# Fileset [IMFP_IX__March_18__2010_st.3.pdf](https://mdr.nims.go.jp/filesets/be9db9cd-f8a7-4eb0-984d-1d2cc4dda4d6/download) ## Creator [Tanuma, Shigeo](https://orcid.org/0000-0003-2628-9941), [Powell, C. J.](https://orcid.org/0000-0001-8990-2286), Penn, D. R. ## Rights ## Other metadata [Calculations of electron inelastic mean free paths. IX. Data for 41 elemental solids over the 50 eV to 30 keV range](https://mdr.nims.go.jp/datasets/f9222d77-030b-44e8-b8d5-5661ab007778) ## Fulltext IMFP_IX, March 18, 2010_st 37/60 Table 4. Calculated IMFPs for the 41 elemental solids as a function of electron kinetic energy E. Inelastic mean free path (Å) E (eV) Li Be C (graphite) C (diamond) C (glassy) Na Mg 54.6 4.84 3.56 4.57 6.25 5.75 5.25 4.10 60.3 5.12 3.60 4.40 5.69 5.77 5.56 4.26 66.7 5.43 3.68 4.30 5.26 5.77 5.90 4.45 73.7 5.77 3.78 4.27 4.96 5.84 6.27 4.66 81.5 6.14 3.91 4.29 4.77 5.96 6.66 4.89 90.0 6.54 4.07 4.35 4.68 6.12 7.08 5.15 99.5 6.98 4.25 4.44 4.65 6.30 7.53 5.42 109.9 7.45 4.45 4.57 4.68 6.54 8.01 5.72 121.5 7.97 4.68 4.73 4.76 6.80 8.53 6.06 134.3 8.53 4.94 4.92 4.88 7.11 9.09 6.41 148.4 9.15 5.22 5.14 5.04 7.44 9.70 6.80 164.0 9.81 5.53 5.39 5.23 7.83 10.4 7.22 181.3 10.5 5.87 5.67 5.46 8.26 11.1 7.67 200.3 11.3 6.24 5.99 5.71 8.81 11.8 8.16 221.4 12.1 6.65 6.33 6.00 9.34 12.7 8.69 244.7 13.1 7.09 6.72 6.33 9.86 13.6 9.27 270.4 14.1 7.58 7.14 6.70 10.5 14.6 9.90 298.9 15.1 8.11 7.61 7.10 11.2 15.7 10.6 330.3 16.4 8.76 8.12 7.52 12.0 17.0 11.4 365.0 17.7 9.38 8.69 8.02 12.8 18.3 12.2 403.4 19.2 10.1 9.31 8.56 13.8 19.7 13.1 445.9 20.7 10.8 9.99 9.16 14.8 21.2 14.0 492.7 22.4 11.6 10.7 9.81 15.9 22.9 15.1 544.6 24.3 12.5 11.5 10.5 17.1 24.7 16.2 601.8 26.3 13.5 12.4 11.3 18.4 26.7 17.5 665.1 28.5 14.5 13.4 12.1 19.8 28.9 18.9 735.1 30.9 15.7 14.4 13.0 21.4 31.3 20.4 812.4 33.5 16.9 15.5 14.0 23.0 33.8 22.0 897.8 36.4 18.3 16.8 15.1 24.8 36.7 23.8 992.3 39.5 19.8 18.1 16.3 26.8 39.8 25.7 1096.6 42.9 21.4 19.6 17.6 29.0 43.1 27.8 1212.0 46.6 23.2 21.1 19.0 31.4 46.8 30.2 1339.4 50.7 25.1 22.9 20.5 33.9 50.9 32.7 1480.3 55.1 27.3 24.8 22.1 36.7 55.2 35.4 1636.0 59.9 29.6 26.8 24.0 39.8 60.0 38.4 38/60 1808.0 65.2 32.1 29.1 25.9 43.1 65.3 41.7 1998.2 71.0 34.8 31.5 28.1 46.8 71.0 45.3 2208.3 77.3 37.8 34.2 30.4 50.8 77.2 49.2 2440.6 84.2 41.1 37.1 33.0 55.1 84.0 53.5 2697.3 91.7 44.7 40.3 35.8 59.9 91.4 58.1 2981.0 99.9 48.6 43.8 38.8 65.0 99.6 63.2 3294.5 108.9 52.8 47.6 42.1 70.7 108.4 68.7 3640.9 118.7 57.5 51.7 45.8 76.9 118.1 74.8 4023.9 129.4 62.6 56.3 49.7 83.6 128.6 81.4 4447.1 141.1 68.1 61.2 54.0 90.9 140.2 88.6 4914.8 153.9 74.2 66.6 58.8 99.0 152.8 96.4 5431.7 167.9 80.8 72.5 63.9 107.7 166.6 105.0 6002.9 183.2 88.0 78.9 69.5 117.3 181.6 114.4 6634.2 199.9 95.9 85.9 75.6 127.8 198.1 124.7 7332.0 218.2 104.5 93.6 82.3 139.2 216.1 135.9 8103.1 238.2 113.9 102.0 89.6 151.7 235.8 148.1 8955.3 260.1 124.2 111.1 97.6 165.3 257.3 161.5 9897.1 284.0 135.5 121.1 106.3 180.2 280.8 176.1 10938.0 310.2 147.8 132.0 115.9 196.5 306.5 192.1 12088.4 338.8 161.2 144.0 126.3 214.3 334.7 209.6 13359.7 370.1 175.9 157.0 137.6 233.8 365.4 228.7 14764.8 404.4 192.0 171.3 150.1 255.1 399.1 249.6 16317.6 441.9 209.6 186.9 163.6 278.4 435.9 272.4 18033.7 483.0 228.8 204.0 