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A Simple Answer |
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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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