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PHY.K02UF Molecular and Solid State Physics | ||||
In the range of scattering vectors between 0 < q < 25 Å-1, the atomic form factor is well approximated by the expression, [1]
f(q)≈5∑i=1aiexp(−bi(q4π)2),
where the values of ai, and bi are tabulated below. The different atomic form factors for the elements can be plotted using the form below.
|
Element | a1 |
b1 |
a2 |
b2 |
a3 |
b3 |
a4 |
b4 |
a5 |
b5 |
H | 0.0088 | 0.1152 | 0.0449 | 1.0867 | 0.1481 | 4.9755 | 0.2356 | 16.5591 | 0.0914 | 43.2743 |
He | 0.0084 | 0.0596 | 0.0443 | 0.536 | 0.1314 | 2.4274 | 0.1671 | 7.7852 | 0.0666 | 20.3126 |
Li | 0.0478 | 0.2258 | 0.2048 | 2.1032 | 0.5253 | 12.9349 | 1.5225 | 50.7501 | 0.9853 | 136.628 |
Be | 0.0423 | 0.1445 | 0.1874 | 1.418 | 0.6019 | 8.1165 | 1.4311 | 27.9705 | 0.7891 | 74.8684 |
B | 0.0436 | 0.1207 | 0.1898 | 1.1595 | 0.6788 | 6.2474 | 1.3273 | 21.046 | 0.5544 | 59.3619 |
C | 0.0489 | 0.114 | 0.2091 | 1.0825 | 0.7537 | 5.4281 | 1.142 | 17.8811 | 0.3555 | 51.1341 |
N | 0.0267 | 0.0541 | 0.1328 | 0.5165 | 0.5301 | 2.8207 | 1.102 | 10.6297 | 0.4215 | 34.3764 |
O | 0.0365 | 0.0652 | 0.1729 | 0.6184 | 0.5805 | 2.9449 | 0.8814 | 9.6298 | 0.3121 | 28.2194 |
F | 0.0382 | 0.0613 | 0.1822 | 0.5753 | 0.5972 | 2.6858 | 0.7707 | 8.8214 | 0.213 | 25.6668 |
Ne | 0.038 | 0.0554 | 0.1785 | 0.5087 | 0.5494 | 2.2639 | 0.6942 | 7.3316 | 0.1918 | 21.6912 |
Na | 0.126 | 0.1684 | 0.6442 | 1.715 | 0.8893 | 8.8386 | 1.8197 | 50.8265 | 1.2988 | 147.2073 |
Mg | 0.113 | 0.1356 | 0.5575 | 1.3579 | 0.9046 | 6.9255 | 2.158 | 32.3165 | 1.4735 | 92.1138 |
Al | 0.1165 | 0.1295 | 0.5504 | 1.2619 | 1.0179 | 6.8242 | 2.6295 | 28.4577 | 1.5711 | 88.475 |
Si | 0.0567 | 0.0582 | 0.3365 | 0.6155 | 0.8104 | 3.2522 | 2.496 | 16.7929 | 2.1186 | 57.6767 |
P | 0.1005 | 0.0977 | 0.4615 | 0.9084 | 1.0663 | 4.9654 | 2.5854 | 18.5471 | 1.2725 | 54.3648 |
S | 0.0915 | 0.0838 | 0.4312 | 0.7788 | 1.0847 | 4.3462 | 2.4671 | 15.5846 | 1.0852 | 44.6365 |
Cl | 0.0799 | 0.0694 | 0.3891 | 0.6443 | 1.0037 | 3.5351 | 2.3332 | 12.5058 | 1.0507 | 35.8633 |
Ar | 0.1044 | 0.0853 | 0.4551 | 0.7701 | 1.4232 | 4.4684 | 2.1533 | 14.5864 | 0.4459 | 41.2474 |
K | 0.2149 | 0.166 | 0.8703 | 1.6906 | 2.4999 | 8.7447 | 2.3591 | 46.7825 | 3.0318 | 165.6923 |
Ca | 0.2355 | 0.1742 | 0.9916 | 1.8329 | 2.3959 | 8.8407 | 3.7252 | 47.4583 | 2.5647 | 134.9613 |
Sc | 0.4636 | 0.3682 | 2.0802 | 4.0312 | 2.9003 | 22.6493 | 1.4193 | 71.82 | 2.4323 | 103.3691 |
