Question about size of object relative to effective radius given in DDAconvert

In the DDSCAT+ user guide it is specified that the effective radius aeff = (3V/4*pi)1/3 where V is the volume represented by an array of N dipoles with lattice spacing d, then V = Nd3

For a rectangular prism of 17732 dipoles and dipole spacing of d = 0.5nm then, the volume is V = 2216.5 nm3. The effective radius would then be aeff = 8.088nm.

However, in actual use with a rectangular prism shaped array of 17732 dipoles and 0.5nm dipole spacing the effective radius given by the software is aeff = 32.353nm. This would be the effective radius were d = 2nm used for the spacing rather than d = 0.5nm as is specified in the same file as the given effective radius.

This is also true for the same shape with a dipole density of 3 per nanometer. The given dipole spacing and effective radius seem to not match up. Now the number of dipoles is N = 62040 and the file says d = 0.33nm but the given aeff = 73.674nm which would be true were d = 3nm.

It seems to me that the program uses a certain dipole spacing, but when calculating the effective radius it uses the reciprocal of that spacing. Am I incorrect, or missing something?

### 1 Responses

1. You are right about the definition, effective radius = (3/4pi*Volume in cu. nm)^0.3333
Effective radius does not depend on dipole distance as you will see from the formula above.

Effective radius is a fixed property of the nanostructure of given dimensions, it does not care what dipole density you use. If you increase dipole distance, you simply pack less dipoles within the structure. If you decrease dipole distance, you pack more within the same structure. The volume stays fixed and so does the effective radius. In essence, you choose the dimensions of your structure and that is what sets the effective radius.

Therefore, you can specify the dimensions of the object (in Blender) and then in DDAConvert you specify the dipole density. That will automatically set the number of dipoles. As long as you use the same dimesions for the object, the effective radius ought not to change. Can you try this and let me know whether you still have trouble? This is a critical issue and so I want to make sure all our users are able to set the effective radius reliably.

1. Dear Jain,

I have question regarding effective radius and precision of the simulation results. just for example, I have constructed a sphere in blender with diameter 10 units and in DDAConvert i choosed dipoles per nanometer to 1 which results a sphere with NBX NBY NBZ=10 10 10 in size (other parameters are NAT=486, The spacing between dipoles for the current density is: 1 nm and effective radius of: 4.87 nm). in second case i constructed a similar sphere with  diameter 0.1 units and in DDAConvert dipoles per nanometer was set to 10 which again results with a sphere of size NBX NBY NBZ=10 10 10 (other parameters are NAT=488, The spacing between dipoles for the current density is: 0.1 nm and effective radius of:48.7 nm). Now apparently the size of the object remains the same so does the optical results but the effective radius and spacing between the dipoles is different. following are the questions

1. why we have different spacing and effective radius?

2. If I would like to have precise simulation results (meaning reasonable size and geometry of the object) what values are best for effective radius and spacing between dipoles whether it should be low or high or somewhere in the middle?

3. another question is related to the adding more dipoles in the same size and geometry of the object. As mentioned above what should i do to increase number of dipoles lets say twice with the same size of the sphere 10 10 10?