Identifying single phases from a completely unknown mixture of compounds by powder diffraction data can be a long and exhausting work. If nothing else is known about the mixture (e.g. which elemnts are in it) and there is no major phase in it to start the search with it can become almost impossible. If one works with the Hannawalt index the three strongest lines have to be chosen and then try to find a match for it. Most times this doesn´t work at once. In such a case the strongest lines can be permutated and hopefully after some time at least one phase can be indexed. After cancelling out the reflexes from the known phase the remaining lines can again be searched for the three strongest lines and so on, until no reflexes remain. Other impurities and further phases can be existent but are to weak to be seen in the powder diffraction data. A much easier way would be to use computer software which has access to a powder diffraction databank.

Step 1:

For this assignment such machine power is not necessary at all, due to the fact that one of the phases is already known. First thing is to look up the PDF entry for calcite and cancel or mark all reflexes which belong to it. After that one takes the next three most intensive lines and tries to find a next match.

Step 2:

The next three now most intensive lines are at d = 3.343, 4.27 and 1.817 Å. After searching the index this yields synthetic quartz as second phase. This is also consistent with the result from the microprobe analysis, that silicium is in the sample.

Step 3:

Having found another phase it is again started with step 1, cancelling out the reflexes which belong to the synthetic quartz and then detemining the three strongest remaining reflexes. These are at d = 2.742, 2.102 and 1.700 Å. This gives synthetic MgCO₃ as result after looking up the index.

Result:

Finally after marking all the reflexes for the carbonate one realizes, that all apparent reflexes in the powder diffraction data are now used once or twice. The overlapping peaks clearly show a broader FWHM as the single ones. Having found calcite, synthetic quartz and synthetic MgCO₃ I would suggest to call the police and arrest the person who has uncovered the "ancient" palster figures for betrayal. If the figures would be really ancient there would not be a synthetic product in it.
Try and make money with that, but not with a chemist who knows the ways of powder diffraction measurements.