178.5 303.8 476.3 297.4 19930.4 527.9 249.8 222.6 194.7 331.6 520.3 324.7 22026.5 577.1 272.8 243.0 212.4 362.1 568.6 354.6 24343.0 631.0 298.0 265.3 231.8 395.4 621.4 387.3 26903.2 689.9 325.5 289.7 253.0 431.8 679.2 423.0 29732.6 754.5 355.6 316.4 276.2 471.6 742.5 462.2 39/60 Table 4. (Continued.) Inelastic mean free path (Å) E (eV) Al Si K Sc Ti V Cr 54.6 3.58 4.18 7.39 4.58 4.11 4.54 4.34 60.3 3.68 4.29 7.72 4.57 4.09 4.49 4.26 66.7 3.82 4.42 8.08 4.57 4.09 4.48 4.21 73.7 3.97 4.59 8.48 4.60 4.12 4.49 4.21 81.5 4.15 4.78 8.95 4.67 4.19 4.54 4.24 90.0 4.34 5.00 9.42 4.76 4.28 4.62 4.30 99.5 4.56 5.25 9.93 4.88 4.40 4.71 4.40 109.9 4.81 5.52 10.5 5.00 4.51 4.82 4.51 121.5 5.08 5.82 11.2 5.15 4.64 4.97 4.66 134.3 5.37 6.16 11.9 5.33 4.79 5.12 4.82 148.4 5.69 6.52 12.7 5.56 4.98 5.30 5.01 164.0 6.03 6.92 13.6 5.84 5.21 5.50 5.21 181.3 6.41 7.35 14.6 6.15 5.47 5.73 5.44 200.3 6.82 7.81 15.6 6.50 5.77 5.99 5.70 221.4 7.28 8.32 16.8 6.89 6.10 6.29 6.00 244.7 7.75 8.88 18.1 7.32 6.47 6.63 6.32 270.4 8.28 9.49 19.4 7.80 6.88 7.01 6.69 298.9 8.84 10.2 21.0 8.33 7.32 7.42 7.09 330.3 9.56 11.0 22.8 8.91 7.82 7.86 7.53 365.0 10.2 11.8 24.6 9.55 8.36 8.37 8.02 403.4 10.9 12.6 26.6 10.2 8.95 8.93 8.55 445.9 11.7 13.5 28.7 11.0 9.60 9.54 9.13 492.7 12.6 14.5 31.1 11.8 10.3 10.2 9.77 544.6 13.5 15.5 33.6 12.7 11.1 10.9 10.5 601.8 14.5 16.7 36.4 13.7 11.9 11.7 11.2 665.1 15.6 18.0 39.5 14.8 12.8 12.6 12.1 735.1 16.9 19.4 42.8 15.9 13.9 13.6 13.0 812.4 18.2 20.9 46.3 17.2 14.9 14.6 14.0 897.8 19.6 22.5 50.2 18.6 16.1 15.8 15.0 992.3 21.2 24.3 54.5 20.1 17.4 17.0 16.2 1096.6 22.9 26.3 59.1 21.8 18.9 18.4 17.5 1212.0 24.8 28.5 64.1 23.5 20.4 19.8 18.9 1339.4 26.9 30.8 69.6 25.5 22.1 21.4 20.5 1480.3 29.1 33.4 75.6 27.6 23.9 23.2 22.1 1636.0 31.6 36.2 82.1 29.9 25.8 25.1 23.9 1808.0 34.2 39.2 89.2 32.4 28.0 27.1 25.9 1998.2 37.1 42.5 97.0 35.1 30.3 29.4 28.0 40/60 2208.3 40.3 46.2 105.5 38.1 32.9 31.8 30.3 2440.6 43.8 50.1 114.8 41.3 35.7 34.5 32.9 2697.3 47.6 54.5 125.0 44.9 38.7 37.4 35.6 2981.0 51.7 59.2 136.0 48.7 42.0 40.5 38.6 3294.5 56.2 64.3 148.1 53.0 45.7 44.0 41.9 3640.9 61.1 70.0 161.4 57.6 49.6 47.7 45.5 4023.9 66.5 76.1 175.8 62.6 53.9 51.9 49.4 4447.1 72.4 82.8 191.6 68.1 58.6 56.3 53.7 4914.8 78.8 90.1 208.8 74.1 63.8 61.2 58.4 5431.7 85.8 98.1 227.7 80.6 69.4 66.6 63.5 6002.9 93.4 106.9 248.3 87.8 75.5 72.4 69.0 6634.2 101.7 116.4 270.8 95.6 82.2 78.8 75.1 7332.0 110.8 126.8 295.4 104.1 89.5 85.7 81.7 8103.1 120.8 138.2 322.4 113.4 97.5 93.3 88.9 8955.3 131.7 150.6 351.8 123.6 106.2 101.6 96.8 9897.1 143.6 164.2 384.0 134.7 115.7 110.7 105.4 10938.0 156.5 179.1 419.2 146.8 126.1 120.6 114.9 12088.4 170.7 195.3 457.7 160.1 137.5 131.4 125.2 13359.7 186.3 213.0 499.8 174.6 149.9 143.2 136.4 14764.8 203.2 232.4 545.9 190.4 163.5 156.1 148.7 16317.6 221.8 253.6 596.3 207.8 178.3 170.2 162.1 18033.7 242.1 276.8 651.4 226.7 194.6 185.6 176.8 19930.4 264.2 302.2 711.8 247.4 212.3 202.5 192.8 22026.5 288.5 329.9 777.8 270.1 231.7 220.9 210.4 24343.0 315.1 360.3 850.1 294.8 252.9 241.0 229.5 26903.2 344.1 393.5 929.2 321.9 276.1 263.0 250.5 29732.6 375.9 429.8 1015.8 351.5 301.5 287.1 273.4 41/60 Table 4. (Continued.) Inelastic mean free path (Å) E (eV) Fe Co Ni Cu Ge Y 