SILICON

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SILICON= tells XDS what the absorption coefficient of the detector material is. This needs to be known for two reasons:

  1. in case of oblique incidence of diffracted x-rays on the detector, the path through the detector's absorbing material is longer than for vertical incidence, so more x-rays are absorbed
  2. in that situation, the center of gravity of the absorbed x-rays is not at the same position as for an infinitely thin detector, so a positional correction is required

Both corrections are usually only required at very high resolution, or rather, high two-theta.


Usage for CCD detectors

Actually, if the detector material is silicon, the absorption coefficient is calculated internally within XDS, thus SILICON= is not required. If however the detector material is GADOX (gadolinium oxysulphide, as used e.g. for ADSC and Mar/Rayonix CCD detectors; colloquially called Phosphor), then the absorption coefficient can be obtained from the table below, and should be entered manually into the line that has SILICON= in XDS.INP (if required, after uncommenting that line).

Speifying SILICON is only useful if SENSOR_THICKNESS is also specified. For the Pilatus detector, the value to be used can usually be obtained from the frame header. For CCD detectors, a typical value of SENSOR_THICKNESS is 0.031, and the SILICON= values in the table are correct for that.

Thanks to James Holton and Jason Price for coming up (by actually measuring it) with the SENSOR_THICKNESS value of 0.031, and the table of SILICON= values! The latter assumes that 40% of the 0.031 mm is air, and uses the measured weight of GADOX sheets. Then, specifying a density of 4.2 (which is about 60% of the density of Gd2O2S, 7.32 g/cm^3) on http://henke.lbl.gov/optical_constants/atten2.html one obtains a list of absorption coefficients that can be converted to values close to the SILICON values given in the table below, by using <table_value>=1000/<absorption_coefficient>.

The actual values below are obtained from elemental absorption coefficients (e.g. obtained from http://skuld.bmsc.washington.edu/scatter/data/Gd.dat ) and an equation found at the LBL site. Specifically, this:

SILICON = 2000*r0*lambda*fpp*N_Avogadro*density/atomic_mass
where:
r0 = 2.817941e-15 meters
lambda = wavelength in meters
N_Avogadro = 6.02214179e+23 molecules/mol
fpp = f-double-prime (electron equivalents)
density = bulk density of material in g/cm^3
atomic_mass is in g/mol

Granted, this is only for one element at a time, but if you sum the results for each element (using the appropriate g/cm^3 for each atom type in the material), then you should get the right value for SILICON= of any compound.


