原子散乱因子(電子)

Last update:

Neutral atoms: Peng et al. (1996), Acta Cryst. A52, 257-276.
Ionized atoms:  Peng (1998), Acta Cryst. A54, 481-485.
電子に対する原子散乱因子 \(f\) は以下の近似式で求めることが出来ます。$$ f(\sin\theta/\lambda) = \sum_{i=1}^5 a_i \exp(-b_i \sin^2\theta/\lambda^2)$$

ZSymbolNote\(a_1\)\(b_1\)\(a_2\)\(b_2\)\(a_3\)\(b_3\)\(a_4\)\(b_4\)\(a_5\)\(b_5\)
1HH: HF0.03490.53470.12013.58670.19712.34710.057318.95250.119538.6269
H1-: HF0.140.9840.6498.671.3738.90.3371110.787166
2HeHe: RHF0.03170.25070.08381.47510.15264.49380.133412.66460.016431.1653
3LiLi: RHF0.0750.38640.22492.93830.554815.38291.495453.55450.9354138.7337
Li1+: RHF0.00460.03580.01650.2390.04350.8790.06492.640.0277.09
4BeBe: RHF0.0780.31310.2212.23810.67410.15171.386730.90610.692578.3273
Be2+: RHF0.00340.02670.01030.1620.02330.5310.03251.480.0123.88
5BB: RHF0.09090.29950.25512.11550.77388.38161.213624.12920.460663.1314
6CC: RHF0.08930.24650.25631.710.7576.40941.048718.61130.357550.2523
7NN: RHF0.10220.24510.32191.74810.79826.19250.819717.38940.171548.1431
8OO: RHF0.09740.20670.29211.38150.6914.69430.69912.71050.203932.4726
O1-: HF0.2050.3970.6282.641.178.81.0327.10.2991.8
O2-: HF0.04210.06090.210.5590.8522.961.8211.51.1737.7
9FF: RHF0.10830.20570.31751.34390.64874.27880.584611.39320.142128.7881
F1-: RHF0.1340.2280.3911.470.8144.680.92813.20.34736
10NeNe: RHF0.12690.220.35351.37790.55824.02030.46749.49340.14623.1278
ZSymbolNote\(a_1\)\(b_1\)\(a_2\)\(b_2\)\(a_3\)\(b_3\)\(a_4\)\(b_4\)\(a_5\)\(b_5\)
11NaNa: RHF0.21420.33340.68532.34460.769210.0831.658948.30371.4482138.27
Na1+: RHF0.02560.03970.09190.2870.2971.180.5143.750.19910.8
12MgMg: RHF0.23140.32780.68662.2720.967710.92412.188239.28981.1339101.9748
Mg2+: HF0.0210.03310.06720.2220.1980.8380.3682.480.1746.75
13AlAl: RHF0.2390.31380.65732.10631.201110.41632.558634.45521.231298.5344
Al3+: HF0.01920.03060.05790.1980.1630.7130.2842.040.1145.25
14SiSi: RHF0.25190.30750.63722.01741.37959.67462.508229.37441.0580.4732
Si4+: RHF0.1920.3590.2891.960.19.34-0.072811.10.001213.4
15PP: RHF0.25480.29080.61061.8741.45418.51762.320424.34340.847763.2996
16SS: RHF0.24970.26810.56281.67111.38997.02672.186519.53770.771550.3888
17ClCl: RHF0.24430.24680.53971.52421.39196.15372.019716.66870.662142.3086
Cl1-: RHF0.2650.2520.5961.561.66.212.6917.81.2347.8
18ArAr: RHF0.23850.22890.50171.36941.34285.25611.889914.09280.607935.5361
19KK: RHF0.41150.37031.40313.38742.278413.10292.674268.95922.2162194.4329
K1+: RHF0.1990.1920.3961.10.9283.911.459.750.4523.4
20CaCa: RHF0.40540.34991.3883.09912.160211.96083.753253.93532.2063142.3892
Ca2+: RHF0.1640.1570.3270.8940.7433.151.167.670.30717.7
ZSymbolNote\(a_1\)\(b_1\)\(a_2\)\(b_2\)\(a_3\)\(b_3\)\(a_4\)\(b_4\)\(a_5\)\(b_5\)
21ScSc: RHF0.37870.31331.21812.58562.05949.58133.261841.76882.387116.7282
Sc3+: HF0.1630.1570.3070.8990.7163.060.887.050.13916.1
