Changeset 1127c32 in sasview


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Timestamp:
Apr 15, 2014 10:08:31 AM (10 years ago)
Author:
smk78
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, costrafo411, magnetic_scatt, release-4.1.1, release-4.1.2, release-4.2.2, release_4.0.1, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, ticket885, unittest-saveload
Children:
d4117ccb
Parents:
bf8c07b
Message:

More updates by SMK

File:
1 edited

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  • src/sans/models/media/model_functions.rst

    rbf8c07b r1127c32  
    186186-------- 
    187187 
    188 - LamellarModel 
    189 - LamellarFFHGModel 
    190 - LamellarPSModel 
    191 - LamellarPSHGModel 
     188- LamellarModel_ 
     189- LamellarFFHGModel_ 
     190- LamellarPSModel_ 
     191- LamellarPSHGModel_ 
    192192 
    193193Paracrystals 
    194194------------ 
    195195 
    196 - LamellarPCrystalModel 
     196- LamellarPCrystalModel_ 
    197197- SCCrystalModel 
    198198- FCCrystalModel 
    … …  
    23562356**2.1.29. LamellarModel** 
    23572357 
    2358 This model provides the scattering intensity, I( *q*), for a lyotropic 
    2359 lamellar phase where a uniform SLD and random distribution in solution 
    2360 are assumed. The ploydispersion in the bilayer thickness can be 
    2361 applied from the GUI. 
    2362  
    2363 The scattering intensity I(q) is: 
    2364  
    2365  
    2366  
    2367 The form factor is, 
    2368  
    2369  
    2370  
    2371 where d = bilayer thickness. 
    2372  
    2373 The 2D scattering intensity is calculated in the same way as 1D, where 
    2374 the *q* vector is defined as . 
    2375  
    2376  
    2377  
    2378 The returned value is in units of |cm^-1|, on absolute scale. In the 
    2379 parameters, sld_bi = SLD of the bilayer, sld_sol = SLD of the solvent, 
    2380 and bi_thick = the thickness of the bilayer. 
     2358This model provides the scattering intensity, *I(q)*, for a lyotropic lamellar phase where a uniform SLD and random 
     2359distribution in solution are assumed. Polydispersity in the bilayer thickness can be applied from the GUI. 
     2360 
     2361*2.1.29.1. Definition* 
     2362 
     2363The scattering intensity *I(q)* is 
     2364 
     2365.. image:: img/image133.PNG 
     2366 
     2367The form factor is 
     2368 
     2369.. image:: img/image134.PNG 
     2370 
     2371where |delta| = bilayer thickness. 
     2372 
     2373The 2D scattering intensity is calculated in the same way as 1D, where the *q* vector is defined as 
     2374 
     2375.. image:: img/image040.GIF 
     2376 
     2377The returned value is in units of |cm^-1|, on absolute scale. In the parameters, *sld_bi* = SLD of the bilayer, 
     2378*sld_sol* = SLD of the solvent, and *bi_thick* = thickness of the bilayer. 
    23812379 
    23822380==============  ========  ============= 
    … …  
    23902388==============  ========  ============= 
    23912389 
    2392  
     2390.. image:: img/image135.JPG 
    23932391 
    23942392*Figure. 1D plot using the default values (w/1000 data point).* 
    23952393 
    2396 Our model uses the form factor calculations implemented in a c-library 
    2397 provided by the NIST Center for Neutron Research (Kline, 2006): 
     2394Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research 
     2395(Kline, 2006). 
    23982396 
    23992397REFERENCE 
    … …  
    24092407**2.1.30. LamellarFFHGModel** 
    24102408 
    2411 This model provides the scattering intensity, I( *q*), for a lyotropic 
    2412 lamellar phase where a random distribution in solution are assumed. 
    2413 The SLD of the head region is taken to be different from the SLD of 
    2414 the tail region. 
    2415  
    2416 The scattering intensity I(q) is: 
    2417  
    2418  
    2419  
    2420 The form factor is, 
    2421  
    2422  
    2423  
    2424 where dT = tail length (or t_length), dH = heasd thickness (or 
    2425 h_thickness) , DrH = SLD (headgroup) - SLD(solvent), and DrT = SLD 
    2426 (tail) - SLD(headgroup). 
