho|\ T = SLD(tail) - SLD(headgroup). 2554 2554 Here *d* = (repeat) spacing, *K* = smectic bending elasticity, *B* = compression modulus, and N = number of lamellar 2555 2555 plates (*n_plates*). … … 3124 3124 .. _Debye: 3125 3125 3126 **2.2.1. Debye ( Model)**3126 **2.2.1. Debye (Gaussian Coil Model)** 3127 3127 3128 3128 The Debye model is a form factor for a linear polymer chain. In addition … … 3138 3138 ============== ======== ============= 3139 3139 Parameter name Units Default value 3140 3141 ============== ======== ============= 3142 | scale None 1.0 3143 3144 | rg Ã⊠50.0 3145 3146 | background | cm-1 0.0 3140 ============== ======== ============= 3141 scale None 1.0 3142 rg |Ang| 50.0 3143 background |cm^-1| 0.0 3147 3144 ============== ======== ============= 3148 3145 … … 3160 3157 .. _BroadPeakModel: 3161 3158 3162 **2.2.2. BroadPeak 3159 **2.2.2. BroadPeakModel** 3163 3160 3164 3161 Calculate an empirical functional form for SANS data characterized by a … … 3183 3180 .. image:: img/image040.GIF 3184 3181 3185 ============== ======== ============= 3186 Parameter name Units Default value 3187 ============== ======== ============= 3188 | scale\_l (= C) |  10 3189 3190 | scale\_p (=A) |  1e-05 3191 3192 | length\_l (=x) | Ã⊠50 3193 3194 | q\_peak (= Q0) | ÃâŠ-1 0.1 3195 3196 | exponent\_p (=n) |  2 3197 3198 | exponent\_l (=m) |  3 3199 3200 | Background (=B) | cm-1 0.1 3201 ============== ======== ============= 3182 =============== ======== ============= 3183 Parameter name Units Default value 3184 =============== ======== ============= 3185 scale_l (=C) None 10 3186 scale_p (=A) None 1e-05 3187 length_l (=x) |Ang| 50 3188 q_peak (=Q0) |Ang^-1| 0.1 3189 exponent_p (=n) None 2 3190 exponent_l (=m) None 3 3191 Background (=B) |cm^-1| 0.1 3192 =============== ======== ============= 3202 3193 3203 3194 .. image:: img/image175.JPG … … 3215 3206 .. _CorrLength: 3216 3207 3217 **2.2.3. CorrLength (Correlation LengthModel)**3208 **2.2.3. CorrLength (Correlation Length Model)** 3218 3209 3219 3210 Calculate an empirical functional form for SANS data characterized by a … … 3239 3230 .. image:: img/image040.GIF 3240 3231 3241 ============== ======== ============= 3242 Parameter name Units Default value 3243 ============== ======== ============= 3244 | scale\_l (= C) |  10 3245 3246 | scale\_p (=A) |  1e-06 3247 3248 | length\_l (=x) | Ã⊠50 3249 3250 | exponent\_p (=n) |  2 3251 3252 | exponent\_l (=m) |  3 3253 3254 | Background (=B) | cm-1 0.1 3255 ============== ======== ============= 3232 =============== ======== ============= 3233 Parameter name Units Default value 3234 =============== ======== ============= 3235 scale_l (=C) None  10 3236 scale_p (=A) None  1e-06 3237 length_l (=x) |Ang| 50 3238 exponent_p (=n) None  2 3239 exponent_l (=m) None 3 3240 Background (=B) |cm^-1| 0.1 3241 =============== ======== ============= 3256 3242 3257 3243 .. image:: img/image177.JPG … … 3270 3256 .. _Lorentz: 3271 3257 3272 **2.2.4. (Ornstein-Zernicke) Lorentz (Model)**3258 **2.2.4. Lorentz (Ornstein-Zernicke Model)** 3273 3259 3274 3260 The Ornstein-Zernicke model is defined by: … … 3285 3271 Parameter name Units Default value 3286 3272 ============== ======== ============= 