22TiTi: RHF0.38250.3041.25982.48632.00089.27833.061739.07512.0694109.4583
Ti2+: HF0.3990.3761.042.741.218.1-0.079714.20.35223.2
Ti3+: HF0.3640.3640.9192.671.358.18-0.93311.80.58914.9
Ti4+: HF0.1160.1080.2560.6550.5652.380.7725.510.13212.3
23VV: RHF0.38760.29671.2752.3781.91098.79812.831435.95281.8979101.7201
V2+: RHF0.3170.2690.9392.091.497.22-1.3115.21.4717.6
V3+: HF0.3410.3210.8052.230.9425.990.078313.40.15616.9
V5+: HF0.03670.0330.1240.2220.2440.8240.7232.80.4356.7
24CrCr: RHF0.40460.29861.36962.39581.89419.14062.0837.47011.2196113.7121
Cr2+: HF0.2370.1770.6341.351.234.30.71312.20.085939.0
Cr3+: HF0.3930.3591.052.571.628.68-1.1511.00.40715.8
Cr4+: HF0.1320.1090.2920.6950.7032.390.6925.650.095914.7
25MnMn: RHF0.37960.26991.20942.04551.78157.47262.54231.06041.593791.5622
Mn2+: RHF0.05760.03980.210.2840.6041.291.324.230.65914.5
Mn3+: HF0.1160.01170.5230.8760.8813.060.5896.440.21414.3
Mn4+: HF0.3810.3541.832.72-1.333.470.9955.470.061816.1
26FeFe: RHF0.39460.27171.27252.04431.70317.60072.31429.97141.479586.2265
Fe2+: RHF0.3070.230.8381.621.114.870.2810.70.27719.2
Fe3+: RHF0.1980.1540.3870.8930.8892.620.7096.650.11718
27CoCo: RHF0.41180.27421.31612.03721.64937.72052.19329.9681.28384.9383
Co2+: RHF0.2130.1480.4880.9390.9982.780.8287.310.2320.7
Co3+: HF0.3310.2670.4871.410.7292.890.6086.450.13115.8
28NiNi: RHF0.3860.24781.17651.7661.54516.31072.07325.22041.381474.3146
Ni2+: RHF0.3380.2370.9821.671.325.73-3.5611.43.6212.1
Ni3+: HF0.3470.260.8771.710.794.750.05387.510.19213.0
29CuCu: RHF0.43140.26941.32081.92231.52367.34741.467128.98920.856290.6246
Cu1+: RHF0.3120.2010.8121.311.113.80.79410.50.25728.2
Cu2+: HF0.2240.1450.5440.9330.972.690.7277.110.18219.4
30ZnZn: RHF0.42880.25931.26461.79981.44726.751.829425.5861.093473.5284
Zn2+: RHF0.2520.1610.61.010.9172.760.6637.080.16119
ZSymbolNote\(a_1\)\(b_1\)\(a_2\)\(b_2\)\(a_3\)\(b_3\)\(a_4\)\(b_4\)\(a_5\)\(b_5\)
31GaGa: RHF0.48180.28251.40321.97851.65618.75462.460532.52381.105498.5523
Ga3+: HF0.3910.2640.9471.650.694.820.070910.70.065315.2
32GeGe: RHF0.46550.26471.30141.79261.60887.60712.699826.55411.300377.5238
Ge4+: HF0.3460.2320.831.450.5994.080.094913.2-0.021729.5
33AsAs: RHF0.45170.24931.22291.64361.58526.81542.795822.36811.263862.039
34SeSe: RHF0.44770.24051.16781.54421.58436.32312.808719.4611.195652.0233
35BrBr: RHF0.47980.25041.19481.59631.86956.96532.695319.84920.820350.3233
Br1-: RHF0.1250.0530.5630.4691.432.153.5211.13.2238.9
36KrKr: RHF0.45460.23091.09931.42791.76965.94492.706816.67520.867242.2243
37RbRb: RHF1.0160.48532.85285.09253.546625.7851-7.7804130.451512.1148138.6775
Rb1+: RHF0.3680.1870.8841.121.143.982.2610.90.88126.6
38SrSr: RHF0.67030.3191.49262.22873.336810.35044.4652.32913.1501151.2216
Sr2+: RHF0.3460.1760.8041.040.9883.591.899.320.60921.4
39YY: *RHF0.68940.31891.54742.29043.24510.00624.212644.07712.9764125.012
Y2+: *DS0.4650.240.9231.432.416.45-2.319.972.4812.2