    2427  
    2428 The 2D scattering intensity is calculated in the same way as 1D, where 
    2429 the *q* vector is defined as . 
    2430  
    2431  
    2432  
    2433 The returned value is in units of |cm^-1|, on absolute scale. In the 
    2434 parameters, sld_tail = SLD of the tail group, and sld_head = SLD of 
    2435 the head group. 
     2409This model provides the scattering intensity, *I(q)*, for a lyotropic lamellar phase where a random distribution in 
     2410solution are assumed. The SLD of the head region is taken to be different from the SLD of the tail region. 
     2411 
     2412*2.1.31.1. Definition* 
     2413 
     2414The scattering intensity *I(q)* is 
     2415 
     2416.. image:: img/image136.PNG 
     2417 
     2418The form factor is 
     2419 
     2420.. image:: img/image137.JPG 
     2421 
     2422where |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(headgroup). 
     2424 
     2425The 2D scattering intensity is calculated in the same way as 1D, where the *q* vector is defined as 
     2426 
     2427.. image:: img/image040.GIF 
     2428 
     2429The returned value is in units of |cm^-1|, on absolute scale. In the parameters, *sld_tail* = SLD of the tail group, 
     2430and *sld_head* = SLD of the head group. 
    24362431 
    24372432==============  ========  ============= 
    … …  
    24472442==============  ========  ============= 
    24482443 
    2449  
     2444.. image:: img/image138.JPG 
    24502445 
    24512446*Figure. 1D plot using the default values (w/1000 data point).* 
    24522447 
    2453 Our model uses the form factor calculations implemented in a c-library 
    2454 provided by the NIST Center for Neutron Research (Kline, 2006): 
     2448Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research 
     2449(Kline, 2006). 
    24552450 
    24562451REFERENCE 
    … …  
    24662461**2.1.31. LamellarPSModel** 
    24672462 
    2468 This model provides the scattering intensity ( *form factor* \* 
    2469 *structure factor*), I( *q*), for a lyotropic lamellar phase where a 
    2470 random distribution in solution are assumed. 
    2471  
    2472 The scattering intensity I(q) is: 
    2473  
    2474  
     2463This model provides the scattering intensity, *I(q)* = *P(q)* \* *S(q)*, for a lyotropic lamellar phase where a random 
     2464distribution in solution are assumed. 
     2465 
     2466*2.1.31.1. Definition* 
     2467 
     2468The scattering intensity *I(q)* is 
     2469 
     2470.. image:: img/image139.PNG 
    24752471 
    24762472The form factor is 
    24772473 
    2478  
    2479  
    2480 and the structure is 
    2481  
    2482  
     2474.. image:: img/image134.PNG 
     2475 
     2476and the structure factor is 
     2477 
     2478.. image:: img/image140.PNG 
    24832479 
    24842480where 
    24852481 
    2486  
    2487  
    2488  
    2489  
    2490  
    2491  
    2492 Here d= (repeat) spacing, d = bilayer thickness, the contrast Dr = SLD 
    2493 (headgroup) - SLD(solvent), K=smectic bending elasticity, 
    2494 B=compression modulus, and N = number of lamellar plates (n_plates). 
    2495  
    2496 NB: When the Caille parameter is greater than approximately 0.8 to 
    2497 1.0, the assumptions of the model are incorrect. And due to the 
    2498 complication of the model function, users are responsible to make sure 
    2499 that all the assumptions are handled accurately: see the original 
    2500 reference (below) for more details. 
    2501  
    2502 The 2D scattering intensity is calculated in the same way as 1D, where 
    2503 the *q* vector is defined as . 
     2482.. image:: img/image141.PNG 
     2483 
     2484Here *d* = (repeat) spacing, |delta| = bilayer thickness, the contrast |bigdelta|\ |rho| = SLD(headgroup) - SLD(solvent), 
     2485K = smectic bending elasticity, B = compression modulus, and N = number of lamellar plates (*n_plates*). 
     2486 
     2487NB: **When the Caille parameter is greater than approximately 0.8 to 1.0, the assumptions of the model are incorrect.** 
     2488And due to a complication of the model function, users are responsible for making sure that all the assumptions are 
     2489handled accurately (see the original reference below for more details). 
