source: sans/Analysis/trunk/Put in User Procedures/SANS_Models_v3.00/EffectiveDiameter.ipf @ 42

#pragma rtGlobals=1             // Use modern global access method.

// these routines are used to calculate an effective spherical diameter for
// a non-spherical object, either a cylinder or an  ellipsoid
//
// the functions calculate the 2nd virial coefficient for the non-spherical
// object, then find the diameter of sphere that has this value of virial
// coefficient
//
// - so the calculation at least has some thermodynamic basis, rather than
// some simplistic volume correction
//

//prolate OR oblate ellipsoids
//aa is the axis of rotation
//if aa>bb, then PROLATE
//if aa<bb, then OBLATE
// A. Isihara, J. Chem. Phys. 18, 1446 (1950)
//returns DIAMETER

Function DiamEllip(aa,bb)
        Variable aa,bb
        
        Variable ee,e1,bd,b1,bL,b2,del,ddd,diam
        
        if(aa>bb)
                ee = (aa^2 - bb^2)/aa^2
        else
                ee = (bb^2 - aa^2)/bb^2
        Endif
        
        bd = 1-ee
        e1 = sqrt(ee)
        b1 = 1 + asin(e1)/(e1*sqrt(bd))
        bL = (1+e1)/(1-e1)
        b2 = 1 + bd/2/e1*ln(bL)
        del = 0.75*b1*b2
        
        ddd = 2*(del+1)*aa*bb*bb                //volume is always calculated correctly
        diam = ddd^(1/3)
        
        return (diam)
End

//effective DIAMETER of a cylinder of total height hcyl and radius rcyl
//
Function DiamCyl(hcyl,rcyl)
        Variable hcyl,rcyl
        
        Variable diam,a,b,t1,t2,ddd
        
        a = rcyl
        b = hcyl/2
        t1 = a*a*2*b/2
        t2 = 1 + (b/a)*(1+a/b)*(1+pi*a/b/2)
        ddd = 3*t1*t2
        diam = ddd^(1/3)
        
        return (diam)
End