GADOX0.031-graph.png


wave-   ene- mu_
length  rgy  energy
[A]     [eV] absorp SILICON=

3.0996 4000 244.537 248.401
3.0919 4010 243.005 246.854
3.0842 4020 241.486 245.321
3.0765 4030 239.979 243.801
3.0689 4040 238.486 242.293
3.0613 4050 237.005 240.799
3.0538 4060 235.536 239.316
3.0463 4070 234.08 237.847
3.0388 4080 232.636 236.389
3.0314 4090 231.204 234.944
3.024 4100 229.784 233.511
3.0166 4110 228.376 232.089
3.0093 4120 226.979 230.68
3.002 4130 225.595 229.282
2.9948 4140 224.221 227.895
2.9876 4150 222.859 226.521
2.9804 4160 221.508 225.157
2.9732 4170 220.169 223.805
2.9661 4180 218.84 222.463
2.9591 4190 217.522 221.133
2.952 4200 216.215 219.813
2.945 4210 214.919 218.505
2.938 4220 213.633 217.206
2.9311 4230 212.358 215.919
2.9242 4240 211.093 214.642
2.9173 4250 209.838 213.375
2.9104 4260 208.593 212.118
2.9036 4270 207.359 210.871
2.8968 4280 206.134 209.635
2.8901 4290 204.919 208.408
2.8834 4300 203.714 207.191
2.8767 4310 202.518 205.984
2.87 4320 201.332 204.786
2.8634 4330 200.156 203.598
2.8568 4340 198.988 202.42
2.8502 4350 197.83 201.25
2.8437 4360 196.681 200.09
2.8372 4370 195.541 198.939
2.8307 4380 194.411 197.797
2.8242 4390 193.289 196.664
2.8178 4400 192.175 195.54
2.8114 4410 191.071 194.425
2.8051 4420 189.975 193.318
2.7987 4430 188.888 192.22
2.7924 4440 187.809 191.131
2.7862 4450 186.738 190.05
2.7799 4460 185.676 188.977
2.7737 4470 184.622 187.912
2.7675 4480 183.576 186.856
2.7613 4490 182.538 185.808
2.7552 4500 181.508 184.768
2.7491 4510 180.486 183.736
2.743 4520 179.472 182.712
2.737 4530 178.465 181.695
2.7309 4540 177.466 180.686
2.7249 4550 176.475 179.685
2.719 4560 175.491 178.692
2.713 4570 174.515 177.706
2.7071 4580 173.546 176.727
2.7012 4590 172.585 175.756
2.6953 4600 171.63 174.792
2.6895 4610 170.683 173.836
2.6836 4620 169.743 172.886
2.6778 4630 168.81 171.944
2.6721 4640 167.884 171.009
2.6663 4650 166.964 170.08
2.6606 4660 166.052 169.159
2.6549 4670 165.146 168.244
2.6492 4680 164.247 167.337
2.6436 4690 163.355 166.435
2.638 4700 162.469 165.541
2.6324 4710 161.59 164.653
2.6268 4720 160.717 163.772
2.6212 4730 159.851 162.897
2.6157 4740 158.991 162.028
2.6102 4750 158.137 161.166
2.6047 4760 157.29 160.31
2.5993 4770 156.449 159.461
2.5938 4780 155.613 158.617
2.5884 4790 154.784 157.78
2.583 4800 153.961 156.948
2.5776 4810 153.144 156.123
2.5723 4820 152.332 155.304
2.567 4830 151.527 154.49
2.5617 4840 150.727 153.682
2.5564 4850 149.933 152.881
2.5511 4860 149.145 152.084
2.5459 4870 148.362 151.294
2.5407 4880 147.585 150.509
2.5355 4890 146.813 149.73
2.5303 4900 146.047 148.956
2.5251 4910 145.287 148.188
2.52 4920 144.531 147.425
2.5149 4930 143.781 146.668
2.5098 4940 143.037 145.916
2.5047 4950 142.297 145.169
2.4997 4960 141.563 144.427
2.4947 4970 140.834 143.691