Ti | 0.2123 | 0.1399 | 0.896 | 1.4568 | 2.1765 | 6.7534 | 3.0436 | 33.1168 | 2.4439 | 101.8238 |
V | 0.2369 | 0.1505 | 1.0774 | 1.6392 | 2.1894 | 7.5691 | 3.0825 | 36.8741 | 1.719 | 107.8517 |
Cr | 0.197 | 0.1197 | 0.8228 | 1.1985 | 2.02 | 5.4097 | 2.1717 | 25.2361 | 1.7516 | 94.429 |
Mn | 0.1943 | 0.1135 | 0.819 | 1.1313 | 1.9296 | 5.0341 | 2.4968 | 24.1798 | 2.0625 | 80.5598 |
Fe | 0.1929 | 0.1087 | 0.8239 | 1.0806 | 1.8689 | 4.7637 | 2.3694 | 22.85 | 1.906 | 76.7309 |
Co | 0.2186 | 0.1182 | 0.9861 | 1.23 | 1.854 | 5.4177 | 2.3258 | 25.7602 | 1.4685 | 80.8542 |
Ni | 0.2313 | 0.121 | 1.0657 | 1.2691 | 1.8229 | 5.687 | 2.2609 | 27.0917 | 1.1883 | 83.0285 |
Cu | 0.3501 | 0.1867 | 1.6558 | 1.9917 | 1.9582 | 11.3396 | 0.2134 | 53.2619 | 1.4109 | 63.252 |
Zn | 0.178 | 0.0876 | 0.8096 | 0.865 | 1.6744 | 3.8612 | 1.9499 | 18.8726 | 1.4495 | 64.7016 |
Ga | 0.2135 | 0.102 | 0.9768 | 1.0219 | 1.6669 | 4.6275 | 2.5662 | 22.8742 | 1.679 | 80.1535 |
Ge | 0.2135 | 0.0989 | 0.9761 | 0.9845 | 1.6555 | 4.5527 | 2.8938 | 21.5563 | 1.6356 | 70.3903 |
As | 0.2059 | 0.0926 | 0.9518 | 0.9182 | 1.6372 | 4.3291 | 3.049 | 19.2996 | 1.4756 | 58.9329 |
Se | 0.1574 | 0.0686 | 0.7614 | 0.6808 | 1.4834 | 3.1163 | 3.0016 | 14.3458 | 1.7978 | 44.0455 |
Br | 0.1899 | 0.081 | 0.8983 | 0.7957 | 1.6358 | 3.9054 | 3.1845 | 15.7701 | 1.1518 | 45.6124 |
Kr | 0.1742 | 0.0723 | 0.8447 | 0.7123 | 1.5944 | 3.5192 | 3.1507 | 13.7724 | 1.1338 | 39.1148 |
Rb | 0.3781 | 0.1557 | 1.4904 | 1.5347 | 3.5753 | 9.9947 | 3.0031 | 51.4251 | 3.3272 | 185.9828 |
Sr | 0.3723 | 0.148 | 1.4598 | 1.4643 | 3.5124 | 9.232 | 4.4612 | 49.8807 | 3.3031 | 148.0937 |
Y | 0.3234 | 0.1244 | 1.2737 | 1.1948 | 3.2115 | 7.2756 | 4.0563 | 34.143 | 3.7962 | 111.2079 |
Zr | 0.2997 | 0.1121 | 1.1879 | 1.0638 | 3.1075 | 6.3891 | 3.974 | 28.7081 | 3.5769 | 97.4289 |
Nb | 0.168 | 0.0597 | 0.937 | 0.6524 | 2.73 | 4.4317 | 3.815 | 19.554 | 3.0053 | 85.5011 |
Mo | 0.3069 | 0.1101 | 1.1714 | 1.0222 | 3.2293 | 5.9613 | 3.4254 | 25.1965 | 2.1224 | 93.5831 |
Tc | 0.2928 | 0.102 | 1.1267 | 0.9481 | 3.1675 | 5.4713 | 3.6619 | 23.8153 | 2.5942 | 82.8991 |
Ru | 0.2604 | 0.0887 | 1.0442 | 0.824 | 3.0761 | 4.8278 | 3.2175 | 19.8977 | 1.9448 | 80.4566 |
Rh | 0.2713 | 0.0907 | 1.0556 | 0.8324 | 3.1416 | 4.7702 | 3.0451 | 19.7862 | 1.7179 | 80.254 |
Pd | 0.2003 | 0.0659 | 0.8779 | 0.6111 | 2.6135 | 3.5563 | 2.8594 | 12.7638 | 1.0258 | 44.4283 |
Ag | 0.2739 | 0.0881 | 1.0503 | 0.8028 | 3.1564 | 4.4451 | 2.7543 | 18.7011 | 1.4328 | 79.2633 |
