(* :Title: XRayAttenuation *) (* :Author: John Schweppe *) (* :Summary: This package provides functions describing the attenuation and energy absorption of x-rays in various materials, based on NIST report 5632, by J. Hubbell and S.M. Seltzer. *) (* :Context: XRayAttenuation *) (* :Package Version: 1.0 *) (* :Copyright: Copyright 2002, John Schweppe *) (* :History: Original version by John Schweppe, February, 2002. *) (* :Keywords: *) (* :Source: J. Hubbell and S.M. Seltzer, "Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients 1 keV to 20 MeV for Elements Z = 1 to 92 and 48 Additional Substances of Dosimetric Interest," National Institute of Standards and Technology report NISTIR 5632 (1995). Also available at: http://physics.nist.gov/PhysRefData/XrayMassCoef/cover.html *) (* :Warning: Arguments are passed to the functions XRayTransmission and XRayAbsorption, which call the Exp function, without checking whether Exp will underflow or overflow. *) (* :Mathematica Version: Tested with Versions 3.0 and 4.1. *) (* :Limitation: Needs the following standard packages: "DiscreteMath`Tree`" "Miscellaneous`ChemicalElements`" "Miscellaneous`Units`" "Miscellaneous`SIUnits`" "Miscellaneous`PhysicalConstants`" *) (* :Discussion: The tables in NIST 5632 report give x-ray mass attenuation coefficients (MAC) and mass energy absorption coefficients (MEAC) for the first 92 elements, from hydrogen through uranium, and for 48 additional radiological materials. The tables cover the energy range from 0.001 MeV to 20 MeV. The tables give coefficients in cm^2/g against energy in MeV. The report also gives the density in g/cm^3 assumed for each material. The values in the table for gases appear to be for 20 degrees C at 1 atmosphere. The values for ceric ammonium sulfate solution are for 0.015 Molar solution. Interpolation is done to Log of coefficients against Log of energy, because of the near power-law dependence of coefficients against energy over much of the energy range. The final result is then taken as the Exp of the interpolation: coefficient = Exp[Interpolation[Log[energy]]]. At each absorption edge the coefficients undergo a discontinuous change, so the interpolation is done separately for each region of the table, between pairs of absorption edges. The order of the polynomial interpolating function is set to 3, except for regions of the table with only three points between absorptiion edges, where it is set to 2. The tables include at least 3 points between each pair of absorption edges. The Tree functions used to find the correct part of each table, between absorption edges, do not include the last energy in each table, at 20 MeV, so the value for the interpolation at 20 MeV must be added back in separately. The names of the first 92 elements are taken from the Miscellaneous`ChemicalElements` package, in order to be consistent with that package. The densities of materials, used to calculate mean free path, transmission, and absorption, are taken from the NIST report, rather than from the Miscellaneous`ChemicalElements` package, in order to be consistent with the NIST report. I corrected 2 apparent typos in the tables taken from the NIST web site: - changed MAC for Chromium at 0.0059892 MeV from 597.7 to 516.0 cm^2/g. - changed MAC for Thulium at 0.0593896 MeV from 12.00 to 14.60 cm^2/g. I removed 3 points that were so close to an absorption edge that round-off error caused problems with the interpolating polynomial: - removed the point at 0.006 MeV for Chromium, both MAC and MEAC. - removed the point at 0.06 MeV for Thulium, both MAC and MEAC. - removed the point at 0.02 MeV for Molybdenum, both MAC and MEAC. *) BeginPackage["XRayAttenuation`", "DiscreteMath`Tree`", "Miscellaneous`ChemicalElements`", "Miscellaneous`Units`", "Miscellaneous`SIUnits`", "Miscellaneous`PhysicalConstants`"] XRayAttenuation::usage = "The XRayAttenuation package describes the attenuation and energy absorption of x-rays in the first 92 elements and in 48 additional radiological materials for x-ray energy from 1 keV to 20 MeV. It defines the functions XRayMAC, XRayMEAC, XRayAMFP, XRayEAMFP, XRayTransmission, and XRayAbsorption for all these materials. It defines the functions MixtureMAC, MixtureAMFP, and MixtureTransmission for mixtures of all these materials. It defines the functions CompoundMAC, CompoundAMFP, and CompoundTransmission for chemical compounds of the first 92 elements. It defines the functions WaveLengthToEnergy, EnergyToWaveLength, FrequencyToEnergy, and EnergyToFrequency. It define the additional radiological materials RadiologicalMaterials." RadiologicalMaterials::usage = "RadiologicalMaterials is a list of the materials covered by the XRayAttenuation package in addition to the first 92 elements." XRayMAC::usage = "XRayMAC[material, energy] gives the x-ray mass attenuation coefficient of the specified material at the specified x-ray energy. The energy argument requires proper units." XRayMEAC::usage = "XRayMEAC[material, energy] gives the x-ray mass energy absorption coefficient of the specified material at the specified x-ray energy. The energy argument requires proper units." XRayAMFP::usage = "XRayAMFP[material, energy] gives the x-ray attenuation mean free path of the specified material at the specified x-ray energy. The energy argument requires proper units." XRayEAMFP::usage = "XRayEAMFP[material, energy] gives the x-ray energy absorption mean free path of the specified material at the specified x-ray energy. The energy argument requires proper units." XRayTransmission::usage = "XRayTransmission[material, energy, thickness] gives the x-ray transmission fraction through the specified thickness of the specified material at the specified x-ray energy. The energy and thickness arguments require proper units." XRayAbsorption::usage = "XRayAbsorption[material, energy, thickness] gives the x-ray energy absorption fraction in the specified thickness of the specified material at the specified x-ray energy. The energy and thickness arguments require proper units." MixtureMAC::usage = "MixtureMAC[mixture, energy] gives the x-ray mass attenuation coefficient of the specified mixture at the specified x-ray energy. The mixture is given in the form {{material1, fraction1}, {material2, fraction2}, ...}, where each fraction is the fraction by weight of that material in the mixture. The energy argument requires proper units." MixtureAMFP::usage = "MixtureAMFP[mixture, density, energy] gives the x-ray attenuation mean free path of the specified mixture with specified density at the specified x-ray energy. The mixture is given in the form {{material1, fraction1}, {material2, fraction2}, ...}, where each fraction is the fraction by weight of that material in the mixture. The density and energy arguments require proper units." MixtureTransmission::usage = "MixtureTransmission[mixture, density, energy, thickness] gives the x-ray transmission fraction through the specified thickness of the specified mixture with specified density at the specified x-ray energy. The mixture is given in the form {{material1, fraction1}, {material2, fraction2}, ...}, where each fraction is the fraction by weight of that material in the mixture. The density, energy, and thickness arguments require proper units." CompoundMAC::usage = "CompoundMAC[compound, energy] gives the x-ray mass attenuation coefficient of the specified chemical compound at the specified x-ray energy. The compound is given in the form {{element1, number1}, {element2, number2}, ...}, where each number is the number of atoms per molecule of the element in the compound. The energy argument requires proper units." CompoundAMFP::usage = "CompoundAMFP[compound, density, energy] gives the x-ray attenuation mean free path of the specified chemical compound with specified density at the specified x-ray energy. The compound is given in the form {{element1, number1}, {element2, number2}, ...}, where each number is the number of atoms per molecule of the element in the compound. The density and energy arguments require proper units." CompoundTransmission::usage = "CompoundTransmission[compound, density, energy, thickness] gives the x-ray transmission fraction through the specified thickness of the specified chemical compound with specified density at the specified x-ray energy. The compound is given in the form {{element1, number1}, {element2, number2}, ...}, where each number is the number of atoms per molecule of the element in the compound. The density, energy, and thickness arguments require proper units." WaveLengthToEnergy::usage = "WaveLengthToEnergy[wavelength] gives the x-ray energy corresponding to the specified x-ray wave length. The wave length argument requires proper units." EnergyToWaveLength::usage = "EnergyToWaveLength[energy] gives the x-ray wave length corresponding to the specified x-ray energy. The energy argument requires proper units." FrequencyToEnergy::usage = "FrequencyToEnergy[frequency] gives the x-ray energy corresponding to the specified x-ray frequency. The frequency argument requires proper units." EnergyToFrequency::usage = "EnergyToFrequency[energy] gives the x-ray frequency corresponding to the specified x-ray energy. The energy argument requires proper units." RadiologicalMaterials = { A150TissueEquivalentPlastic, AdiposeTissue, DryAir, Alanine, B100BoneEquivalentPlastic, Bakelite, WholeBlood, CorticalBone, GreyWhiteMatterBrain, BreastTissue, C552AirEquivalentPlastic, CadmiumTelluride, CalciumFluoride, CalciumSulfate, CericAmmoniumSulfateSolution, CesiumIodide, OrdinaryConcrete, BariteConcrete, EyeLens, FerrousSulfate, GadoliniumOxysulfide, GafchromicSensor, GalliumArsenide, BorosilicateGlass, LeadGlass, LithiumFluoride, LithiumTetraborate, LungTissue, MagnesiumTetraborate, MercuricIodide, SkeletalMuscle, Ovary, KodakTypeAAPhotographicEmulsion, StandardNuclearPhotgraphicEmulsion, PlasticScintillator, Polyethylene, PolyethyleneTerepthalate, PolymethylMethacrylate, Polystyrene, Polytetrafluoroethylene, PolyvinylChloride, RadiochromicDyeFilm, Testis, SoftTissue, FourComponentSoftTissue, MethaneBasedTissueEquivalentGas, PropaneBasedTissueEquivalentGas, LiquidWater}; Map[(#::"usage" = StringJoin[ToString[#], " is a radiological material described in the XRayAttenuation package."])&, RadiologicalMaterials] (* Define equivalent names for some of the radiological materials *) Map[(Evaluate[#[[1]]]::"usage" = StringJoin[ToString[#[[1]]],", also known as ", ToString[#[[2]]], ", is a radiological material described in the XRayAttenuation package."])&, { {A150, A150TissueEquivalentPlastic}, {TissueEquivalentPlastic, A150TissueEquivalentPlastic}, {Air, DryAir}, {B100, B100BoneEquivalentPlastic}, {BoneEquivalentPlastic, B100BoneEquivalentPlastic}, {Blood, WholeBlood}, {Bone, CorticalBone}, {Brain, GreyWhiteMatterBrain}, {Breast, BreastTissue}, {C552, C552AirEquivalentPlastic}, {AirEquivalentPlastic, C552AirEquivalentPlastic}, {Concrete, OrdinaryConcrete}, {StandardFricke, FerrousSulfate}, {Pyrex, BorosilicateGlass}, {Lung, LungTissue}, {Muscle, SkeletalMuscle}, {KodakEmulsion, KodakTypeAAPhotographicEmulsion}, {NuclearEmulsion, StandardNuclearPhotgraphicEmulsion}, {Vinyltoluene, PlasticScintillator}, {Mylar, PolyethyleneTerepthalate}, {Teflon, Polytetrafluoroethylene}, {Water, LiquidWater}}]; Begin["`Private`"] (*** Table Data ***) (* The table of x-ray mass attenuation coefficients (mac) and mass energy absorption coefficients (meac). The data structure has the form {{name1, density1, table1}, {name2, density2, table2}, ...