how might you identify and differentiate between a single- and double-chain silicate?

Answer 1

Most of the time, you can not readily tell this difference in the field or even with a microscope. I recommend you trying to identify the mineral first, then working back towards it chemical structure.

Answer 2

With X-ray diffraction you can identify the crystalline structure of a mineral. If you do Rietveld refinement after the X-ray pattern is obtained you can model the crystalline structure and account for possible substitutions and solid solutions.

Just for your information there are also triple chain silicates, they are rare, but they do occur in nature.

Another way to know if it is single, double, or triple chain silicate is by analyzing your sample with a High Resolution Transmission electron microscope, in which you can almost see every atom and you can clearly see how the mineral is organized. You can really see the number of chains and count them, you can see solid solutions, defects, etc. This technique is quite amazing.

But as a first approach, looking under a polarized microscope will be helpful. The 2 direction cleavage of single chained silicates form an angle close to 90 degrees, while for double chained silicates is close to 60 degrees(check a book for exact numbers).
X-ray diffraction is the fingerprint of minerals (or I should say the "DNA" of a mineral, now that we are in the DNA era).

Answer 3

Well, a quick-n-dirty method is to identify the cleavages. It won't be perfect, but it'll be close. Otherwise, you're in for some "quality lab time".