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PHY.K02UF Molecular and Solid State Physics

Electron atomic form factors

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.

Electron atomic form factor for He

f(q) 
0
5
10
15
20
25
0.00
0.10
0.20
0.30
0.40
0.50

q [Å-1]


 

 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/.