} where each table has the form {{energy1, mac1, meac1}, {energy2, mac2, meac2}, ...}. Density is in g/cm^3, energy is in MeV, and both mac and meac are in cm^2/g. *) xRayAttenuationData = {{Hydrogen,0.00008375, {{0.001,7.217,6.82},{0.0015,2.148,1.752},{0.002,1.059,0.6643}, {0.003,0.5612,0.1693},{0.004,0.4546,0.06549},{0.005,0.4193,0.03278}, {0.006,0.4042,0.01996},{0.008,0.3914,0.0116},{0.01,0.3854,0.009849}, {0.015,0.3764,0.01102},{0.02,0.3695,0.01355},{0.03,0.357,0.01863}, {0.04,0.3458,0.02315},{0.05,0.3355,0.02709},{0.06,0.326,0.03053}, {0.08,0.3091,0.0362},{0.1,0.2944,0.04063},{0.15,0.2651,0.04813}, {0.2,0.2429,0.05254},{0.3,0.2112,0.05695},{0.4,0.1893,0.0586}, {0.5,0.1729,0.059},{0.6,0.1599,0.05875},{0.8,0.1405,0.05739}, {1.,0.1263,0.05556},{1.25,0.1129,0.05311},{1.5,0.1027,0.05075}, {2.,0.08769,0.0465},{3.,0.06921,0.03992},{4.,0.05806,0.03523}, {5.,0.05049,0.03174},{6.,0.04498,0.02905},{8.,0.03746,0.02515}, {10.,0.03254,0.02247},{15.,0.02539,0.01837},{20.,0.02153,0.01606}}}, {Helium,0.0001663, {{0.001,60.84,60.45},{0.0015,16.76,16.38},{0.002,6.863,6.503}, {0.003,2.007,1.681},{0.004,0.9329,0.6379},{0.005,0.5766,0.3061}, {0.006,0.4195,0.1671},{0.008,0.2933,0.06446},{0.01,0.2476,0.0326}, {0.015,0.2092,0.01246},{0.02,0.196,0.00941},{0.03,0.1838,0.01003}, {0.04,0.1763,0.0119},{0.05,0.1703,0.01375},{0.06,0.1651,0.01544}, {0.08,0.1562,0.01826},{0.1,0.1486,0.02047},{0.15,0.1336,0.02424}, {0.2,0.1224,0.02647},{0.3,0.1064,0.02868},{0.4,0.09535,0.02951}, {0.5,0.08707,0.02971},{0.6,0.08054,0.02959},{0.8,0.07076,0.0289}, {1.,0.06362,0.02797},{1.25,0.05688,0.02674},{1.5,0.05173,0.02555}, {2.,0.04422,0.02343},{3.,0.03503,0.02019},{4.,0.02949,0.0179}, {5.,0.02577,0.01622},{6.,0.02307,0.01493},{8.,0.0194,0.01308}, {10.,0.01703,0.01183},{15.,0.01363,0.009948},{20.,0.01183,0.008914}}}, {Lithium,0.534, {{0.001,233.9,233.5},{0.0015,66.68,66.29},{0.002,27.07,26.72}, {0.003,7.549,7.249},{0.004,3.114,2.84},{0.005,1.619,1.364}, {0.006,0.9875,0.7477},{0.008,0.5054,0.2888},{0.01,0.3395,0.1387}, {0.015,0.2176,0.0391},{0.02,0.1856,0.01885},{0.03,0.1644,0.01138}, {0.04,0.1551,0.01131},{0.05,0.1488,0.01237},{0.06,0.1438,0.01361}, {0.08,0.1356,0.01588},{0.1,0.1289,0.01776},{0.15,0.1158,0.02098}, {0.2,0.106,0.0229},{0.3,0.0921,0.02481},{0.4,0.08249,0.02552}, {0.5,0.07532,0.02569},{0.6,0.06968,0.02559},{0.8,0.06121,0.02499}, {1.,0.05503,0.02419},{1.25,0.04921,0.02312},{1.5,0.04476,0.0221}, {2.,0.0383,0.02028},{3.,0.03043,0.01753},{4.,0.02572,0.01561}, {5.,0.02257,0.01422},{6.,0.0203,0.01316},{8.,0.01725,0.01167}, {10.,0.01529,0.01066},{15.,0.01252,0.009182},{20.,0.01109,0.008385}}}, {Beryllium,1.848, {{0.001,604.1,603.5},{0.0015,179.7,179.1},{0.002,74.69,74.22}, {0.003,21.27,20.9},{0.004,8.685,8.367},{0.005,4.369,4.081}, {0.006,2.527,2.26},{0.008,1.124,0.8839},{0.01,0.6466,0.4255}, {0.015,0.307,0.1143},{0.02,0.2251,0.0478},{0.03,0.1792,0.01898}, {0.04,0.164,0.01438},{0.05,0.1554,0.01401},{0.06,0.1493,0.01468}, {0.08,0.1401,0.01658},{0.1,0.1328,0.01836},{0.15,0.119,0.02157}, {0.2,0.1089,0.02353},{0.3,0.09463,0.02548},{0.4,0.08471,0.0262}, {0.5,0.07739,0.02639},{0.6,0.07155,0.02627},{0.8,0.06286,0.02565}, {1.,0.05652,0.02483},{1.25,0.05054,0.02373},{1.5,0.04597,0.02268}, {2.,0.03938,0.02083},{3.,0.03138,0.01806},{4.,0.02664,0.01617}, {5.,0.02347,0.01479},{6.,0.02121,0.01377},{8.,0.01819,0.01233}, {10.,0.01627,0.01138},{15.,0.01361,0.01001},{20.,0.01227,0.009294}}}, {Boron,2.37, {{0.001,1229.,1228.},{0.0015,376.6,375.9},{0.002,159.7,159.1}, {0.003,46.67,46.17},{0.004,19.27,18.86},{0.005,9.683,9.332}, {0.006,5.538,5.223},{0.008,2.346,2.072},{0.01,1.255,1.006}, {0.015,0.4827,0.2698},{0.02,0.3014,0.1084},{0.03,0.2063,0.03506}, {0.04,0.1793,0.02084},{0.05,0.1665,0.01737},{0.06,0.1583,0.0168}, {0.08,0.1472,0.01785},{0.1,0.1391,0.0194},{0.15,0.1243,0.02255}, {0.2,0.1136,0.02453},{0.3,0.09862,0.02654},{0.4,0.08834,0.02731}, {0.5,0.08065,0.02749},{0.6,0.0746,0.02737},{0.8,0.06549,0.02671}, {1.,0.0589,0.02586},{1.25,0.05266,0.02472},{1.5,0.04791,0.02362}, {2.,0.04108,0.02171},{3.,0.03284,0.01889},{4.,0.02798,0.01698}, {5.,0.02476,0.01562},{6.,0.02248,0.01461},{8.,0.01945,0.01322}, {10.,0.01755,0.01232},{15.,0.01495,0.01104},{20.,0.01368,0.01039}}}, {Carbon,1.7, {{0.001,2211.,2209.},{0.0015,700.2,699.},{0.002,302.6,301.6}, {0.003,90.33,89.63},{0.004,37.78,37.23},{0.005,19.12,18.66}, {0.006,10.95,10.54},{0.008,4.576,4.242},{0.01,2.373,2.078}, {0.015,0.8071,0.5627},{0.02,0.442,0.2238},{0.03,0.2562,0.06614}, {0.04,0.2076,0.03343},{0.05,0.1871,0.02397},{0.06,0.1753,0.02098}, {0.08,0.161,0.02037},{0.1,0.1514,0.02147},{0.15,0.1347,0.02449}, {0.2,0.1229,0.02655},{0.3,0.1066,0.0287},{0.4,0.09546,0.0295}, {0.5,0.08715,0.02969},{0.6,0.08058,0.02956},{0.8,0.07076,0.02885}, {1.,0.06361,0.02792},{1.25,0.0569,0.02669},{1.5,0.05179,0.02551}, {2.,0.04442,0.02345},{3.,0.03562,0.02048},{4.,0.03047,0.01849}, {5.,0.02708,0.0171},{6.,0.02469,0.01607},{8.,0.02154,0.01468}, {10.,0.01959,0.0138},{15.,0.01698,0.01258},{20.,0.01575,0.01198}}}, {Nitrogen,0.001165, {{0.001,3311.,3306.},{0.0015,1083.,1080.},{0.002,476.9,475.5}, {0.003,145.6,144.7},{0.004,61.66,60.94},{0.005,31.44,30.86}, {0.006,18.09,17.59},{0.008,7.562,7.17},{0.01,3.879,3.545}, {0.015,1.236,0.9715},{0.02,0.6178,0.3867},{0.03,0.3066,0.1099}, {0.04,0.2288,0.05051},{0.05,0.198,0.03217},{0.06,0.1817,0.02548}, {0.08,0.1639,0.02211},{0.1,0.1529,0.02231},{0.15,0.1353,0.02472}, {0.2,0.1233,0.02665},{0.3,0.1068,0.02873},{0.4,0.09557,0.02952}, {0.5,0.08719,0.02969},{0.6,0.08063,0.02956},{0.8,0.07081,0.02886}, {1.,0.06364,0.02792},{1.25,0.05693,0.02669},{1.5,0.0518,0.0255}, {2.,0.0445,0.02347},{3.,0.03579,0.02057},{4.,0.03073,0.01867}, {5.,0.02742,0.01734},{6.,0.02511,0.01639},{8.,0.02209,0.01512}, {10.,0.02024,0.01434},{15.,0.01782,0.01332},{20.,0.01673,0.01285}}}, {Oxygen,0.001332, {{0.001,4590.,4576.},{0.0015,1549.,1545.},{0.002,694.9,692.6}, {0.003,217.1,215.8},{0.004,93.15,92.21},{0.005,47.9,47.15}, {0.006,27.7,27.08},{0.008,11.63,11.16},{0.01,5.952,5.565}, {0.015,1.836,1.545},{0.02,0.8651,0.6179},{0.03,0.3779,0.1729}, {0.04,0.2585,0.0753},{0.05,0.2132,0.04414},{0.06,0.1907,0.03207}, {0.08,0.1678,0.02468},{0.1,0.1551,0.02355},{0.15,0.1361,0.02506}, {0.2,0.1237,0.02679},{0.3,0.107,0.02877},{0.4,0.09566,0.02953}, {0.5,0.08729,0.02971},{0.6,0.0807,0.02957},{0.8,0.07087,0.02887}, {1.,0.06372,0.02794},{1.25,0.05697,0.02669},{1.5,0.05185,0.02551}, {2.,0.04459,0.0235},{3.,0.03597,0.02066},{4.,0.031,0.01882}, {5.,0.02777,0.01757},{6.,0.02552,0.01668},{8.,0.02263,0.01553}, {10.,0.02089,0.01483},{15.,0.01866,0.01396},{20.,0.0177,0.0136}}}, {Fluorine,0.00158, {{0.001,5649.,5615.},{0.0015,1979.,1969.},{0.002,904.7,900.5}, {0.003,288.8,287.},{0.004,125.6,124.4},{0.005,65.14,64.24}, {0.006,37.89,37.16},{0.008,16.02,15.48},{0.01,8.205,7.776}, {0.015,2.492,2.186},{0.02,1.133,0.8796},{0.03,0.4487,0.2451}, {0.04,0.2828,0.1036},{0.05,0.2214,0.05747},{0.06,0.192,0.03903}, {0.08,0.1639,0.02676},{0.1,0.1496,0.02394},{0.15,0.1298,0.02417}, {0.2,0.1176,0.02554},{0.3,0.1015,0.02729},{0.4,0.09073,0.028}, {0.5,0.08274,0.02815},{0.6,0.07649,0.02801},{0.8,0.06717,0.02734}, {1.,0.06037,0.02645},{1.25,0.05399,0.02527},{1.5,0.04915,0.02416}, {2.,0.04228,0.02226},{3.,0.03422,0.01964},{4.,0.0296,0.01797}, {5.,0.02663,0.01685},{6.,0.02457,0.01607},{8.,0.02195,0.01508}, {10.,0.02039,0.01451},{15.,0.01846,0.01382},{20.,0.01769,0.01357}}}, {Neon,0.0008385, {{0.001,7409.,7326.},{0.0015,2666.,2645.},{0.002,1243.,1234.}, {0.003,405.1,402.1},{0.004,178.5,176.7},{0.005,93.39,92.14}, {0.006,54.67,53.69},{0.008,23.28,22.6},{0.01,11.97,11.43}, {0.015,3.613,3.253},{0.02,1.606,1.317},{0.03,0.5923,0.3676}, {0.04,0.3473,0.1528},{0.05,0.2579,0.08182},{0.06,0.2161,0.05287}, {0.08,0.1781,0.03273},{0.1,0.16,0.02733},{0.15,0.137,0.0259}, {0.2,0.1236,0.02697},{0.3,0.1064,0.02862},{0.4,0.09502,0.02931}, {0.5,0.08664,0.02946},{0.6,0.08006,0.0293},{0.8,0.07029,0.0286}, {1.,0.06316,0.02766},{1.25,0.05646,0.02641},{1.5,0.05145,0.02526}, {2.,0.0443,0.0233},{3.,0.03594,0.02061},{4.,0.03122,0.01894}, {5.,0.02818,0.01784},{6.,0.0261,0.01709},{8.,0.02348,0.01616}, {10.,0.02197,0.01564},{15.,0.02013,0.01508},{20.,0.01946,0.01491}}}, {Sodium,0.971, {{0.001,654.2,652.2},{0.00103542,596.,594.1},{0.0010721,542.9,541.}, {0.0010721,6435.,6320.},{0.0015,3194.,3151.},{0.002,1521.,1504.}, {0.003,507.,502.3},{0.004,226.1,223.8},{0.005,119.4,117.8}, {0.006,70.3,69.15},{0.008,30.18,29.41},{0.01,15.57,14.99}, {0.015,4.694,4.313},{0.02,2.057,1.759},{0.03,0.7197,0.4928}, {0.04,0.3969,0.2031},{0.05,0.2804,0.1063},{0.06,0.2268,0.06625}, {0.08,0.1796,0.03761},{0.1,0.1585,0.02931},{0.15,0.1335,0.02579}, {0.2,0.1199,0.02635},{0.3,0.1029,0.02771},{0.4,0.09185,0.02833}, {0.5,0.08372,0.02845},{0.6,0.07736,0.0283},{0.8,0.06788,0.0276}, {1.,0.061,0.02669},{1.25,0.05454,0.02549},{1.5,0.04968,0.02437}, {2.,0.04282,0.02249},{3.,0.03487,0.01997},{4.,0.03037,0.01842}, {5.,0.02753,0.01743},{6.,0.02559,0.01675},{8.,0.02319,0.01595}, {10.,0.02181,0.01552},{15.,0.02023,0.01508},{20.,0.0197,0.01496}}}, {Magnesium,1.74, {{0.001,922.5,920.3},{0.00114237,647.4,645.2},{0.001305,453.,450.9}, {0.001305,5444.,5310.},{0.0015,4004.,3918.},{0.002,1932.,1899.}, {0.003,658.5,649.9},{0.004,297.4,293.7},{0.005,158.3,156.1}, {0.006,93.81,92.27},{0.008,40.61,39.65},{0.01,21.05,20.36}, {0.015,6.358,5.925},{0.02,2.763,2.432},{0.03,0.9306,0.6855}, {0.04,0.4881,0.2815},{0.05,0.3292,0.1451},{0.06,0.257,0.0882}, {0.08,0.1951,0.04671},{0.1,0.1686,0.0341},{0.15,0.1394,0.02766}, {0.2,0.1245,0.02761},{0.3,0.1065,0.02871},{0.4,0.09492,0.02928}, {0.5,0.08647,0.02938},{0.6,0.07988,0.02921},{0.8,0.07008,0.02848}, {1.,0.06296,0.02753},{1.25,0.05629,0.02629},{1.5,0.05129,0.02514}, {2.,0.04426,0.02322},{3.,0.03613,0.02067},{4.,0.03159,0.01915}, {5.,0.02873,0.01819},{6.,0.02681,0.01756},{8.,0.02445,0.01683}, {10.,0.02313,0.01646},{15.,0.02168,0.01614},{20.,0.02127,0.01609}}}, {Aluminium,2.699, {{0.001,1185.,1183.},{0.0015,402.2,400.1},{0.0015596,362.1,360.}, {0.0015596,3957.,3829.},{0.002,2263.,2204.},{0.003,788.,773.2}, {0.004,360.5,354.5},{0.005,193.4,190.2},{0.006,115.3,113.3}, {0.008,50.33,49.18},{0.01,26.23,25.43},{0.015,7.955,7.487}, {0.02,3.441,3.094},{0.03,1.128,0.8778},{0.04,0.5685,0.3601}, {0.05,0.3681,0.184},{0.06,0.2778,0.1099},{0.08,0.2018,0.05511}, {0.1,0.1704,0.03794},{0.15,0.1378,0.02827},{0.2,0.1223,0.02745}, {0.3,0.1042,0.02816},{0.4,0.09276,0.02862},{0.5,0.08445,0.02868}, {0.6,0.07802,0.02851},{0.8,0.06841,0.02778},{1.,0.06146,0.02686}, {1.25,0.05496,0.02565},{1.5,0.05006,0.02451},{2.,0.04324,0.02266}, {3.,0.03541,0.02024},{4.,0.03106,0.01882},{5.,0.02836,0.01795}, {6.,0.02655,0.01739},{8.,0.02437,0.01678},{10.,0.02318,0.0165}, {15.,0.02195,0.01631},{20.,0.02168,0.01633}}}, {Silicon,2.33, {{0.001,1570.,1567.},{0.0015,535.5,533.1},{0.0018389,309.2,307.}, {0.0018389,3192.,3059.},{0.002,2777.,2669.},{0.003,978.4,951.6}, {0.004,452.9,442.7},{0.005,245.,240.},{0.006,147.,143.9}, {0.008,64.68,63.13},{0.01,33.89,32.89},{0.015,10.34,9.794}, {0.02,4.464,4.076},{0.03,1.436,1.164},{0.04,0.7012,0.4782}, {0.05,0.4385,0.243},{0.06,0.3207,0.1434},{0.08,0.2228,0.06896}, {0.1,0.1835,0.04513},{0.15,0.1448,0.03086},{0.2,0.1275,0.02905}, {0.3,0.1082,0.02932},{0.4,0.09614,0.02968},{0.5,0.08748,0.02971}, {0.6,0.08077,0.02951},{0.8,0.07082,0.02875},{1.,0.06361,0.02778}, {1.25,0.05688,0.02652},{1.5,0.05183,0.02535},{2.,0.0448,0.02345}, {3.,0.03678,0.02101},{4.,0.0324,0.01963},{5.,0.02967,0.01878}, {6.,0.02788,0.01827},{8.,0.02574,0.01773},{10.,0.02462,0.01753}, {15.,0.02352,0.01746},{20.,0.02338,0.01757}}}, {Phosphorus,2.2, {{0.001,1913.,1910.