Models

FISH Models

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! )

richard.heenan@stfc.ac.uk

07/01/2003

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