40ZrZr: *RHF0.67190.30361.46842.12493.16688.92363.955736.84582.892108.2049
Zr4+: *DS0.2340.1130.6420.7360.7472.541.476.720.37714.7
ZSymbolNote\(a_1\)\(b_1\)\(a_2\)\(b_2\)\(a_3\)\(b_3\)\(a_4\)\(b_4\)\(a_5\)\(b_5\)
41NbNb: *RHF0.61230.27091.26771.76833.03487.24893.384127.94652.368398.5624
Nb3+: *DS0.3770.1840.7491.021.293.81.619.440.48125.7
Nb5+: *DS0.08280.03690.2710.2610.6540.9571.243.940.8299.44
42MoMo: *RHF0.67730.2921.47982.06063.17888.11293.082430.53361.8384100.0658
Mo3+: *DS0.4010.1910.7561.061.383.841.589.380.49724.6
Mo5+: *DS0.4790.2410.8461.4615.66.79-15.27.131.610.4
Mo6+: *DS0.2030.09710.5670.6470.6462.281.165.610.17112.4
43TeTe: *RHF0.70820.29761.63922.21063.19938.52463.432733.14561.871196.6377
44RuRu: *RHF0.67350.27731.49341.97163.09667.32492.725426.68911.559790.5581
Ru3+: *DS0.4280.1910.7731.091.553.821.469.080.48621.7
Ru4+: *DS0.2820.1250.6530.7531.142.851.537.010.41817.5
45RhRh: *RHF0.64130.2581.3691.77212.98546.38542.695223.25491.543385.1517
Rh3+: *DS0.3520.1510.7230.8781.53.281.638.160.49920.7
Rh4+: *DS0.3970.1770.7251.011.513.621.198.560.25118.9
46PdPd: *RHF0.59040.23241.17751.50192.65195.15912.287515.54280.868946.8213
Pd2+: *DS0.9350.3933.114.0624.643.1-43.65421.169.8
Pd4+: *DS0.3480.1510.640.8321.222.851.456.590.42715.6
47AgAg: RHF0.63770.24661.3791.69742.82945.76562.363120.09431.455376.7372
Ag1+: *DS0.5030.1990.941.192.174.051.9911.30.72632.4
Ag2+: *DS0.4310.1750.7560.9791.723.31.788.240.52621.4
48CdCd: RHF0.63640.24071.42471.68232.78025.65882.597320.72191.788669.1109
Cd2+: *DS0.4250.1680.7450.9441.733.141.747.840.48720.4
49InIn: RHF0.67680.25221.65891.85452.7746.29363.183525.14572.132684.5448
In3+: *DS0.4170.1640.7550.961.593.081.367.030.45116.1
50SnSn: RHF0.72240.26511.9612.06042.71617.30113.560327.54931.897281.3349
Sn2+: RHF0.7970.3172.132.512.159.04-1.6424.22.7226.4
Sn4+: RHF0.2610.09570.6420.6251.532.511.366.310.17715.9
ZSymbolNote\(a_1\)\(b_1\)\(a_2\)\(b_2\)\(a_3\)\(b_3\)\(a_4\)\(b_4\)\(a_5\)\(b_5\)
51SbSb: RHF0.71060.25621.92471.96462.61496.88523.832224.76481.889968.9168
Sb3+: *DS0.5520.2121.141.421.874.211.3612.50.41429
Sb5+: *DS0.3770.1510.5880.8121.222.41.185.270.24411.9
52TeTe: *RHF0.69470.24591.8691.85422.53566.44114.001322.1731.895559.2206
53II: RHF0.70470.24551.94841.86382.5946.76394.152621.80071.505756.4395
I1+: RHF0.9010.3122.82.595.6114.1-8.6934.412.639.5
54XeXe: RHF0.67370.23051.79081.6892.41295.82184.2118.39281.705847.2496
55CsCs: RHF1.27040.43563.80184.20585.661823.43420.9205136.77834.8105171.7561
Cs1+: RHF0.5870.21.41.381.874.123.48131.6731.8
56BaBa: RHF0.90490.30662.60762.43634.849812.18215.160354.61354.7388161.9978
Ba2+: *DS0.7330.2582.051.962311.8-15214.413414.9
57LaLa: *RHF0.84050.27912.38632.1414.613910.345.151441.91484.7949132.0204
La3+: *DS0.4930.1671.11.111.53.112.79.611.0821.2
58CeCe: *RHF0.85510.28052.39152.124.577210.18085.027842.06334.5118130.9893