},{0.0015,654.7,652.2},{0.002,301.8,299.6}, {0.0021455,249.4,247.3},{0.0021455,2473.,2343.},{0.003,1118.,1074.}, {0.004,524.2,507.9},{0.005,286.,278.2},{0.006,172.6,168.2}, {0.008,76.6,74.57},{0.01,40.35,39.12},{0.015,12.39,11.79}, {0.02,5.352,4.939},{0.03,1.7,1.422},{0.04,0.8096,0.585}, {0.05,0.4916,0.2965},{0.06,0.3494,0.1735},{0.08,0.2324,0.08083}, {0.1,0.1865,0.05068},{0.15,0.1432,0.03188},{0.2,0.125,0.02899}, {0.3,0.1055,0.0287},{0.4,0.09359,0.02892},{0.5,0.08511,0.02891}, {0.6,0.07854,0.02869},{0.8,0.06884,0.02793},{1.,0.06182,0.02698}, {1.25,0.05526,0.02575},{1.5,0.05039,0.02462},{2.,0.04358,0.02279}, {3.,0.0359,0.02049},{4.,0.03172,0.01921},{5.,0.02915,0.01846}, {6.,0.02747,0.01801},{8.,0.02552,0.0176},{10.,0.02452,0.01747}, {15.,0.02364,0.01754},{20.,0.02363,0.01771}}}, {Sulfur,2., {{0.001,2429.,2426.},{0.0015,834.2,831.4},{0.002,385.3,382.8}, {0.002472,216.8,214.5},{0.002472,2070.,1935.},{0.003,1339.,1265.}, {0.004,633.8,606.6},{0.005,348.7,336.},{0.006,211.6,204.6}, {0.008,94.65,91.71},{0.01,50.12,48.47},{0.015,15.5,14.77}, {0.02,6.708,6.235},{0.03,2.113,1.809},{0.04,0.9872,0.7466}, {0.05,0.5849,0.3779},{0.06,0.4053,0.2199},{0.08,0.2585,0.1}, {0.1,0.202,0.06052},{0.15,0.1506,0.03516},{0.2,0.1302,0.0308}, {0.3,0.1091,0.02983},{0.4,0.09665,0.02991},{0.5,0.08781,0.02984}, {0.6,0.08102,0.02959},{0.8,0.07098,0.02878},{1.,0.06373,0.0278}, {1.25,0.05697,0.02652},{1.5,0.05193,0.02535},{2.,0.04498,0.02349}, {3.,0.03715,0.02118},{4.,0.03293,0.01993},{5.,0.03036,0.01923}, {6.,0.02872,0.01884},{8.,0.02682,0.0185},{10.,0.02589,0.01845}, {15.,0.02517,0.01864},{20.,0.02529,0.01889}}}, {Chlorine,0.002995, {{0.001,2832.,2829.},{0.0015,977.1,974.2},{0.002,452.,449.4}, {0.0028224,177.4,175.2},{0.0028224,1637.,1506.},{0.003,1473.,1361.}, {0.004,703.7,662.6},{0.005,390.1,371.1},{0.006,238.4,228.2}, {0.008,107.5,103.4},{0.01,57.25,55.1},{0.015,17.84,17.}, {0.02,7.739,7.227},{0.03,2.425,2.114},{0.04,1.117,0.8756}, {0.05,0.6483,0.4433},{0.06,0.4395,0.257},{0.08,0.2696,0.1148}, {0.1,0.205,0.06745},{0.15,0.148,0.03639},{0.2,0.1266,0.03067}, {0.3,0.1054,0.02898},{0.4,0.09311,0.02887},{0.5,0.08453,0.02874}, {0.6,0.07795,0.02847},{0.8,0.06826,0.02767},{1.,0.06128,0.02671}, {1.25,0.05478,0.02549},{1.5,0.04994,0.02436},{2.,0.04328,0.02258}, {3.,0.03585,0.02043},{4.,0.03188,0.01931},{5.,0.0295,0.01871}, {6.,0.02798,0.01839},{8.,0.02628,0.01819},{10.,0.02549,0.01824}, {15.,0.02496,0.01861},{20.,0.0252,0.01899}}}, {Argon,0.001662, {{0.001,3184.,3180.},{0.0015,1105.,1102.},{0.002,512.,509.3}, {0.003,170.3,168.2},{0.0032029,142.4,140.3},{0.0032029,1275.,1153.}, {0.004,757.2,697.9},{0.005,422.5,395.3},{0.006,259.3,244.9}, {0.008,118.,112.5},{0.01,63.16,60.38},{0.015,19.83,18.86}, {0.02,8.629,8.074},{0.03,2.697,2.382},{0.04,1.228,0.9907}, {0.05,0.7012,0.502},{0.06,0.4664,0.2904},{0.08,0.276,0.128}, {0.1,0.2043,0.07344},{0.15,0.1427,0.03703},{0.2,0.1205,0.02998}, {0.3,0.09953,0.02757},{0.4,0.08776,0.02727},{0.5,0.07958,0.02708}, {0.6,0.07335,0.02679},{0.8,0.06419,0.02601},{1.,0.05762,0.0251}, {1.25,0.0515,0.02394},{1.5,0.04695,0.02288},{2.,0.04074,0.02123}, {3.,0.03384,0.01927},{4.,0.03019,0.01827},{5.,0.02802,0.01777}, {6.,0.02667,0.01753},{8.,0.02517,0.01742},{10.,0.02451,0.01754}, {15.,0.02418,0.018},{20.,0.02453,0.01842}}}, {Potassium,0.862, {{0.001,4058.,4053.},{0.0015,1418.,1415.},{0.002,659.2,656.3}, {0.003,219.8,217.4},{0.0036074,132.7,130.6},{0.0036074,1201.,1065.}, {0.004,925.6,830.4},{0.005,518.9,475.2},{0.006,320.5,297.4}, {0.008,146.9,138.3},{0.01,79.07,74.9},{0.015,25.03,23.7}, {0.02,10.93,10.23},{0.03,3.413,3.045},{0.04,1.541,1.272}, {0.05,0.8679,0.6454},{0.06,0.5678,0.373},{0.08,0.3251,0.1628}, {0.1,0.2345,0.09161},{0.15,0.1582,0.04346},{0.2,0.1319,0.03378}, {0.3,0.108,0.03015},{0.4,0.09495,0.02959},{0.5,0.086,0.02929}, {0.6,0.07922,0.02895},{0.8,0.06929,0.02807},{1.,0.06216,0.02707}, {1.25,0.05556,0.02581},{1.5,0.05068,0.02467},{2.,0.04399,0.0229}, {3.,0.03666,0.02084},{4.,0.03282,0.01985},{5.,0.03054,0.01935}, {6.,0.02915,0.01914},{8.,0.02766,0.0191},{10.,0.02704,0.01928}, {15.,0.02687,0.01983},{20.,0.02737,0.02029}}}, {Calcium,1.55, {{0.001,4867.,4861.},{0.0015,1714.,1710.},{0.002,799.9,796.6}, {0.003,267.6,265.},{0.004,121.8,119.7},{0.0040381,118.7,116.6}, {0.0040381,1023.,888.7},{0.005,602.6,537.3},{0.006,373.1,338.7}, {0.008,172.6,160.},{0.01,93.41,87.44},{0.015,29.79,28.04}, {0.02,13.06,12.2},{0.03,4.08,3.665},{0.04,1.83,1.538}, {0.05,1.019,0.7822},{0.06,0.6578,0.452},{0.08,0.3656,0.1958}, {0.1,0.2571,0.1085},{0.15,0.1674,0.04876},{0.2,0.1376,0.03639}, {0.3,0.1116,0.03146},{0.4,0.09783,0.0306},{0.5,0.08851,0.03019}, {0.6,0.08148,0.02979},{0.8,0.07122,0.02884},{1.,0.06388,0.0278}, {1.25,0.05709,0.0265},{1.5,0.05207,0.02532},{2.,0.04524,0.02352}, {3.,0.0378,0.02147},{4.,0.03395,0.02052},{5.,0.0317,0.02007}, {6.,0.03035,0.01992},{8.,0.02892,0.01997},{10.,0.02839,0.02022}, {15.,0.02838,0.02088},{20.,0.02903,0.0214}}}, {Scandium,2.989, {{0.001,5238.,5231.},{0.0015,1858.,1853.},{0.002,870.6,867.2}, {0.003,292.2,289.6},{0.004,133.2,131.1},{0.0044928,96.87,94.9}, {0.0044928,814.8,691.1},{0.005,630.5,543.6},{0.006,393.3,347.4}, {0.008,182.8,166.1},{0.01,99.52,91.75},{0.015,32.02,29.88}, {0.02,14.09,13.11},{0.03,4.409,3.975},{0.04,1.969,1.677}, {0.05,1.087,0.8552},{0.06,0.6932,0.4944},{0.08,0.3753,0.2132}, {0.1,0.2577,0.1167},{0.15,0.1619,0.04998},{0.2,0.131,0.03586}, {0.3,0.1052,0.02997},{0.4,0.09193,0.02887},{0.5,0.08305,0.02837}, {0.6,0.07639,0.02795},{0.8,0.06675,0.02703},{1.,0.05985,0.02603}, {1.25,0.05347,0.0248},{1.5,0.04878,0.0237},{2.,0.04243,0.02202}, {3.,0.03554,0.02016},{4.,0.03202,0.01933},{5.,0.02999,0.01897}, {6.,0.02878,0.01887},{8.,0.02756,0.019},{10.,0.02715,0.01929}, {15.,0.02732,0.02},{20.,0.02804,0.02052}}}, {Titanium,4.54, {{0.001,5869.,5860.},{0.0015,2096.,2091.},{0.002,986.,982.4}, {0.003,332.3,329.5},{0.004,151.7,149.4},{0.0049664,83.8,81.88}, {0.0049664,687.8,568.4},{0.005,683.8,565.7},{0.006,432.3,369.1}, {0.008,202.3,179.3},{0.01,110.7,100.1},{0.015,35.87,33.11}, {0.02,15.85,14.65},{0.03,4.972,4.488},{0.04,2.214,1.904}, {0.05,1.213,0.9737},{0.06,0.7661,0.5634},{0.08,0.4052,0.2422}, {0.1,0.2721,0.1312},{0.15,0.1649,0.05393},{0.2,0.1314,0.03726}, {0.3,0.1043,0.03007},{0.4,0.09081,0.02864},{0.5,0.08191,0.02804}, {0.6,0.07529,0.02756},{0.8,0.06572,0.02661},{1.,0.05891,0.02561}, {1.25,0.05263,0.02439},{1.5,0.04801,0.0233},{2.,0.0418,0.02166}, {3.,0.03512,0.01989},{4.,0.03173,0.01913},{5.,0.02982,0.01884}, {6.,0.02868,0.01879},{8.,0.02759,0.01899},{10.,0.02727,0.01933}, {15.,0.02762,0.02013},{20.,0.02844,0.02067}}}, {Vanadium,6.11, {{0.001,6495.,6483.},{0.0015,2342.,2336.},{0.002,1106.,1102.}, {0.003,374.3,371.3},{0.004,171.2,168.8},{0.005,92.91,90.89}, {0.0054651,72.77,70.9},{0.0054651,587.,471.7},{0.006,468.7,384.1}, {0.008,221.7,190.8},{0.01,121.8,107.7},{0.015,39.83,36.27}, {0.02,17.68,16.2},{0.03,5.564,5.015},{0.04,2.472,2.14}, {0.05,1.347,1.098},{0.06,0.8438,0.6364},{0.08,0.4371,0.2731}, {0.1,0.2877,0.1469},{0.15,0.1682,0.05821},{0.2,0.1318,0.03879}, {0.3,0.1034,0.03019},{0.4,0.08965,0.02843},{0.5,0.08074,0.0277}, {0.6,0.07414,0.02717},{0.8,0.06466,0.02618},{1.,0.05794,0.02518}, {1.25,0.05175,0.02396},{1.5,0.04722,0.02289},{2.,0.04115,0.0213}, {3.,0.03466,0.01961},{4.,0.03141,0.01892},{5.,0.0296,0.01869}, {6.,0.02855,0.01869},{8.,0.02759,0.01896},{10.,0.02738,0.01937}, {15.,0.02786,0.02022},{20.,0.02877,0.02079}}}, {Chromium,7.18, {{0.001,7405.,7388.},{0.0015,2694.,2687.},{0.002,1277.,1272.}, {0.003,433.9,430.5},{0.004,198.8,196.1},{0.005,108.,105.7}, {0.0059892,65.74,63.83},{0.0059892,516.,402.7},(*{0.006,516.,402.7},*) {0.008,251.3,208.7},{0.01,138.6,119.3},{0.015,45.71,40.93}, {0.02,20.38,18.46},{0.03,6.434,5.78},{0.04,2.856,2.482}, {0.05,1.55,1.278},{0.06,0.9639,0.742},{0.08,0.4905,0.3182}, {0.1,0.3166,0.1701},{0.15,0.1788,0.06536},{0.2,0.1378,0.04211}, {0.3,0.1067,0.0316},{0.4,0.09213,0.02938},{0.5,0.08281,0.02849}, {0.6,0.07598,0.02788},{0.8,0.0662,0.0268},{1.,0.0593,0.02576}, {1.25,0.05295,0.0245},{1.5,0.04832,0.0234},{2.,0.04213,0.02178}, {3.,0.03559,0.02011},{4.,0.03235,0.01947},{5.,0.03057,0.01929}, {6.,0.02956,0.01933},{8.,0.02869,0.0197},{10.,0.02855,0.02016}, {15.,0.0292,0.02112},{20.,0.03026,0.02174}}}, {Manganese,7.44, {{0.001,8093.,8069.},{0.0015,2984.,2975.},{0.002,1421.,1415.}, {0.003,485.1,481.5},{0.004,222.9,220.1},{0.005,121.2,118.8}, {0.006,73.5,71.5},{0.006539,58.03,56.19},{0.006539,452.,341.5}, {0.008,273.4,217.7},{0.01,151.4,126.2},{0.015,50.27,44.14}, {0.02,22.53,20.15},{0.03,7.141,6.382},{0.04,3.169,2.757}, {0.05,1.714,1.425},{0.06,1.06,0.8294},{0.08,0.5306,0.3558}, {0.1,0.3367,0.1894},{0.15,0.1838,0.07085},{0.2,0.1391,0.04421}, {0.3,0.1062,0.03196},{0.4,0.09133,0.02932},{0.5,0.08192,0.02827}, {0.6,0.07509,0.0276},{0.8,0.06537,0.02647},{1.,0.05852,0.02541}, {1.25,0.05224,0.02416},{1.5,0.04769,0.02307},{2.,0.04162,0.02149}, {3.,0.03524,0.01989},{4.,0.03213,0.01933},{5.,0.03045,0.0192}, {6.,0.02952,0.0193},{8.,0.02875,0.01973},{10.,0.02871,0.02025}, {15.,0.02951,0.02127},{20.,0.03068,0.02193}}}, {Iron,7.874, {{0.001,9085.,9052.},{0.0015,3399.,3388.},{0.002,1626.,1620.}, {0.003,557.6,553.5},{0.004,256.7,253.6},{0.005,139.8,137.2}, {0.006,84.84,82.65},{0.007112,53.19,51.33},{0.007112,407.6,297.8}, {0.008,305.6,231.6},{0.01,170.6,136.9},{0.015,57.08,48.96}, {0.02,25.68,22.6},{0.03,8.176,7.251},{0.04,3.629,3.155}, {0.05,1.958,1.638},{0.06,1.205,0.9555},{0.08,0.5952,0.4104}, {0.1,0.3717,0.2177},{0.15,0.1964,0.07961},{0.2,0.146,0.04825}, {0.3,0.1099,0.03361},{0.4,0.094,0.03039},{0.5,0.08414,0.02914}, {0.6,0.07704,0.02836},{0.8,0.06699,0.02714},{1.,0.05995,0.02603}, {1.25,0.0535,0.02472},{1.5,0.04883,0.0236},{2.,0.04265,0.02199}, {3.,0.03621,0.02042},{4.,0.03312,0.0199},{5.,0.03146,0.01983}, {6.,0.03057,0.01997},{8.,0.02991,0.0205},{10.,0.02994,0.02108}, {15.,0.03092,0.02221},{20.,0.03224,0.02292}}}, {Cobalt,8.9, {{0.001,9796.,9750.},{0.0015,3697.,3682.},{0.002,1779.,1771.}, {0.003,612.9,608.4},{0.004,283.,279.6},{0.005,154.3,151.5}, {0.006,93.7,91.38},{0.0077089,47.1,45.3},{0.0077089,355.5,250.7}, {0.008,324.8,232.2},{0.01,184.1,141.3},{0.015,62.01,51.78}, {0.02,28.03,24.21},{0.03,8.962,7.873},{0.04,3.981,3.45}, {0.05,2.144,1.799},{0.06,1.314,1.052},{0.08,0.6414,0.4528}, {0.1,0.3949,0.2397},{0.15,0.2023,0.08597},{0.2,0.1476,0.05071}, {0.3,0.1094,0.03406},{0.4,0.09311,0.03034},{0.5,0.08315,0.0289}, {0.6,0.07604,0.02805},{0.8,0.06604,0.02677},{1.,0.05906,0.02564}, {1.25,0.0527,0.02434},{1.5,0.0481,0.02323},{2.,0.04204,0.02165}, {3.,0.0358,0.02016},{4.,0.03283,0.01971},{5.,0.03127,0.01969}, {6.,0.03045,0.01988},{8.,0.02991,0.02048},{10.,0.03002,0.0211}, {15.,0.03115,0.0223},{20.,0.03256,0.02303}}}, {Nickel,8.902, {{0.001,9855.,9797.},{0.00100404,9753.,9697.},{0.0010081,9654.,9598.}, {0.0010081,10990.,10930.},{0.0015,4234.,4214.},{0.002,2049.,2039.}, {0.003,709.4,704.2},{0.004,328.2,324.4},{0.005,179.3,176.1}, {0.006,109.,106.4},{0.008,49.52,47.58},{0.0083328,44.28,42.42}, {0.0083328,329.4,224.},{0.01,209.,152.4},{0.015,70.81,57.34}, {0.02,32.2,27.22},{0.03,10.34,8.982},{0.04,4.6,3.967}, {0.05,2.474,2.078},{0.06,1.512,1.219},{0.08,0.7306,0.5259}, {0.1,0.444,0.2781},{0.15,0.2208,0.09812},{0.2,0.1582,0.05649}, {0.3,0.1154,0.03659},{0.4,0.09765,0.03209},{0.5,0.08698,0.03036}, {0.6,0.07944,0.02937},{0.8,0.06891,0.02795},{1.,0.0616,0.02674}, {1.25,0.05494,0.02536},{1.5,0.05015,0.0242},{2.,0.04387,0.02257}, {3.,0.03745,0.02107},{4.,0.03444,0.02066},{5.,0.03289,0.0207}, {6.,0.0321,0.02094},{8.,0.03164,0.02163},{10.,0.03185,0.02234}, {15.,0.0332,0.02368},{20.,0.03476,0.02446}}}, {Copper,8.96, {{0.001,10570.,10490.},{0.00104695,9307.,9241.},{0.0010961,8242.,8186.