     2490 
     2491The 2D scattering intensity is calculated in the same way as 1D, where the *q* vector is defined as 
     2492 
     2493.. image:: img/image040.GIF 
    25042494 
    25052495The returned value is in units of |cm^-1|, on absolute scale. 
    … …  
    25172507==============  ========  ============= 
    25182508 
    2519  
     2509.. image:: img/image142.JPG 
    25202510 
    25212511*Figure. 1D plot using the default values (w/6000 data point).* 
    25222512 
    2523 Our model uses the form factor calculations implemented in a c-library 
    2524 provided by the NIST Center for Neutron Research (Kline, 2006): 
     2513Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research 
     2514(Kline, 2006). 
    25252515 
    25262516REFERENCE 
    … …  
    25362526**2.1.32. LamellarPSHGModel** 
    25372527 
    2538 This model provides the scattering intensity ( *form factor* \* 
    2539 *structure factor*), I( *q*), for a lyotropic lamellar phase where a 
    2540 random distribution in solution are assumed. The SLD of the head 
    2541 region is taken to be different from the SLD of the tail region. 
    2542  
    2543 The scattering intensity I(q) is: 
    2544  
    2545  
    2546  
    2547 The form factor is, 
    2548  
    2549  
     2528This model provides the scattering intensity, *I(q)* = *P(q)* \* *S(q)*, for a lyotropic lamellar phase where a random 
     2529distribution in solution are assumed. The SLD of the head region is taken to be different from the SLD of the tail 
     2530region. 
     2531 
     2532*2.1.32.1. Definition* 
     2533 
     2534The scattering intensity *I(q)* is 
     2535 
     2536.. image:: img/image139.PNG 
     2537 
     2538The form factor is 
     2539 
     2540.. image:: img/image143.PNG 
    25502541 
    25512542The structure factor is 
    25522543 
    2553  
     2544.. image:: img/image140.PNG 
    25542545 
    25552546where 
    25562547 
    2557  
    2558  
    2559  
    2560  
    2561  
    2562  
    2563 where dT = tail length (or t_length), dH = heasd thickness (or 
    2564 h_thickness) , DrH = SLD (headgroup) - SLD(solvent), and DrT = SLD 
    2565 (tail) - SLD(headgroup). Here d= (repeat) spacing, K=smectic bending 
    2566 elasticity, B=compression modulus, and N = number of lamellar plates 
    2567 (n_plates). 
    2568  
    2569 NB: When the Caille parameter is greater than approximately 0.8 to 
    2570 1.0, the assumptions of the model are incorrect. And due to the 
    2571 complication of the model function, users are responsible to make sure 
    2572 that all the assumptions are handled accurately: see the original 
    2573 reference (below) for more details. 
    2574  
    2575 The 2D scattering intensity is calculated in the same way as 1D, where 
    2576 the *q* vector is defined as . 
    2577  
    2578  
    2579  
    2580 The returned value is in units of |cm^-1|, on absolute scale. In the 
    2581 parameters, sld_tail = SLD of the tail group, sld_head = SLD of the 
    2582 head group, and sld_solvent = SLD of the solvent. 
     2548.. image:: img/image141.PNG 
     2549 
     2550where |delta|\ T = tail length (or *t_length*), |delta|\ H = head thickness (or *h_thickness*), 
     2551|bigdelta|\ |rho|\ H = SLD(headgroup) - SLD(solvent), and |bigdelta|\ |rho|\ T = SLD(tail) - SLD(headgroup). 
     2552Here *d* = (repeat) spacing, *K* = smectic bending elasticity, *B* = compression modulus, and N = number of lamellar 
     2553plates (*n_plates*). 
     2554 
     2555NB: **When the Caille parameter is greater than approximately 0.8 to 1.0, the assumptions of the model are incorrect.** 
     2556And due to a complication of the model function, users are responsible for making sure that all the assumptions are 
     2557handled accurately (see the original reference below for more details). 
     2558 
     2559The 2D scattering intensity is calculated in the same way as 1D, where the *q* vector is defined as 
     2560 
     2561.. image:: img/image040.GIF 
     2562 
     2563The returned value is in units of |cm^-1|, on absolute scale. In the parameters, *sld_tail* = SLD of the tail group, 
     2564*sld_head* = SLD of the head group, and *sld_solvent* = SLD of the solvent. 