54.6 4.28 4.84 4.77 4.94 4.08 5.04 60.3 4.25 4.68 4.68 4.87 4.18 5.05 66.7 4.26 4.58 4.59 4.84 4.31 5.09 73.7 4.30 4.52 4.58 4.84 4.45 5.16 81.5 4.37 4.51 4.55 4.87 4.62 5.25 90.0 4.47 4.52 4.59 4.93 4.80 5.36 99.5 4.57 4.55 4.63 5.00 5.02 5.50 109.9 4.70 4.61 4.70 5.11 5.25 5.67 121.5 4.86 4.70 4.80 5.24 5.51 5.89 134.3 5.05 4.83 4.92 5.40 5.79 6.15 148.4 5.25 4.98 5.07 5.58 6.09 6.46 164.0 5.47 5.13 5.24 5.79 6.43 6.81 181.3 5.71 5.30 5.45 6.02 6.79 7.20 200.3 5.98 5.50 5.67 6.29 7.18 7.64 221.4 6.28 5.74 5.91 6.58 7.61 8.13 244.7 6.61 6.00 6.19 6.90 8.07 8.66 270.4 6.97 6.30 6.49 7.25 8.58 9.24 298.9 7.38 6.63 6.83 7.64 9.13 9.88 330.3 7.85 7.00 7.23 8.15 9.86 10.7 365.0 8.33 7.41 7.64 8.60 10.5 11.5 403.4 8.86 7.85 8.09 9.11 11.2 12.3 445.9 9.44 8.35 8.60 9.67 12.0 13.2 492.7 10.1 8.89 9.15 10.3 12.8 14.2 544.6 10.8 9.49 9.75 10.9 13.7 15.3 601.8 11.5 10.1 10.4 11.7 14.7 16.4 665.1 12.4 10.9 11.1 12.5 15.8 17.7 735.1 13.3 11.6 11.9 13.4 16.9 19.1 812.4 14.3 12.5 12.8 14.3 18.2 20.6 897.8 15.4 13.4 13.8 15.4 19.6 22.2 992.3 16.6 14.5 14.8 16.6 21.1 23.9 1096.6 17.9 15.6 15.9 17.8 22.8 25.8 1212.0 19.3 16.8 17.2 19.2 24.6 27.9 1339.4 20.8 18.1 18.5 20.7 26.6 30.2 1480.3 22.5 19.6 20.0 22.3 28.7 32.7 1636.0 24.3 21.1 21.6 24.1 31.1 35.3 1808.0 26.3 22.9 23.4 26.1 33.6 38.3 1998.2 28.5 24.7 25.3 28.2 36.4 41.5 42/60 2208.3 30.9 26.8 27.4 30.5 39.5 45.0 2440.6 33.4 29.0 29.7 33.1 42.8 48.8 2697.3 36.2 31.4 32.1 35.8 46.5 53.0 2981.0 39.3 34.0 34.8 38.8 50.4 57.5 3294.5 42.6 36.9 37.7 42.1 54.8 62.5 3640.9 46.3 40.0 40.9 45.6 59.5 67.9 4023.9 50.2 43.4 44.4 49.5 64.7 73.8 4447.1 54.5 47.1 48.2 53.7 70.3 80.3 4914.8 59.3 51.2 52.3 58.3 76.4 87.3 5431.7 64.4 55.6 56.9 63.4 83.1 95.0 6002.9 70.0 60.4 61.8 68.8 90.4 103.4 6634.2 76.2 65.7 67.2 74.8 98.4 112.6 7332.0 82.9 71.5 73.1 81.4 107.1 122.6 8103.1 90.2 77.7 79.5 88.5 116.6 133.5 8955.3 98.2 84.6 86.5 96.3 127.0 145.5 9897.1 106.9 92.1 94.1 104.8 138.3 158.5 10938.0 116.4 100.3 102.5 114.1 150.7 172.8 12088.4 126.8 109.2 111.6 124.3 164.2 188.3 13359.7 138.2 118.9 121.6 135.4 179.0 205.3 14764.8 150.6 129.6 132.4 147.5 195.2 223.9 16317.6 164.2 141.2 144.3 160.7 212.9 244.3 18033.7 179.0 153.9 157.3 175.2 232.2 266.5 19930.4 195.2 167.8 171.5 191.0 253.4 290.8 22026.5 212.9 183.0 187.0 208.2 276.5 317.4 24343.0 232.3 199.6 204.0 227.1 301.8 346.4 26903.2 253.5 217.8 222.5 247.7 329.4 378.2 29732.6 276.7 237.6 242.8 270.3 359.6 413.0 43/60 Table 4. (Continued.) Inelastic mean free path (Å) E (eV) Nb Mo Ru Rh Pd Ag In 54.6 5.50 4.77 4.68 4.57 4.64 5.91 4.79 60.3 5.36 4.56 4.46 4.37 4.44 5.63 4.86 66.7 5.26 4.44 4.29 4.21 4.27 5.39 4.95 73.7 5.21 4.37 4.16 4.08 4.16 5.18 5.05 81.5 5.20 4.34 4.09 4.01 4.08 5.05 5.16 90.0 5.24 4.35 4.05 3.96 4.04 4.94 5.28 99.5 5.30 4.39 4.05 3.96 4.04 4.88 5.43 109.9 5.38 4.47 4.09 3.99 4.07 4.87 5.59 121.5 5.47 4.56 4.15 4.05 4.13 4.89 5.78 134.3 5.59 4.66 4.25 4.14 4.21 4.94 6.00 148.4 5.75 4.79 4.37 4.25 4.33 5.01 6.24 164.0 5.95 4.96 4.51 4.39 4.47 5.13 6.51 181.3 6.20 5.16 4.67 4.54 4.63 5.28 6.81 200.3 6.49 5.40 4.86 4.72 4.81 5.46 7.15 221.4 6.82 5.68 5.08 4.92 5.02 5.66 7.52 244.7 7.20 5.99 5.34 5.16 5.26 5.89 7.93 270.4 7.62 6.34 5.63 5.43 5.53 6.16 8.37 298.9 8.09 6.72 5.96 