}, {0.0010961,9347.,9282.},{0.0015,4418.,4393.},{0.002,2154.,2142.}, {0.003,748.8,743.},{0.004,347.3,343.2},{0.005,189.9,186.6}, {0.006,115.6,112.8},{0.008,52.55,50.54},{0.0089789,38.29,36.52}, {0.0089789,278.4,182.4},{0.01,215.9,148.4},{0.015,74.05,57.88}, {0.02,33.79,27.88},{0.03,10.92,9.349},{0.04,4.862,4.163}, {0.05,2.613,2.192},{0.06,1.593,1.29},{0.08,0.763,0.5581}, {0.1,0.4584,0.2949},{0.15,0.2217,0.1027},{0.2,0.1559,0.05781}, {0.3,0.1119,0.03617},{0.4,0.09413,0.03121},{0.5,0.08362,0.02933}, {0.6,0.07625,0.02826},{0.8,0.06605,0.02681},{1.,0.05901,0.02562}, {1.25,0.05261,0.02428},{1.5,0.04803,0.02316},{2.,0.04205,0.0216}, {3.,0.03599,0.02023},{4.,0.03318,0.01989},{5.,0.03177,0.01998}, {6.,0.03108,0.02027},{8.,0.03074,0.021},{10.,0.03103,0.02174}, {15.,0.03247,0.02309},{20.,0.03408,0.02387}}}, {Zinc,7.133, {{0.001,1553.,1548.},{0.0010098,1518.,1513.},{0.0010197,1484.,1478.}, {0.0010197,3804.,3777.},{0.00103119,5097.,5057.},{0.0010428,6518.,6464.}, {0.0010428,8274.,8202.},{0.00111565,8452.,8382.},{0.0011936,7371.,7312.}, {0.0011936,8396.,8328.},{0.0015,4825.,4791.},{0.002,2375.,2359.}, {0.003,831.1,824.4},{0.004,386.5,382.},{0.005,211.8,208.2}, {0.006,129.,126.1},{0.008,58.75,56.6},{0.0096586,35.05,33.32}, {0.0096586,253.6,159.9},{0.01,233.1,149.7},{0.015,81.17,60.99}, {0.02,37.19,29.86},{0.03,12.07,10.18},{0.04,5.384,4.57}, {0.05,2.892,2.419},{0.06,1.76,1.429},{0.08,0.8364,0.6203}, {0.1,0.4973,0.3278},{0.15,0.2341,0.1128},{0.2,0.1617,0.06225}, {0.3,0.1141,0.03764},{0.4,0.09539,0.03195},{0.5,0.0845,0.02979}, {0.6,0.07695,0.02861},{0.8,0.06656,0.02704},{1.,0.05941,0.0258}, {1.25,0.05296,0.02443},{1.5,0.04834,0.02329},{2.,0.04235,0.02174}, {3.,0.03634,0.02041},{4.,0.0336,0.02014},{5.,0.03225,0.02028}, {6.,0.0316,0.02061},{8.,0.03138,0.02143},{10.,0.03175,0.02223}, {15.,0.03335,0.02367},{20.,0.03509,0.02451}}}, {Gallium,5.904, {{0.001,1697.,1692.},{0.00105613,1492.,1487.},{0.0011154,1312.,1307.}, {0.0011154,3990.,3955.},{0.00112877,4887.,4842.},{0.0011423,5664.,5611.}, {0.0011423,7405.,7332.},{0.00121752,7138.,7070.},{0.0012977,6358.,6299.}, {0.0012977,7206.,7139.},{0.0015,5087.,5044.},{0.002,2515.,2496.}, {0.003,885.7,878.2},{0.004,413.,408.2},{0.005,226.6,222.9}, {0.006,138.2,135.2},{0.008,63.02,60.82},{0.01,34.21,32.5}, {0.0103671,30.99,29.36},{0.0103671,221.4,134.4},{0.015,85.37,61.35}, {0.02,39.28,30.59},{0.03,12.81,10.61},{0.04,5.726,4.81}, {0.05,3.076,2.56},{0.06,1.868,1.518},{0.08,0.8823,0.6613}, {0.1,0.5197,0.3497},{0.15,0.2387,0.1193},{0.2,0.1619,0.06463}, {0.3,0.1123,0.03782},{0.4,0.09325,0.03156},{0.5,0.08236,0.0292}, {0.6,0.07487,0.02793},{0.8,0.06466,0.02631},{1.,0.05767,0.02506}, {1.25,0.05139,0.02371},{1.5,0.04692,0.0226},{2.,0.04113,0.0211}, {3.,0.03538,0.01986},{4.,0.0328,0.01966},{5.,0.03156,0.01985}, {6.,0.03099,0.02021},{8.,0.03086,0.02108},{10.,0.0313,0.02191}, {15.,0.033,0.02339},{20.,0.03479,0.02425}}}, {Germanium,5.323, {{0.001,1893.,1887.},{0.00110304,1502.,1496.},{0.0012167,1190.,1185.}, {0.0012167,4389.,4343.},{0.00123215,4734.,4684.},{0.0012478,4974.,4922.}, {0.0012478,6698.,6622.},{0.00132844,6348.,6279.},{0.0014143,5554.,5495.}, {0.0014143,6287.,6221.},{0.0015,5475.,5420.},{0.002,2711.,2688.}, {0.003,961.3,952.7},{0.004,449.7,444.5},{0.005,247.2,243.3}, {0.006,150.9,147.7},{0.008,68.9,66.6},{0.01,37.42,35.64}, {0.0111031,28.11,26.53},{0.0111031,198.1,115.7},{0.015,91.52,62.56}, {0.02,42.22,31.78},{0.03,13.85,11.26},{0.04,6.207,5.152}, {0.05,3.335,2.759},{0.06,2.023,1.642},{0.08,0.9501,0.7184}, {0.1,0.555,0.3803},{0.15,0.2491,0.1288},{0.2,0.1661,0.06865}, {0.3,0.1131,0.03891},{0.4,0.09327,0.03193},{0.5,0.08212,0.0293}, {0.6,0.07452,0.0279},{0.8,0.06426,0.02618},{1.,0.05727,0.02489}, {1.25,0.05101,0.02353},{1.5,0.04657,0.02242},{2.,0.04086,0.02094}, {3.,0.03524,0.01977},{4.,0.03275,0.01962},{5.,0.03158,0.01987}, {6.,0.03107,0.02027},{8.,0.03103,0.0212},{10.,0.03156,0.02208}, {15.,0.0334,0.02364},{20.,0.03528,0.02452}}}, {Arsenic,5.73, {{0.001,2121.,2116.},{0.00115026,1523.,1517.},{0.0013231,1092.,1087.}, {0.0013231,4513.,4459.},{0.00134073,4469.,4416.},{0.0013586,4452.,4398.}, {0.0013586,6093.,6015.},{0.0015,5227.,5164.},{0.0015265,4997.,4938.}, {0.0015265,5653.,5585.},{0.002,2931.,2902.},{0.003,1049.,1039.}, {0.004,492.,486.2},{0.005,270.9,266.7},{0.006,165.6,162.2}, {0.008,75.73,73.3},{0.01,41.15,39.28},{0.0118667,25.77,24.25}, {0.0118667,179.2,100.8},{0.015,98.56,63.71},{0.02,45.64,33.1}, {0.03,15.06,11.98},{0.04,6.76,5.537},{0.05,3.635,2.983}, {0.06,2.203,1.783},{0.08,1.03,0.7837},{0.1,0.5971,0.4155}, {0.15,0.2622,0.1399},{0.2,0.1719,0.0735},{0.3,0.115,0.04043}, {0.4,0.09414,0.03261},{0.5,0.08259,0.02966},{0.6,0.07483,0.02813}, {0.8,0.0644,0.02628},{1.,0.05735,0.02494},{1.25,0.05106,0.02355}, {1.5,0.04661,0.02243},{2.,0.04093,0.02096},{3.,0.03539,0.01984}, {4.,0.03296,0.01974},{5.,0.03187,0.02005},{6.,0.03141,0.02049}, {8.,0.03146,0.02148},{10.,0.03207,0.02241},{15.,0.03405,0.02404}, {20.,0.03603,0.02495}}}, {Selenium,4.5, {{0.001,2317.,2312.},{0.00119825,1512.,1506.},{0.0014358,981.4,976.}, {0.0014358,4347.,4287.},{0.00145586,4057.,4002.},{0.0014762,3907.,3855.}, {0.0014762,5186.,5112.},{0.0015,5336.,5260.},{0.0016539,4342.,4284.}, {0.0016539,4915.,4849.},{0.002,3098.,3062.},{0.003,1116.,1104.}, {0.004,525.2,518.7},{0.005,289.6,285.1},{0.006,177.3,173.7}, {0.008,81.16,78.65},{0.01,44.14,42.21},{0.0126578,23.18,21.73}, {0.0126578,158.9,85.99},{0.015,103.3,62.7},{0.02,48.18,33.52}, {0.03,15.96,12.4},{0.04,7.184,5.796},{0.05,3.864,3.143}, {0.06,2.341,1.886},{0.08,1.09,0.8332},{0.1,0.6278,0.4426}, {0.15,0.2703,0.1483},{0.2,0.1742,0.07695},{0.3,0.1144,0.04113}, {0.4,0.09299,0.03261},{0.5,0.08129,0.02941},{0.6,0.0735,0.02775}, {0.8,0.06314,0.02581},{1.,0.05619,0.02446},{1.25,0.04999,0.02306}, {1.5,0.04564,0.02195},{2.,0.0401,0.02052},{3.,0.03476,0.01947}, {4.,0.03247,0.01944},{5.,0.03145,0.01978},{6.,0.03105,0.02025}, {8.,0.03119,0.0213},{10.,0.03186,0.02226},{15.,0.03395,0.02394}, {20.,0.03599,0.02487}}}, {Bromine,0.007072, {{0.001,2624.,2618.},{0.0015,1002.,996.4},{0.0015499,925.5,920.}, {0.0015499,4289.,4223.},{0.00157278,3838.,3780.},{0.001596,3587.,3534.}, {0.001596,5097.,5014.},{0.00168644,4595.,4523.},{0.001782,3969.,3910.}, {0.001782,4495.,4427.},{0.002,3407.,3360.},{0.003,1231.,1216.}, {0.004,581.5,574.},{0.005,321.3,316.3},{0.006,196.8,193.}, {0.008,90.26,87.56},{0.01,49.12,47.06},{0.0134737,21.76,20.33}, {0.0134737,147.1,76.68},{0.015,111.9,63.36},{0.02,52.66,35.02}, {0.03,17.53,13.28},{0.04,7.9,6.267},{0.05,4.264,3.431}, {0.06,2.582,2.068},{0.08,1.198,0.9185},{0.1,0.6861,0.489}, {0.15,0.2899,0.1634},{0.2,0.1838,0.08378},{0.3,0.1186,0.0436}, {0.4,0.09563,0.03398},{0.5,0.08328,0.03036},{0.6,0.07515,0.02851}, {0.8,0.06443,0.0264},{1.,0.05728,0.02496},{1.25,0.05094,0.0235}, {1.5,0.0465,0.02237},{2.,0.04089,0.02092},{3.,0.03552,0.01991}, {4.,0.03327,0.01995},{5.,0.03229,0.02036},{6.,0.03194,0.0209}, {8.,0.03218,0.02207},{10.,0.03293,0.02314},{15.,0.03521,0.02507}, {20.,0.03738,0.02618}}}, {Krypton,0.003478, {{0.001,2854.,2848.},{0.0015,1093.,1087.},{0.0016749,836.1,830.5}, {0.0016749,3909.,3842.},{0.00170085,3409.,3352.},{0.0017272,3166.,3114.}, {0.0017272,4566.,4484.},{0.00182152,4014.,3945.},{0.001921,3482.,3425.}, {0.001921,3948.,3882.},{0.002,3599.,3541.},{0.003,1305.,1288.}, {0.004,618.6,610.1},{0.005,342.5,337.1},{0.006,210.1,206.}, {0.008,96.51,93.71},{0.01,52.57,50.44},{0.0143256,19.71,18.36}, {0.0143256,131.3,66.04},{0.015,116.8,61.12},{0.02,55.48,35.09}, {0.03,18.54,13.65},{0.04,8.389,6.538},{0.05,4.523,3.596}, {0.06,2.739,2.178},{0.08,1.267,0.9729},{0.1,0.7221,0.5192}, {0.15,0.2998,0.1731},{0.2,0.1872,0.08787},{0.3,0.1186,0.04459}, {0.4,0.0948,0.03414},{0.5,0.08226,0.03023},{0.6,0.0741,0.02825}, {0.8,0.0634,0.02603},{1.,0.05631,0.02456},{1.25,0.05005,0.0231}, {1.5,0.04569,0.02197},{2.,0.0402,0.02055},{3.,0.03501,0.01961}, {4.,0.03286,0.01969},{5.,0.03196,0.02014},{6.,0.03168,0.02071}, {8.,0.03199,0.02192},{10.,0.0328,0.02302},{15.,0.03518,0.02497}, {20.,0.03741,0.0261}}}, {Rubidium,1.532, {{0.001,3174.,3168.},{0.0015,1219.,1213.},{0.0018044,778.2,772.6}, {0.0018044,3096.,3040.},{0.00183391,2969.,2915.},{0.0018639,2861.,2810.}, {0.0018639,3957.,3880.},{0.002,3410.,3347.},{0.0020651,3153.,3096.}, {0.0020651,3606.,3540.},{0.003,1418.,1397.},{0.004,674.8,664.8}, {0.005,374.4,368.2},{0.006,230.,225.5},{0.008,105.8,102.8}, {0.01,57.66,55.41},{0.015,19.09,17.75},{0.0151997,18.42,17.09}, {0.0151997,120.8,58.64},{0.02,59.8,35.81},{0.03,20.09,14.36}, {0.04,9.112,6.963},{0.05,4.918,3.858},{0.06,2.979,2.349}, {0.08,1.375,1.056},{0.1,0.7799,0.5649},{0.15,0.3187,0.1881}, {0.2,0.196,0.09465},{0.3,0.1219,0.0469},{0.4,0.0967,0.03531}, {0.5,0.0836,0.03098},{0.6,0.0751,0.02878},{0.8,0.06412,0.02638}, {1.,0.05689,0.02484},{1.25,0.05053,0.02332},{1.5,0.04613,0.02217}, {2.,0.04061,0.02074},{3.,0.03545,0.01983},{4.,0.03335,0.01996}, {5.,0.0325,0.02045},{6.,0.03227,0.02105},{8.,0.03267,0.02231}, {10.,0.03357,0.02343},{15.,0.0361,0.02538},{20.,0.03845,0.02645}}}, {Strontium,2.54, {{0.001,3494.,3487.},{0.0015,1347.,1341.},{0.0019396,720.7,715.2}, {0.0019396,2864.,2807.},{0.002,2589.,2539.},{0.0020068,2571.,2521.}, {0.0020068,3577.,3501.},{0.00210895,3201.,3134.},{0.0022163,2842.,2786.}, {0.0022163,3241.,3176.},{0.003,1525.,1500.},{0.004,729.7,718.1}, {0.005,405.8,398.8},{0.006,249.6,244.6},{0.008,115.,111.8}, {0.01,62.74,60.37},{0.015,20.79,19.38},{0.0161046,17.14,15.85}, {0.0161046,110.8,52.},{0.02,63.86,36.02},{0.03,21.57,14.93}, {0.04,9.818,7.346},{0.05,5.306,4.103},{0.06,3.214,2.511}, {0.08,1.481,1.135},{0.1,0.8365,0.6093},{0.15,0.3369,0.2028}, {0.2,0.2042,0.1013},{0.3,0.1247,0.04906},{0.4,0.09811,0.03634}, {0.5,0.08443,0.03156},{0.6,0.0757,0.02917},{0.8,0.06447,0.0266}, {1.,0.05714,0.02498},{1.25,0.05072,0.02342},{1.5,0.0463,0.02225}, {2.,0.04079,0.02082},{3.,0.03569,0.01995},{4.,0.03365,0.02013}, {5.,0.03286,0.02066},{6.,0.03268,0.0213},{8.,0.03317,0.0226}, {10.,0.03414,0.02377},{15.,0.03683,0.02578},{20.,0.03927,0.02684}}}, {Yttrium,4.469, {{0.001,3864.,3857.},{0.0015,1493.,1487.},{0.002,742.2,736.5}, {0.00208,673.8,668.2},{0.00208,2627.,2569.},{0.00211741,2466.,2412.}, {0.0021555,2342.,2292.},{0.0021555,3264.,3187.},{0.0022614,2916.,2849.}, {0.0023725,2597.,2540.},{0.0023725,2962.,2897.},{0.003,1654.,1623.}, {0.004,793.6,779.8},{0.005,442.4,434.4},{0.006,272.5,267.}, {0.008,125.8,122.4},{0.01,68.71,66.19},{0.015,22.79,21.3}, {0.0170384,16.12,14.86},{0.0170384,102.9,46.72},{0.02,68.55,36.2}, {0.03,23.3,15.58},{0.04,10.65,7.79},{0.05,5.764,4.388}, {0.06,3.493,2.699},{0.08,1.607,1.228},{0.1,0.9047,0.6616}, {0.15,0.3595,0.2203},{0.2,0.2149,0.1093},{0.3,0.1289,0.05186}, {0.4,0.1006,0.03779},{0.5,0.08613,0.03249},{0.6,0.07703,0.02986}, {0.8,0.06546,0.02708},{1.,0.05795,0.02537},{1.25,0.05141,0.02375}, {1.5,0.04692,0.02254},{2.,0.04137,0.02109},{3.,0.03628,0.02026}, {4.,0.03428,0.02048},{5.,0.03355,0.02107},{6.,0.03341,0.02174}, {8.,0.03399,0.02311},{10.,0.03504,0.02432},{15.,0.0379,0.02638}, {20.,0.04048,0.02746}}}, {Zirconium,6.506, {{0.001,4210.,4203.},{0.0015,1631.,1625.},{0.002,811.5,805.7}, {0.0022223,625.8,620.1},{0.0022223,2392.,2335.},{0.00226411,2239.,2186.}, {0.0023067,2120.,2071.},{0.0023067,2953.,2878.},{0.00241654,2641.,2575.}, {0.0025316,2359.,2303.},{0.0025316,2691.,2627.},{0.003,1772.,1734.}, {0.004,850.7,834.4},{0.005,475.5,466.4},{0.006,293.5,287.3}, {0.008,135.6,132.},{0.01,74.17,71.5},{0.015,24.63,23.08}, {0.0179976,15.01,13.8},{0.0179976,94.7,41.64},{0.02,72.37,35.55}, {0.03,24.85,16.