Ce3+: *DS0.560.191.351.31.593.932.6310.70.70623.8
Ce4+: *DS0.4830.1651.091.11.343.022.458.850.79718.8
59PrPr: *RMF0.90960.29392.53132.24714.526610.82664.637648.88424.369147.602
Pr3+: *DS0.6630.2261.731.612.356.330.351111.5916.9
Pr4+: *DS0.5210.1771.191.171.333.282.368.940.6919.3
60NdNd: *RHF0.88070.28022.41832.08364.444810.03574.685847.45064.1725146.9976
Nd3+: *DS0.5010.1621.181.081.453.062.538.80.9219.6
ZSymbolNote\(a_1\)\(b_1\)\(a_2\)\(b_2\)\(a_3\)\(b_3\)\(a_4\)\(b_4\)\(a_5\)\(b_5\)
61PmPm: *RHF0.94710.29772.54632.22764.352310.57624.478949.36193.908145.358
Pm3+: *DS0.4960.1561.21.051.473.072.438.560.94319.2
62SmSm: *RHF0.96990.30032.58372.24474.277810.64874.457550.79943.5985146.4179
Sm3+: *DS0.5180.1631.241.081.433.112.48.520.78119.1
63EuEu: RHF0.86940.26532.24131.8593.91968.39983.969436.73974.5498125.7089
Eu2+: *DS0.6130.191.531.271.844.182.4610.70.71426.2
Eu3+: *DS0.4960.1521.211.011.452.952.368.180.77418.5
64GdGd: *RHF0.96730.29092.47022.10144.11489.70674.497243.4273.2099125.9474
Gd3+: *DS0.490.1481.190.9741.422.812.37.780.79517.7
65TbTb: *RHF0.93250.27612.36731.95113.87918.92963.967441.59373.7996131.0122
Tb3+: *DS0.5030.151.220.9821.422.862.247.770.7117.7
66DyDy: *RHF0.95050.27732.37051.94693.82188.88624.047143.09383.4451133.1396
Dy3+: *DS0.5030.1481.240.971.442.882.177.730.64317.6
67HoHo: *RHF0.92480.2662.24281.81833.61827.96553.79133.11293.7912101.8139
Ho3+: *DS0.4560.1291.170.8691.432.612.157.240.69216.7
68ErEr: *RHF1.03730.29442.48242.07973.65589.41563.892545.80563.0056132.772
Er3+: *DS0.5220.151.280.9641.462.932.057.720.50817.8
69TmTm: *RHF1.00750.28162.37871.94863.5448.71623.693241.8423.1759125.032
Tm3+: *DS0.4750.1321.20.8641.422.62.057.090.58416.6
70YbYb: *RHF1.03470.28552.39111.96793.46198.76193.655642.33043.0052125.6499
Yb2+: *DS0.5080.1361.370.9221.763.122.238.720.58423.7
Yb3+: *DS0.4980.1381.220.8811.392.631.976.990.55916.3
ZSymbolNote\(a_1\)\(b_1\)\(a_2\)\(b_2\)\(a_3\)\(b_3\)\(a_4\)\(b_4\)\(a_5\)\(b_5\)
71LuLu: *RHF0.99270.27012.24361.80733.35547.81123.781334.48493.0994103.3526
Lu3+: *DS0.4830.1311.210.8451.412.571.946.880.52216.2
72HfHf: *RHF1.02950.27612.29111.86253.4118.09613.949734.27122.492598.5295
Hf4+: *DS0.5220.1451.220.8961.372.741.686.910.31216.1
73TaTa: *RHF1.0190.26942.22911.79623.40977.69443.925231.09422.267991.1089
Ta5+: *DS0.5690.1611.260.9720.9792.761.295.40.55110.9
74WW: *RHF0.98530.25692.11671.67453.3577.00983.798126.92342.279881.391
W6+: *DS0.1810.01180.8730.4421.181.521.484.350.5629.42
75ReRe: *RHF0.99140.25482.08581.65183.45316.88453.881226.72341.852681.7215
76OsOs: *RHF0.98130.24872.03221.59733.36656.47373.623523.28171.974170.9254
Os4+: *DS0.5860.1551.310.9381.633.191.717.840.5419.3
77IrIr: *RHF1.01940.25542.06451.64753.44256.59663.491423.22691.697670.0272
Ir3+: *DS0.6920.1821.371.041.83.471.978.510.80421.2
