**A summary of the models available in FISH**

Each model has a number (LM) , and often a "sub-type" (LTYP) where LTYP=1,11,21,31 etc. These numbers are used when generating the "model file" as part of the input to the FISH program, which enables different models to be combined. The table below identifies most of the currently available models. The full manual contains details of the SANS equations used and references to the literature where appropriate.

The models here are grouped by functionality rather than in their (largely historical) numerical order. Where not otherwise specified they are for fitting small-angle diffraction data ! A structure factor S(Q) multiplies the previously accumulated form factor(s) and corrects for shape or polydispersity ( see note at end).

MODEL (LM) | LTYP | Models in FISH |

| | PARTICLE FORM FACTORS |

1 | 1 | Spherical particle - simple monodisperse solid sphere |

12 | 1 | Guinier radius ( direct fit, useful to include flat background) |

10 or 8 | 1 | Spherical shell, sharp step ( repeat for multiple shells ) |

10 or 8 | 11 | Spherical shell, linear, diffuse step |

10 or 8 | 21 | Spherical shell, decreasing exponential, to infinity |

10 or 8 | 31 | Spherical shell, decreasing exponential, truncated |

10 or 8 | 41 | Spherical shell, increasing exponential from R=0 |

10 or 8 | 51 | Spherical shell, increasing exponential, from previous R |

9 | 1 | square operation, use after model 8 monodisperse shells |

18 | 1 | Rod/disc - rigid, monodisperse, randomly oriented, core/shell, with shell at ends (useful for core/shell disc ) |

18 | 11 | Rod/disc - rigid, randomly oriented, core/shell, without shell at ends (useful for hollow cylinder) |

18 | 21 & 31 | Rods, as above, oriented in shear flow, Hayter & Penfold, fit to 1d averaged wedges of 2d data. |

18 | 41 & 51 | Rods, as above, nematic “Maier-Saupe, DeGennes” distribution. |

18 | 61 & 71 | Rods, as above, nematic “Maier-Saupe, DeGennes” distribution, viewed end-on. |

1 | 11 | "end on" view of a monodisperse cylinder |

10 or 8 | 61 | End-on view of mono/polydisperse fixed rod, multi-shell, sharp step |

21 | 1 | Solid ellipsoid, use model 24 instead. |

24 | 1 | Ellipsoid, core/shell with outer/inner radius ratio constant |

24 | 11 | Ellipsoid, core/shell with constant thickness shell |

24 | 21 &31 | Ellipsoids as above, but with molecular constraints for surfactant micelles. |

| | POLYDISPERSITY used with Model 10 |

1 | 21 | Polydisperse solid spheres - analytic equations for Schultz distribution |

6 | 11 | Schultz distribution (all model 6 use numerical integration) |

6 | 21 | symmetric parabola |

6 | 31 | triangular decreasing |

6 | 41 | concave decreasing |

6 | 51 | flat “hat” |

6 | 1 | cubic polynomial |

6 | 61 | alternative cubic polynomial |

6 | 71 | stick model ( for bimodal ) |

6 | 81 | power law between R1 & R2 |

6 | 91 | log-normal distribution |

5 | 1 | test of a maximum entropy condition on polydispersity |

| | PARTICLE STRUCTURE FACTORS |

7 | 1 | Critical scattering “attractive” S(Q) |

19 | 1 | Correlation hole S(Q) |

22 | 1 | Hard sphere S(Q) |

22 | 11 | Hard sphere S(Q) with attractive/repulsive square well |

23 | 1 | Hayter-Penfold charged sphere S(Q) (using their routines) |

25 | 1 | as model 23, with additional critical scattering term. |

11 | 21 | P(Q) = Constant ( useful for fitting just S(Q) ) |

| | POLYMERS |

14 | 1 | Debye Gaussian coil - for polymers |

14 | 11 | Polydisperse Debye Gaussian coil |

14 | 21 | attempt at Kratky-Porod worm-like persistence chain, (14 - 71 is better) |

14 | 31 | Benoit f-branched star Debye coil |

14 | 41 | Dozier star polymer |

14 | 51 | Leibler diblock copolymer |

14 | 61 | H-shaped copolymer with deuterated tips (D.J.Read) |

14 | 71 | Kholodenko worm – mono/polydisperse with Guinier Raxial |

14 | 81 | Kholodenko worm – mono/polydisperse with core/shell rod |

| | SURFACES, SHEETS & FRACTALS |

20 | 1 | Q**n term ( compare LM=11 ) |

12 | 11 | Porod surface, with optional diffuse interface |

12 | 21 | Porod surface, with diffuse layer of different scattering density. |

26 | 1 | Surface fractal form factor |

13 | 1 | Volume fractal S(Q) |

26 | 11 | Andrew Allen, “cement” surface fractal |

13 | 11 | Andrew Allen “cement” volume fractal |

28 | 1 & 11 | Polydisperse sheet, with Lorentz “waviness” |

28 | 21 | Core/shell sheet, with Lorentz “waviness” |

28 | 31 | Core/exponential shell sheet, with Lorentz “waviness” |

29 | 1 | One dimensional paracrystalline stack, Kotlarchyk & Ritzau. (useful even for a bilayer ) |

29 | 11 | Wenig & Bramer, flat, 3 phase paracrystal, allows gaps between stacks to have different scattering densities |

| | GENERIC GELS & 2 PHASE MODELS |

16 | 1 &11 | Teubner & Strey 2 phase “peak” |

17 | 11 | Debye random 2 phase |

27 | 1 | Gels - Lorentzian plus Debye-Beuche |

| | PEAK FITTING |

27 | 21 | Gaussian peak |

27 | 71 | Stretched Gaussian peak ( as used for LOQ resolution) |

27 | 31 | Voigt peak ( Gaussian convoluted with Lorentzian) |

27 | 51 | Gaussian peak, going to exponential, with continuous first derivative. |

27 | 61 | Ikeda-Carpenter equation for neutron moderator time distributions |

27 | 81 | Gaussian convoluted by exponential |

| | QUASIELASTIC |

4 | 11 | “Vanadium” resolution function for neutron quasielastic scattering |

11 | 31 | Delta function, as alternative to LM=4, LTYP=11 for quasielastic data. |

27 | 11 | Lorentzian, for quasielastic neutrons |

| | GENERAL |

2 | 1 | does nothing - allows parameters to be introduced into constraints |

3 | 11 | Simple flat background ( note background is stored separately and is not resolution smeared) |

3 | 1 | Quadratic background |

11 | 1 | General polynomial to order 7 |

4 | 1 | Scaled subtraction of a “background” data set. |

11 | 21 | P(Q) = Constant ( useful for fitting just S(Q) ) |

15 | 21 &31 | Resolution smearing by a constant width Gaussian |

15 | 41 | Resolution smearing by input curve |

15 | 51,61 & 71 | Resolution smearing, estimated for LOQ at ISIS |

5 | -n | Predicate observation - allows weighting of parameters towards “known” values, see manual. |

88 | 0 or n | Allows multiple data sets, following lines are for all (0) or just set n. |

99 | 1 | ALWAYS needed to end the calculation |

Note S(Q) is corrected for shape and/or polydispersity where appropriate, except that mixtures of particles with different contrasts will not automatically be handled correctly. ( This is because in general the number of particles N and their contrast are lumped together in a single scale factor. In a mixture with other particles the distinction between a few particles at high contrast and a lot of particles at low contrast becomes important! )

07/01/2003

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