Giao Trinh PTKH610

7/21/2019 Giao Trinh PTKH610

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Chng 1

CC NGUYN TC C BN CA PHP PHN TCH HUNH QUANG TIA X

1.1. Tng quan v phng php phn tch hunh quang tia X

Nm 1895, Wilhelm Roentgen khm ph ra tia X, lnh vc ng dng u tin catia X l Y hc. Nhng mi n nm 1910 Barkla mi pht hin ph pht x tia X ctrng, v ba nm sau (1913), chnh H. G. J. Moseley thit lp h thc lin quan gia tns ca bc x tia X vi bc s nguyn t ca nguyn t pht ra n, l c s cho phng

php hunh quang tia X ngy nay. Nm 1966 detector tia X bn dn u tin ra i phng th nghim Lawrence Berkeley nh du s pht trin ph k hunh quang tia X.Sau s pht trin ca ngnh in t ht nhn, c bit l s ch to v s hon thin ccloi detector bn dn nh Ge, Si(Li) cho php xy dng c cc ph k c hiu sut

ghi cao, tc phn tch nhanh v thun tin trong nhiu yu cu s dng, nn phngphp phn tch hunh quang tia X c vai tr ngy cng quan trng trong phn tch nguynt.

Tia X l bc x in t c bc sng trong khong 10 -5 100 , c to ra dos hm t ngt in t nng lng cao hay bi s dch chuyn in t t qu o caosang qu o thp trong nguyn t. Tng ng vi hai nguyn nhn , ta c hai loi bcx tia X: bc x hm v bc x c trng. Trong phng php phn tch ph hunh quangtia X, chng ta quan tm n bc x c trng v n gip ta phn tch nh tnh v nhlng nguyn t pht ra n.

Mun mt nguyn t pht bc x hunh quang tia X c trng, th ta phi dng mtngun kch. Ngun kch ny c th l my gia tc ht tch in, hoc my pht tia X, hocmt ngun ng v pht tia gamma, tia X.

n nay tnh u vit ca phng php phn tch hunh quang tia X c khngnh nh sau:

- Khng ph mu.- C th phn tch nhanh vi chnh xc cao.- C th phn tch cng lc nhiu nguyn t (t Z = 9) n gii hn pht hin

nh lng c th t n mcppm (10 -6g/g).

- Sai s phn tch c th t ti gi tr cc nh: %1,0C

C

- i tng phn tch a dng: rn, lng v kh.- C th thit lp h thng phn tch t ng kim tra sn phm trn dy

chuyn sn xut.Do nhng u im c bn ni trn, phng php phn tch hunh quang tia X c

phm vi ng dng ngy cng rng ri. nc ta trong mi nm gn y, phng phpphn tch vi lng bng bc x hunh quang tia X c p dng trong mt s lnh vcsau:

- Trong ngnh luyn kim: xc nh thnh phn nguyn t trong hp kim.- Qung m: iu tra khong sn.- Phn tch nguyn liu cho gm, s, xi mng, thy tinh v cc ha phm.- Xc nh b dy lp m.

1


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- nh tui ca kim loi qu nh Au, Ag, Pt,...- Nhn din qu.- Xc nh hm lng K, Ca, F, P,... trong phn bn.

- Trong k ngh phim nh: xc nh hm lng Ag.- Phn tch mi sinh: xc nh hm lng Pb, Hg, Sb, Cu trong mi trng khngkh.