Cd | 0.3072 | 0.0966 | 1.1303 | 0.8856 | 3.2046 | 4.6273 | 2.9329 | 20.6789 | 1.656 | 73.4723 |
In | 0.3564 | 0.1091 | 1.3011 | 1.0452 | 3.2424 | 5.09 | 3.4839 | 24.6578 | 2.0459 | 88.0513 |
Sn | 0.2966 | 0.0896 | 1.1157 | 0.8268 | 3.0973 | 4.2242 | 3.8156 | 20.69 | 2.5281 | 71.3399 |
Sb | 0.2725 | 0.0809 | 1.0651 | 0.7488 | 2.994 | 3.871 | 4.0697 | 18.88 | 2.5682 | 60.6499 |
Te | 0.2422 | 0.0708 | 0.9692 | 0.6472 | 2.8114 | 3.3609 | 4.1509 | 16.0752 | 2.8161 | 50.1724 |
I | 0.2617 | 0.0749 | 1.0325 | 0.6914 | 2.8097 | 3.4634 | 4.4809 | 16.3603 | 2.319 | 48.2522 |
Xe | 0.2334 | 0.0655 | 0.9496 | 0.605 | 2.6381 | 3.0389 | 4.468 | 14.0809 | 2.502 | 41.0005 |
Cs | 0.5713 | 0.1626 | 2.4866 | 1.8213 | 4.9795 | 11.1049 | 4.0198 | 49.0568 | 4.4403 | 202.9987 |
Ba | 0.5229 | 0.1434 | 2.2874 | 1.6019 | 4.7243 | 9.4511 | 5.0807 | 42.7685 | 5.6389 | 148.4969 |
La | 0.5461 | 0.1479 | 2.3856 | 1.6552 | 5.0653 | 10.0059 | 5.7601 | 47.3245 | 4.0463 | 145.8464 |
Ce | 0.2227 | 0.0571 | 1.076 | 0.5946 | 2.9482 | 3.2022 | 5.8496 | 16.4253 | 7.1834 | 95.703 |
Pr | 0.5237 | 0.136 | 2.2913 | 1.5068 | 4.6161 | 8.8213 | 4.7233 | 41.9536 | 4.8173 | 141.2424 |
Nd | 0.5368 | 0.1378 | 2.3301 | 1.514 | 4.6058 | 8.8719 | 4.6621 | 43.5967 | 4.4622 | 141.8065 |
Pm | 0.5232 | 0.1317 | 2.2627 | 1.4336 | 4.4552 | 8.3087 | 4.4787 | 40.601 | 4.5073 | 135.9196 |
Sm | 0.5162 | 0.1279 | 2.2302 | 1.3811 | 4.3449 | 7.9629 | 4.3598 | 39.1213 | 4.4292 | 132.7846 |
Eu | 0.5272 | 0.1285 | 2.2844 | 1.3943 | 4.3361 | 8.1081 | 4.3178 | 40.9631 | 4.0908 | 134.1233 |
Gd | 0.9664 | 0.2641 | 3.4052 | 2.6586 | 5.0803 | 16.2213 | 1.4991 | 80.206 | 4.2528 | 92.5359 |
Tb | 0.511 | 0.121 | 2.157 | 1.2704 | 4.0308 | 7.1368 | 3.9936 | 35.0354 | 4.2466 | 123.5062 |
Dy | 0.4974 | 0.1157 | 2.1097 | 1.2108 | 3.8906 | 6.7377 | 3.81 | 32.415 | 4.3084 | 116.9225 |
Ho | 0.4679 | 0.1069 | 1.9693 | 1.0994 | 3.7191 | 5.9769 | 3.9632 | 27.1491 | 4.2432 | 96.3119 |
Er | 0.5034 | 0.1141 | 2.1088 | 1.1769 | 3.8232 | 6.6087 | 3.7299 | 33.4332 | 3.8963 | 116.4913 |
Tm | 0.4839 | 0.1081 | 2.0262 | 1.1012 | 3.6851 | 6.1114 | 3.5874 | 30.3728 | 4.0037 | 110.5988 |
Yb | 0.5221 | 0.1148 | 2.1695 | 1.186 | 3.7567 | 6.752 | 3.6685 | 35.6807 | 3.4274 | 118.0692 |
Lu | 0.468 | 0.1015 | 1.9466 | 1.0195 | 3.5428 | 5.6058 | 3.849 | 27.4899 | 3.6594 | 95.2846 |
Hf | 0.4048 | 0.0868 | 1.737 | 0.8585 | 3.3399 | 4.6378 | 3.9448 | 21.69 | 3.7293 | 80.2408 |
Ta | 0.3835 | 0.081 | 1.6747 | 0.802 | 3.2986 | 4.3545 | 4.0462 | 19.9644 | 3.4303 | 73.6337 |
