Biological Small Angle Scattering Group
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ATSAS v. 2.3.2
Written by P.V. Konarev, V.V Volkov and D.I. Svergun.
Post all your questions about MIXTURE to the ATSAS Forum.
© ATSAS Team, 2003-2009
- Manual
- Introduction
- Running MIXTURE
- MIXTURE Input Files
- MIXTURE Output FIles
- Useful references
- Examples
Manual
Program MIXTURE makes the fitting to the experimental scattering curve by modelling the multicomponent system represented by simple geometrical bodies taking into account interparticle interactions.
If you use results from MIXTURE in your own publication, please cite:
Introduction
The model scattering intensity may be represented by the linear combination of four several types of particles:
The scattering intensity can be expressed as follows:
where νk and Ik(s) are the volume fraction and the scattering intensity from the k-th component, respectively. For mixtures of different types of particles with possible polydispersity ad interactions between particles of the same components, the scattering intensity from a component can be represented as
where Δρk(R), Vk(R) and iok(s,R) denote the contrast, volume and normalized scattering intensity (form factor) of the particle with size R (these functions are defined by the shape and internal structure of the particles, and iok(0,R)=1 ), whereas Sk(s) is the sturcture factor describing the inteference effects for the k-th component. Each component can be monodisperse or polydispers and in the second case the size polydispersity Dk(R) is described by a two-parametric monomodal Gaussian or Schultz distribution characterized by the average dimension Rok(R) and dispersion ΔRk(R)
The spheres and cylinders may have complicated features:
1. polydispersity on radius with Gauss or Schultz distribution
2. two shells with different contrasts (zero contrast of the inner shell means the hole sphere or cylinder).
The interparticle interactions between sphere particles can be described by structure factor calculated within Percus-Yevick approximation for hard-sphere or sticky hard-sphere potential.(see [4] Baxter, 1968) described by two parameters: the hard-sphere interaction radius Rkhs and the "stickiness" τk.
MIXTURE allows one to model mixtures containing up to ten different components (i.e. different types of particles)
Running MIXTURE
Configuration
Below there is the list of the fitting parameters for each type of particles:
SPHERE (PHASE 1)
| Parameters | Description |
|---|---|
| Volume fraction | 0 < νk < 1 |
| Internal Shell Radius | Rin (if Rin=0, the sphere is solid) |
| Internal Shell Contrast | ρin (if ρin=ρout, the sphere is uniform) |
| External Shell Radius | Rout |
| External Shell Contrast | ρout |
| Polydispersity | dRout |
| Volume concentration | Proportion of volume taken by all particles (from 0 to 1), is needed to calculate structure factor |
| Hard sphere radius | Rhs: this should be fulfiled: Rout <= Rhs |
| Stickiness parameter | τ: 0.1<τ<100, τ=100 (Hard-sphere case), τ=0 no interactions |
Possible variants:
monodisperse or polydisperse spheres,
solid spheres or spheres with hollows
interactive or non-interactive spheres
CYLINDER (PHASE 2)
| Parameters | Description |
|---|---|
| Volume fraction | 0 < νk < 1 |
| Internal Shell Radius | Rin (if Rin=0, the sphere is solid) |
| Internal Shell Contrast | ρin (if ρin=ρout, the sphere is uniform) |
| External Shell Radius | Rout |
| External Shell Contrast | ρout |
| Polydispersity (on the radius) | dRout |
| Height | Hcyl, it is fixed during the minimization |
Possible variants:
monodisperse or polydisperse cylinders,
solid cylinders or cylinders with hollows
ELLIPSOID (PHASE 3)
(ellipsoid of rotation with R, R, v*R semiaxes)
| Parameters | Description |
|---|---|
| Volume fraction | 0 < νk < 1 |
| semiaxis of ellipsoid | R |
| ellipsoid ratio | v |
Possible variants:
monodisperse ellipsoids
DUMB-BELL (PHASE 4)
(two sticked spheres)
parameters the same as for SPHERE (PHASE 1)
Running Output
To start the program one has to have both mixture.exe and mixture.cmd
(see MIXTURE Input Files ) files in one directory and
run with the following command: MIXTURE.EXE < MIXTURE.CMD
_/_/ _/_/_/_/_/ _/_/_/_/_/_/ _/_/_/_/_/_/ _/_/_/_/ _/_/_/_/_/
_/_/ _/_/ _/_/ _/_/ _/_/ _/_/ _/_/ _/_/
_/_/ _/_/ _/_/ _/_/ _/_/ _/_/ _/_/
_/_/ _/_/ _/_/ _/_/ _/_/ _/_/ _/_/_/_/_/
_/_/ _/_/ _/_/_/_/_/_/ _/_/ _/_/ _/_/
_/_/ _/_/ _/_/ _/_/ _/_/ _/_/ _/_/
_/_/_/_/_/ _/_/ _/_/ _/_/_/_/ _/_/_/_/_/ _/_/
DIALOGUE SERVICE PROGRAM FOR MINIMIZATION OF NONLINEAR MULTIVARIATE
FUNCTIONS.