3287 | scale None 1.0 3288 3289 | length Ã⊠50.0 3290 3291 | background | cm-1 0.0 3273 scale None 1.0 3274 length |Ang| 50.0 3275 background |cm^-1| 0.0 3292 3276 ============== ======== ============= 3293 3277 … … 3300 3284 .. _DABModel: 3301 3285 3302 **2.2.5. DAB (Debye-Anderson-Brumberger) Model**3286 **2.2.5. DABModel (Debye-Anderson-Brumberger Model)** 3303 3287 3304 3288 Calculates the scattering from a randomly distributed, two-phase system … … 3321 3305 Parameter name Units Default value 3322 3306 ============== ======== ============= 3323 | scale None 1.0 3324 3325 | length Ã⊠50.0 3326 3327 | background | cm-1 0.0 3307 scale None 1.0 3308 length |Ang| 50.0 3309 background |cm^-1| 0.0 3328 3310 ============== ======== ============= 3329 3311 … … 3347 3329 .. _AbsolutePower_Law: 3348 3330 3349 **2.2.6. Absolute Power\_Law**3331 **2.2.6. AbsolutePower_Law** 3350 3332 3351 3333 This model describes a power law with background. … … 3358 3340 Parameter name Units Default value 3359 3341 ============== ======== ============= 3360 | Scale None 1.0 3361 3362 | m None 4 3363 3364 | Background | cm-1 0.0 3342 Scale None 1.0 3343 m None 4 3344 Background |cm^-1| 0.0 3365 3345 ============== ======== ============= 3366 3346 … … 3387 3367 Parameter name Units Default value 3388 3368 ============== ======== ============= 3389 | scale None 0.1 3390 3391 | c1 None -30.0 3392 3393 | c2 None 5000.0 3394 3395 | background | cm-1 0.0 3369 scale None 0.1 3370 c1 None -30.0 3371 c2 None 5000.0 3372 background |cm^-1| 0.0 3396 3373 ============== ======== ============= 3397 3374 … … 3411 3388 .. _FractalModel: 3412 3389 3413 **2.2.8. 3390 **2.2.8. FractalModel** 3414 3391 3415 3392 Calculates the scattering from fractal-like aggregates built from … … 3434 3411 Parameter name Units Default value 3435 3412 ============== ======== ============= 3436 | scale None 0.05 3437 3438 | radius Ã⊠5.0 3439 3440 | fractal\_dim | None 2 3441 3442 | corr\_length | Ã⊠100.0 3443 3444 | block\_sld | ÃâŠ-2 2e-6 3445 3446 | solvent\_sld | ÃâŠ-2 6e-6 3447 3448 | background | cm-1 0.0 3413 scale None 0.05 3414 radius |Ang| 5.0 3415 fractal_dim None 2 3416 corr_length |Ang| 100.0 3417 block_sld |Ang^-2| 2e-6 3418 solvent_sld |Ang^-2| 6e-6 3419 background |cm^-1| 0.0 3449 3420 ============== ======== ============= 3450 3421 … … 3473 3444 scattering length density of particles. 3474 3445 3475 Note:  The mass fractal dimension is valid for 1<mass\_dim<6. 3476 3477 ============== ======== ============= 3478 Parameter name Units Default value 3479 ============== ======== ============= 3480 | scale None 1 3481 3482 | radius Ã⊠10.0 3483 3484 | mass\_dim | None 1.9 3485 3486 | co\_length | Ã⊠100.0 3487 3488 | background |  0.0 3446 Note:  The mass fractal dimension is valid for 1<mass_dim<6. 3447 3448 ============== ======== ============= 3449 Parameter name Units Default value 3450 ============== ======== ============= 3451 scale None 1 3452 radius |Ang| 10.0 3453 mass_dim None 1.9 3454 co_length |Ang| 100.0 3455 background |cm^-1| 0.0 3489 3456 ============== ======== ============= 3490 3457 … … 3515 3482 scattering length density of particles. 