    25832565 
    25842566==============  ========  ============= 
    … …  
    25972579==============  ========  ============= 
    25982580 
    2599  
    2600  
     2581.. image:: img/image144.JPG 
    26012582 
    26022583*Figure. 1D plot using the default values (w/6000 data point).* 
    26032584 
    2604 Our model uses the form factor calculations implemented in a c-library 
    2605 provided by the NIST Center for Neutron Research (Kline, 2006): 
     2585Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research 
     2586(Kline, 2006). 
    26062587 
    26072588REFERENCE 
    … …  
    26172598**2.1.33. LamellarPCrystalModel** 
    26182599 
    2619 Lamella ParaCrystal Model: Calculates the scattering from a stack of 
    2620 repeating lamellar structures. The stacks of lamellae (infinite in 
    2621 lateral dimension) are treated as a paracrystal to account for the 
    2622 repeating spacing. The repeat distance is further characterized by a 
    2623 Gaussian polydispersity. This model can be used for large 
    2624 multilamellar vesicles. 
    2625  
    2626 The scattering intensity I(q) is calculated as: 
    2627  
    2628  
    2629  
    2630 The form factor of the bilayer is approximated as the cross section of 
    2631 an infinite, planar bilayer of thickness t. 
    2632  
    2633  
    2634  
    2635 Here, the scale factor is used instead of the mass per area of the 
    2636 bilayer (G). The scale factor is the volume fraction of the material 
    2637 in the bilayer, not the total excluded volume of the paracrystal. 
    2638 ZN(q) describes the interference effects for aggregates consisting of 
    2639 more than one bilayer. The equations used are (3-5) from the Bergstrom 
    2640 reference below. 
    2641  
    2642 Non-integer numbers of stacks are calculated as a linear combination 
    2643 of the lower and higher values: 
    2644  
    2645  
    2646  
    2647 The 2D scattering intensity is the same as 1D, regardless of the 
    2648 orientation of the *q* vector which is defined as . 
    2649  
    2650 The parameters of the model are the following (Nlayers= no. of layers, 
    2651 pd_spacing= polydispersity of spacing): 
     2600This model calculates the scattering from a stack of repeating lamellar structures. The stacks of lamellae (infinite 
     2601in lateral dimension) are treated as a paracrystal to account for the repeating spacing. The repeat distance is further 
     2602characterized by a Gaussian polydispersity. **This model can be used for large multilamellar vesicles.** 
     2603 
     2604*2.1.33.1. Definition* 
     2605 
     2606The scattering intensity *I(q)* is calculated as 
     2607 
     2608.. image:: img/image145.JPG 
     2609 
     2610The form factor of the bilayer is approximated as the cross section of an infinite, planar bilayer of thickness *t* 
     2611 
     2612.. image:: img/image146.JPG 
     2613 
     2614Here, the scale factor is used instead of the mass per area of the bilayer (*G*). The scale factor is the volume 
     2615fraction of the material in the bilayer, *not* the total excluded volume of the paracrystal. *ZN(q)* describes the 
     2616interference effects for aggregates consisting of more than one bilayer. The equations used are (3-5) from the 
     2617Bergstrom reference below. 
     2618 
     2619Non-integer numbers of stacks are calculated as a linear combination of the lower and higher values 
     2620 
     2621.. image:: img/image147.JPG 
     2622 
     2623The 2D scattering intensity is the same as 1D, regardless of the orientation of the *q* vector which is defined as 
     2624 
     2625.. image:: img/image040.GIF 
     2626 
     2627The parameters of the model are *Nlayers* = no. of layers, and *pd_spacing* = polydispersity of spacing. 
    26522628 
    26532629==============  ========  ============= 
    … …  
    26642640==============  ========  ============= 
    26652641 
    2666  
    2667  
    2668 *Figure. 1D plot using the default values above (w/20000 data 
    2669 point).* 
    2670  
    2671 Our model uses the form factor calculations implemented in a c-library 
    2672 provided by the NIST Center for Neutron Research (Kline, 2006). 
    2673  
    2674 See the reference for details. 
     2642.. image:: img/image148.JPG 
     2643 
     2644*Figure. 1D plot using the default values above (w/20000 data point).* 
     2645 
     2646Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research 
     2647(Kline, 2006). 
    26752648 
    26762649REFERENCE 
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