Ir4+: *DS0.6530.1741.290.9921.53.141.747.220.68317.2
78PtPt: *RHF0.91480.22631.80961.38133.21345.32433.295317.59871.575460.0171
Pt2+: *DS0.8720.2231.681.352.634.991.9313.60.47533
Pt4+: *DS0.550.1421.210.8331.622.811.957.210.6117.7
79AuAu: RHF0.96740.23581.89161.47123.39935.67583.052418.71191.260761.5286
Au1+: *DS0.8110.2011.571.182.634.252.6812.10.99834.4
Au3+: *DS0.7220.1841.391.061.943.581.948.560.69920.4
80HgHg: RHF1.00330.24131.94691.52983.43965.80093.154819.4521.41860.5753
Hg1+: *DS0.7960.1941.561.142.724.212.7612.41.1836.2
Hg2+: *DS0.7730.1911.491.122.454.002.2310.80.5727.6
ZSymbolNote\(a_1\)\(b_1\)\(a_2\)\(b_2\)\(a_3\)\(b_3\)\(a_4\)\(b_4\)\(a_5\)\(b_5\)
81TITI: *RHF1.06890.2542.10381.67153.60396.35093.492723.15311.828378.7099
Tl1+: *DS0.820.1971.571.162.784.232.8212.71.3135.7
Tl3+: *DS0.8360.2081.431.20.3942.572.514.861.513.5
82PbPb: RHF1.08910.25522.18671.71743.6166.51313.803123.9171.899474.7039
Pb2+: *DS0.7550.1811.441.052.483.752.4510.61.0327.9
Pb4+: *DS0.5830.1441.140.7961.62.582.066.220.66214.8
83BiBi: RHF1.10070.25462.23061.73513.56896.49484.154923.64642.038270.378
Bi3+: *DS0.7080.171.350.9812.283.442.189.410.79723.7
Bi5+: *DS0.6540.1621.180.9051.252.681.665.140.77811.2
84PoPo: *RHF1.15680.26482.43531.87863.64597.17494.406425.17661.717969.2821
85AtAt: *RHF1.09090.24662.19761.67073.38316.01974.6720.76572.127757.2663
86RnRn: RHF1.07560.24022.1631.61693.31785.76444.885219.45682.048952.5009
87FrFr: *RHF1.42820.31833.50812.68895.676713.48164.196454.38663.8946200.8321
88RaRa: *RHF1.31270.28873.12432.28975.298810.82765.389143.53895.4133145.6109
Ra2+: *DS0.9110.2041.651.262.534.033.6212.61.5830
89AcAc: *RHF1.31280.28613.10212.25095.338510.52875.961141.77964.7562128.2973
Ac3+: *DS0.9150.2051.641.282.263.923.1811.31.2525.1
90ThTh: *RHF1.25530.27012.91782.06365.08629.30516.120634.59774.7122107.92
ZSymbolNote\(a_1\)\(b_1\)\(a_2\)\(b_2\)\(a_3\)\(b_3\)\(a_4\)\(b_4\)\(a_5\)\(b_5\)
91PaPa: *RHF1.32180.28273.14442.2255.437110.24545.644441.11624.0107124.4449
92UU: RHF1.33820.28383.20432.24525.455810.25195.483941.72513.6342124.9023
U3+: *DS1.140.252.481.843.617.391.13180.922.7
U4+: *DS1.090.2432.321.75127.79-9.118.312.1516.5
U6+: *DS0.6870.1541.140.8611.832.582.537.70.95715.9
93NpNp: *RHF1.51930.32134.00532.82066.532714.8878-0.140268.91036.748981.7257
94PuPu: *RHF1.35170.28133.29372.24185.32139.99524.646642.79393.5714132.1739
95AmAm: *RHF1.21350.24832.79621.84374.75457.54214.573129.38414.4786112.4579
96CmCm: *RHF1.29370.26383.112.03415.03938.71014.754635.29923.5031109.4972
97BkBk: *RHF1.29150.26113.10232.00234.93098.43774.600934.15593.4661105.8911
98CfCf: *RHF1.20890.24212.73911.74874.34826.72624.004723.21534.649780.3108
ZSymbolNote\(a_1\)\(b_1\)\(a_2\)\(b_2\)\(a_3\)\(b_3\)\(a_4\)\(b_4\)\(a_5\)\(b_5\)

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Stupidity has a certain charm; ignorance does not. Frank Zappa