- Trong k ngh du th v cao su: xc nh hm lng Cu, Ni, S.- X l g: xc nh hm lng Cr, Cu, As.- K ngh giy: xc nh hm lng Ti.Trong phng php phn tch hunh quang tia X, t c nhy v nng sut

phn gii cao, ngi ta ang quan tm nhiu n vic ci tin k thut phn tch, nh tng ha qu trnh thay mu trong bung chiu; gn h phn tch vi my tnh x lngay kt qu thc nghim, lm trn ph bng tnh ton, th d nh bng phng php bnh

phng ti thiu tuyn tnh hoc phi tuyn nh dng phn mm AXIL (Analysis of X-ray

spectra by Iterative Least squares fitting).Bn cnh nhng thun li nu trn, vn ang c quan tm l s khc phc nh

hng ca cc hiu ng xu i vi kt qu phn tch, v d nh hiu ng giao thoa cacc nguyn t trong mu nhiu thnh phn; do cn phi hiu chnh cng vch phc trng nguyn t phn tch i vi c hiu ng hp th ln hiu ng tng cng bc xdo cc nguyn t khc trong cng mu phn tch pht ra.

hiu chnh nh hng ca hiu ng matrix ngi ta thng dng cc phngphp hi quy nhiu ln tnh ton cc h s nhiu.

1.2. Tng tc ca tia X vi vt chtKhi tia X tng tc vi electron ca cc nguyn t n s b hp th hoc tn x. S

hp th bc x s xy ra do nhng tng tc ring hoc do nhiu tng tc tng qut hn.Cc tng tc ring c vai tr quan trng trong qu trnh kch thch mu, cc tng tctng qut c nh hng quan trng vo cng bc x tia X t mu. Tn x tia X dnn xut hin nn phng trong ph quan st. S hiu bit v tng tc ca tia X vi lp vnguyn t l c s cho vic phn tch bin xung ca ph.

1.2.1. H s suy gimXt mt chm tia X n sc, chun trc c cng I0(E), khi i qua mt lp vt

cht c b dy T(cm), mt nguyn t mi trng (g/cm 3), mt vi photon s tng tcvi h nguyn t mi trng vt cht. Tng tc xy ra c th l hiu ng quang in hoctn x khng kt hp hoc tn x kt hp hoc nhiu x, cn chm tia X nng lng E

truyn qua vt cht m khng tng tc vi vt cht c cng I(E) tun theo nh lutsuy gim:

I(E) = I0(E).exp[-t(E).T] (1.1)

vi t(E) c gi l h s suy gim tuyn tnh, c th nguyn cm-l.

2

Hnh 1.1: S suy gim cng ca chm tia Xkhi xuyn qua vt cht.

T

I(E)I (E)0


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Thng ngi ta dng khi nim h s suy gim khi (E) = t(E)/ (c thnguyn l cm2/g ) ch s suy gim cng trn n v khi lng trn n v din tch.Trong trng hp ny phng trnh (l.l) tr thnh:

I (E) = I0(E). exp[-(E)..T] (l.2)

H s suy gim khi ca mt hp cht s bng tng cc h s suy gim khi thnhphn:

=i

iiw (1.3)

vi wi l hm lng (%) ca nguyn t i ( 1wi

i = ).Do tng tc vi lp v electron ca nguyn t, nn h s suy gim khi tng theo

bc s nguyn t Z ca nguyn t vt liu bia. H s suy gim khi cn l c trng ca

mt cht ng vi mt gi tr no ca nng lng tia X ti. i vi mt nguyn t chotrc, h s suy gim khi thay i theo bc sng tia X ti. 34KZ = (1.4)vi l di sng ca tia X ti, tnh theo n v cm; K l h s thay i theo mi giihn hp th ca nguyn t bia.

V vy khi mt chm tia X i qua mu, cng chm tia s b suy gim. Cnhiu loi tng tc khc bit nhau ca tia X vi h nguyn t ca mi trng vt cht.Cc tng tc ny l cc qu trnh tn x kt hp, khng kt hp v qu trnh hp thquang in nh ta thy trn hnh 1.2. Do , h s suy gim l tng cc h s tn x v hpth xy ra khi tia X i qua mu:

3

TN X KHNGKT HP

Ekkh

= E0

- EHIU NG QUANG INTia X c trngQuang- in t

in t Auger

TN X KT HP

H s suy gim = +

kkh+

kh

Chm tia ti I0(E0) Chm tia truyn qua I(E0)

Chm tia tn x: gc tn x

Hnh 1.2: S tng tc ca tia X vi vt cht.