5.73 5.85 6.47 8.87 330.3 8.62 7.15 6.30 6.04 6.16 6.74 9.34 365.0 9.21 7.63 6.71 6.43 6.56 7.15 9.96 403.4 9.85 8.16 7.16 6.85 7.00 7.61 10.6 445.9 10.6 8.74 7.66 7.32 7.48 8.11 11.4 492.7 11.3 9.37 8.20 7.84 8.01 8.66 12.2 544.6 12.1 10.1 8.79 8.40 8.58 9.26 13.1 601.8 13.0 10.8 9.44 9.01 9.21 9.92 14.1 665.1 14.0 11.6 10.1 9.68 9.90 10.6 15.1 735.1 15.0 12.5 10.9 10.4 10.6 11.4 16.3 812.4 16.1 13.4 11.7 11.2 11.5 12.3 17.6 897.8 17.4 14.4 12.6 12.1 12.3 13.2 18.9 992.3 18.7 15.5 13.6 13.0 13.3 14.2 20.4 1096.6 20.1 16.7 14.6 14.0 14.3 15.2 22.1 1212.0 21.7 18.0 15.8 15.1 15.4 16.4 23.9 1339.4 23.4 19.4 17.0 16.2 16.7 17.7 25.8 1480.3 25.3 21.0 18.3 17.5 18.0 19.0 27.9 1636.0 27.3 22.6 19.8 18.9 19.4 20.5 30.1 1808.0 29.5 24.5 21.4 20.4 21.0 22.2 32.6 1998.2 31.9 26.4 23.1 22.1 22.7 23.9 35.3 44/60 2208.3 34.5 28.6 25.0 23.9 24.5 25.9 38.2 2440.6 37.4 31.0 27.1 25.8 26.6 28.0 41.4 2697.3 40.5 33.6 29.3 28.0 28.8 30.3 44.9 2981.0 43.9 36.4 31.8 30.3 31.2 32.8 48.6 3294.5 47.6 39.5 34.4 32.9 33.8 35.6 52.8 3640.9 51.7 42.8 37.3 35.6 36.7 38.6 57.3 4023.9 56.1 46.5 40.5 38.7 39.8 41.8 62.2 4447.1 60.9 50.5 44.0 42.0 43.2 45.4 67.6 4914.8 66.2 54.8 47.8 45.6 46.9 49.3 73.4 5431.7 71.9 59.6 51.9 49.5 51.0 53.6 79.8 6002.9 78.2 64.8 56.4 53.8 55.4 58.2 86.8 6634.2 85.1 70.4 61.3 58.5 60.2 63.2 94.4 7332.0 92.5 76.6 66.7 63.6 65.5 68.8 102.7 8103.1 100.7 83.4 72.6 69.2 71.3 74.8 111.8 8955.3 109.6 90.7 79.0 75.3 77.5 81.4 121.8 9897.1 119.3 98.8 86.0 82.0 84.4 88.5 132.6 10938.0 129.9 107.5 93.6 89.3 91.9 96.4 144.4 12088.4 141.5 117.1 101.9 97.2 100.1 104.9 157.4 13359.7 154.2 127.6 111.0 105.9 109.0 114.3 171.5 14764.8 168.0 139.1 121.0 115.4 118.8 124.5 186.9 16317.6 183.1 151.6 131.8 125.8 129.5 135.6 203.8 18033.7 199.6 165.2 143.7 137.1 141.1 147.8 222.2 19930.4 217.7 180.2 156.7 149.4 153.9 161.1 242.4 22026.5 237.4 196.5 170.8 162.9 167.8 175.7 264.4 24343.0 259.0 214.3 186.3 177.7 183.0 191.6 288.5 26903.2 282.5 233.8 203.3 193.9 199.6 208.9 314.8 29732.6 308.3 255.1 221.8 211.5 217.8 227.9 343.6 45/60 Table 4. (Continued.) Inelastic mean free path (Å) E (eV) Sn Cs Gd Tb Dy Hf Ta 54.6 5.82 6.57 4.14 4.08 4.44 5.43 4.71 60.3 5.88 6.92 4.15 4.06 4.39 5.37 4.58 66.7 5.94 7.31 4.19 4.06 4.37 5.33 4.51 73.7 6.03 7.74 4.26 4.09 4.40 5.33 4.47 81.5 6.12 8.22 4.36 4.14 4.44 5.34 4.48 90.0 6.26 8.73 4.48 4.21 4.50 5.39 4.49 99.5 6.39 9.29 4.61 4.29 4.59 5.46 4.54 109.9 6.57 9.89 4.79 4.40 4.70 5.55 4.60 121.5 6.78 10.5 5.01 4.54 4.84 5.67 4.70 134.3 7.01 11.3 5.25 4.71 5.01 5.81 4.82 148.4 7.27 12.0 5.51 4.92 5.22 5.98 4.95 164.0 7.55 12.9 5.79 5.15 5.44 6.19 5.11 181.3 7.87 13.8 6.11 5.40 5.71 6.43 5.30 200.3 8.22 14.8 6.46 5.70 6.01 6.72 5.52 221.4 8.62 15.9 6.86 6.02 6.34 7.03 5.77 244.7 9.05 17.1 7.28 6.38 6.70 7.39 6.05 270.4 9.53 18.4 7.74 6.78 7.11 7.79 6.37 298.9 10.1 19.8 8.24 7.21 7.55 8.23 6.72 330.3 10.5 21.4 8.93 7.76 8.13 8.80 7.17 365.0 11.2 23.0 9.51 8.27 8.65 9.34 7.60 403.4 11.9 24.8 10.2 8.83 9.22 9.92 8.07 445.9 12.8 26.8 10.9 9.44 9.84 10.6 8.58 492.7 13.6 28.9 11.6 10.1 10.5 11.2 9.14 544.6 14.6 31.3 12.5 10.8 11.3 12.0 9.74 601.8 15.7 33.8 13.4 11.6 12.1 12.8 10.4 665.1 16.8 36.6 14.4 12.5 13.0 13.7 11.1 735.1 18.1 39.7 15.5 13.5 13.9 14.7 11.9 