3516 3483 3517  Note:  The surface fractal dimension is valid for 1<surface \_dim<3.3484  Note:  The surface fractal dimension is valid for 1<surface_dim<3. 3518 3485  Also it is valid in a limited q range (see the reference for details). 3519 3486 … … 3521 3488 Parameter name Units Default value 3522 3489 ============== ======== ============= 3523 | scale None 1 3524 3525 | radius Ã⊠10.0 3526 3527 | surface\_dim | None 2.0 3528 3529 | co\_length | Ã⊠500.0 3530 3531 | background |  0.0 3490 scale None 1 3491 radius |Ang| 10.0 3492 surface_dim None 2.0 3493 co_length |Ang| 500.0 3494 background |cm^-1| 0.0 3532 3495 ============== ======== ============= 3533 3496 … … 3545 3508 .. _MassSurfaceFractal: 3546 3509 3547 **2.2.11. MassSurfaceFractal **3510 **2.2.11. MassSurfaceFractal (Model)** 3548 3511 3549 3512 A number of natural and commercial processes form high-surface area … … 3572 3535 3573 3536  Note:  The surface and mass fractal dimensions are valid for 3574 0<surface\_dim<6, 0<mass\_dim<6, and (surface\_mass+mass\_dim)<6. 3575 3576 ============== ======== ============= 3577 Parameter name Units Default value 3578 ============== ======== ============= 3579 | scale None 1 3580 3581 | primary\_rg | Ã⊠4000.0 3582 3583 |  cluster\_rg |  Ã⊠ 86.7 3584 3585 | surface\_dim | None 2.3 3586 3587 |  mass\_dim |  None  1.8 3588 3589 | background |  0.0 3537 0<surface_dim<6, 0<mass_dim<6, and (surface_mass+mass_dim)<6. 3538 3539 ============== ======== ============= 3540 Parameter name Units Default value 3541 ============== ======== ============= 3542 scale None 1 3543 primary_rg |Ang| 4000.0 3544 cluster_rg |Ang|  86.7 3545 surface_dim None 2.3 3546 mass_dim None  1.8 3547 background |cm^-1|  0.0 3590 3548 ============== ======== ============= 3591 3549 … … 3604 3562 .. _FractalCoreShell: 3605 3563 3606 **2.2.12. FractalCoreShell(Model)**3564 **2.2.12. FractalCoreShell (Model)** 3607 3565 3608 3566 Calculates the scattering from a fractal structure with a primary … … 3620 3578 .. image:: img/fractcore_eq3.gif 3621 3579 3622 where Df = frac \_dim, ß = cor\_length, rc = (core) radius, and scale3580 where Df = frac_dim, ß = cor_length, rc = (core) radius, and scale 3623 3581 = volfraction. 3624 3582 … … 3639 3597 Parameter name Units Default value 3640 3598 ============== ======== ============= 3641 | volfraction |  0.05 3642 3643 | frac\_dim |  2 3644 3645 | thickness | Ã⊠5.0 3646 3647 | raidus  Ã⊠20.0 3648 3649 | cor\_length | Ã⊠100.0 3650 3651 | core\_sld | ÃâŠ-2 3.5e-6 3652 3653 | shell\_sld | ÃâŠ-2 1e-6 3654 3655 | solvent\_sld | ÃâŠ-2 6.35e-6 3656 3657 | background | cm-1 0.0 3599 volfraction None  0.05 3600 frac_dim None  2 3601 thickness |Ang| 5.0 3602 radius  |Ang| 20.0 3603 cor_length |Ang| 100.0 3604 core_sld |Ang^-2| 3.5e-6 3605 shell_sld |Ang^-2| 1e-6 3606 solvent_sld |Ang^-2| 6.35e-6 3607 background |cm^-1| 0.0 3658 3608 ============== ======== ============= 3659 3609 … … 3670 3620 .. _GaussLorentzGel: 3671 3621 3672 **2.2.13. 