2.4896 4980 140.11 142.96
2.4847 4990 139.391 142.234
2.4797 5000 138.677 141.513
2.4747 5010 137.968 140.797
2.4698 5020 137.264 140.086
2.4649 5030 136.565 139.38
2.46 5040 135.87 138.678
2.4551 5050 135.181 137.982
2.4503 5060 134.496 137.29
2.4454 5070 133.816 136.603
2.4406 5080 133.14 135.921
2.4358 5090 132.469 135.244
2.4311 5100 131.803 134.571
2.4263 5110 131.142 133.903
2.4216 5120 130.484 133.239
2.4168 5130 129.832 132.58
2.4121 5140 129.183 131.925
2.4075 5150 128.54 131.275
2.4028 5160 127.9 130.629
2.3981 5170 127.265 129.987
2.3935 5180 126.634 129.35
2.3889 5190 126.007 128.717
2.3843 5200 125.385 128.089
2.3797 5210 124.767 127.464
2.3752 5220 124.153 126.844
2.3706 5230 123.542 126.228
2.3661 5240 122.937 125.616
2.3616 5250 122.335 125.008
2.3571 5260 121.737 124.404
2.3526 5270 121.143 123.804
2.3482 5280 120.553 123.208
2.3437 5290 119.967 122.616
2.3393 5300 119.384 122.028
2.3349 5310 118.806 121.444
2.3305 5320 118.231 120.864
2.3262 5330 117.66 120.287
2.3218 5340 117.093 119.714
2.3175 5350 116.53 119.145
2.3131 5360 115.97 118.58
2.3088 5370 115.414 118.018
2.3045 5380 114.862 117.46
2.3003 5390 114.313 116.906
2.296 5400 113.768 116.355
2.2918 5410 113.226 115.808
2.2875 5420 112.688 115.264
2.2833 5430 112.153 114.724
2.2791 5440 111.622 114.187
2.2749 5450 111.094 113.654
2.2708 5460 110.569 113.124
2.2666 5470 110.048 112.598
2.2625 5480 109.53 112.075
2.2584 5490 109.016 111.555
2.2543 5500 108.505 111.039
2.2502 5510 107.997 110.526
2.2461 5520 107.492 110.016
2.242 5530 106.99 109.509
2.238 5540 106.492 109.006
2.234 5550 105.997 108.505
2.2299 5560 105.505 108.008
2.2259 5570 105.016 107.514
2.2219 5580 104.53 107.023
2.218 5590 104.047 106.535
2.214 5600 103.567 106.051
2.2101 5610 103.091 105.569
2.2061 5620 102.617 105.09
2.2022 5630 102.146 104.615
2.1983 5640 101.678 104.142
2.1944 5650 101.213 103.672
2.1905 5660 100.751 103.205
2.1867 5670 100.292 102.741
2.1828 5680 99.8352 102.28
2.179 5690 99.3816 101.821
2.1752 5700 98.9308 101.366
2.1714 5710 98.4828 100.913
2.1676 5720 98.0376 100.463
2.1638 5730 97.5951 100.016
2.16 5740 97.1553 99.5716
2.1562 5750 96.7181 99.1298
2.1525 5760 96.2837 98.6908
2.1488 5770 95.8519 98.2544
2.1451 5780 95.4228 97.8207
2.1414 5790 94.9962 97.3896
2.1377 5800 94.5723 96.9611
2.134 5810 94.1509 96.5352
2.1303 5820 93.732 96.1119
2.1267 5830 93.3157 95.6911
2.123 5840 92.902 95.2728
2.1194 5850 92.4907 94.8571
2.1158 5860 92.0818 94.4439
2.1122 5870 91.6755 94.0331
2.1086 5880 91.2716 93.6248
2.105 5890 90.87 93.2189
2.1014 5900 90.4709 92.8154
2.0979 5910 90.0742 92.4143
2.0943 5920 89.6798 92.0156
2.0908 5930 89.2878 91.6193
2.0873 5940 88.8981 91.2253
2.0838 5950 88.5108 90.8337
2.0803 5960 88.1257 90.4443
2.0768 5970 87.7429 90.0573
2.0733 5980 87.3623 89.6725
2.0699 5990 86.984 89.2899