Program MIXTURE uses the optimization program suite OPTIS written by V.V. Volkov (Institute of Crystallography, Moscow, Russia) e-mail: vvo@ns.crys.ras.ru
Dialogue mode [ Interactive / PASSive ] ...... < Inter. >:
OPTIS: OPTIS: Welcome to user's problem
Enter the series title .................................: Enter comment line
.....................................: Enter Number of phases ................
< 0 >: Enter concentration of the system ...... < 0.0 >:
Choose type of data file format:.
1: OTOKO format
2: ASCII format
Enter the format code .................. < 2 >: Enter INTENSITY fil
name .............. < .dat >: 339703.100000000 10.4556000000
00
Angular units in the input file :
4*pi*sin(theta)/lambda [1/angstrom] (1)
4*pi*sin(theta)/lambda [1/nm ] (2)
2* sin(theta)/lambda [1/angstrom] (3)
2* sin(theta)/lambda [1/nm ] (4) < 1 >: Enter Fraction of t
e curve ............ < 0.0 >: 75 101
I(1), I(last) : 339703.100000000 10.7711200000000
s(1), s(last) : 3.229300000000000E-002 0.421600000000000
Err(1), Err(last): 10191.0900000000 0.323133500000000
15-dimensional user's problem
OPTIS: OPTIS: OPTIS: ///////////////////////////////////////////////////////
//////////////
This is the information which was read from the command file.
OPTIS --- Version 5.6 rev. 09 May 02 03:30 reports current information:
08-Oct-2009 time 10:42:37
Objective function -- : User's problem (15-dimensional): 0
Chosen algorithm ---- : B-F-G-S with simple bounds
number of performed function evaluations ----- : 1
number of performed iterations --------------- : 0
number of performed gradient estimations ----- : 0
maximum number of function evaluations ------- : 5250
maximum number of search iterations ---------- : 40
total number of problem variables ------------ : 15
number of problem variables to be varied ----- : 15
maximum allowed number of variables ---------- : 512
function value ------------------------------- : 5.678e-2
rel/abs function tolerance to be attained ---- : 0.0
tolerance multiplier switch ------------------ : 0.0 (OFF)
upper bound on hessian condition number ------ : 0.0 (OFF)
temperature and scedule factor --------------- : 0.0, 0.0
function computation noise (rel/abs) --------- : 0.0
relative machine precision ------------------- : 2.22e-16
message level -------------------------------- : 1
===> Press CR to continue: ---------------------------------------------------
------------------
fixative-vector
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1
----------------------------------------------------------------------
argument values
0.500000 0.00000 0.00000 48.0000 1.00000
5.00000 55.0000 0.00000 0.500000 0.00000
0.00000 40.0000 1.00000 3.00000 300.000
----------------------------------------------------------------------
lower bounds on variables
0.00000 0.00000 0.00000 40.0000 1.00000
0.100000 48.0000 0.00000 0.00000 0.00000
0.00000 30.0000 1.00000 2.10000 300.000
----------------------------------------------------------------------
upper bounds on variables
1.00000 0.00000 0.00000 60.0000 1.00000
25.0000 85.0000 0.00000 1.00000 0.00000
0.00000 60.0000 1.00000 10.1000 300.000
//////////////////////////////////////////////////////////////////////
The information about minimization method (it uses B-F-G-S with simple bounds) and the argument values (its initial values, lower and upper boundaries).
CPU time used: 0 min 0.02 sec Continue? [ Y / N ] < Yes >: E04JAF a|Itr.Rem.| No.of F | F | cond(H | E04JAF a| 40| 0| 5.678e-2| 6.295| E04JAF a| 39| 9| 3.509e-2| 8.380| E04JAF a| 38| 18| 4.007e-3| 17.01| E04JAF a| 37| 27| 3.483e-3| 2.358| E04JAF a| 36| 36| 3.109e-3| 246.7| E04JAF a| 35| 45| 3.099e-3| 170.6| E04JAF a| 34| 56| 3.068e-3| 4.026| E04JAF a| 33| 65| 3.046e-3| 2.668| E04JAF a| 32| 78| 2.715e-3| 476.2| E04JAF a| 31| 86| 2.651e-3| 447.6|
The value of minimization tagret function at each iteration step.
