Course Electron Microprobe Analysis

Transcription

1 Course Electron Mcroprobe Analyss

2 THE ELECTROMAGNETIC SPECTRUM

3 Electron Probe X-ray Mcro-Analyss A) quanttatve chemcal analyss of solds: Be to U 1 mcrometer resoluton up to 10 ppm B) hgh-resoluton scannng mages: backscattered electron secondary electron x-ray (elemental maps) cathodolumnescence

4 ELECTRON-SPECIMEN INTERACTIONS Elastc Scatterng Inelastc Scatterng E 1 = E 0, large e E I <E 0, small, ( e >> )

5 ELASTIC SCATTERING Q(> e ) = 1.62x10-20 (Z 2 /E 2 )cot 2 ( e /2) Q: cross secton (events.cm 2 /e -.atom) e : elastc scatterng angle Z: atomc number E: beam energy

6 Electron Backscatterng Elastc scatterng at hgh angles = n BSE /n B = BSE / B = j C j j

7 INELASTIC SCATTERING Secondary electron = n SE /n B = SE / B Inelastc Scatterng E I <E 0, small, ( e >> ) Bremsstrahlung or Contnuum X-rays Characterstc X-rays

8 Characterstc X-ray generaton Condton: U(=E/Ec) > 1 K: L to K-shell transton K: M to K-shell transton L: M to L-shell transton L: N to L-shell transton M: N to M-shell transton E=h = hc/e = /E h: Planck's constant (6.626x10-34 Joule.sec=6.626x10-34 /1.6021x10-16 kev.sec) : frequency=c/ (c: speed of lght n vacuum ( x10 18 Å/sec) and wavelength)

9 Cross-secton for nner-shell onzaton Q=6.51x10-20 [(n s b s )/(UE c2 )]ln(c s U) n s : # of electrons n the shell b s,c s : constants for the partcular shell; for the K-shell, b s =0.3 and c s =1 at low overvoltages, and b s =0.9 and c s =0.65 n the range 4<U<25 E c (kev): crtcal exctaton energy or, absorpton edge of the shell U : overvoltage, E/E c, where E (kev) s the nstantaneous beam energy.

10 Interacton Volume Contnuous Energy-loss expresson: de/ds = -7.85x10 4 (Z/AE m ) ln (1.166E m /J) where, J (kev) = (9.76Z Z )x10-3 Electron Range: R KO = KE 0n / where, K = A/Z 0.889, n = 1.67 X-ray Range: R = K(E 0n -E cn )/ where, K = 0.064, n = 1.68

11 Depth-dstrbuton functon I ( z) ( z) d( z) gen 0

12 X-ray absorpton electrons x-rays z x=z cosec dz I = I 0 exp -()(x) = I 0 exp-()(z cosec) I: Intensty emtted; I 0 : Intensty generated : mass absorpton coeffcent : densty; z: depth; : take-off angle

13 Mass Absorpton Coeffcent emtter absorber Emtter E K E c(k) emtter-k (/) N (Atomc No.) (kev) (kev) (cm 2 /g) Co(27) N(28) Cu(29) Zn(30)* * ZnK s absorbed by N

14 X-ray fluorescence A consequence of X-ray Absorpton Absorber E K E K E c(k) NK (/) absorber (Atomc No.) (kev) (kev) (kev) (cm 2 /g) Mn(25)* Fe(26)* Co(27) N(28) Cu(29) * NK fluoresces Mn (K and Fe (K Element Radaton causng fluorescence Mn FeK, CoK, CoK, NK, NK, CuK, CuK Fe CoK, NK, NK, CuK, CuK Co NK, CuK, CuK N CuK Cu none

15 MATRIX CORRECTIONS C /C () = [ZAF].k k = I /I () ZAF Correctons: Atomc number correcton (Z) Absorpton correcton (A) Characterstc fluorescence correcton (F) Contnuum fluorescence correcton The (z) correcton procedure

16 Atomc number correcton (Z) R E 0 Q S de Z R E c E 0 * E c Q S * de R = #x-ray photons generated / #photons f there were no backscatter S = -(1/)(dE/ds) de/ds = -7.85x10 4 (Z/AEm)ln(1.166Em/J) Q = 6.51x10-20 [(nsbs)/(uec 2 )]ln(csu)