2.0664 6000 86.608 88.9097
2.063 6010 86.2341 88.5316
2.0595 6020 85.8624 88.1557
2.0561 6030 85.4929 87.7821
2.0527 6040 85.1256 87.4106
2.0493 6050 84.7604 87.0412
2.0459 6060 84.3974 86.6741
2.0426 6070 84.0364 86.309
2.0392 6080 83.6776 85.946
2.0359 6090 83.3208 85.5852
2.0325 6100 82.9661 85.2264
2.0292 6110 82.6135 84.8697
2.0259 6120 82.2629 84.515
2.0226 6130 81.9143 84.1624
2.0193 6140 81.5677 83.8118
2.016 6150 81.2232 83.4632
2.0127 6160 80.8806 83.1166
2.0095 6170 80.5399 82.7719
2.0062 6180 80.2013 82.4292
2.003 6190 79.8645 82.0885
1.9997 6200 79.5297 81.7497
1.9965 6210 79.1968 81.4128
1.9933 6220 78.8658 81.0779
1.9901 6230 78.5366 80.7448
1.9869 6240 78.2093 80.4136
1.9837 6250 77.8839 80.0842
1.9806 6260 77.5604 79.7567
1.9774 6270 77.2386 79.4311
1.9743 6280 76.9187 79.1072
1.9711 6290 76.6006 78.7852
1.968 6300 76.2842 78.465
1.9649 6310 75.9697 78.1466
1.9618 6320 75.6569 77.8299
1.9587 6330 75.3458 77.515
1.9556 6340 75.0365 77.2019
1.9525 6350 74.7289 76.8904
1.9494 6360 74.4231 76.5807
1.9464 6370 74.1189 76.2728
1.9433 6380 73.8164 75.9665
1.9403 6390 73.5156 75.6619
1.9373 6400 73.2165 75.3589
1.9342 6410 72.919 75.0577
1.9312 6420 72.6232 74.7581
1.9282 6430 72.329 74.4601
1.9252 6440 72.0365 74.1638
1.9222 6450 71.7455 73.869
1.9193 6460 71.4561 73.5759
1.9163 6470 71.1684 73.2844
1.9133 6480 70.8822 72.9945
1.9104 6490 70.5975 72.7061
1.9074 6500 70.3145 72.4193
1.9045 6510 70.0329 72.134
1.9016 6520 69.7529 71.8503
1.8987 6530 69.4745 71.5681
1.8958 6540 69.1975 71.2875
1.8929 6550 68.922 71.0083
1.89 6560 68.6481 70.7306
1.8871 6570 68.3756 70.4545
1.8843 6580 68.1046 70.1798
1.8814 6590 67.835 69.9065
1.8785 6600 67.5669 69.6348
1.8757 6610 67.3003 69.3644
1.8729 6620 67.0351 69.0956
1.87 6630 66.7713 68.8281
1.8672 6640 66.5089 68.5621
1.8644 6650 66.2479 68.2974
1.8616 6660 65.9883 68.0342
1.8588 6670 65.7301 67.7724
1.8561 6680 65.4733 67.5119
1.8533 6690 65.2178 67.2528
1.8505 6700 64.9637 66.9951
1.8478 6710 64.7109 66.7387
1.845 6720 64.4595 66.4837
1.8423 6730 64.2094 66.23
1.8395 6740 63.9606 65.9776
1.8368 6750 63.7132 65.7265
1.8341 6760 63.467 65.4768
1.8314 6770 63.2222 65.2283
1.8287 6780 62.9786 64.9812
1.826 6790 62.7363 64.7353
1.8233 6800 62.4953 64.4907
1.8206 6810 62.2555 64.2473
1.818 6820 62.017 64.0053
1.8153 6830 61.7797 63.7644
1.8126 6840 61.5437 63.5248
1.81 6850 61.3089 63.2865
1.8074 6860 61.0753 63.0493
1.8047 6870 60.843 62.8134
1.8021 6880 60.6118 62.5787
1.7995 6890 60.3818 62.3451
1.7969 6900 60.153 62.1128
1.7943 6910 59.9254 61.8817
1.7917 6920 59.699 61.6517
1.7891 6930 59.4737 61.4229
1.7865 6940 59.2496 61.1953
1.7839 6950 59.0267 60.9688
1.7814 6960 58.8049 60.7435
1.7788 6970 58.5842 60.5193
1.7763 6980 58.3646 60.2962
1.7737 6990 58.1462 60.0743
1.7712 7000 57.9289 59.8534