E04JAF a|Itr.Rem.| No.of F | F | cond(H) |
E04JAF a| 30| 94| 1.739e-3| 512.1|
E04JAF a| 29| 104| 1.557e-3| 531.3|
E04JAF a| 28| 113| 1.442e-3| 652.1|
E04JAF a| 27| 122| 1.385e-3| 628.3|
E04JAF a| 26| 131| 1.349e-3| 1082.|
E04JAF a| 25| 140| 1.312e-3| 2145.|
E04JAF a| 24| 149| 1.291e-3| 2115.|
E04JAF a| 23| 158| 1.251e-3| 2370.|
E04JAF a| 22| 167| 1.185e-3| 2259.|
E04JAF a| 21| 176| 1.167e-3| 1794.|
E04JAF a|Itr.Rem.| No.of F | F | cond(H) |
E04JAF a| 20| 185| 1.163e-3| 1680.|
E04JAF a| 19| 194| 1.162e-3| 1485.|
E04JAF a| 18| 202| 1.162e-3| 1383.|
E04JAF a| 17| 211| 1.162e-3| 1302.|
E04JAF a| 16| 227| 1.162e-3| 1444.|
E04JAF a| 15| 244| 1.162e-3| 1456.|
E04JAF b| 14| 260| 1.162e-3| 1731.|
E04JBM --- Local search attempt...
E04JAF c| 14| 268| 1.162e-3| 1731.|
OPTIS: OPTIS: 15-dimensional user's problem
Function no. 20, 301 value = 1.1621442432225761E-03
OPTIS: OPTIS:
Are you sure of the solution? [ Y / N ] < No >:
Remember to save your results before you leave "OPTIS"!
Exit now? [ Y / N ] .................... < No >:
Well, absolute accuracy requires infinite time...
----------------------------- END OF JOB -----------------------------
Final Function value. (In ideal fit it should approach to zero)
Produced function minimum is equal to 0.1162144E-02 at the point: 0.987769 0.00000 0.00000 54.1704 1.00000 7.11431 55.0000 0.00000 0.614604 0.00000 0.00000 45.2565 1.00000 4.02500 300.000
Optimized values for the arguments.
after 301 function evaluations,
0 gradient evaluations,
0 iterations
CPU time used: 0 min 4.61 sec
E4MAIN --- Normal termination
MIXTURE Input Files
For running the program MIXTURE it is necessary to prepare the command file where one has to specify your model and initial values of parameters for this model, i.e. the number of "phases" (components), the type for each component (SPHERE, CYLINDER, ELLIPSOID, DUMBBELL), dimension parameters (relative volume fraction, average sphere radius, its polydispersity, type of distribution function (Gauss or Schultz) etc., the upper and lower boundary values for all fitting parameters.
Below there are two examples of command file for the model containing different types of components (example 1- spheres+cylinders, example 2 - ellipsoids+dumb-bells) one can design the model containing several components of the same type (for example large and small spheres, long and short cylinders etc.), but in all cases one has to follow the thumb rule of describing the model parameters as it is done in this example command file:
Below symbols !! are used for comments. For your convienence it is recommended to keep the comments on each line, the program will automatically detect them.
Example Command File 1 (spheres+cylinders)
Some description !! Comment Line 1 (done by user ) Some description !! Comment Line 2 (done by user ) EXPERIMENT !! MODE FOR FITTING DATA, "TEST" MODE FOR EXPERTS 2 !! Number of Phases (2 for this example) 0.20 !! System Concentration SPHERE !! Type of the first Phase 0.25 0.0 1.0 !! sphere volume Fraction 0.0 0.0 0.0 !! inner shell sphere radius 0.0 0.0 0.0 !! density(contrast) for inner shell (hollow sphere) 48.0 40.0 60.0 !! outer shell sphere radius 1.0 1.0 1.0 !! density(contrast) for outer shell 5.0 0.1 25.0 !! sphere polydispersity 75.0 55.0 95.0 !! interaction radius for spheres (hard sphere radius) 2 !! type of distributions for spheres (1 - Gauss, 2 - Schultz) 0.0 0.0 0.0 !! sticky parameter (0.1 .GT. tau .LT. 100), if tau=0 no interactions CYLINDER !! Type of the second Phase 0.25 0.0 1.0 !! cylinder volume Fraction 0.0 0.0 0.0 !! inner shell cylinder radius 0.0 0.0 0.0 !! density(contrast) for inner shell 40.0 30.0 60.0 !! outer shell cylinder radius 1.0 1.0 1.0 !! density(contrast) for outer shell 3.0 2.1 10.1 !! cylinder outer shell radius polydispersity 2 !! type of distributions for cylinders (1 - Gauss, 2 - Schultz) 300.0 !! cylinder length 2 !! type of data (1 - for OTOKO format, 2 - for ASCII format) test1.dat !! experimental file data 1 !! scale for s-vector in A*(-1) (1 for 1.0 coefficient) 1.0 !! fraction of data taken for evaluation meth sb !! method for minimization (Quasi-Newton with simple bounds) loa maxit 40 !! maximum number of iterations 40 run !! run minimisation process y !! confirm running y !! confirm running mes 14 !! message for saving the output data > eva !! write data mes 1 !! prepare for next set data ex !! exit the program y !! confirm exit y !! confirm exit