17 Duncumb-Reed model for Z Z = (R S *)/(R *S ) R = j C j R j Yakowtz et al: R j = R' 1 - R' 2 ln(r' 3 Z j +25) R' 1 = 8.73x10-3 U U U R' 2 = 2.703x10-3 U x10-2 U U R' 3 = (0.887 U U U )/U 3 S = j C j S j S j = (const) [(2Z j /A j )/(E 0 +E c )]ln[583(e 0 +E c )/J j ] where, J (kev) = (9.76Z Z )x10-3

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19 Absorpton correcton (A) A = f( )/f( )* f( ) s the absorpton functon defned as I (em)/i (gen) f ( ) 0 ( z) exp d( z) 0 z ( zd ) ( z) where, = () cosec

20 Phlbert-Duncumb-Henrch model for f( ) f h h ( ) where, h = 1.2A /Z 2 = 4.5x10 5 / (E E(c) 1.65 ) For compounds, h h C j j j ( / ) ( / ) spec j j j C

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22 Characterstc fluorescence correcton (F) F 1 1 j j I I f j f j I I * If j : ntensty of x-ray "" fluoresced by element j, I : ntensty of electron beam-generated x-ray "". Fluorescence correcton for x-ray emtted by an element "", s the summaton of the effect of fluorescence caused by all the other elements ("j") n the specmen.

23 Castang-Reed model for I f j /I I f j /I = C j Y 0 Y 1 Y 2 Y 3 P j Y 0 = 0.5[(r -1)/r ][ j A /A j ] (r -1)/r = 0.88 for K-lne; 0.75 for L-lne j : fluorescent yeld Y 1 = [(U j -1)/(U -1)] 1.67 Y 2 = (/) j /(/) j spec (/) j : mass absorpton coeffcent of for x-ray j (/) j spec : mass absorpton coeff. of the specmen for x-ray j Y 3 = [ln(1+u)]/u + [ln(1+v)]/v u = [(/) spec/(/) j spec] cosec v = 3.3x10 5 /[(E E c 1.65 )(/) j spec] P j =1 for K fluorescng K; 4.76 for K-L; 0.24 for L-K)

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25 Contnuum fluorescence correcton ntegrated effect over an energy range between the crtcal exctaton energy of the x-ray lne, E c, and the beam energy, E 0. May be gnored f f() < 0.95 C > 0.5 Zstd ~ Zspec

26 (z) correcton ZA 0 0 z ( z) exp d( z) z * ( z ) exp d ( z ) z s modeled n terms of,, and (Packwood and Brown); or, n terms of, Rm and Rx, and the ntegral of the z dstrbuton (Pouchou and Pchor).

27 : the value of (z) at z=0 Rm : the depth at whch (z) s maxmum Rx : the maxmum depth of x-ray producton

28 depends on the overvoltage, U Rm and Rx decrease wth atomc number, Z

29 agan depends on the overvoltage, U Rm and Rx ncrease wth beam energy, E 0

30 Effect of matrx (manly Cu) on the emtted ntensty of AlK, whch s hghly absorbed by Cu; Cu Al = cm 2 /g.

31 Measurement of (z) curve for Cu 1) A (z) thck flm of Zn s deposted on a substrate and coated by successve layers of Cu, each (z) thck. 2) Intensty of ZnK s measured by placng the beam on each successve Cu-layer. 3) Intensty from the thn-flm Zn s measured, whch serves as the solated thn flm n space. 4) The ratos of the ntenstes obtaned n steps 2 and 3 gves the value of (z) at that mass-depth z. 5) Zn s selected as the tracer because Z Zn ~Z Cu, E ZnK ~E CuK but E ZnK s slghtly hgher so that CuK does not fluoresce ZnK CuK Zn =58.6 cm 2 /g].

32 Problem 2 NK (E K =7.478 kev) s hghly absorbed n Fe (E c =7.111 kev) wth () Fe NK =379.6 cm 2 /g Calculate the matrx correctons for FeK and NK at beam energes (E 0 ) of 10, 15, 20, 25 and 30 kev and take-off angles () of 15 o, 40 o and 52.5 o for the followng specmens: Sample Fe (wt%) N(wt%) FN-Ol FN-Ol FN-Ol FN-Ol MA

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