The lowest line is corresponding to cubic lattice and for all values of the radius the value is zero.
Note that the Y-axis values are ranging from 10 -8 to 10 -3. Hence what were appearing to be very different values in the
top right all seem to be contained along the x-axis line for zero in the lower plot. This is precisely it was earlier remarked
that all the values in the above are said to be practically zero. Thus a variation in ellipticity from 1.0 (sphere-the lowest
dark blue line) to 1.25 the top green line on the x-axis when the radius measures from 48 to 186 angstroms there is significant
increase in the sum with ellipticity. Beyond 186 there is a sharp variation in the summed values for all ellipticities. And,
by 240 angstroms all the lines (for all ellipticities) have dropped to coincide with zero line. This establishes the observation
that ellipsoid has the same sum total value as sphere for cubic lattices. The Fig.8 to follow contains the results for summing
for non-cubic lattice and the inner semi micro element for discrete summation is a sphere. The y-axis values range from 10
r.p.of -8 to 10 r.p.of -3 [r.p.of=Abr(raised to power of)]as in the previous case and the different lines
for different lattice constants. This can be provided a comparison with an inner ellipsoid. In Fig.8 the pink line has been
made a special mention of at the caption. It is the lattice constant value corresponding to the pink colored line which is
chosen and held fixed for the next plot as in Fig.9. Thus the Y-axis value for this pink line in Fig.8 will be the convergent
value for all the lines in the graph of Fig.9 as on the Y-axis
Discrete Summation Inner Volume Elments IVE
Lorentz (IVE) Sphere and Ellipsoids; Click on picture for full view
Discrete Summation Inner Volume Element IVE
Sperical IVE ; Noncubic Lattice: CLICK on picture for Full View
Discrete Summation Inner Volume Element (IVE)
Non Cubic Lattice with Ellipsoidal IVE: CLICK on picture for Full View