812.4 19.5 43.0 16.7 14.5 15.0 15.7 12.8 897.8 21.0 46.6 18.0 15.6 16.2 16.9 13.7 992.3 22.6 50.5 19.4 16.8 17.4 18.1 14.7 1096.6 24.4 54.8 21.0 18.2 18.8 19.5 15.8 1212.0 26.4 59.5 22.7 19.6 20.3 21.0 17.0 1339.4 28.5 64.6 24.5 21.2 21.9 22.6 18.3 1480.3 30.8 70.2 26.5 23.0 23.7 24.4 19.7 1636.0 33.3 76.3 28.7 24.8 25.6 26.3 21.3 1808.0 36.0 82.9 31.1 26.9 27.7 28.4 23.0 1998.2 38.9 90.1 33.7 29.1 30.0 30.7 24.8 46/60 2208.3 42.1 98.0 36.5 31.6 32.5 33.2 26.8 2440.6 45.6 106.6 39.6 34.3 35.2 35.9 29.0 2697.3 49.4 115.9 43.0 37.2 38.2 38.9 31.4 2981.0 53.5 126.2 46.6 40.3 41.5 42.1 34.0 3294.5 58.0 137.3 50.7 43.8 45.0 45.6 36.8 3640.9 63.0 149.5 55.0 47.6 48.9 49.5 39.9 4023.9 68.3 162.8 59.8 51.7 53.1 53.7 43.3 4447.1 74.2 177.3 65.0 56.2 57.6 58.3 47.0 4914.8 80.6 193.2 70.6 61.1 62.6 63.3 51.0 5431.7 87.6 210.6 76.8 66.4 68.1 68.7 55.4 6002.9 95.2 229.5 83.5 72.2 74.0 74.6 60.2 6634.2 103.5 250.3 90.9 78.6 80.5 81.1 65.4 7332.0 112.6 272.9 98.9 85.5 87.6 88.1 71.0 8103.1 122.6 297.7 107.6 93.1 95.4 95.8 77.2 8955.3 133.4 324.8 117.2 101.3 103.8 104.2 84.0 9897.1 145.2 354.4 127.7 110.4 113.0 113.4 91.4 10938.0 158.1 386.8 139.1 120.2 123.1 123.4 99.4 12088.4 172.3 422.2 151.6 131.0 134.1 134.3 108.2 13359.7 187.7 460.9 165.2 142.8 146.2 146.3 117.8 14764.8 204.5 503.3 180.1 155.7 159.3 159.3 128.3 16317.6 222.9 549.7 196.4 169.7 173.7 173.6 139.8 18033.7 243.0 600.4 214.2 185.1 189.4 189.1 152.3 19930.4 265.0 655.9 233.7 201.9 206.6 206.1 166.0 22026.5 289.0 716.6 255.0 220.3 225.3 224.7 180.9 24343.0 315.2 783.0 278.2 240.4 245.8 245.0 197.2 26903.2 343.9 855.8 303.7 262.4 268.2 267.2 215.1 29732.6 375.3 935.3 331.5 286.4 292.8 291.5 234.6 47/60 Table 4. (Continued.) Inelastic mean free path (Å) E (eV) W Re Os Ir Pt Au Bi 54.6 5.04 5.04 5.29 5.01 4.81 4.95 4.96 60.3 4.77 4.73 5.01 4.74 4.59 4.75 5.02 66.7 4.60 4.49 4.77 4.53 4.44 4.60 5.09 73.7 4.49 4.32 4.61 4.36 4.30 4.49 5.15 81.5 4.43 4.22 4.50 4.25 4.21 4.41 5.27 90.0 4.41 4.18 4.43 4.19 4.16 4.38 5.40 99.5 4.43 4.17 4.41 4.16 4.15 4.34 5.54 109.9 4.49 4.20 4.44 4.18 4.19 4.36 5.70 121.5 4.57 4.25 4.51 4.23 4.25 4.40 5.88 134.3 4.67 4.33 4.59 4.31 4.34 4.48 6.09 148.4 4.78 4.44 4.69 4.41 4.45 4.58 6.31 164.0 4.92 4.57 4.82 4.55 4.59 4.72 6.57 181.3 5.09 4.71 4.97 4.70 4.75 4.88 6.86 200.3 5.28 4.89 5.14 4.87 4.95 5.07 7.17 221.4 5.51 5.09 5.35 5.07 5.17 5.29 7.53 244.7 5.77 5.32 5.59 5.31 5.41 5.54 7.93 270.4 6.06 5.59 5.86 5.57 5.68 5.82 8.36 298.9 6.38 5.89 6.16 5.86 5.99 6.13 8.85 330.3 6.79 6.25 6.55 6.22 6.36 6.47 9.35 365.0 7.19 6.62 6.93 6.60 6.74 6.87 9.96 403.4 7.63 7.03 7.34 7.00 7.16 7.31 10.6 445.9 8.11 7.47 7.80 7.45 7.62 7.78 11.4 492.7 8.62 7.94 8.29 7.93 8.12 8.29 12.2 544.6 9.19 8.47 8.83 8.45 8.66 8.87 13.0 601.8 9.80 9.03 9.42 9.02 9.24 9.47 14.0 665.1 10.5 9.65 10.1 9.63 9.88 10.1 15.0 735.1 11.2 10.3 10.7 10.3 10.6 10.8 16.1 812.4 12.0 11.1 11.5 11.0 11.3 11.6 17.3 897.8 12.8 11.8 12.3 11.8 12.1 12.5 18.7 992.3 13.8 12.7 13.2 12.7 13.0 13.4 20.1 1096.6 14.8 13.6 14.2 13.6 14.0 14.4 21.7 1212.0 15.9 14.7 15.2 14.6 15.0 15.5 23.3 1339.4 17.1 15.8 16.4 15.7 16.2 16.7 25.2 1480.3 18.4 17.0 17.6 16.9 17.4 18.0 27.2 1636.0 19.9 18.3 19.0 18.2 18.8 19.4 29.4 1808.0 21.4 19.8 20.5 19.7 20.3 