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Electron Microprobe Analysis Slide 4 EPMA: Quantitative analysis WDS spectrum: Intensity is proportional to concentration C i I i Ii where, ki C( i )I i ( ) I() i C i ki [ ZAF i ] C( i ) Ci and C(i): concentration of element ‘i’ in sample and standard Ii and I(i): measured X-ray intensities of element ‘i’ in sample and standard ki : k-ratio of element ‘i’ ZAF : matrix corrections Matrix (ZAF) corrections Z : atomic number correction A : absorption correction F : fluorescence correction Atomic number (Z) correction R = CjRj Ri [ R = #X-ray photons S i generated / #photons if Z i * there were no back-scatter] Ri * S = C S S i j j [ S = -(1/)(dE/ds), * sample stopping power] Z, a function of E0 and composition Duncumb-Reed-Yakowitz method: Ri = j CjRij Rij = R' 1 - R'2 ln(R'3 Zj+25) -3 3 2 R'1 = 8.73x10 U - 0.1669 U + 0.9662 U + 0.4523 -3 3 -2 2 R'2 = 2.703x10 U - 5.182x10 U + 0.302 U - 0.1836 3 2 3 R'3 = (0.887 U - 3.44 U + 9.33 U - 6.43)/U Si = j CjSij Sij = (const) [(2Zj/Aj )/(E0+Ec)]ln[583(E0+Ec)/Jj ] where, J (keV) = (9.76Z + 58.82Z-0.19)x10-3 Z, a function of E0 and composition Al-Cu alloy 1.2 1.2 Pure metal standards Pure metal standards 1.15 1.15 1.1 1.1 1.05 1.05 1 1 AlK C CuK C 0.95 Cu 0.95 Cu Z 0.1 0.1 Z 0.9 0.3 0.9 0.3 0.5 0.5 0.85 0.7 0.85 0.7 0.9 0.9 0.8 0.8 10 15 20 10 15 20 E0 (keV) E0 (keV) 1.2 1.2 CuAl standard CuAl standard 1.15 2 1.15 2 1.1 1.1 1.05 1.05 1 1 AlK C CuK C 0.95 Cu 0.95 Cu Z 0.1 0.1 Z 0.9 0.3 0.9 0.3 0.5 0.5 0.85 0.7 0.85 0.7 0.9 0.9 0.8 0.8 10 15 20 10 15 20 E0 (keV) E0 (keV) X-ray absorption -(/)(x) -(/)( z cosec) I = I0 exp = I0 exp I: Intensity emitted; I0: Intensity generated /: mass absorption coefficient : density; z: depth; : take-off angle energy Mass absorption coefficient,() absorber A function of energy being absorbed energy () Ni Energy Ec(K- shell) (keV) (keV) (cm 2/g) CoK 6.925 53 NiK 7.472 8.331 60 CuK 8.041 49 ZnK 8.632 311 ZnK is absorbed by Ni For compounds, energy energy C ()() compound element 'j' j j Absorption (A) correction Absortion function, p f( i ) Ai * f( i ) f(i) = Ii(emitted)/Ii(generated) * sample A, a function of E0, and composition Philibert method: 1 h i i i ( f )i 1 1 i i 1 hi i energy () specimen where, i = cosec 2 hi = 1.2Ai/Zi 5 1.65 1.65 i = 4.5x10 / (E0 -Ei(c) ) For compounds: h i hj j C j i energy i energy C ()() specimen element 'j' j j A, a function of E0, and composition ANiK in Fe-Ni alloy 1.7 1.6 1.6 CFe CFe CFe 1.6 0.1 1.5 0.1 1.5 0.1 0.3 0.3 0.3 1.5 0.5 0.5 0.5 o o 1.4 1.4 o 0.7 0.7 0.7 1.4 0.9 0.9 0.9 at 40 1.3 1.3 at 52.5 at 15.5 1.3 NiK NiK NiK A A A 1.2 1.2 1.2 1.1 1.1 1.1 1 1 1 10 15 20 25 30 10 15 20 25 30 10 15 20 25 30 E0 (keV) E0 (keV) E0 (keV) Total X-ray intensity: generated versus emitted Generated intensity I n ge( z )0 ( z ) d ( z ) Emitted intensity z I emit nI gep ex z ( z )0 (zp ex ) () d z eh wre, () c ecos Generated and emitted X-ray intensity variation with depth: AlK in Al-Cu alloy Effect of matrix (mainly Cu) on the emitted