variable divergence

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Up Kaolin Spergau Metashale Böhlscheiben Smectite
Copper Shale Variable Divergence Trimer

We want to demonstrate applicability of automatic (variable) divergence slit

Therefore, we use the widely known Round Robin sample PbSO4 as described in
J. Appl. Cryst. 25 (1992) pp. 589-610.

We have learned: irradiated sample length should be at maximum 10mm. Maximum divergence angle should be much less than take-off angle of X-rays from tube anode. The latter angle usually is 6°.

We have collected all results into a table. Table colums are marked as follows:

  1. column RR: Range of results from ibid.
  2. column RR-BGMN: Data as distributed, re-evaluated using BGMN.
  3. column F1: Own measurement of RR sample PbSO4 using fixed divergence slit 1mm.
  4. column V5: Own measurement of RR sample PbSO4 using variable divergence slit, 5mm irradiated sample length.
  5. column V10: Own measurement of RR sample PbSO4 using variable divergence slit, 10mm irradiated sample length.
  6. column X: Single crystal data as described ibid.
Value RR RR-BGMN F1 V5 V10 X
Rexp 1.5%-7.0% 5.36% 6.16% 4.96% 3.70% -
Rwp 8.2%-20% 7.84% 8.36% 7.91% 6.48% -
a/Å 8.4764-8.4859 8.4760(2) 8.4789(6) 8.4786(5) 8.4786(4) 8.482(2)
b/Å 5.3962-5.4024 5.3957(2) 5.3991(4) 5.3989(3) 5.3986(3) 5.398(2)
c/Å 6.9568-6.9650 6.9563(2) 6.9589(5) 6.9588(4) 6.9588(4) 6.959(2)
Pb: x 0.1875-0.1883 0.18790(7) 0.1880(1) 0.1881(1) 0.18790(7) 0.1879(1)
Pb: z 0.1669-0.1683 0.16714(1) 0.1672(2) 0.1674(2) 0.1671(2) 0.1667(1)
Pb: B/Å2 0.9-2.39 1.52(2) 1.44(2) 1.30(2) 1.63(2) 1.48
S: x 0.0621-0.0673 0.0631(4) 0.0636(6) 0.0632(5) 0.0636(4) 0.0633(6)
S: z 0.6799-0.6860 0.6849(5) 0.6878(7) 0.6852(7) 0.6851(5) 0.6842(7)
S: B/Å2 0.29-1.37 0.83(7) 1.0(1) 0.7(1) 1.04(7) 0.74
O1: x 0.902-0.924 0.906(1) 0.907(2) 0.909(1) 0.907(1) 0.908(2)
O1: z 0.585-0.601 0.597(1) 0.598(2) 0.599(2) 0.598(2) 0.596(3)
O1: B/Å2 0.50-4.2 1.2(2) 0.8(2) 0.8(2) 1.0(2) 1.87
O2: x 0.177-0.200 0.191(2) 0.192(2) 0.191(2) 0.191(2) 0.194(2)
O2: z 0.523-0.548 0.547(2) 0.546(2) 0.543(2) 0.545(2) 0.543(2)
O2: B/Å2 0.1-5.8 1.4(2) 1.6(3) 0.6(2) 1.4(2) 1.76
O3: x 0.071-0.080 0.0786(6) 0.0808(8) 0.0810(8) 0.0790(6) 0.082(1)
O3: y 0.018-0.041 0.026(1) 0.024(2) 0.026(2) 0.026(1) 0.026(2)
O3: z 0.806-0.819 0.811(1) 0.807(2) 0.805(2) 0.807(1) 0.809(2)
O3: B/Å2 0.8-4.6 0.9(2) 0.7(2) 0.7(2) 0.8(2) 1.34

Remarks:

Obviously, results of variable divergence measurements are a little less accurate compared to those of fixed divergence measurements (especially Debye-Waller factors B). But, in principle, automatic (variable) divergence slits are usable for Rietveld refinements.