21.0 31.8 1998.2 23.1 21.3 22.1 21.2 21.9 22.6 34.3 48/60 2208.3 25.0 23.0 23.8 22.9 23.6 24.5 37.2 2440.6 27.0 24.9 25.8 24.8 25.5 26.5 40.2 2697.3 29.2 26.9 27.8 26.8 27.6 28.6 43.6 2981.0 31.6 29.2 30.1 29.0 29.9 31.0 47.2 3294.5 34.3 31.6 32.6 31.4 32.4 33.6 51.2 3640.9 37.1 34.2 35.3 34.0 35.1 36.4 55.6 4023.9 40.3 37.1 38.3 36.8 38.0 39.5 60.3 4447.1 43.7 40.2 41.5 39.9 41.2 42.8 65.5 4914.8 47.4 43.6 45.0 43.3 44.7 46.4 71.1 5431.7 51.4 47.4 48.9 47.0 48.6 50.4 77.3 6002.9 55.9 51.5 53.1 51.1 52.7 54.8 84.0 6634.2 60.7 55.9 57.6 55.5 57.3 59.5 91.4 7332.0 65.9 60.7 62.6 60.3 62.2 64.7 99.4 8103.1 71.6 66.0 68.0 65.5 67.6 70.3 108.1 8955.3 77.9 71.8 74.0 71.2 73.6 76.5 117.7 9897.1 84.7 78.0 80.4 77.4 80.0 83.2 128.1 10938.0 92.2 84.9 87.5 84.2 87.0 90.5 139.5 12088.4 100.3 92.4 95.2 91.6 94.7 98.5 152.0 13359.7 109.2 100.6 103.6 99.7 103.1 107.3 165.5 14764.8 118.9 109.5 112.8 108.6 112.2 116.8 180.4 16317.6 129.5 119.2 122.8 118.3 122.2 127.2 196.6 18033.7 141.0 129.9 133.7 128.8 133.2 138.6 214.3 19930.4 153.7 141.5 145.7 140.3 145.1 151.0 233.7 22026.5 167.5 154.2 158.8 152.9 158.1 164.6 254.9 24343.0 182.6 168.1 173.1 166.7 172.4 179.5 278.0 26903.2 199.1 183.3 188.7 181.8 187.9 195.7 303.3 29732.6 217.1 199.9 205.7 198.2 205.0 213.4 331.0 49/60 Table 5. Values of the parameters β, γ, C, and D found in the fits of Eq. (7) to the calculated IMFPs for each elemental solid, values of βopt calculated from Eq. (9), and values of RMS calculated from Eq. (8). Element βopt (eV-1 Å-1) β (eV-1 Å-1) γ (eV-1) C (Å-1) D (eV Å-1) RMS (%) Li 0.0646 0.0653 0.4340 3.091 81.4 0.16 Be 0.0279 0.0290 0.1668 1.591 31.2 0.35 C (graphite) 0.0177 0.0183 0.1333 1.365 23.6 0.20 C (diamond) 0.0135 0.0139 0.1022 1.271 24.9 0.27 C (glassy) 0.0147 0.0153 0.1380 1.072 23.3 0.28 Na 0.1236 0.1258 0.3030 7.846 268.1 0.24 Mg 0.0618 0.0642 0.1648 3.801 126.5 0.49 Al 0.0367 0.0389 0.1258 1.629 50.3 0.61 Si 0.0291 0.0311 0.1186 1.104 30.3 0.63 K 0.1726 0.1759 0.3041 5.119 2.1 0.33 Sc 0.0604 0.0603 0.1587 5.393 119.5 0.42 Ti 0.0378 0.0380 0.1352 3.436 88.3 0.33 V 0.0256 0.0263 0.0942 2.361 73.5 0.51 Cr 0.0196 0.0204 0.0860 1.492 43.0 0.45 Fe 0.0142 0.0151 0.0715 0.981 33.7 0.72 Co 0.0140 0.0149 0.0623 1.186 40.9 0.94 Ni 0.0123 0.0132 0.0587 0.965 34.6 0.92 Cu 0.0108 0.0117 0.0535 0.680 25.8 0.94 Ge 0.0409 0.0444 0.0781 1.592 61.4 0.74 Y 0.0685 0.0708 0.1161 3.261 43.1 0.63 Nb 0.0315 0.0324 0.0811 2.494 69.8 0.60 Mo 0.0274 0.0283 0.0771 2.000 52.0 0.53 Ru 0.0208 0.0214 0.0743 1.740 48.4 0.42 Rh 0.0198 0.0204 0.0732 1.760 51.8 0.42 Pd 0.0184 0.0188 0.0787 1.733 50.5 0.44 Ag 0.0188 0.0196 0.0628 1.933 65.0 0.65 In 0.0672 0.0693 0.0911 5.607 191.8 0.47 Sn 0.0485 0.0505 0.0752 4.016 145.9 0.73 Cs 0.2960 0.3045 0.2512 9.227 247.1 0.16 Gd 0.0279 0.0292 0.0909 1.199 26.9 0.35 Tb 0.0327 0.0337 0.0979 2.236 56.6 0.26 Dy 0.0311 0.0323 0.0846 2.049 55.8 0.29 Hf 0.0529 0.0566 0.0523 3.038 111.4 0.45 Ta 0.0428 0.0460 0.0488 2.378 87.4 0.54 W 0.0342 0.0372 0.0417 1.543 55.6 0.65 Re 0.0296 0.0321 0.0428 1.502 50.6 0.54 Os 0.0241 0.0262 0.0395 1.160 42.6 0.54 Ir 0.0223 0.0241 0.0422 1.132 38.9 0.42 Pt 0.0207 0.0223 0.0444 1.046 35.4 0.38 Au 0.0202 0.0213 0.0524 1.424 48.1 0.31 Bi 0.0576 0.0609 0.0700 3.998 