3622 **2.2.13. GaussLorentzGel(Model)** 3673 3623 3674 3624 Calculates the scattering from a gel structure, typically a physical … … 3699 3649 .. image:: img/image040.GIF 3700 3650 3701 ============== ======== ============= 3702 Parameter name Units Default value 3703 ============== ======== ============= 3704 | dyn\_colength(=Dynamic | Ã⊠20.0 3705 | correlation length) | 3706 3707 | scale\_g(=Gauss scale |  100 3708 | factor) 3709 3710 | scale\_l(=Lorentzian |  50 3711 | scale factor) | 3712 3713 | stat\_colength(=Static | Ã⊠100.0 3714 | correlation Z) | 3715 3716 | background | cm-1 0.0 3717 ============== ======== ============= 3651 =================================== ======== ============= 3652 Parameter name Units Default value 3653 =================================== ======== ============= 3654 dyn_colength (=dynamic corr length) |Ang| 20.0 3655 scale_g (=Gauss scale factor) None  100 3656 scale_l (=Lorentzian scale factor) None 50 3657 stat_colength (=static corr length) |Ang| 100.0 3658 background |cm^-1| 0.0 3659 =================================== ======== ============= 3718 3660 3719 3661 .. image:: img/image190.JPG … … 3730 3672 .. _BEPolyelectrolyte: 3731 3673 3732 **2.2.14. BEPolyelectrolyte Model**3674 **2.2.14. BEPolyelectrolyte (Model)** 3733 3675 3734 3676 Calculates the structure factor of a polyelectrolyte solution with the … … 3750 3692 Parameter name Units Default value 3751 3693 ============== ======== ============= 3752 | K Barns = 10-24 cm2 | 10 3753 3754 | Lb Ã⊠7.1 3755 3756 | h ÃâŠ-3 12 3757 3758 | b Ã⊠10 3759 3760 | Cs Mol/L 0 3761 3762 | alpha None 0.05 3763 3764 | Ca Mol/L 0.7 3765 3766 | background | cm-1 0.0 3767 ============== ======== ============= 3694 K barns 10 3695 Lb |Ang| 7.1 3696 h |Ang^-3| 12 3697 b |Ang| 10 3698 Cs mol/L 0 3699 alpha None 0.05 3700 Ca mol/L 0.7 3701 background |cm^-1| 0.0 3702 ============== ======== ============= 3703 3704 NB: 1 barn = 10\ :sup:`-24` |cm^2| 3768 3705 3769 3706 REFERENCE … … 3797 3734 Parameter name Units Default value 3798 3735 ============== ======== ============= 3799 | scale cm-1 1.0 3800 3801 | Rg Ã⊠0.1 3736 scale |cm^-1| 1.0 3737 Rg |Ang| 0.1 3802 3738 ============== ======== ============= 3803 3739 … … 3863 3799 .. image:: img/image008.PNG 3864 3800 3865 ============== ======== ============= 3866 Parameter name Units Default value 3867 ============== ======== ============= 3868 | Scale(=Guinier scale, | cm-1 1.0 3869 | G) 3870 3871 | rg Ã⊠100 3872 3873 | dim(=Dimensional |  1 3874 | Variable, s) | 3875 3876 | m(=Porod exponent) |  3 3877 3878 | background |  0.1 3879 ============== ======== ============= 3801 ============================== ======== ============= 3802 Parameter name Units Default value 3803 ============================== ======== ============= 3804 scale (=Guinier scale, G) |cm^-1| 1.0 3805 rg |Ang| 100 3806 dim (=dimensional variable, s) None  1 3807 m (=Porod exponent) None  3 3808 background |cm^-1| 0.1 3809 ============================== ======== ============= 3880 3810 3881 3811 .. image:: img/image196.JPG … … 3907 3837 Parameter name Units Default value 3908 3838 ============== ======== ============= 3909 | scale ÃâŠ-4 0.1 3910 3911 | background | cm-1 0 3839 scale |Ang^-4| 0.1 3840 background |cm^-1| 0 3912 3841 ============== ======== ============= 3913 3842 … … 3925 3854 deviation of B. The fwhm is 2.354\*B.  3926 3855 3927 Parameters I0, B, qpk, and BGD can all be adjusted during fitting. 