Crystal Types

The crystal type and orientation determine where, and what type of halo is formed. Ice crystals are made up of water molecules bound in a hexagonal lattice, because of this the crystals are hexagonal.

Figure 1: Diagram of a hexagonal crystal. For ice a=4.5 angstroms and c=7.3 angstroms. The center dots are not actually part of the lattice but are there to show the geometry of the basal plane. All other points represent oxygen atoms. Image courtesy of Wikipedia

When light enters one face and exits the other it experiences a deflection angle (D) based on the refractive index(n), this relationship is given by:

n =	sin(.5(A_R + D))
	sin(.5A_R)

where A_R is the relative angle between crystal faces[Unpublished Manuscript by Martin Truffer, UAF Physics Department]. Depending on the face entered and exited by the light, different halos can be formed. Although most ice crystals are hexagonal, they have different types. Thin crystals are refered to as plates, while longer crystals are refered to as columns. How they orient themselves produces differing types of halos. In the following pages I will outline each orientation type and show a computer simulation of the specific halos produced at 10 degrees elevation(Fairbanks winter day) and 60 degrees(Winter Day near the equator) These simulations are done using HaloSim3 developed by Les Cowley and Michael Schroeder. The program uses mathematical models of ice crystals and does several million ray tracings to generate the images. It is available for download here www.atoptics.co.uk. It works on Windows as well as Ubuntu 9.04 under Wine, I have not tried it on Mac because using them causes me physical pain.