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)E()E()E()E( kkhkh ++= (1.5)Trong cng thc (1.5): (E) l h s hp th khi quang in, ( )kh E l tng h s tn x

khi kt hp,( )

kkhE

l tng h s tn x khi khng kt hp. C( )

khE

v( )

kkhE

uc tnh vi tt c cc gc tn x c th c.

4

1 10

100

10-2

10-1

1

10

102

103

Nng lng (keV)

LEADZ = 82

kh

kk

h

104

K Edge

(cm

2/g)

L Edge

MEdge

1000

1 10

100

10-2

10-1

1

10

102

103

Nng lng (keV)

IRONZ = 26

kh

kkh

104

K Edge

(cm

2/g)

1000

Hnh 1.3b: H s suy gim khi i vi St (Fe) v Ch (Pb) nh l hmnng lng photon ti.

Hnh 1.3a: H s suy gim khi i vi Cacbon (C) v Nhm (Al) nh lhm nng lng photon ti.

1 10

100 1000

10-2

10

-1

1

10

102

103

Nng lng (keV)

(cm

2/g)

CARBONZ = 6

k

h

k

kh

(cm

2/g)

1 10

100

10-2

10-1

1

10

102

103

Nng lng (keV)

ALUMINUMZ = 13

kh

kk

h

104K Edge

1000


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Mt cch tng qut, ta c th m t cc qu trnh xy ra khi chm tia X c nnglng E0 cng I0(E0) p vo vt cht c m t nh hnh 1.2 trn.

Hnh 1.3 sau y cho thy vi bc s nguyn t Z cho trc, h s suy gim khi

gim theo s gia tng nng lng ca photon ti.

1.2.2. Qu trnh tn xKhi tia X p vo m my electron ca v nguyn t ca nguyn t bia, n s

tng tc vi electron v b tn x nh trong hnh 1.4.Tn x tia X trong mu, ch yu gy ra tng ngoi ca v nguyn t v l ngun

gc chnh ca phng trong ph tia X s tn x c th l n hi, y photon tn x ccng nng lng vi photon ti, v gi l tn x kt hp, hay cn gi l tn x Rayleigh.ng i ca tia X b lch, v vy c s ng gp biu kin vo h s suy gim khi. Nus va chm l khng n tnh th tia X b mt nng lng mt electron thot ra v tn xtia X c gi l khng kt hp hay tn x Compton. ng i ca tia X b lch v nng

lng gim.

Hai nhn xt quan trng lin quan n tn x i vi ph k tia X l:- Mc d s tn x tng cng tng theo bc s nguyn t Z, nhng i vi mu cbc s nguyn t Z cao th phn ln cc bc x tn x b hp th ngay trong mu, nn tnx quan st c t mu s t. Cn i vi mu c bc s nguyn t Z thp th tn x quanst c t mu li nhiu hn do s hp th bi mu l nh.

- i vi nguyn t nh th tn x Compton xy ra vi xc sut ln, do t scng tn x Compton v Rayleigh tng, khi bc s nguyn t Z ca mu gim.

1.2.2.1 Tng tc ca tia X vi electron t doTng tc ca tia X vi electron t do, ch yu l qu trnh tn x. Gi l gc tn

x, Ie l cng tn x ln mt electron t do. Cng I e c nh ngha nh l nng

lng tn x trn mt n v gc khi trong mt n v thi gian gy ra bi s tng tc

5

Hnh l.4: Tn x Rayleigh v tn x Compton ca tia X.