3856 Parameters I0, B, qpk, and BGD can all be adjusted during fitting. **NB: These don't match the table!** 3928 3857 3929 3858 REFERENCE … … 3938 3867 Parameter name Units Default value 3939 3868 ============== ======== ============= 3940 | scale cm-1 100 3941 3942 | q0 Ã⊠0.05 3943 3944 | B  0.005 3945 3946 | background |  1 3869 scale |cm^-1| 100 3870 q0 |Ang^-1| 0.05 3871 B  |Ang^-1| 0.005 3872 background |cm^-1| 1 3947 3873 ============== ======== ============= 3948 3874 … … 3964 3890 (half-width-half-maximum) of B. 3965 3891 3966 The parameters I0, B, qpk, and BGD can all be adjusted during fitting. 3892 The parameters I0, B, qpk, and BGD can all be adjusted during fitting. **NB: These don't match the table!** 3967 3893 3968 3894 REFERENCE … … 3977 3903 Parameter name Units Default value 3978 3904 ============== ======== ============= 3979 | scale cm-1 100 3980 3981 | q0 Ã⊠0.05 3982 3983 | B  0.005 3984 3985 | background |  1 3905 scale |cm^-1| 100 3906 q0 |Ang^-1| 0.05 3907 B  |Ang^-1| 0.005 3908 background |cm^-1| 1 3986 3909 ============== ======== ============= 3987 3910 … … 4023 3946 TEST DATASET 4024 3947 4025  This example dataset is produced by running the Poly\_GaussCoil, using 4026 200 data points, qmin = 0.001 ÃâŠ-1, qmax = 0.7 ÃâŠ-1  and the default 4027 values below. 4028 4029 ============== ======== ============= 4030 Parameter name Units Default value 4031 ============== ======== ============= 4032 | Scale None 1.0 4033 4034 | rg Ã⊠60.0 4035 4036 | poly\_m Mw/Mn 2 4037 4038 | background | cm-1 0.001 3948 This example dataset is produced by running the Poly_GaussCoil, using 200 data points, *qmin* = 0.001 |Ang^-1|\ , 3949 qmax = 0.7 |Ang^-1| and the default values below. 3950 3951 ============== ======== ============= 3952 Parameter name Units Default value 3953 ============== ======== ============= 3954 scale None 1.0 3955 rg |Ang| 60.0 3956 poly_m (Mw/Mn) None 2 3957 background |cm^-1| 0.001 4039 3958 ============== ======== ============= 4040 3959 … … 4130 4049 TEST DATASET 4131 4050 4132  This example dataset is produced, using 200 data points, qmin = 0.001 4133 ÃâŠ-1, qmax = 0.2 ÃâŠ-1  and the default values below. 4134 4135 ============== ======== ============= 4136 Parameter name Units Default value 4137 ============== ======== ============= 4138 | Scale None 1.0 4139 4140 | rg Ã⊠60.0 4141 4142 | m(=Porod exponent) |  3 4143 4144 | background | cm-1 0.0 4145 ============== ======== ============= 4051 This example dataset is produced, using 200 data points, qmin = 0.001 |Ang^-1|\ , qmax = 0.2 |Ang^-1|  and the 4052 default values below. 4053 4054 =================== ======== ============= 4055 Parameter name Units Default value 4056 =================== ======== ============= 4057 scale None 1.0 4058 rg |Ang| 60.0 4059 m (=Porod exponent) None  3 4060 background |cm^-1| 0.0 4061 =================== ======== ============= 4146 4062 4147 4063 .. image:: img/image214.JPG … … 4210 4126 Fitting parameters for Case0 Model 4211 4127 4212 ============== ======== ============= 4213 Parameter name Units Default value 4214 ============== ======== ============= 4215 | background | cm-1 0.0 4216 4217 | scale  1 4218 4219 | bc(=Seg. Length bc) |  5 4220 4221 | bd(=Seg. Length bd) |  