},{0.04,11.39,8.129},{0.05,6.173,4.621}, {0.06,3.744,2.859},{0.08,1.721,1.31},{0.1,0.9658,0.708}, {0.15,0.379,0.2361},{0.2,0.2237,0.1164},{0.3,0.1318,0.0542}, {0.4,0.1018,0.03885},{0.5,0.08693,0.03311},{0.6,0.07756,0.03025}, {0.8,0.06571,0.02726},{1.,0.0581,0.02547},{1.25,0.0515,0.0238}, {1.5,0.047,0.02257},{2.,0.04146,0.02112},{3.,0.03644,0.02033}, {4.,0.03451,0.02061},{5.,0.03384,0.02123},{6.,0.03374,0.02193}, {8.,0.03441,0.02335},{10.,0.03554,0.0246},{15.,0.03855,0.0267}, {20.,0.04122,0.02778}}}, {Niobium,8.57, {{0.001,4600.,4592.},{0.0015,1786.,1780.},{0.002,889.3,883.2}, {0.0023705,584.4,578.6},{0.0023705,2181.,2125.},{0.00241714,2045.,1992.}, {0.0024647,1935.,1886.},{0.0024647,2694.,2619.},{0.00257857,2412.,2347.}, {0.0026977,2161.,2104.},{0.0026977,2470.,2405.},{0.003,1906.,1859.}, {0.004,916.4,897.},{0.005,513.4,502.7},{0.006,317.2,310.3}, {0.008,146.9,142.9},{0.01,80.38,77.54},{0.015,26.72,25.08}, {0.0189856,14.09,12.91},{0.0189856,87.84,37.46},{0.02,77.12,34.93}, {0.03,26.66,16.48},{0.04,12.23,8.511},{0.05,6.644,4.884}, {0.06,4.032,3.04},{0.08,1.852,1.403},{0.1,1.037,0.7608}, {0.15,0.4023,0.2542},{0.2,0.2344,0.1247},{0.3,0.1357,0.05705}, {0.4,0.104,0.04026},{0.5,0.08831,0.03396},{0.6,0.07858,0.03085}, {0.8,0.06642,0.02764},{1.,0.05866,0.02575},{1.25,0.05196,0.02402}, {1.5,0.04741,0.02276},{2.,0.04185,0.0213},{3.,0.03686,0.02054}, {4.,0.03498,0.02086},{5.,0.03436,0.02153},{6.,0.03432,0.02227}, {8.,0.03508,0.02375},{10.,0.03628,0.02503},{15.,0.03944,0.02718}, {20.,0.04224,0.02828}}}, {Molybdenum,10.22, {{0.001,4942.,4935.},{0.0015,1925.,1918.},{0.002,959.3,953.1}, {0.0025202,541.5,535.8},{0.0025202,1979.,1924.},{0.00257212,1854.,1802.}, {0.0026251,1750.,1703.},{0.0026251,2433.,2360.},{0.00274267,2183.,2119.}, {0.0028655,1961.,1906.},{0.0028655,2243.,2179.},{0.003,2011.,1956.}, {0.004,970.3,947.5},{0.005,545.,532.8},{0.006,337.3,329.5}, {0.008,156.5,152.2},{0.01,85.76,82.75},{0.015,28.54,26.84}, {0.0199995,13.08,11.93},{0.0199995,80.55,32.93},(*{0.02,80.54,32.93},*) {0.03,28.1,16.64},{0.04,12.94,8.757},{0.05,7.037,5.074}, {0.06,4.274,3.178},{0.08,1.962,1.477},{0.1,1.096,0.8042}, {0.15,0.4208,0.2693},{0.2,0.2423,0.1316},{0.3,0.1379,0.05919}, {0.4,0.1047,0.04117},{0.5,0.08848,0.03437},{0.6,0.07851,0.03104}, {0.8,0.06619,0.02764},{1.,0.05837,0.02567},{1.25,0.05167,0.0239}, {1.5,0.04713,0.02263},{2.,0.04163,0.02118},{3.,0.03675,0.02046}, {4.,0.03496,0.02084},{5.,0.03439,0.02153},{6.,0.0344,0.02231}, {8.,0.03523,0.02382},{10.,0.0365,0.02513},{15.,0.03978,0.02731}, {20.,0.04264,0.0284}}}, {Technetium,11.5, {{0.001,5356.,5348.},{0.0015,2092.,2085.},{0.002,1044.,1037.}, {0.0026769,507.2,501.4},{0.0026769,1812.,1758.},{0.00273443,1699.,1648.}, {0.0027932,1602.,1555.},{0.0027932,2223.,2151.},{0.003,1862.,1805.}, {0.0030425,1800.,1745.},{0.0030425,2059.,1995.},{0.004,1036.,1009.}, {0.005,583.6,569.4},{0.006,361.9,353.},{0.008,168.3,163.5}, {0.01,92.31,89.08},{0.015,30.76,28.98},{0.02,14.1,12.9}, {0.021044,12.29,11.17},{0.021044,74.81,30.14},{0.03,29.93,16.93}, {0.04,13.81,9.075},{0.05,7.521,5.312},{0.06,4.571,3.348}, {0.08,2.099,1.568},{0.1,1.169,0.8572},{0.15,0.4449,0.288}, {0.2,0.2534,0.1403},{0.3,0.1418,0.06214},{0.4,0.1066,0.04257}, {0.5,0.08968,0.03521},{0.6,0.07935,0.03159},{0.8,0.06674,0.02797}, {1.,0.05876,0.02589},{1.25,0.05197,0.02406},{1.5,0.0474,0.02276}, {2.,0.04189,0.02129},{3.,0.03705,0.02061},{4.,0.03532,0.02103}, {5.,0.03482,0.02178},{6.,0.03487,0.02258},{8.,0.03578,0.02415}, {10.,0.03712,0.02549},{15.,0.04055,0.02774},{20.,0.04353,0.02884}}}, {Ruthenium,12.41, {{0.001,5718.,5709.},{0.0015,2240.,2233.},{0.002,1120.,1113.}, {0.0028379,470.4,464.6},{0.0028379,1644.,1591.},{0.00290168,1542.,1492.}, {0.0029669,1452.,1407.},{0.0029669,2317.,2233.},{0.003,1963.,1894.}, {0.003224,1638.,1584.},{0.003224,1874.,1811.},{0.004,1095.,1063.}, {0.005,616.5,600.},{0.006,383.2,373.1},{0.008,178.5,173.3}, {0.01,98.,94.56},{0.015,32.7,30.85},{0.02,14.99,13.76}, {0.0221172,11.43,10.35},{0.0221172,68.76,27.},{0.03,31.39,16.89}, {0.04,14.52,9.251},{0.05,7.926,5.477},{0.06,4.822,3.476}, {0.08,2.215,1.641},{0.1,1.232,0.9012},{0.15,0.4647,0.3037}, {0.2,0.2618,0.1475},{0.3,0.144,0.06445},{0.4,0.1074,0.04355}, {0.5,0.08992,0.03567},{0.6,0.07933,0.03182},{0.8,0.06647,0.02796}, {1.,0.05846,0.02581},{1.25,0.05166,0.02393},{1.5,0.0471,0.02262}, {2.,0.04164,0.02115},{3.,0.03692,0.02052},{4.,0.03527,0.02098}, {5.,0.03482,0.02176},{6.,0.03491,0.02259},{8.,0.03591,0.02419}, {10.,0.0373,0.02556},{15.,0.04084,0.02783},{20.,0.04387,0.02893}}}, {Rhodium,12.41, {{0.001,6169.,6160.},{0.0015,2426.,2419.},{0.002,1214.,1207.}, {0.003,444.1,438.2},{0.0030038,442.7,436.8},{0.0030038,1513.,1461.}, {0.00307413,1422.,1372.},{0.0031461,1337.,1292.},{0.0031461,1847.,1777.}, {0.00327631,1671.,1608.},{0.0034119,1512.,1458.},{0.0034119,1731.,1669.}, {0.004,1170.,1132.},{0.005,658.9,639.6},{0.006,410.1,398.5}, {0.008,191.5,185.7},{0.01,105.3,101.5},{0.015,35.18,33.22}, {0.02,16.13,14.84},{0.0232199,10.79,9.736},{0.0232199,64.14,24.58}, {0.03,33.3,16.99},{0.04,15.44,9.52},{0.05,8.448,5.706}, {0.06,5.147,3.649},{0.08,2.365,1.737},{0.1,1.314,0.9581}, {0.15,0.4916,0.3241},{0.2,0.2742,0.1571},{0.3,0.1485,0.06776}, {0.4,0.1097,0.04517},{0.5,0.09134,0.03663},{0.6,0.08035,0.03247}, {0.8,0.06711,0.02834},{1.,0.05894,0.02608},{1.25,0.05204,0.02413}, {1.5,0.04744,0.02278},{2.,0.04197,0.02131},{3.,0.03728,0.02071}, {4.,0.03568,0.02122},{5.,0.03529,0.02204},{6.,0.03542,0.0229}, {8.,0.0365,0.02456},{10.,0.03797,0.02597},{15.,0.04166,0.02831}, {20.,0.04481,0.02943}}}, {Palladium,12.02, {{0.001,6538.,6529.},{0.0015,2579.,2571.},{0.002,1292.,1285.}, {0.003,473.,466.8},{0.0031733,410.6,404.7},{0.0031733,1355.,1305.}, {0.00325085,1287.,1238.},{0.0033303,1215.,1171.},{0.0033303,1664.,1597.}, {0.00346459,1518.,1456.},{0.0036043,1379.,1326.},{0.0036043,1582.,1520.}, {0.004,1227.,1182.},{0.005,691.2,668.8},{0.006,430.8,417.5}, {0.008,201.7,195.3},{0.01,111.,107.},{0.015,37.15,35.11}, {0.02,17.04,15.71},{0.0243503,10.03,9.016},{0.0243503,58.98,22.08}, {0.03,34.65,16.69},{0.04,16.14,9.611},{0.05,8.85,5.833}, {0.06,5.399,3.759},{0.08,2.481,1.804},{0.1,1.377,1.}, {0.15,0.5115,0.3397},{0.2,0.2827,0.1644},{0.3,0.1506,0.07007}, {0.4,0.1103,0.04611},{0.5,0.09134,0.03704},{0.6,0.0801,0.03262}, {0.8,0.06669,0.02828},{1.,0.05849,0.02594},{1.25,0.05159,0.02395}, {1.5,0.04702,0.02259},{2.,0.04162,0.02112},{3.,0.03704,0.02056}, {4.,0.03552,0.02111},{5.,0.03518,0.02196},{6.,0.03537,0.02284}, {8.,0.03651,0.02453},{10.,0.03802,0.02595},{15.,0.04181,0.02832}, {20.,0.04501,0.02944}}}, {Silver,10.5, {{0.001,7039.,7029.},{0.0015,2790.,2782.},{0.002,1401.,1393.}, {0.003,513.6,507.3},{0.0033511,388.7,382.7},{0.0033511,1274.,1223.}, {0.00343632,1200.,1151.},{0.0035237,1126.,1082.},{0.0035237,1547.,1479.}, {0.00366203,1409.,1348.},{0.0038058,1282.,1229.},{0.0038058,1468.,1406.}, {0.004,1305.,1252.},{0.005,738.5,712.2},{0.006,461.,445.7}, {0.008,216.4,209.2},{0.01,119.3,114.9},{0.015,39.98,37.8}, {0.02,18.36,16.95},{0.025514,9.527,8.534},{0.025514,55.39,20.31}, {0.03,36.68,16.6},{0.04,17.2,9.869},{0.05,9.444,6.066}, {0.06,5.766,3.938},{0.08,2.651,1.907},{0.1,1.47,1.062}, {0.15,0.5426,0.3622},{0.2,0.2972,0.1751},{0.3,0.156,0.07392}, {0.4,0.1131,0.04803},{0.5,0.09321,0.03822},{0.6,0.08153,0.03347}, {0.8,0.06766,0.02881},{1.,0.05921,0.02632},{1.25,0.05217,0.02425}, {1.5,0.04754,0.02284},{2.,0.04209,0.02135},{3.,0.03754,0.02082}, {4.,0.03606,0.02142},{5.,0.03577,0.02232},{6.,0.03601,0.02324}, {8.,0.03723,0.02499},{10.,0.03882,0.02647},{15.,0.04276,0.02889}, {20.,0.04609,0.03005}}}, {Cadmium,8.65, {{0.001,7350.,7340.},{0.0015,2931.,2922.},{0.002,1473.,1466.}, {0.003,541.4,535.},{0.0035375,357.5,351.7},{0.0035375,1152.,1103.}, {0.00363101,1083.,1036.},{0.003727,1013.,971.5},{0.003727,1389.,1324.}, {0.004,1170.,1118.},{0.004018,1157.,1106.},{0.004018,1324.,1264.}, {0.005,768.5,738.3},{0.006,479.3,461.9},{0.008,225.4,217.4}, {0.01,124.4,119.7},{0.015,41.78,39.52},{0.02,19.2,17.76}, {0.0267112,8.809,7.863},{0.0267112,50.65,18.21},{0.03,37.65,15.94}, {0.04,17.78,9.812},{0.05,9.779,6.115},{0.06,5.975,4.001}, {0.08,2.751,1.957},{0.1,1.524,1.096},{0.15,0.5593,0.3753}, {0.2,0.3038,0.1813},{0.3,0.1571,0.0758},{0.4,0.1129,0.04868}, {0.5,0.0925,0.03838},{0.6,0.08064,0.03339},{0.8,0.0667,0.02854}, {1.,0.05826,0.02597},{1.25,0.05129,0.02387},{1.5,0.04673,0.02247}, {2.,0.04139,0.02099},{3.,0.03698,0.02051},{4.,0.03559,0.02114}, {5.,0.03536,0.02206},{6.,0.03563,0.023},{8.,0.03691,0.02477}, {10.,0.03853,0.02625},{15.,0.04253,0.02869},{20.,0.04587,0.02985}}}, {Indium,7.31, {{0.001,7809.,7797.},{0.0015,3131.,3122.},{0.002,1578.,1570.}, {0.003,580.8,574.3},{0.0037301,335.6,329.8},{0.0037301,1046.,998.9}, {0.00383264,993.,946.5},{0.003938,931.3,890.5},{0.003938,1261.,1199.}, {0.004,1231.,1170.},{0.0042375,1066.,1016.},{0.0042375,1223.,1164.}, {0.005,813.4,778.},{0.006,507.2,487.1},{0.008,239.1,230.1}, {0.01,132.1,126.9},{0.015,44.45,42.06},{0.02,20.44,18.93}, {0.0279399,8.316,7.395},{0.0279399,47.33,16.7},{0.03,39.49,15.53}, {0.04,18.73,9.911},{0.05,10.3,6.262},{0.06,6.306,4.135}, {0.08,2.907,2.043},{0.1,1.609,1.15},{0.15,0.5876,0.396}, {0.2,0.3167,0.1913},{0.3,0.1614,0.07923},{0.4,0.1149,0.05031}, {0.5,0.09371,0.03932},{0.6,0.08138,0.03398},{0.8,0.06707,0.02883}, {1.,0.05849,0.02615},{1.25,0.05144,0.02398},{1.5,0.04684,0.02254}, {2.,0.04151,0.02105},{3.,0.03715,0.0206},{4.,0.03582,0.02127}, {5.,0.03564,0.02223},{6.,0.03596,0.02321},{8.,0.0373,0.02502}, {10.,0.03898,0.02653},{15.,0.04311,0.02903},{20.,0.04654,0.0302}}}, {Tin,7.31, {{0.001,8157.,8144.},{0.0015,3296.,3287.},{0.002,1665.,1657.}, {0.003,614.3,607.7},{0.0039288,311.4,305.8},{0.0039288,928.5,884.5}, {0.004,939.3,894.5},{0.0041561,846.9,807.4},{0.0041561,1145.,1084.}, {0.00430764,1060.,1002.},{0.0044647,971.2,922.1},{0.0044647,1117.,1059.}, {0.005,847.1,806.4},{0.006,529.4,506.5},{0.008,250.,240.}, {0.01,138.4,132.7},{0.015,46.64,44.13},{0.02,21.46,19.9}, {0.0292001,7.76,6.876},{0.0292001,43.6,15.14},{0.03,41.21,14.9}, {0.04,19.42,9.835},{0.05,10.7,6.314},{0.06,6.564,4.211}, {0.08,3.029,2.101},{0.1,1.676,1.189},{0.15,0.6091,0.4119}, {0.2,0.326,0.199},{0.3,0.1639,0.08179},{0.4,0.1156,0.05138}, {0.5,0.09374,0.0398},{0.6,0.08113,0.03417},{0.8,0.06662,0.02878}, {1.,0.058,0.02601},{1.25,0.05095,0.02379},{1.5,0.04638,0.02233}, {2.,0.04112,0.02085},{3.,0.03686,0.02044},{4.,0.03561,0.02115}, {5.,0.03548,0.02213},{6.,0.03583,0.02312},{8.,0.03724,0.02496}, {10.,0.03895,0.02649},{15.,0.04315,0.02901},{20.,0.04662,0.03018}}}, {Antimony,6.691, {{0.001,8582.,8568.},{0.0015,3491.,3481.},{0.002,1767.,1759.}, {0.003,653.6,646.9},{0.004,316.9,311.3},{0.0041322,291.8,286.3}, {0.0041322,869.1,825.2},{0.00425449,830.8,786.5},{0.0043804,777.6,739.2}, {0.0043804,1050.,990.6},{0.00453657,974.3,917.8},{0.0046983,893.9,845.7}, {0.0046983,1029.,972.5},{0.005,884.6,837.7},{0.006,556.9,530.5}, {0.008,263.1,251.8},{0.01,145.9,139.6},{0.015,49.23,46.57}, {0.02,22.68,21.05},{0.03,7.631,6.755},{0.0304912,7.307,6.452}, {0.0304912,40.73,13.91},{0.04,20.27,9.789},{0.05,11.2,6.4}, {0.06,6.879,4.311},{0.08,3.176,2.173},{0.1,1.758,1.237}, {0.15,0.6361,0.4312},{0.2,0.3381,0.2084},{0.3,0.1677,0.08504}, {0.4,0.1172,0.05288},{0.5,0.09453,0.04061},{0.6,0.08153,0.03465}, {0.8,0.0667,0.02896},{1.,0.05797,0.02608},{1.25,0.05086,0.02378}, {1.5,0.04628,0.0223},{2.,0.04105,0.02081},{3.,0.03686,0.02043}, {4.,0.03567,0.02118},{5.,0.03559,0.02219},{6.,0.03598,0.02321}, {8.,0.03745,0.02509},{10.,0.03921,0.02664},{15.,0.04351,0.0292}, {20.,0.04704,0.03038}}}, {Tellurium,6.24, {{0.001,8434.,8419.},{0.001003,8380.,8365.},{0.001006,8326.,8311.}, {0.001006,8684.,8668.},{0.0015,3608.,3598.},{0.002,1832.,1824.}, {0.003,679.2,672.6},{0.004,329.7,324.