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ca chm tia X khng phn cc c mt nng thng in ln mt electron t do. Theo nhlut Thompson ta c:

226

0

1 cos

7,90 10 2eI x I

+

= (1.6)Trong tn x Compton, photon X ti ch truyn mt phn nng lng ca mnh cho

mt electron lin kt yu v phn nng lng cn li xut hin nh l mt tia X th cp.Tn x Compton xy ra khi nng lng ca photon ti vo khong m0c2, ngha l ln xem cc electron lin kt yu nh l t do. Compton l ngi u tin chng minh rng tiaX tn x ln electron t do c dch chuyn bc sng theo biu thc sau:

( )00

1 cosh

m c = = (1.7)

Trong cng thc (1.7), l bc sng bc x tn x Compton, 0 l bc sng photon Xti, h l hng s Planck (6,6 x 10 -27erg/giy), m0 l khi lng electron (9,11 x 10-31kg),

c l vn tc bc x in t (3 x 1010cm/giy) v l gc gia tia ti v tia tn x.T cng thc (1.7), ta c: 0, 0243(1 cos ) = , y tnh bng n v

Angstrom ().Nng lng bc x tn x Compton cho bi phng trnh:

( )

0

02

0

1 1 cosm c

=

+ (1.8)

Vi m0c2 = 511 keV.

1.2.2.2 Tng tc ca tia X vi electron lin kt

C lng t v tr cng nh thc nghim chng minh rng: trong vng nnglng ca tia X xp x 10 keV tn x ca tia X ln cc electron lin kt tun theo ccnguyn tc tng qut sau:

- C tn x kt hp v khng kt hp u xy ra.- Tn x ton phn cng tun theo nh lut Thompson (1.6)Bin tn x kt hp ln nguyn t bng tng cc bin tn x ln mi electron

trong nguyn t. Nu fe l bin tn x kt hp ca mt electron lin kt tnh theo n velectron (eu) th fe c nh ngha nh sau:

fe=

Nu m my electron ring l c gi s c dng hnh cu bn knh r, chng tac:

2

0

sin4 ( )e

krf r r dr

kr

= (1.9) y: (r) l mt phn b in t, k = (4sin) / v = /2

Bin tn x i vi nguyn t Z electron l:

=

=

==Z

n

n

Z

n

ne drkr

krrrfF

10

2

1

sin)(4)( (1.10)

6

Bin tn x kt hp ln mt in t lin kt

Tng bin tn x ln mt in t lin kt


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V vy, vi mt nguyn t bt k, f l mt hm ca (sin )/, v khi (sin)/0,

th: f =

Z

n

ndrrr

10

2)(4 Z. (v

=

Z

n

ndrrr

10

2)(4 = 1: xc xut tm thy

electron trong nguyn t)Lu rng, (sin)/ 0 khi 0 (gc tn x nh) hoc khi rt ln (nng lng

thp).

1 2.2.3. Tn x khng ht hp ln cc nguyn ti vi bc x tn x khng kt hp th khng c giao thoa gia cc sng tn x,

v tng cng tn x ln cc electron trong m my electron quanh nhn c tnhbi:

2 2

1 1

1 ( ) ( )e

Z Z

kkh e e e

n n

I f I Z f I= =

= =

(1.11)

Th d vi Li (Z = 3), Al (Z =13), Cu (Z = 29), s ph thuccng tn x kt hp v khngkt hp vo (sin)/ c m t trncc th hnh 1.5 cho thy: ivi Li th nh hng ca tn x rtln. Cn i vi Al v Cu th nhhng khng ng k khi sin()khng qu b. V vy, phn tch

nguyn t nh bng phng phphunh quang tia X l khng tt.

T cc th trn hnh 1.5cho ta cc nhn xt sau:

- i vi cc nguyn t cbc s nguyn t Z cng ln th nhhng ca tn x khng kt hpcng nh.

- Nu chn gc tn x ln, tac th b qua nh hng ca tn xkt hp.

- Nu photon X ti c nnglng ln hn nng lng lin ktca electron qu o rt nhiu th tnx khng kt hp s chim u th.Khi nng lng photon X ti xp xnng ng lin kt th tn x kt hpchim u th.