1.7687 7010 57.7127 59.6337
1.7662 7020 57.4976 59.4151
1.7636 7030 57.2836 59.1976
1.7611 7040 57.0707 58.9811
1.7586 7050 56.8588 58.7658
1.7562 7060 56.648 58.5515
1.7537 7070 56.4383 58.3383
1.7512 7080 56.2297 58.1262
1.7487 7090 56.0221 57.9151
1.7463 7100 55.8155 57.705
1.7438 7110 55.61 57.496
1.7414 7120 55.4055 57.288
1.7389 7130 55.202 57.0811
1.7365 7140 54.9996 56.8752
1.734 7150 54.7981 56.6703
1.7316 7160 54.5977 56.4663
1.7292 7170 54.3983 56.2634
1.7268 7180 54.1998 56.0615
1.7244 7190 54.0024 55.8606
1.722 7200 53.8059 55.6607
1.7196 7210 53.6104 55.4617
1.7172 7220 53.4159 55.2637
1.7149 7230 53.2223 55.0667
1.7125 7240 53.0297 54.8707
1.7101 7250 99.6913 138.768
1.7078 7260 99.6724 138.279
1.7054 7270 99.6536 137.791
1.7031 7280 99.6349 137.306
1.7007 7290 99.6163 136.823
1.6984 7300 99.5978 136.343
1.6961 7310 99.5794 135.865
1.6938 7320 99.5611 135.389
1.6915 7330 99.5429 134.916
1.6892 7340 99.5247 134.445
1.6869 7350 99.5067 133.976
1.6846 7360 99.4888 133.51
1.6823 7370 99.4709 133.046
1.68 7380 99.4532 132.584
1.6777 7390 99.4355 132.124
1.6755 7400 99.4179 131.667
1.6732 7410 99.4004 131.211
1.6709 7420 99.383 130.758
1.6687 7430 99.3657 130.307
1.6665 7440 99.3485 129.859
1.6642 7450 99.3313 129.412
1.662 7460 99.3143 128.968
1.6598 7470 99.2973 128.525
1.6575 7480 99.2804 128.085
1.6553 7490 99.2636 127.647
1.6531 7500 99.2469 127.211
1.6509 7510 99.2303 126.777
1.6487 7520 99.2137 126.345
1.6465 7530 99.1973 125.915
1.6444 7540 99.1809 125.488
1.6422 7550 99.1646 125.062
1.64 7560 99.1484 124.638
1.6378 7570 99.1322 124.216
1.6357 7580 99.1162 123.796
1.6335 7590 99.1002 123.379
1.6314 7600 99.0843 122.963
1.6292 7610 99.0685 122.549
1.6271 7620 99.0527 122.137
1.625 7630 99.037 121.727
1.6228 7640 99.0214 121.319
1.6207 7650 99.0059 120.913
1.6186 7660 98.9905 120.508
1.6165 7670 98.9751 120.106
1.6144 7680 98.9598 119.705
1.6123 7690 98.9446 119.307
1.6102 7700 98.9295 118.91
1.6081 7710 98.9144 118.515
1.606 7720 98.8994 118.122
1.6039 7730 98.8845 117.73
1.6019 7740 98.8697 117.341
1.5998 7750 98.8549 116.953
1.5977 7760 98.8402 116.567
1.5957 7770 98.8255 116.183
1.5936 7780 98.811 115.8
1.5916 7790 98.7965 115.42
1.5895 7800 98.7821 115.041
1.5875 7810 98.7677 114.664
1.5855 7820 98.7534 114.288
1.5835 7830 98.7392 113.914
1.5814 7840 98.7251 113.542
1.5794 7850 98.711 113.172
1.5774 7860 98.697 112.803
1.5754 7870 98.683 112.436
1.5734 7880 98.6692 112.071
1.5714 7890 98.6554 111.707
1.5694 7900 98.6416 111.345
1.5674 7910 98.6279 110.985
1.5655 7920 98.6143 110.626
1.5635 7930 98.6008 110.269
1.5615 7940 121.24 148.376
1.5596 7950 121.227 147.916
1.5576 7960 121.214 147.458
1.5556 7970 121.2 147.001
1.5537 7980 121.187 146.547
1.5517 7990 121.174 146.095
1.5498 8000 121.161 145.644
1.5479 8010 121.148 145.196
1.5459 8020 121.135 144.749