},{0.0043414,267.8,262.5}, {0.0043414,788.2,746.},{0.00447465,750.4,707.8},{0.004612,699.5,662.9}, {0.004612,944.5,888.},{0.0047728,878.2,823.7},{0.0049392,806.2,760.}, {0.0049392,929.2,874.4},{0.005,901.4,848.7},{0.006,572.1,542.3}, {0.008,270.2,257.8},{0.01,150.1,143.3},{0.015,50.78,48.02}, {0.02,23.41,21.75},{0.03,7.878,6.997},{0.0318138,6.738,5.929}, {0.0318138,37.19,12.51},{0.04,20.64,9.48},{0.05,11.45,6.33}, {0.06,7.041,4.306},{0.08,3.255,2.195},{0.1,1.801,1.256}, {0.15,0.6492,0.4409},{0.2,0.3429,0.2132},{0.3,0.1679,0.08646}, {0.4,0.1163,0.05326},{0.5,0.09328,0.04055},{0.6,0.08022,0.0344}, {0.8,0.06538,0.02854},{1.,0.05669,0.02559},{1.25,0.04967,0.02327}, {1.5,0.04518,0.02179},{2.,0.04009,0.02033},{3.,0.03606,0.01998}, {4.,0.03494,0.02075},{5.,0.03492,0.02177},{6.,0.03534,0.02279}, {8.,0.03683,0.02466},{10.,0.0386,0.0262},{15.,0.0429,0.02873}, {20.,0.04642,0.02989}}}, {Iodine,4.93, {{0.001,9096.,9078.},{0.00103542,8465.,8448.},{0.0010721,7863.,7847.}, {0.0010721,8198.,8181.},{0.0015,3919.,3908.},{0.002,1997.,1988.}, {0.003,742.,735.1},{0.004,360.7,354.8},{0.0045571,259.2,253.7}, {0.0045571,755.,712.1},{0.00470229,712.3,672.4},{0.0048521,663.6,627.}, {0.0048521,894.3,837.5},{0.005,843.,790.3},{0.0051881,766.5,719.8}, {0.0051881,883.7,828.3},{0.006,617.3,582.2},{0.008,292.2,277.7}, {0.01,162.6,154.8},{0.015,55.12,52.08},{0.02,25.43,23.63}, {0.03,8.561,7.622},{0.0331694,6.553,5.744},{0.0331694,35.82,11.88}, {0.04,22.1,9.616},{0.05,12.32,6.573},{0.06,7.579,4.518}, {0.08,3.51,2.331},{0.1,1.942,1.342},{0.15,0.6978,0.4742}, {0.2,0.3663,0.2295},{0.3,0.1771,0.09257},{0.4,0.1217,0.0565}, {0.5,0.09701,0.04267},{0.6,0.08313,0.03598},{0.8,0.06749,0.02962}, {1.,0.05841,0.02646},{1.25,0.05111,0.02399},{1.5,0.04647,0.02243}, {2.,0.04124,0.02092},{3.,0.03716,0.02059},{4.,0.03607,0.02142}, {5.,0.03608,0.0225},{6.,0.03655,0.02357},{8.,0.03815,0.02553}, {10.,0.04002,0.02714},{15.,0.04455,0.0298},{20.,0.04823,0.03101}}}, {Xenon,0.005485, {{0.001,9413.,9393.},{0.00107191,8151.,8132.},{0.001149,7035.,7019.}, {0.001149,7338.,7321.},{0.0015,4085.,4073.},{0.002,2088.,2078.}, {0.003,778.,770.9},{0.004,378.7,372.8},{0.0047822,240.8,235.5}, {0.0047822,694.1,652.4},{0.005,639.2,601.5},{0.0051037,604.4,569.3}, {0.0051037,818.1,763.},{0.00527536,757.9,707.9},{0.0054528,699.1,653.9}, {0.0054528,806.4,752.7},{0.006,637.6,597.9},{0.008,303.2,287.1}, {0.01,169.,160.5},{0.015,57.43,54.2},{0.02,26.52,24.65}, {0.03,8.93,7.969},{0.0345614,6.129,5.352},{0.0345614,33.16,10.86}, {0.04,22.7,9.323},{0.05,12.72,6.54},{0.06,7.825,4.541}, {0.08,3.633,2.374},{0.1,2.011,1.376},{0.15,0.7202,0.4894}, {0.2,0.376,0.2373},{0.3,0.1797,0.09522},{0.4,0.1223,0.05761}, {0.5,0.09699,0.04317},{0.6,0.08281,0.03617},{0.8,0.06696,0.02956}, {1.,0.05785,0.0263},{1.25,0.05054,0.02378},{1.5,0.04594,0.02221}, {2.,0.04078,0.0207},{3.,0.03681,0.02042},{4.,0.03577,0.02128}, {5.,0.03583,0.0224},{6.,0.03634,0.0235},{8.,0.03797,0.02553}, {10.,0.03987,0.0272},{15.,0.04445,0.03002},{20.,0.04815,0.03139}}}, {Caesium,1.873, {{0.001,9365.,9343.},{0.00103199,8775.,8754.},{0.001065,8214.,8194.}, {0.001065,8685.,8663.},{0.00113851,7576.,7557.},{0.0012171,6584.,6567.}, {0.0012171,6888.,6870.},{0.0015,4335.,4322.},{0.002,2226.,2216.}, {0.003,831.9,824.6},{0.004,405.5,399.4},{0.005,230.3,225.1}, {0.0050119,229.,223.7},{0.0050119,667.4,624.8},{0.00518274,618.4,576.3}, {0.0053594,564.5,529.9},{0.0053594,769.2,714.2},{0.00553401,714.6,661.}, {0.0057143,655.6,610.8},{0.0057143,754.7,701.5},{0.006,671.1,625.3}, {0.008,321.4,302.9},{0.01,179.3,169.7},{0.015,61.04,57.53}, {0.02,28.22,26.23},{0.03,9.507,8.502},{0.0359846,5.863,5.102}, {0.0359846,31.43,10.17},{0.04,23.81,9.185},{0.05,13.4,6.618}, {0.06,8.248,4.653},{0.08,3.836,2.464},{0.1,2.124,1.438}, {0.15,0.7589,0.5154},{0.2,0.3941,0.2502},{0.3,0.1863,0.1}, {0.4,0.1257,0.06003},{0.5,0.09912,0.04463},{0.6,0.08431,0.03717}, {0.8,0.06789,0.03014},{1.,0.05854,0.02671},{1.25,0.05108,0.02408}, {1.5,0.04641,0.02246},{2.,0.04121,0.02091},{3.,0.03725,0.02064}, {4.,0.03625,0.02153},{5.,0.03635,0.02268},{6.,0.03689,0.0238}, {8.,0.0386,0.02583},{10.,0.04057,0.0275},{15.,0.04529,0.03026}, {20.,0.0491,0.03152}}}, {Barium,3.5, {{0.001,8543.,8521.},{0.00103063,7990.,7969.},{0.0010622,7465.,7445.}, {0.0010622,8547.,8524.},{0.00109882,7957.,7935.},{0.0011367,7404.,7384.}, {0.0011367,7837.,7815.},{0.00121224,6861.,6841.},{0.0012928,5985.,5968.}, {0.0012928,6255.,6237.},{0.0015,4499.,4485.},{0.002,2319.,2308.}, {0.003,869.6,862.2},{0.004,424.6,418.4},{0.005,241.4,236.1}, {0.005247,213.5,208.4},{0.005247,609.8,568.9},{0.00543204,563.4,526.3}, {0.0056236,516.9,483.5},{0.0056236,701.6,648.6},{0.00580333,650.7,602.5}, {0.0059888,601.3,557.7},{0.0059888,693.,641.2},{0.006,689.8,638.3}, {0.008,333.4,312.7},{0.01,186.,175.4},{0.015,63.47,59.72}, {0.02,29.38,27.3},{0.03,9.904,8.875},{0.0374406,5.498,4.768}, {0.0374406,29.19,9.346},{0.04,24.57,8.842},{0.05,13.79,6.534}, {0.06,8.511,4.66},{0.08,3.963,2.501},{0.1,2.196,1.47}, {0.15,0.7828,0.5309},{0.2,0.4046,0.2583},{0.3,0.1891,0.1028}, {0.4,0.1265,0.06125},{0.5,0.09923,0.04521},{0.6,0.0841,0.03743}, {0.8,0.06744,0.03011},{1.,0.05803,0.02657},{1.25,0.05058,0.02388}, 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{0.08,4.177,2.587},{0.1,2.315,1.532},{0.15,0.8239,0.5576}, {0.2,0.4239,0.2718},{0.3,0.1961,0.1079},{0.4,0.1301,0.06382}, {0.5,0.1015,0.04677},{0.6,0.0857,0.03849},{0.8,0.06843,0.03073}, {1.,0.05876,0.027},{1.25,0.0511,0.02418},{1.5,0.0464,0.02249}, {2.,0.04122,0.0209},{3.,0.03737,0.02068},{4.,0.03646,0.02161}, {5.,0.03664,0.0228},{6.,0.03726,0.02395},{8.,0.03907,0.02602}, {10.,0.04113,0.02769},{15.,0.04603,0.03043},{20.,0.04996,0.03163}}}, {Cerium,6.657, {{0.001,9711.,9679.},{0.00108876,7991.,7964.},{0.0011854,6563.,6541.}, {0.0011854,7545.,7519.},{0.00122832,6984.,6960.},{0.0012728,6465.,6442.}, {0.0012728,6853.,6829.},{0.00135222,6031.,6010.},{0.0014366,5293.,5273.}, {0.0014366,5532.,5512.},{0.0015,5033.,5015.},{0.002,2607.,2595.}, {0.003,985.7,977.6},{0.004,481.1,474.5},{0.005,274.,268.4}, {0.0057234,194.3,189.2},{0.0057234,545.4,504.6},{0.006,490.8,455.}, {0.0061642,455.4,422.8},{0.0061642,618.8,566.5},{0.00635359,575.6,527.8}, 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{0.0142135,61.62,57.38},{0.0142135,146.1,114.},{0.015,127.9,100.8}, {0.0167847,94.17,75.76},{0.0167847,130.2,96.7},{0.0171352,133.8,92.64}, {0.017493,118.1,88.47},{0.017493,136.,101.},{0.02,97.04,74.46}, {0.03,34.42,28.12},{0.04,16.38,13.61},{0.05,9.196,7.637}, {0.06,5.748,4.729},{0.08,2.769,2.2},{0.0957299,1.777,1.361}, {0.0957299,6.895,1.935},{0.1,6.174,1.897},{0.15,2.249,1.112}, {0.2,1.118,0.6369},{0.3,0.4491,0.2718},{0.4,0.2565,0.1522}, {0.5,0.1765,0.1012},{0.6,0.1354,0.07517},{0.8,0.09495,0.05055}, {1.,0.07538,0.03934},{1.25,0.06189,0.03181},{1.5,0.05479,0.02791}, {2.,0.04821,0.02478},{3.,0.04424,0.02427},{4.,0.04383,0.02556}, {5.,0.04461,0.0271},{6.,0.04585,0.02859},{8.,0.04883,0.03113}, {10.,0.05195,0.03311},{15.,0.05918,0.03619},{20.,0.06493,0.03739}}}, {Radon,0.009066, {{0.001,5826.,5812.},{0.00104738,5354.,5340.},{0.001097,4909.,4895.}, {0.001097,5013.,5000.},{0.0015,2719.,2706.},{0.002,1490.,1478.}, {0.0028924,663.4,652.6},{0.0028924,2319.,2243.},{0.003,1554.,1507.}, 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{0.05,9.525,7.851},{0.06,5.959,4.881},{0.08,2.871,2.283}, {0.1,1.655,1.261},{0.101137,1.61,1.224},{0.101137,6.089,1.71}, {0.15,2.295,1.087},{0.2,1.141,0.6351},{0.3,0.4577,0.275}, {0.4,0.2601,0.1542},{0.5,0.178,0.1025},{0.6,0.1358,0.07597}, {0.8,0.09444,0.05067},{1.,0.0745,0.0392},{1.25,0.06087,0.03151}, {1.5,0.05376,0.02752},{2.,0.04721,0.02432},{3.,0.04324,0.02372}, {4.,0.04283,0.02495},{5.,0.04358,0.02644},{6.,0.04479,0.02788}, {8.,0.04769,0.03033},{10.,0.05077,0.03227},{15.,0.05786,0.03525}, {20.,0.0635,0.03641}}}, {Radium,5., {{0.001,6201.,6187.},{0.0010284,5895.,5881.},{0.0010576,5602.,5588.}, {0.0010576,5683.,5669.},{0.00113049,5019.,5005.},{0.0012084,4424.,4411.}, {0.0012084,4516.,4502.},{0.0015,2950.,2937.},{0.002,1620.,1608.}, {0.003,666.4,655.5},{0.0031049,616.9,606.1},{0.0031049,1715.,1657.}, {0.00317584,1506.,1457.},{0.0032484,1374.,1331.},{0.0032484,2039.,1965.}, {0.0035096,1647.,1587.},{0.0037918,1342.,1297.},{0.0037918,1558.,1506.}, 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{15.,0.05815,0.03549},{20.,0.06383,0.03668}}}, {Actinium,10.07, {{0.001,6469.,6455.},{0.00103923,6034.,6020.},{0.00108,5622.,5608.}, {0.00108,5702.,5688.},{0.00117069,4905.,4891.},{0.001269,4203.,4190.}, {0.001269,4289.,4275.},{0.0015,3082.,3069.},{0.002,1696.,1683.}, {0.003,698.1,687.},{0.003219,595.9,585.1},{0.003219,1537.,1485.}, {0.00329373,1404.,1358.},{0.0033702,1307.,1264.},{0.0033702,1892.,1822.}, {0.00362962,1564.,1508.},{0.003909,1296.,1252.},{0.003909,1504.,1453.}, {0.004,1426.,1377.},{0.004656,974.5,942.8},{0.004656,1034.,1000.}, {0.005,868.7,840.8},{0.005002,867.8,839.9},{0.005002,905.1,876.1}, {0.006,582.9,564.1},{0.008,287.8,277.3},{0.01,165.3,158.}, {0.015,60.02,55.83},{0.015871,52.13,48.23},{0.015871,121.4,92.24}, {0.0174031,104.2,73.5},{0.0190832,74.26,58.65},{0.0190832,103.6,74.48}, {0.0194579,107.9,71.33},{0.01984,94.03,68.31},{0.01984,108.2,77.74}, {0.02,106.2,76.45},{0.03,38.11,30.},{0.04,18.23,14.79}, {0.05,10.27,8.396},{0.06,6.433,5.242},{0.08,3.1,2.465}, {0.1,1.786,1.367},{0.106756,1.525,1.15},{0.106756,5.622,1.582}, {0.15,2.434,1.1},{0.2,1.213,0.6581},{0.3,0.4859,0.2896}, {0.4,0.2749,0.1632},{0.5,0.1872,0.1085},{0.6,0.1421,0.08018}, {0.8,0.09804,0.05311},{1.,0.07686,0.0408},{1.25,0.06251,0.03258}, {1.5,0.05504,0.02831},{2.,0.04822,0.0249},{3.,0.04409,0.02419}, {4.,0.04363,0.02539},{5.,0.04438,0.02688},{6.,0.0456,0.02832}, {8.,0.04856,0.03079},{10.,0.05171,0.03275},{15.,0.05895,0.03575}, {20.,0.06473,0.03692}}}, {Thorium,11.72, {{0.001,6614.,6600.},{0.00108088,5747.,5733.},{0.0011683,4976.,4962.}, {0.0011683,5048.,5034.},{0.0012463,4463.,4449.},{0.0013295,3937.,3924.}, {0.0013295,4017.,4003.},{0.0015,3161.,3148.},{0.002,1742.,1729.}, {0.003,718.,707.},{0.003332,567.1,556.5},{0.003332,1394.,1346.}, {0.00341048,1304.,1260.},{0.0034908,1226.,1185.},{0.0034908,1749.,1683.}, {0.004,1253.,1208.},{0.0040461,1217.,1174.},{0.0040461,1415.,1364.}, {0.00442089,1137.,1098.},{0.0048304,910.3,879.7},{0.0048304,965.5,933.}, {0.005,887.8,858.1},{0.0051823,812.9,785.9},{0.0051823,847.7,819.6}, {0.006,594.5,574.9},{0.008,293.9,283.},{0.01,168.9,161.5}, {0.015,61.41,57.18},{0.0163003,49.91,46.11},{0.0163003,115.6,87.32}, {0.0179166,99.24,69.24},{0.0196932,69.84,54.92},{0.0196932,95.27,68.36}, {0.02,93.68,67.14},{0.0204721,88.51,63.83},{0.0204721,101.8,72.59}, {0.03,38.92,30.32},{0.04,18.65,15.03},{0.05,10.52,8.558}, {0.06,6.592,5.355},{0.08,3.178,2.526},{0.1,1.83,1.403}, {0.109651,1.465,1.1},{0.109651,5.336,1.502},{0.15,2.472,1.09}, {0.2,1.234,0.6603},{0.3,0.4939,0.2931},{0.4,0.2789,0.1656}, {0.5,0.1895,0.1101},{0.6,0.1435,0.08128},{0.8,0.09861,0.05366}, {1.,0.07709,0.04109},{1.25,0.06251,0.03269},{1.5,0.05498,0.02834}, {2.,0.04812,0.02487},{3.,0.04396,0.02411},{4.,0.04347,0.02528}, {5.,0.04421,0.02674},{6.,0.04542,0.02817},{8.,0.04836,0.0306}, {10.,0.05149,0.03253},{15.,0.05871,0.0355},{20.,0.06447,0.03664}}}, {Protactinium,15.37, {{0.001,6530.,6515.},{0.00100334,6490.,6476.},{0.0010067,6451.,6437.}, 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{0.03,0.3778,0.1596},{0.04,0.2687,0.07125},{0.05,0.2266, 0.04315}, {0.06,0.2053,0.0324},{0.08,0.1828,0.02611},{0.1,0.1699, 0.02547}, {0.15,0.1497,0.02753},{0.2,0.1363,0.02952},{0.3,0.118, 0.03175}, {0.4,0.1055,0.03261},{0.5,0.09633,0.03281},{0.6,0.08906, 0.03266}, {0.8,0.07822,0.03188},{1.,0.07032,0.03086},{1.25,0.06288, 0.02949}, {1.5,0.05722,0.02818},{2.,0.04914,0.02593},{3.,0.03945, 0.02268}, {4.,0.03382,0.02053},{5.,0.03012,0.01903},{6.,0.02752, 0.01793}, {8.,0.02411,0.01646},{10.,0.02202,0.01554},{15.,0.01924, 0.01428}, {20.,0.01796,0.01368}}}, {SoftTissue,1.06, {{0.001,3712.,3701.