146.3 0.49 50/60 Table 6. Root-mean-square (RMS) deviations between IMFPs from the TPP-2M equation [Eqs. (7) and (13)] and IMFPs calculated from optical data for the indicated elemental solids and for energies between 50 eV and 30 keV. Element RMS deviation (%) Li 14.7 Be 23.7 C (graphite) 47.9 C (diamond) 71.7 C (glassy) 1.6 Na 4.6 Mg 9.0 Al 11.4 Si 3.0 K 2.1 Sc 24.8 Ti 20.6 V 8.2 Cr 5.8 Fe 2.6 Co 6.7 Ni 7.2 Cu 11.9 Ge 5.6 Y 14.3 Nb 2.9 Mo 6.6 Ru 4.3 Rh 6.2 Pd 4.4 Ag 8.2 In 20.6 Sn 4.9 Cs 36.7 Gd 6.6 Tb 11.4 Dy 5.3 Hf 12.9 Ta 17.0 W 8.8 Re 6.3 Os 6.6 Ir 6.6 Pt 9.1 Au 9.4 Bi 13.6 51/60 Figure captions Fig. 1. Plots of Zeff from Eq. (5) (solid line) and Peff from Eq. (6) (short-dashed line) as a function of for aluminum. Fig. 2. Plots of Zeff from Eq. (5) (solid line) and Peff from Eq. (6) (short-dashed line) as a function of for bismuth. Fig. 3. Plot of errors of KK- sum rule [Eq. (6)] versus errors of f-sum rule [Eq. (5)] for the 41 elemental solids. Fig. 4. Plots of electron inelastic mean free paths as a function of electron energy for Li, Be, graphite, diamond, glassy carbon and Na. The solid circles show calculated IMFPs from the Penn algorithm (Table 4). The solid lines show fits to these IMFPs with the modified Bethe equation [Eq. (7)] and the derived parameters in Table 5. The long-dashed lines indicate IMFPs calculated from the TPP-2M equation [Eqs. (7) and (13)]. The ordinate scale on the right indicates the IMFP scale for Li. Successive plots have been displaced vertically for clarity, and the ordinate scale at the left indicates these displacements. Fig. 5. Plots of electron inelastic mean free paths as a function of electron energy for Mg, Al, Si, K, Sc and Ti. See caption to Fig. 4. Fig. 6. Plots of electron inelastic mean free paths as a function of electron energy for V, Cr, Fe, Co, Ni, and Cu. See caption to Fig. 4. Fig. 7. Plots of electron inelastic mean free paths as a function of electron energy for Ge, Y, Nb, Mo and Ru. See caption to Fig. 4. Fig. 8. Plots of electron inelastic mean free paths as a function of electron energy for Rh, Pd, Ag, In, Sn and Cs. See caption to Fig. 4. 52/60 Fig. 9. Plots of electron inelastic mean free paths as a function of electron energy for Gd, Tb, Dy, Hf, Ta and W. See caption to Fig. 4. Fig. 10. Plots of electron inelastic mean free paths as a function of electron energy for Re, Os, Ir, Pt, Au and Bi. See caption to Fig. 4. Fig. 11. Plots of the ratio of the IMFPs in Table 4 for Ti, V, Cr, Fe, Cu Y, Nb, Mo, Ru, Rh, Pd, Hf, Ta, W, Re, Os, Ir, and Au with the newer ELFs that we used ( ) to the corresponding IMFPs that we published previously ( ) in Ref. 4. Fig. 12. Plots of slopes of Fano plots for Li, Ni and Si from Eqs. (10)-(12) as a function of the upper energy limit, , used in the evaluation of from Eq. (9) or of electron energy Ei. The dashed lines indicate values of the slopes calculated from Eq. (10). The solid diamonds indicate slopes calculated from the optical IMFPs (Table 4) using Eq. (11). The solid lines show slopes calculated from Eq. (12) with parameter values from Table 5 for each elemental solid. The discontinuities in the vicinity of 300 eV are artifacts associated with use of the FPA for