A quick and qualitative way to determine purity would be by XRF. If you're impurities are in the ppm range it would be best to dissolve a known quantity of powder in an acid (usually HCl) and perform ICP analysis on the solution.

I agree with James, and I add neutron activation analysis as another appropriate technique for this purpose.

RBS is easier and faster than Neutron activation..

the first method is probably the most convenient and available.

SIMS is a choice too.

NRA (neutron activation) is probably the most sensitive (needs a nuclear reactor!). Not sure how to compare RBS or SIMS to the ICP/OES method in terms of sensitivity, but the first two will definitively tell which contaminants are in.

The quantitative analysis will need some standards, but the people running these tools must have them.

The easiest method is XRF and XRD, but these do not detect low levels of impurities. You can try Inductively Coupled Plasma optical emmission spectrometry (ICP-OES) and /or Inductively Coupled Plasma mass spectrometry (ICP-MS). You would need to dissolve the sample preferrably in nitric acid and make up the solution so that the concentration of nitric acid is less than 3% in the sample solution. Then run the solutions through the instruments making sure that you put in standards, internal standards and international standards as well as replicates in order to get a good result.

There are two ways to determine purity would be by XRF and XRD. If the impurities are in the ppm range the sample powder should be dissolved in acid (usually HCl) and perform ICP analysis on the solution.

For concentration below 50 ppm there are not too many experimental methods able to measure this content with enough certainty. But XRF which is a non-destructive techniques can measure the impurity concentration till < 1 ppm in the sample of your interest. Follow the above said instruction by many authors.