Example Command File 2 (ellipsoids+dumbbells)
Some description !! Comment Line 1 (done by user ) Some description !! Comment Line 2 (done by user ) EXPERIMENT !! MODE FOR FITTING DATA, "TEST" MODE FOR EXPERTS 2 !! Number of Phases (2 for this example) 0.20 !! System Concentration ELLIPSOID !! Type of the third Phase ( sph, cyl, dmb, ell) 0.25 0.0 1.0 !! ellipsoid Fraction 90.0 20.0 100.0 !! SemiAxis for Ellipsoid (Radius r) 1.5 0.5 3.0 !! Ratio of SemiAxes "v" for Ellipsoid (semiaxes r,r,v*r) DUMBBELL !! Type of the fourth Phase ( sph, cyl, dmb, ell) 0.25 0.0 1.0 !! volume Fraction of dumbbells 0.0 0.0 0.0 !! inner sphere radius 0.0 0.0 0.0 !! density(contrast) for inner shell 62.3 40.0 80.0 !! outer sphere radius 1.0 1.0 1.0 !! density(contrast) for outer shell 2.0 0.1 25.0 !! sphere polydispersity 2 !! type of distributions for spheres in dumbbell 2 !! type of data (1 - for OTOKO format, 2 - for ASCII format) test1.dat !! experimental file data 1 !! scale for s-vector in A*(-1) (1 for 1.0 coefficient) 1.0 !! fraction of data taken for evaluation meth sb !! method for minimization (Quasi-Newton with simple bounds) loa maxit 40 !! maximum number of iterations 40 run !! run minimisation process y !! confirm running y !! confirm running mes 14 !! message for saving the output data > eva !! write data mes 1 !! prepare for next set data ex !! exit the program y !! confirm exit y !! confirm exit
To start the program one has to have both mixture.exe and mixture.cmd files in one directory and run with the following command: MIXTURE.EXE < MIXTURE.CMD
MIXTURE Output Files
The output files of the program mixture are the following: 3 files with extensions *.fit, *.pam, *.str, where the names of files coincide with the file name of experimental data as well as mixture.log file
| File extensions | Description |
|---|---|
| *.fit |
In *.fit files there are three columns, the first column is the S-vector axis, the second column - experimental data, the third column - fit to the data. |
*.pam |
In *.pam files the number of column is equal to Number of phases in your model plus one (Nph+1). The first column is S-vector axis and the others columns contain partial intensities from each component of your model. |
*.str |
In *.str files there is information about structure factor if you used spheres with interactions. The first column is S-vector axis, the second column - structure factor with SHS (sticky hard-sphere potential) calculated for the values of the parameters in your model, the third column - structure factor with HS (hard-sphere potential) calculated with the same parameters. |
Mixture.log file contains information about the file name of experimental data and obtained fitting parameters for your model for each component. After each run the program mixture adds information to this file, so you will have the whole history of running the program in this file.
Useful references
Useful References:
1. D. I. Svergun, L. A. Feigin, Structure Analysis by Small-Angle X-ray and Neutron Scattering, edited by G.W. Taylor, (Sec. Ed. New York: Plenum Press 1989).
2. D.I. Svergun, P.V.Konarev, V.V.Volkov, M.H.J. Koch, W.F.C. Sager, J. Smeeth and E.M. Blokhuis // A Small Angle X-ray Scattering Study of the Droplet-Cylinder Transition in Oil-Rich Sodium Bis(2-ethylhexyl) Sulfosuccinate Microemulsions. Journal of .Chemical Physics 2000, V.113, N. 4, p. 1651-1665.
3. C. Robertus, W. H. Philipse, J. G. H. Joosten, and Y. K. Levine, Solution of the Percus-Yevick approximation of the multicomponent adhesive spheres system applied to the small anglex-ray scattering from microemulsions, J. Chem. Phys. 90, 4482-4489 (1989).
4. R.J.Baxter J.Chem.Phys. 49, (1968), 2270-2273.
Examples
All examples are included in the documentation directory of the installation package.Last edited :
July 7, 2010