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A Simple Answer

Using Bragg's Law you should be able to calculate the d spacings for the given values of 2θ:

                  d = λ/2sinθ = 0.771/sinθ.
You should also normalise the intensities giving a value of 100% to the strongest line (which is the third line at 9450) so that 4750 becomes 50%, 3795 becomes 40% and so on. Then the list of peaks becomes:

d (Å): 2.475 2.305 2.088 1.688 1.343 1.332 1.237 1.173 1.153 1.124 1.090 1.046
I (%): 50 42 100 30 25 20 1 21 6 16 2 5
The three strongest lines are, in order Nos. 3, 1, 2 with intensities 100, 50, 42 respectively, the fourth (1.688 at 30) being sufficiently less intense so as not to confuse the order. Therefore the Hanawalt index should be:
2.088, 2.475, 2.305.
The only match with the metals set appears to be with Zinc (No. 4-831) which has a Hanawalt index of:
2.09, 2.47, 2.31.
The next stage is to compare these first 12 lines with those of the full pattern for Zn in the PDF database (see below)

Click here to see PDF Card image for Zinc

The comparison reads as follows: First, the first 12 d spacings, which taken to the third decimal place are:

here: 2.475 2.305 2.088 1.688 1.343 1.332 1.237 1.173 1.153 1.124 1.090 1.046
PDF: 2.473 2.308 2.091 1.687 1.342 1.332 1.237 1.173 1.154 1.124 1.090 1.046

and correspondingly for intensity the comparison is:

here: 50 42 100 30 25 20 1 21 6 16 2 5
PDF: 53 40 100 28 25 21 2 23 5 17 3 5
The general agreement with both the d spacings and intensities is convincingly good and we can be confident that the unknown metal is zinc. Further since there no unaccounted extra lines we can assume that the sample is pure in the sense that there is no second minor crystalline phase present. Also since the d spacings are close in value to the PDF values with no systematic bias, as would be if all d spacings were greater or all less than the PDF values, then we can also assume that the zinc sample was pure in a structural sense.


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© Copyright 1997-2006.  Birkbeck College, University of London.
 
Author(s): Paul Barnes
Martin Vickers