energies between 10 eV and 300 eV and the SPA for energies between 330 eV and 30 keV. Fig. 13. Plots of slopes of Fano plots for Ag and Pt. See caption to Fig. 12. Fig. 14. Ratio of IMFPs calculated from the TPP-2M equation [Eqs. (7) and (13)] to IMFPs calculated from optical data as a function of electron energy for the 41 elemental solids. Fig. 15. Comparison of IMFPs calculated from optical data for Al by Mao et al. (solid line, Refs. 48 and 49) with our IMFPs that were obtained with the single-pole approximation [solid circles and dashed line, TPP (SPA)] and the full Penn algorithm [solid squares, TPP (FPA)]. 53/60 Fig. 16. Comparison of IMFPs calculated from optical data for Cu by Mao et al. (solid line, Refs. 48 and 49) with our IMFPs that were obtained with the single-pole approximation [solid circles and dashed line, TPP (SPA)] and the full Penn algorithm [solid squares, TPP (FPA)]. Fig. 17. Comparison of IMFPs calculated from optical data for Al by Denton et al. (solid line, Ref. 38) with our IMFPs that were obtained with the single-pole approximation [solid circles and dashed line, TPP (SPA)] and the full Penn algorithm [solid squares, TPP (FPA)]. Fig. 18. Comparison of IMFPs calculated from optical data for Au by Denton et al. (solid line, Ref. 38) with our IMFPs that were obtained with the single-pole approximation [solid circles and dashed line, TPP (SPA)] and the full Penn algorithm [solid squares, TPP (FPA)]. Fig. 19. Comparison of Fano plots for graphite with E/λ plotted as a function of electron energy. The solid circles are values of E/λ with IMFPs from our optical IMFPs. The solid line indicates values of E/λ with IMFPs calculated from the TPP-2M equation [Eqs. (7) and (13)]. The dashed and dotted lines show E/λ values from IMFPs calculated with Eq. (14) using parameters obtained from the EPES experiments of Tanuma et al. (Ref. 47) and Werner et al. (Refs. 83 and 84), respectively. Fig. 20. Comparison of Fano plots for silicon with E/λ plotted as a function of electron energy. See caption to Fig. 18. Fig. 21. Comparison of Fano plots for iron with E/λ plotted as a function of electron energy. See caption to Fig. 18. Fig.22. Comparison of Fano plots for silver with E/λ plotted as a function of electron energy. 54/60 See caption to Fig. 18. Fig. 23. Comparison of Fano plots for gold with E/λ plotted as a function of electron energy. See caption to Fig. 18. Fig. 24. Plot of βEPES values from the EPES experiments of Tanuma et al. (Ref. 47, solid circles) and Werner et al. (Refs. 83 and 84, solid squares) versus values of from Eq. (15) (evaluated with parameter values from Table 5 and for an energy of 1 keV) for the elemental solids common to our calculations and each set of EPES measurements. Fig. 25. Summary plot of calculated IMFPs for the 41 elemental solids (Table 4) as a function of electron energy. 55/60 References 1 C. J. Powell, A. Jablonski, Nucl. Instr. Methods Phys. Res. A. 2009, 54, 601. 2 C. J. Powell, A. Jablonski A, J. Electron Spectrosc. Relat. Phenom. (in press). 3 S. Tanuma, C. J. Powell, D. R. Penn, Surf. Interface Anal. 1988, 11, 577. 4 S. Tanuma, C. J. Powell, D. R. Penn, Surf. 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