1.544 8030 121.122 144.305
1.5421 8040 121.109 143.862
1.5402 8050 121.096 143.422
1.5383 8060 121.083 142.983
1.5364 8070 121.071 142.546
1.5345 8080 121.058 142.111
1.5326 8090 121.046 141.678
1.5307 8100 121.033 141.246
1.5288 8110 121.021 140.817
1.5269 8120 121.008 140.389
1.525 8130 120.996 139.963
1.5231 8140 120.984 139.539
1.5213 8150 120.971 139.117
1.5194 8160 120.959 138.697
1.5176 8170 120.947 138.278
1.5157 8180 120.935 137.861
1.5138 8190 120.923 137.446
1.512 8200 120.911 137.033
1.5102 8210 120.899 136.621
1.5083 8220 120.887 136.212
1.5065 8230 120.876 135.804
1.5047 8240 120.864 135.397
1.5028 8250 120.852 134.993
1.501 8260 120.841 134.59
1.4992 8270 120.829 134.188
1.4974 8280 120.818 133.789
1.4956 8290 120.806 133.391
1.4938 8300 120.795 132.995
1.492 8310 120.783 132.6
1.4902 8320 120.772 132.207
1.4884 8330 120.761 131.816
1.4866 8340 120.75 131.426
1.4848 8350 120.738 131.038
1.4831 8360 120.727 130.652
1.4813 8370 120.716 130.267
1.4795 8380 125.012 149.343
1.4778 8390 124.753 148.904
1.476 8400 124.494 148.467
1.4742 8410 124.235 148.031
1.4725 8420 123.976 147.596
1.4708 8430 123.717 147.164
1.469 8440 123.457 146.733
1.4673 8450 123.198 146.303
1.4655 8460 122.938 145.875
1.4638 8470 122.679 145.449
1.4621 8480 122.419 145.025
1.4604 8490 122.16 144.602
1.4586 8500 121.9 144.18
1.4569 8510 121.641 143.76
1.4552 8520 121.381 143.342
1.4535 8530 121.122 142.925
1.4518 8540 120.862 142.51
1.4501 8550 120.603 142.096
1.4484 8560 120.344 141.684
1.4467 8570 120.084 141.274
1.445 8580 119.825 140.865
1.4434 8590 119.566 140.457
1.4417 8600 119.307 140.051
1.44 8610 119.048 139.647
1.4383 8620 118.789 139.244
1.4367 8630 118.53 138.842
1.435 8640 118.271 138.443
1.4333 8650 118.013 138.044
1.4317 8660 117.754 137.647
1.43 8670 117.496 137.252
1.4284 8680 117.238 136.857
1.4267 8690 116.98 136.465
1.4251 8700 116.722 136.074
1.4235 8710 116.464 135.684
1.4218 8720 116.206 135.296
1.4202 8730 115.949 134.909
1.4186 8740 115.692 134.524
1.417 8750 115.435 134.14
1.4153 8760 115.178 133.757
1.4137 8770 114.922 133.376
1.4121 8780 114.665 132.996
1.4105 8790 114.409 132.618
1.4089 8800 114.153 132.241
1.4073 8810 113.897 131.865
1.4057 8820 113.642 131.491
1.4041 8830 113.387 131.119
1.4025 8840 113.132 130.747
1.401 8850 112.877 130.377
1.3994 8860 112.623 130.008
1.3978 8870 112.368 129.641
1.3962 8880 112.115 129.275
1.3946 8890 111.861 128.91
1.3931 8900 111.608 128.547
1.3915 8910 111.354 128.185
1.39 8920 111.102 127.825
1.3884 8930 110.849 127.465
1.3868 8940 110.597 127.107
1.3853 8950 110.345 126.751
1.3838 8960 110.094 126.395
1.3822 8970 109.842 126.041
1.3807 8980 109.591 125.688
1.3791 8990 109.341 125.337
1.3776 9000 109.091 124.987
1.3761 9010 108.841 124.638
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