W | 0.3661 | 0.0761 | 1.6191 | 0.7543 | 3.2455 | 4.0952 | 4.0856 | 18.2886 | 3.2064 | 68.0967 |
Re | 0.3933 | 0.0806 | 1.6973 | 0.7972 | 3.4202 | 4.4237 | 4.1274 | 19.5692 | 2.6158 | 68.7477 |
Os | 0.3854 | 0.0787 | 1.6555 | 0.7638 | 3.4129 | 4.2441 | 4.1111 | 18.37 | 2.4106 | 65.1071 |
Ir | 0.351 | 0.0706 | 1.562 | 0.6904 | 3.2946 | 3.8266 | 4.0615 | 16.0812 | 2.4382 | 58.7638 |
Pt | 0.3083 | 0.0609 | 1.4158 | 0.5993 | 2.9662 | 3.1921 | 3.9349 | 12.5285 | 2.1709 | 49.7675 |
Au | 0.3055 | 0.0596 | 1.3945 | 0.5827 | 2.9617 | 3.1035 | 3.899 | 11.9693 | 2.0026 | 47.9106 |
Hg | 0.3593 | 0.0694 | 1.5736 | 0.6758 | 3.5237 | 3.8457 | 3.8109 | 15.6203 | 1.6953 | 56.6614 |
Tl | 0.3511 | 0.0672 | 1.5489 | 0.6522 | 3.5676 | 3.742 | 4.09 | 15.9791 | 2.5251 | 65.1354 |
Pb | 0.354 | 0.0668 | 1.5453 | 0.6465 | 3.5975 | 3.6968 | 4.3152 | 16.2056 | 2.7743 | 61.4909 |
Bi | 0.353 | 0.0661 | 1.5258 | 0.6324 | 3.5815 | 3.5906 | 4.5532 | 15.9962 | 3.0714 | 57.576 |
Po | 0.3673 | 0.0678 | 1.5772 | 0.6527 | 3.7079 | 3.7396 | 4.8582 | 17.0668 | 2.844 | 55.9789 |
At | 0.3547 | 0.0649 | 1.5206 | 0.6188 | 3.5621 | 3.4696 | 5.0184 | 15.609 | 3.0075 | 49.4818 |
Rn | 0.4586 | 0.0831 | 1.7781 | 0.784 | 3.9877 | 4.3599 | 5.7273 | 20.0128 | 1.546 | 62.1535 |
Fr | 0.8282 | 0.1515 | 2.9941 | 1.6163 | 5.6597 | 9.7752 | 4.9292 | 42.848 | 4.2889 | 190.7366 |
Ra | 1.4129 | 0.2921 | 4.4269 | 3.1381 | 7.046 | 19.6767 | -1.0573 | 102.0436 | 8.643 | 113.9798 |
Ac | 0.7169 | 0.1263 | 2.571 | 1.29 | 5.1791 | 7.3686 | 6.3484 | 32.449 | 5.6474 | 118.0558 |
Th | 0.6958 | 0.1211 | 2.4936 | 1.2247 | 5.1269 | 6.9398 | 6.6988 | 30.0991 | 5.0799 | 105.196 |
Pa | 1.2502 | 0.2415 | 4.2284 | 2.6442 | 7.0489 | 16.3313 | 1.139 | 73.5757 | 5.8222 | 91.9401 |
U | 0.641 | 0.1097 | 2.2643 | 1.0644 | 4.8713 | 5.7907 | 5.9287 | 25.0261 | 5.3935 | 101.3899 |
Np | 0.6938 | 0.1171 | 2.4652 | 1.1757 | 5.1227 | 6.4053 | 5.5965 | 27.5217 | 4.8543 | 103.0482 |
Pu | 0.6902 | 0.1153 | 2.4509 | 1.1545 | 5.1284 | 6.2291 | 5.0339 | 27.0741 | 4.8575 | 111.315 |
Am | 0.7577 | 0.1257 | 2.7264 | 1.3044 | 5.4184 | 7.1035 | 4.8198 | 32.4649 | 4.1013 | 118.8647 |
Cm | 0.7567 | 0.1239 | 2.7565 | 1.2979 | 5.4364 | 7.0798 | 5.1918 | 32.7871 | 3.5643 | 110.1512 |
Bk | 0.7492 | 0.1217 | 2.7267 | 1.2651 | 5.3521 | 6.8101 | 5.0369 | 31.6088 | 3.5321 | 106.4853 |
Cf | 0.81 | 0.131 | 3.0001 | 1.4038 | 5.4635 | 7.6057 | 4.1756 | 34.0186 | 3.5066 | 90.5226 |
[1] The electron atomic form factors were taken from the International Tables for Crystallography: http://it.iucr.org/Cb/ch4o3v0001/sec4o3o2/.