intensity of AlK, which is highly absorbed in Cu; AlKα 2 () Cu = 4837.5 cm /g (z) matrix correction The combined atomic number and absorption corrections is the ratio of emitted intensities * in standard (I emit) to sample (I emit) z I emit (z)0 (z )p ex d ( z) * * z Iemit ( z 0) ( z p) ex d() z i z 0 i (z )p ex d() z ZAi i * i z 0 i ( z p) ex d() z (z) matrix correction 0 : the value of (z) at z=0 Rm : the depth at which (z) is maximum (m) Rx : the maximum depth of X-ray production (X-ray range) ZiAi is modeled in terms of 0, Rm, Rx and the integral of the (z) function (Pouchou and Pichoir: PAP method) (z) dependence on Z and E0 Rm and Rx • decrease with increase in atomic number, Z • increase with beam energy, E0 (0) increases with beam energy, E0 X-ray fluorescence A consequence of X-ray absorption when Eabsorbed X-ray > Ec(absorber shell) NiK )( Absorber Absorber EK EK Ec(K) (Atomic No.) (keV) (keV) (keV) (cm2/g) Mn(25)* 5.895 6.492 6.537 344 Fe(26)* 6.4 7.059 7.111 380 Co(27) 6.925 7.649 7.709 53 Ni(28) 7.472 8.265 8.331 59 Cu(29) 8.041 8.907 8.98 65.5 * NiK fluoresces Mn and Fe Element Radiation causing fluorescence Mn FeK, CoK, CoK, NiK, NiK, CuK, CuK Fe CoK, NiK, NiK, CuK, CuK Co NiK, CuK, CuK Ni CuK Cu none Characteristic fluorescence (F) correction f f I ij : intensity of X-ray ‘i’ 1 I ij i I j fluoresced by element j Fi * f 1 I ij i I Ii : intensity of X-ray ‘i’ j generated by electron * sample beam Fluorescence correction for an element includes the summation of fluoresced intensities by other elements in the compound F, a function of E0 and composition Castaing-Reed method: I fij /Ii = CjY0Y1Y2Y3Pij Y0 = 0.5[(ri-1)/ri][j Ai/Aj] j : fluorescent yield 1.67 Y1 = [(Uj-1)/(Ui-1)] j j Y2 = (/) i/(/) spec Y3 = [ln(1+u)]/u + [ln(1+v)]/v i j u = [(/) spec/(/) spec] cosec 5 1.65 1.65 j v = 3.3x10 /[(E0 -Ec )(/) spec] Pij=1 for K fluorescing K; 4.76 for K fluorescing L; 0.24 for L fluorescing K F, a function of E0 and composition FFeK in Fe-Ni alloy 1.1 1.1 1.1 1 1 1 o o o 0.9 0.9 0.9 at 40 CFe CFe at 52.5 at 15.5 CFe 0.1 0.1 0.1 FeK FeK FeK 0.3 F 0.3 F F 0.3 0.8 0.8 0.8 0.5 0.5 0.5 0.7 0.7 0.7 0.9 0.9 0.9 0.7 0.7 0.7 10 15 20 25 30 10 15 20 25 30 10 15 20 25 30 E0 (keV) E0 (keV) E0 (keV) 1.7 1.6 1.6 CFe CFe CFe 1.6 0.1 1.5 0.1 1.5 0.1 0.3 0.3 0.3 1.5 0.5 0.5 0.5 o o 1.4 1.4 0.7 o 0.7 0.7 1.4 0.9 0.9 1.3 1.3 0.9 at 40 at 52.5 at 15.5 1.3 NiK NiK NiK 1.2 1.2 A A A 1.2 1.1 1.1 1.1 1 1 1 10 15 20 25 30 10 15 20 25 30 10 15 20 25 30 E0 (keV) E0 (keV) E0 (keV) ANiK in Fe-Ni alloy Matrix correction flowchart Concentrations are calculated through an iterative procedure: k ------------ ZAF1 ----------- C1 ( = k * ZAF1) C1 ----------- ZAF2 ----------- C2 ( = k * ZAF2) (if C2 = C1, stop here) C2 ----------- ZAF3 ----------- C3 ( = k * ZAF3) (if C3 = C2, stop here) and so on.... MIT OpenCourseWare http://ocw.mit.edu 12.141 Electron Microprobe Analysis January (IAP) 2012 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. .
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