5 4222 4223 | Kcd(Chi Param. Kcd) |  -0.0004 4224 ============== ======== ============= 4128 ======================= ======== ============= 4129 Parameter name Units Default value 4130 ======================= ======== ============= 4131 background |cm^-1| 0.0 4132 scale  None 1 4133 bc (=segment Length_bc) **unit** 5 4134 bd (=segment length_bd) **unit** 5 4135 Kcd (=chi_cd) **unit** -0.0004 4136 ======================= ======== ============= 4225 4137 4226 4138 Fixed parameters for Case0 Model 4227 4139 4228 ============== ======== ============= 4229 Parameter name Units Default value 4230 ============== ======== ============= 4231 | Lc(= Scatter. |  1e-12 4232 | Length\_c) | 4233 4234 | Ld(= Scatter. |  0 4235 | Length\_d) | 4236 4237 | Nc(=Deg.Polym.c) |  1000 4238 4239 | Nd(=Deg.Polym.d) |  1000 4240 4241 | Phic(=Vol. fraction of |  0.25 4242 | c) 4243 4244 | Phid(=Vol. fraction of |  0.25 4245 | d) 4246 4247 | vc(=Spec. vol. of c) |  100 4248 4249 | vd(=Spec. vol. of d) |  100 4250 ============== ======== ============= 4140 ======================= ======== ============= 4141 Parameter name Units Default value 4142 ======================= ======== ============= 4143 Lc (=scatter. length_c) **unit** 1e-12 4144 Ld (=scatter. length_d) **unit** 0 4145 Nc (=degree polym_c) None 1000 4146 Nd (=degree polym_d) None  1000 4147 Phic (=vol. fraction_c) None  0.25 4148 Phid (=vol. fraction_d) None  0.25 4149 vc (=specific volume_c) **unit** 100 4150 vd (=specific volume_d) **unit** 100 4151 ======================= ======== ============= 4251 4152 4252 4153 .. image:: img/image215.JPG … … 4259 4160 .. _TwoLorentzian: 4260 4161 4261 **2.2.23. TwoLorentzian (Model)**4162 **2.2.23. TwoLorentzian (Model)** 4262 4163 4263 4164 Calculate an empirical functional form for SANS data characterized by a … … 4285 4186 **Default input parameter values** 4286 4187 4287 ============== ======== ============= 4288 Parameter name Units Default value 4289 ============== ======== ============= 4290 | scale\_1(=A) |  10 4291 4292 | scale\_2(=C) |  1 4293 4294 | 1ength\_1 (=Correlation | Ã⊠100 4295 | length1) | 4296 4297 | 1ength\_2(=Correlation | Ã⊠10 4298 | length2) | 4299 4300 | exponent\_1(=n) |  3 4301 4302 | exponent\_2(=m) |  2 4303 4304 | Background(=B) | cm-1 0.1 4305 ============== ======== ============= 4188 =============================== ======== ============= 4189 Parameter name Units Default value 4190 =============================== ======== ============= 4191 scale_1 (=A) None  10 4192 scale_2 (=C) None  1 4193 1ength_1 (=correlation length1) |Ang| 100 4194 1ength_2 (=correlation length2) |Ang| 10 4195 exponent_1 (=n) None  3 4196 exponent_2 (=m) None  2 4197 background (=B) |cm^-1| 0.1 4198 =============================== ======== ============= 4306 4199 4307 4200 .. image:: img/image217.JPG … … 4317 4210 .. _TwoPowerLaw: 4318 4211 4319 **2.2.24. TwoPowerLaw (Model)**4212 **2.2.24. TwoPowerLaw (Model)** 4320 4213 4321 4214 Calculate an empirical functional form for SANS data characterized by … … 4342 4235 Parameter name Units Default value 4343 4236 ============== ======== ============= 4344 | coef\_A  1.0 4345 4346 | qc ÃâŠ-1 0.04 4347 4348 | power\_1(=m1) |  4 4349 