},{0.00103542,3386.,3376.},{0.0010721,3087., 3079.}, {0.0010721,3099.,3090.},{0.0015,1251.,1247.},{0.002,559.6, 557.7}, {0.0021455,458.3,456.6},{0.0021455,465.,462.9},{0.00230297, 380.,378.2}, {0.002472,310.2,308.6},{0.002472,315.8,313.7},{0.0026414, 261.2,259.4}, {0.0028224,215.8,214.2},{0.0028224,218.8,216.9},{0.003, 183.6,181.9}, {0.0036074,107.3,106.1},{0.0036074,110.5,108.9},{0.004, 81.61,80.3}, {0.005,42.24,41.35},{0.006,24.56,23.89},{0.008,10.42, 9.935}, {0.01,5.379,4.987},{0.015,1.699,1.402},{0.02,0.823, 0.5663}, {0.03,0.379,0.1616},{0.04,0.2688,0.07216},{0.05,0.2264, 0.0436}, {0.06,0.2048,0.03264},{0.08,0.1823,0.02617},{0.1,0.1693, 0.02545}, {0.15,0.1492,0.02745},{0.2,0.1358,0.02942},{0.3,0.1175, 0.03164}, {0.4,0.1052,0.03249},{0.5,0.09598,0.03269},{0.6,0.08873, 0.03254}, {0.8,0.07793,0.03176},{1.,0.07006,0.03074},{1.25,0.06265, 0.02938}, {1.5,0.05701,0.02807},{2.,0.04895,0.02583},{3.,0.03931, 0.02259}, {4.,0.03369,0.02045},{5.,0.03,0.01895},{6.,0.02741, 0.01786}, {8.,0.02401,0.01639},{10.,0.02193,0.01547},{15.,0.01915, 0.01422}, {20.,0.01787,0.01362}}}, {FourComponentSoftTissue,1., {{0.001,3829.,3818.},{0.0015,1286.,1283.},{0.002,575.5,573.6}, {0.003, 179.2,178.1},{0.004,76.81,75.98},{0.005,39.47,38.8}, {0.006,22.83, 22.26},{0.008,9.604,9.163},{0.01,4.937,4.564}, {0.015,1.558, 1.266},{0.02,0.7616,0.507},{0.03,0.3604,0.1438}, {0.04,0.2609, 0.06474},{0.05,0.2223,0.03987},{0.06,0.2025,0.03051}, {0.08,0.1813, 0.0253},{0.1,0.1688,0.02501},{0.15,0.149,0.02732}, {0.2,0.1356, 0.02936},{0.3,0.1175,0.03161},{0.4,0.1051,0.03247}, {0.5,0.09593, 0.03267},{0.6,0.0887,0.03252},{0.8,0.07789,0.03175}, {1.,0.07003, 0.03073},{1.25,0.06262,0.02937},{1.5,0.05699,0.02806}, {2.,0.04893, 0.02582},{3.,0.03929,0.02258},{4.,0.03367,0.02044}, {5.,0.02998, 0.01894},{6.,0.02739,0.01785},{8.,0.024,0.01638}, {10.,0.02191, 0.01546},{15.,0.01913,0.0142},{20.,0.01785, 0.0136}}}, {MethaneBasedTissueEquivalentGas,0.001064, {{0.001,2993.,2986.},{0.0015,987.8,985.4},{0.002,437.6, 436.1}, {0.003,134.7,133.8},{0.004,57.34,56.65},{0.005,29.35, 28.78}, {0.006,16.94,16.45},{0.008,7.124,6.73},{0.01,3.679, 3.338}, {0.015,1.197,0.9207},{0.02,0.6129,0.3685},{0.03,0.3177, 0.1063}, {0.04,0.2431,0.05002},{0.05,0.2132,0.03278},{0.06,0.1972, 0.02663}, {0.08,0.179,0.0238},{0.1,0.1675,0.0243},{0.15,0.1486, 0.02714}, {0.2,0.1355,0.0293},{0.3,0.1174,0.03161},{0.4,0.1051, 0.03248}, {0.5,0.09594,0.03269},{0.6,0.08871,0.03254},{0.8,0.0779, 0.03177}, {1.,0.07004,0.03075},{1.25,0.06264,0.02938},{1.5,0.057, 0.02809}, {2.,0.0489,0.02583},{3.,0.03919,0.02254},{4.,0.03351, 0.02035}, {5.,0.02976,0.01881},{6.,0.02711,0.01767},{8.,0.02363, 0.01614}, {10.,0.02146,0.01516},{15.,0.01855,0.01383},{20.,0.01717, 0.01318}}}, {PropaneBasedTissueEquivalentGas,0.001826, {{0.001,2721.,2715.},{0.0015,890.9,888.8},{0.002,392.8, 391.5}, {0.003,120.2,119.4},{0.004,51.03,50.38},{0.005,26.07, 25.53}, {0.006,15.03,14.56},{0.008,6.32,5.941},{0.01,3.272, 2.94}, {0.015,1.08,0.8087},{0.02,0.5648,0.3236},{0.03,0.304, 0.09413}, {0.04,0.2375,0.04526},{0.05,0.2104,0.0305},{0.06,0.1955, 0.02538}, {0.08,0.1783,0.02332},{0.1,0.1672,0.02408},{0.15,0.1485, 0.02709}, {0.2,0.1355,0.02929},{0.3,0.1175,0.03162},{0.4,0.1052, 0.0325}, {0.5,0.09599,0.03271},{0.6,0.08876,0.03256},{0.8,0.07795, 0.03179}, {1.,0.07008,0.03077},{1.25,0.06267,0.02941},{1.5,0.05703, 0.02811}, {2.,0.04892,0.02584},{3.,0.03918,0.02254},{4.,0.03347, 0.02033}, {5.,0.0297,0.01877},{6.,0.02703,0.01762},{8.,0.02352, 0.01605}, {10.,0.02133,0.01505},{15.,0.01837,0.01368},{20.,0.01695, 0.01301}}}, {LiquidWater,1., {{0.001,4078.,4065.},{0.0015,1376.,1372.},{0.002,617.3,615.2}, {0.003, 192.9,191.7},{0.004,82.78,81.91},{0.005,42.58,41.88}, {0.006,24.64, 24.05},{0.008,10.37,9.915},{0.01,5.329,4.944}, {0.015,1.673, 1.374},{0.02,0.8096,0.5503},{0.03,0.3756,0.1557}, {0.04,0.2683, 0.06947},{0.05,0.2269,0.04223},{0.06,0.2059,0.0319}, {0.08,0.1837, 0.02597},{0.1,0.1707,0.02546},{0.15,0.1505,0.02764}, {0.2,0.137, 0.02967},{0.3,0.1186,0.03192},{0.4,0.1061,0.03279}, {0.5,0.09687, 0.03299},{0.6,0.08956,0.03284},{0.8,0.07865,0.03206}, {1.,0.07072, 0.03103},{1.25,0.06323,0.02965},{1.5,0.05754,0.02833}, {2.,0.04942, 0.02608},{3.,0.03969,0.02281},{4.,0.03403,0.02066}, {5.,0.03031, 0.01915},{6.,0.0277,0.01806},{8.,0.02429,0.01658}, {10.,0.02219, 0.01566},{15.,0.01941,0.01441},{20.,0.01813,0.01382}}}}; (* Define equivalent names for some of the radiological materials *) A150 = A150TissueEquivalentPlastic; TissueEquivalentPlastic = A150TissueEquivalentPlastic; Air = DryAir; B100 = B100BoneEquivalentPlastic; BoneEquivalentPlastic = B100BoneEquivalentPlastic; Blood = WholeBlood; Bone = CorticalBone; Brain = GreyWhiteMatterBrain; Breast = BreastTissue; C552 = C552AirEquivalentPlastic; AirEquivalentPlastic = C552AirEquivalentPlastic; Concrete = OrdinaryConcrete; StandardFricke = FerrousSulfate; Pyrex = BorosilicateGlass; Lung = LungTissue; Muscle = SkeletalMuscle; KodakEmulsion = KodakTypeAAPhotographicEmulsion; NuclearEmulsion = StandardNuclearPhotgraphicEmulsion; Vinyltoluene = PlasticScintillator; Mylar = PolyethyleneTerepthalate; Teflon = Polytetrafluoroethylene; Water = LiquidWater; (*** Warning Messages ***) xRayFunctions = {XRayMAC, XRayMEAC, XRayAMFP, XRayEAMFP, XRayTransmission, XRayAbsorption}; (* Warning messages if the material is not in the table. *) Scan[(#::"material" = "The material `1` is not one of the first 92 elements or 48 additional radiological materials in the table.")&, xRayFunctions]; (* Warning messages if the input energy is outside of the table range from 0.001 MeV to 20 MeV. *) Scan[(#::"energyRange" = "The energy argument `1` is outside the table range from 0.001 MeV to 20 MeV.")&, xRayFunctions]; (* Warning messages if an input argument has the wrong units. *) Scan[(#::"energyUnit" = "The energy argument `1` does not have correct units of energy.")&, xRayFunctions]; Scan[(#::"thicknessUnit" = "The thickness argument `1` does not have correct units of thickness.")&, {XRayTransmission, XRayAbsorption}]; mixtureFunctions = {MixtureMAC, MixtureAMFP, MixtureTransmission}; (* Warning messages if the mixture contains improper elements. *) Scan[(#::"mixture" = "The mixture `1` does not have the proper form {{material1, fraction1}, {material2, fraction2}, ...}.")&, mixtureFunctions]; Scan[(#::"material" = "The material `1` in the description of the mixture is not one of the first 92 elements or 48 additional radiological materials in the table.")&, mixtureFunctions]; Scan[(#::"fraction" = "The expression `1` in the description of the mixture is not numeric.")&, mixtureFunctions]; (* Warning messages if an input argument has the wrong units. *) Scan[(#::"energyUnit" = "The energy argument `1` does not have correct units of energy.")&, mixtureFunctions]; Scan[(#::"densityUnit" = "The density argument `1` does not have correct units of density.")&, mixtureFunctions]; Scan[(#::"thicknessUnit" = "The thickness argument `1` does not have correct units of thickness.")&, mixtureFunctions]; compoundFunctions = {CompoundMAC, CompoundAMFP, CompoundTransmission}; (* Warning messages if the compound contains improper elements. *) Scan[(#::"compound" = "The compound `1` does not have the proper form {{element1, number1}, {element2, number2}, ...}.")&, compoundFunctions]; Scan[(#::"element" = "The material `1` in the description of the chemical compound is not one of the first 92 elements.")&, compoundFunctions]; Scan[(#::"number" = "The expression `1` in the description of the chemical compound is not numeric.")&, compoundFunctions]; (* Warning messages if an input argument has the wrong units. *) Scan[(#::"energyUnit" = "The energy argument `1` does not have correct units of energy.")&, compoundFunctions]; Scan[(#::"densityUnit" = "The density argument `1` does not have correct units of density.")&, compoundFunctions]; Scan[(#::"thicknessUnit" = "The thickness argument `1` does not have correct units of thickness.")&, compoundFunctions]; (*** Internal Functions ***) (* A function to check for error messages when evaluating an expression without printing out the messages. If no error messages are found, the evaluated expression is returned. If error messages are found, the error argument is returned. *) myCheck[expression_, errorReturn_] := Module[{answer, flag}, answer = Block[{$Messages = {}}, Check[expression, flag]]; If[answer === flag, errorReturn, answer]]; SetAttributes[myCheck, HoldAll]; (* A function to make a list from the table consisting of the minimum energy in the table, all the absorption edge energies in the table, and the maximum energy in the table. *) findTableEnergies[table_] := Module[{energyList}, energyList = First[Transpose[table]]; Append[Map[First, Split[energyList, UnsameQ]], Last[energyList]]]; (* A function to divide the table into separate parts at each absorption edge. *) splitTable[table_] := Split[table, (First[#1] != First[#2])&]; (* A function to create an interpolationg function for each part of the table. The tables have at least 3 points in each part, between absorption edges. *) interpolateTable[table_] := If[ Length[table] > 3, Interpolation[Log[table], InterpolationOrder->3], Interpolation[Log[table], InterpolationOrder->2]]; (* A list of the names of the materials. For consistency, use the element names from "Miscellaneous`ChemicalElements`", rather than from the table above. *) first92Elements = Take[Elements, 92]; materialName = Join[first92Elements, RadiologicalMaterials]; (* A list of the densities of the materials. For consistency, use the material densities from the NIST report, rather than from "Miscellaneous`ChemicalElements`". *) materialDensity = Transpose[xRayAttenuationData][[2]]; (* Gram / (Centi Meter)^3 *) (* Extract the x-ray mass attenuation coefficients part of the table, columns 1 and 2, and the x-ray mass energy absorption coefficients part of the table, columns 1 and 3. *) macTable = Map[Take[#, 2]&, Transpose[xRayAttenuationData][[3]], {2}]; (* {Mega ElectronVolt, (Centi Meter)^2 / Gram} *) meacTable = Map[Drop[#, {2}]&, Transpose[xRayAttenuationData][[3]], {2}]; (* {Mega ElectronVolt, (Centi Meter)^2 / Gram} *) (* Build a tree of the absorption edge energies for each material, for determining which part of the interpolation, between absorption edges, to use. *) energyTree = Map[MakeTree, Map[findTableEnergies, macTable]]; (* Mega ElectronVolt *) (* Build the interpolation of the x-ray mass attenuation coefficients and the interpolation of the x-ray mass energy absorption coefficients *) macInterpolation = Map[interpolateTable, Map[splitTable, macTable], {2}]; (* {Mega ElectronVolt, (Centi Meter)^2 / Gram} *) meacInterpolation = Map[interpolateTable, Map[splitTable, meacTable], {2}]; (* {Mega ElectronVolt, (Centi Meter)^2 / Gram} *) (* Internal functions to interpolate the x-ray mass attenuation coefficient and the x-ray mass energy absorption coefficient, given the index of the material in the table and the x-ray energy. Add the value for the end of each table, at 20. MeV, not included by the Tree function. Check that the energy input has proper units. Check that the energy is in the correct range from 0.001 MeV to 20 MeV. *) mac[index_, energy_] := Catch[ Module[ { e = myCheck[Convert[energy, Mega * ElectronVolt] / (Mega * ElectronVolt), Throw[energy, "energyUnit"]], macUnit = (Centi * Meter)^2 / Gram}, If[(e >= 0.001 && e < 20.), Exp[macInterpolation[[index, TreeFind[energyTree[[index]], e]]][Log[e]]] * macUnit, If[(e == 20.), Last[Last[macTable[[index]]]] * macUnit, Throw[energy, "energyRange"]]]], _, (Message[MessageName[XRayMAC, #2], #1])&]; meac[index_, energy_] := Catch[ Module[ { e = myCheck[Convert[energy, Mega * ElectronVolt] / (Mega * ElectronVolt), Throw[energy, "energyUnit"]], meacUnit = (Centi * Meter)^2 / Gram}, If[(e >= 0.001 && e < 20.), Exp[meacInterpolation[[index, TreeFind[energyTree[[index]], e]]][Log[e]]] * meacUnit, If[(e == 20.), Last[Last[meacTable[[index]]]] * meacUnit, Throw[energy, "energyRange"]]]], _, (Message[MessageName[XRayMEAC, #2], #1])&]; (* Internal functions to calculate the x-ray attenuation mean free path and the x-ray energy absorption mean free path, given the index of the material in the table and the x-ray energy. Check that the energy input has proper units. Check that the energy is in the correct range from 0.001 MeV to 20 MeV. *) amfp[index_, energy_] := Catch[ Module[ { e = myCheck[Convert[energy, Mega * ElectronVolt] / (Mega * ElectronVolt), Throw[energy, "energyUnit"]], densityUnit = Gram / (Centi * Meter)^3}, If[(e >= 0.001 && e <= 20.), 1. / (mac[index, energy] * materialDensity[[index]] * densityUnit), Throw[energy, "energyRange"]]], _, (Message[MessageName[XRayAMFP, #2], #1])&]; eamfp[index_, energy_] := Catch[ Module[ { e = myCheck[Convert[energy, Mega * ElectronVolt] / (Mega * ElectronVolt), Throw[energy, "energyUnit"]], densityUnit = Gram / (Centi * Meter)^3}, If[(e >= 0.001 && e <= 20.), 1. / (meac[index, energy] * materialDensity[[index]] * densityUnit), Throw[energy, "energyRange"]]], _, (Message[MessageName[XRayEAMFP, #2], #1])&]; (* Internal functions to calculate the fractional x-ray transnission through material and the fractional x-ray energy absorption in a material, given the index of the material in the table, the x-ray energy, and the thickness of the material. Check that the energy input and the thickness input have proper units. Check that the energy is in the correct range from 0.001 MeV to 20 MeV. *) transmission[index_, energy_, thickness_] := Catch[ Module[ { e = myCheck[Convert[energy, Mega * ElectronVolt] / (Mega * ElectronVolt), Throw[energy, "energyUnit"]], t = myCheck[Convert[thickness, Centi * Meter] / (Centi * Meter), Throw[thickness, "thicknessUnit"]], macUnit = (Centi * Meter)^2 / Gram}, If[(e >= 0.001 && e <= 20.), Exp[-t * materialDensity[[index]] * mac[index, energy] / macUnit], Message[XRayTransmission::"energyRange", energy]]], _, (Message[MessageName[XRayTransmission, #2], #1])&]; absorption[index_, energy_, thickness_] := Catch[ Module[ { e = myCheck[Convert[energy, Mega * ElectronVolt] / (Mega * ElectronVolt), Throw[energy, "energyUnit"]], t = myCheck[Convert[thickness, Centi * Meter] / (Centi * Meter), Throw[thickness, "thicknessUnit"]], meacUnit = (Centi * Meter)^2 / Gram}, If[(e >= 0.001 && e <= 20.), 1. - Exp[-t * materialDensity[[index]] * meac[index, energy] / meacUnit], Message[XRayAbsorption::"energyRange", energy]]], _, (Message[MessageName[XRayAbsorption, #2], #1])&]; (*** External Functions ***) (* External functions to interpolate the x-ray mass attenuation coefficient and the x-ray mass energy absorption coefficient, given the name of the material and the x-ray energy. Check that the material is included in the tables. *) XRayMAC[material_ /; !MemberQ[materialName, material], energy_] := Message[XRayMAC::"material", material]; Scan[(# /: XRayMAC[#, energy_] := mac[First[Flatten[Position[materialName, #]]], energy])&, materialName]; XRayMEAC[material_ /; !MemberQ[materialName, material], energy_] := Message[XRayMEAC::"material", material]; Scan[(# /: XRayMEAC[#, energy_] := meac[First[Flatten[Position[materialName, #]]], energy])&, materialName]; (* External functions to calculate the x-ray attenuation mean free path and the x-ray energy absorption mean free path, given the name of the material and the x-ray energy. Check that the material is included in the tables. *) XRayAMFP[material_ /; !MemberQ[materialName, material], energy_] := Message[XRayAMFP::"material", material]; Scan[(# /: XRayAMFP[#, energy_] := amfp[First[Flatten[Position[materialName, #]]], energy])&, materialName]; XRayEAMFP[material_ /; !MemberQ[materialName, material], energy_] := Message[XRayEAMFP::"material", material]; Scan[(# /: XRayEAMFP[#, energy_] := eamfp[First[Flatten[Position[materialName, #]]], energy])&, materialName]; (* External functions to calculate the x-ray mass attenuation coefficient for mixtures and for chemical compounds. Check that the mixture or compound has the correct form. Check that the materials are included in the tables. *) (* External functions to calculate the x-ray transmission through a material and the x-ray energy absorption in a material, given the name of the material, the x-ray energy, and the thickness of the material. Check that the material is included in the tables. *) XRayTransmission[material_ /; !MemberQ[materialName, material], energy_, thickness_] := Message[XRayTransmission::"material", material]; Scan[(# /: XRayTransmission[#, energy_, thickness_] := transmission[First[Flatten[Position[materialName, #]]], energy, thickness])&, materialName]; XRayAbsorption[material_ /; !MemberQ[materialName, material], energy_, thickness_] := Message[XRayAbsorption::"material", material]; Scan[(# /: XRayAbsorption[#, energy_, thickness_] := absorption[First[Flatten[Position[materialName, #]]], energy, thickness])&, materialName]; MixtureMAC[mixture_ /; !MatrixQ[mixture], energy_] := Message[MixtureMAC::"mixture", mixture]; MixtureMAC[mixture_, energy_] := Catch[ Module[{material, fraction, badMaterial, badFraction}, {material, fraction} = Transpose[mixture]; badMaterial = Select[material, !MemberQ[materialName, #]&]; badFraction = Select[fraction, !NumericQ[#]&]; If[badMaterial != {}, Throw[First[badMaterial], "material"]]; If[badFraction != {}, Throw[First[badFraction], "fraction"]]; Apply[Plus, Map[(Last[#] * myCheck[XRayMAC[First[#], energy], Throw[energy, "energyUnit"]])&, mixture]] / Apply[Plus, Map[Last, mixture]]], _, (Message[MessageName[MixtureMAC, #2], #1])&]; CompoundMAC[compound_ /; !MatrixQ[compound], energy_] := Message[CompoundMAC::"compound", compound]; CompoundMAC[compound_, energy_] := Catch[ Module[{element, number, badElement, badNumber, weight, mixture}, {element, number} = Transpose[compound]; badElement = Select[element, !MemberQ[first92Elements, #]&]; badNumber = Select[number, !NumericQ[#]&]; If[badElement != {}, Throw[First[badElement], "element"]]; If[badNumber != {}, Throw[First[badNumber], "number"]]; weight = AtomicWeight[element] * number; mixture = Transpose[{element, weight / Apply[Plus, weight]}]; myCheck[MixtureMAC[mixture, energy],Throw[energy, "energyUnit"]]], _, (Message[MessageName[CompoundMAC, #2], #1])&]; (* External functions to calculate the x-ray attenuation mean free path for mixtures and for chemical compounds. Check that the mixture or compound has the correct form. Check that the materials are included in the tables. *) MixtureAMFP[mixture_ /; !MatrixQ[mixture], density_, energy_] := Message[MixtureAMFP::"mixture", mixture]; MixtureAMFP[mixture_, density_, energy_] := Catch[ Module[{material, fraction, badMaterial, badFraction}, {material, fraction} = Transpose[mixture]; badMaterial = Select[material, !MemberQ[materialName, #]&]; badFraction = Select[fraction, !NumericQ[#]&]; If[badMaterial != {}, Message[MixtureAMFP::"material", First[badMaterial]], If[badFraction != {}, Message[MixtureAMFP::"fraction", First[badFraction]], 1. / (myCheck[MixtureMAC[mixture, energy], Throw[energy, "energyUnit"]] * myCheck[Convert[density, Gram / (Centi Meter)^3], Throw[density, "densityUnit"]])]]], _, (Message[MessageName[MixtureAMFP, #2], #1])&]; CompoundAMFP[compound_ /; !MatrixQ[compound], density_, energy_] := Message[CompoundAMFP::"compound", compound]; CompoundAMFP[compound_, density_, energy_] := Catch[ Module[{element, number, badElement, badNumber, weight, mixture}, {element, number} = Transpose[compound]; badElement = Select[element, !MemberQ[first92Elements, #]&]; badNumber = Select[number, !NumericQ[#]&]; If[badElement != {}, Message[CompoundAMFP::"element", First[badElement]], If[badNumber != {}, Message[CompoundAMFP::"number", First[badNumber]], 1. / (myCheck[CompoundMAC[compound, energy], Throw[energy, "energyUnit"]] * myCheck[Convert[density, Gram / (Centi Meter)^3], Throw[density, "densityUnit"]])]]], _, (Message[MessageName[CompoundAMFP, #2], #1])&]; (* External functions to calculate the x-ray transmission through mixtures and through chemical compounds. Check that the mixture or compound has the correct form. Check that the materials are included in the tables. *) MixtureTransmission[mixture_ /; !MatrixQ[mixture], density_, energy_, thickness_] := Message[MixtureTransmission::"mixture", mixture]; MixtureTransmission[mixture_, density_, energy_, thickness_] := Catch[ Module[{material, fraction, badMaterial, badFraction}, {material, fraction} = Transpose[mixture]; badMaterial = Select[material, !MemberQ[materialName, #]&]; badFraction = Select[fraction, !NumericQ[#]&]; If[badMaterial != {}, Message[MixtureTransmission::"material", First[badMaterial]], If[badFraction != {}, Message[MixtureTransmission::"fraction", First[badFraction]], Exp[-myCheck[MixtureMAC[mixture, energy], Throw[energy, "energyUnit"]] * myCheck[Convert[density, Gram / (Centi Meter)^3], Throw[density, "densityUnit"]] * myCheck[Convert[thickness, Centi Meter], Throw[thickness, "thicknessUnit"]]]]]], _, (Message[MessageName[MixtureTransmission, #2], #1])&]; CompoundTransmission[compound_ /; !MatrixQ[compound], density_, energy_, thickness_] := Message[CompoundTransmission::"compound", compound]; CompoundTransmission[compound_, density_, energy_, thickness_] := Catch[ Module[{element, number, badElement, badNumber, weight, mixture}, {element, number} = Transpose[compound]; badElement = Select[element, !MemberQ[first92Elements, #]&]; badNumber = Select[number, !NumericQ[#]&]; If[badElement != {}, Message[CompoundTransmission::"element", First[badElement]], If[badNumber != {}, Message[CompoundTransmission::"number", First[badNumber]], Exp[-myCheck[CompoundMAC[compound, energy], Throw[energy, "energyUnit"]] * myCheck[Convert[density, Gram / (Centi Meter)^3], Throw[density, "densityUnit"]] * myCheck[Convert[thickness, Centi Meter], Throw[thickness, "thicknessUnit"]]]]]], _, (Message[MessageName[CompoundTransmission, #2], #1])&]; (* External functions to convert x-ray wave length to energy and energy to wave length. Requires the Miscellaneous`PhysicalConstants` package. *) WaveLengthToEnergy[waveLength_] := Convert[PlanckConstant * SpeedOfLight / waveLength, ElectronVolt]; EnergyToWaveLength[energy_] := Convert[PlanckConstant * SpeedOfLight / energy, Meter]; (* External functions to convert x-ray frequency to energy and energy to frequency. Requires the Miscellaneous`PhysicalConstants` package. *) FrequencyToEnergy[frequency_] := Convert[PlanckConstant * frequency, ElectronVolt]; EnergyToFrequency[energy_] := Convert[energy / PlanckConstant, Hertz]; End[] (* Private *) Protect[XRayMAC, XRayMEAC, XRayAMFP, XRayEAMFP, XRayTransmission, XRayAbsorption, MixtureMAC, MixtureAMFP, MixtureTransmission, CompoundMAC, CompoundAMFP, CompoundTransmission, WaveLengthToEnergy, EnergyToWaveLength, FrequencyToEnergy, EnergyToFrequency ]; EndPackage[] (* XRayAttenuation *)