4350 | power\_2(=m2) |  4 4351 4352 | background | cm-1 0.0 4237 coef_A  None 1.0 4238 qc |Ang^-1| 0.04 4239 power_1 (=m1) None  4 4240 power_2 (=m2) None  4 4241 background |cm^-1| 0.0 4353 4242 ============== ======== ============= 4354 4243 … … 4361 4250 .. _UnifiedPowerRg: 4362 4251 4363 **2.2.25. UnifiedPower (Law and)Rg(Model)**4252 **2.2.25. UnifiedPowerRg (Beaucage Model)** 4364 4253 4365 4254 The returned value is scaled to units of |cm^-1|, absolute scale. … … 4397 4286 Parameter name Units Default value 4398 4287 ============== ======== ============= 4399 | scale  1.0 4400 4401 | Rg2 Ã⊠21 4402 4403 | power2  2 4404 4405 | G2 cm-1sr-1 | 3 4406 4407 | B2 cm-1sr-1 | 0.0006 4408 4409 | Rg1 Ã⊠15.8 4410 4411 | power1  4 4412 4413 | G1 cm-1sr-1 | 400 4414 4415 | B1 cm-1sr-1 | 4.5e-006 | 4416 4417 | background | cm-1 0.0 4288 scale  None 1.0 4289 Rg2 |Ang| 21 4290 power2  None 2 4291 G2 |cm^-1| 3 4292 B2 |cm^-1| 0.0006 4293 Rg1 |Ang| 15.8 4294 power1  None 4 4295 G1 |cm^-1| 400 4296 B1 |cm^-1| 4.5e-6 | 4297 background |cm^-1| 0.0 4418 4298 ============== ======== ============= 4419 4299 … … 4440 4320 where A and B are the coefficients of the first and second order terms. 4441 4321 4442 **Note:** For 2D plot, *I(q)* = I(qx)\*I(qy) which is defined differently4322 **Note:** For 2D plot, *I(q)* = *I(qx)* / *I(qy)* which is defined differently 4443 4323 from other shape independent models. 4444 4324 … … 4446 4326 Parameter name Units Default value 4447 4327 ============== ======== ============= 4448 | A cm-1 1.0 4449 4450 | B Ã⊠1.0 4328 A |cm^-1| 1.0 4329 B |Ang| 1.0 4451 4330 ============== ======== ============= 4452 4331 … … 4486 4365    Same as the ReflectivityModel except that the it is more 4487 4366 customizable. More interfacial functions are supplied. The number of 4488 points (npts \_inter) for each interface can be choosen.    The constant4367 points (npts_inter) for each interface can be choosen.    The constant 4489 4368 (A below but 'nu' as a parameter name of the model) for exp, erf, or 4490 4369 power-law is an input. The SLD at the interface between layers, 4491 *rinter \_i*, is calculated with a function chosen by a user, where the4370 *rinter_i*, is calculated with a function chosen by a user, where the 4492 4371 functions are: 4493 4372 … … 4537 4416 **Default input parameter values** 4538 4417 4539 ============== ======== ============= 4540 Parameter name Units Default value 4541 ============== ======== ============= 4542 | Background | cm-1 0.01 4543 4544 | Guinier scale | cm-1 1.7 4545 4546 | Lorentzian scale | cm-1 3.5 4547 4548 | Radius of gyration | Ã⊠104 4549 4550 | Fractal exponent |  2 4551 4552 | Correlation length | Ã⊠16 4553 ============== ======== ============= 4418 ================== ======== ============= 4419 Parameter name Units Default value 4420 ================== ======== ============= 4421 Background |cm^-1| 0.01 4422 Guinier scale |cm^-1| 1.7 4423 Lorentzian scale |cm^-1| 3.5 4424 Radius of gyration |Ang| 104 4425 Fractal exponent None  2 4426 Correlation length |Ang| 16 4427 ================== ======== ============= 4554 4428 4555 4429 .. image:: img/image235.GIF
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