1.2.2.4. Tn x trn h nguyn tlin kt

Khi tn x xy ra trn mt hnguyn t lin kt, cc bc x tn x kt hp (nng lng khng i) s lch pha nhau,

7

Hnh 1.5: S ph thuc cng tn x kt hp vkhng kt hp vo sin()/ ca Li(Z = 3),Al(Z=13) v

Cu(Z=29)

0

2

4

6

8

Ikkh

Ikh

LiZ = 3

0

50

150

100

Ikkh

Ikh

AlZ = 13

eu

2

eu

2

1000

200

400

600

800

Ikkh

Ikh

Cu

Z = 29

0.1 0.3 0.5 0.7 0.9 1.1

eu

2

841

169

Sin()/


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hnh thnh cc cc i tng ng vi s giao thoa gia cc sng, tn x kt hp. Hiu ngny t c trong mt khi cht kt tinh m trong gn nh cc tn x kt hp tp hpthnh cc nh. Hnh 1.6 biu din cng tn x kt hp v khng kt hp hiu chnh

ca qung thy tinh (SiO2)

1.2.2.5. Nng lng ca bc x tn x khng kt hpPhng trnh (1.7) trn l biu thc lin h gia cc bc sng bc x tn x kt

hp (0) v khng kt hp (kkh) v gc tn x . Hnh 1.7 cho thy gc tn x v milin h ca n vi gc ti trung bnh 1 ca chm s cp, v gc l 2 trong mt h phk tia X.

8

40

0

300

200

100

0.16 0.32 0.48 0.60 sin

I(eu

2)

(A)

(B)

Hnh 1.6: Cng tn x o c i vi SiO2

kch thch

bi bc x Cu-K(A): cng tn x kt hp;(B): cng tn x khng kt hp.

Mu

Detector

Ngun

1 2

1: gc ti trung bnh

2: gc l trung bnh

: gc tn x

Hnh 1.7: Tia ti v tia l trong ph k tia X


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Trong cc ph k tia X ta c th b tr xp x 900, khi t phng trnh (1.7)ta tnh c dch chuyn ca bc sng Compton vo khong 0,0243. T phngtrnh (1.8) ta ch ra c rng dch chuyn nng lng ca photon X tn x Compton

ph thuc vo c gc tn x v nng lng E0 ca photon ti.

)cos1(E511

)cos1(E

)cos1(511

E1

11EEEE

0

2

0

0

0kkh

+

=

+==

(1.12)

y, E0 tnh bng n v keV

1.2.3 Qu trnh hp thTia X tng tc vi electron ca nguyn t s b hp th hoc tn x. S lin h gia

qu trnh hp th vi bc s nguyn t Z l mt yu t quan trng trong qu trnh chniu kin hot ng ti u ca h ph k tia X.1.2.3.1 Cnh hp th

Trong hnh 1.8 di y ta thy c nhng im bt lin tc c gi l cnh hp th(gii hn hp th). Nng lng cc tiu c th pht quang mt electron t mt qu otrong nguyn t ca nguyn t cho trc c gi l nng lng cnh hp th. Mt nguynt c nhiu cnh hp th:

- Tng K c mt cnh hp th ng vi nng lng cnh hp th l Kht.- Tng L c ba cnh hp th, ng vi LIht, LIIht, LIIIht- v.v.

Cng mt nguyn t, nng lng cnh hp th tun theo Kht > LIht > LIIht > LIIIht, v.v,i vi mt tng electron xc nh, nguyn t c bc s nguyn t Z cng ln thnng lng cnh hp th tng ng cng cao.

9

Hnh 1.8: ng cong biu din h s suy gim khica nguyn t uranium theo bc sng photon ti.


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Hnh v 1.9 biu din cc tng electron ca nguyn t. Cc tng K, L, M c cc slng t chnh tng ng l 1, 2, 3. S lng t chnh cng nh th nng lng cn thit gii phng mt electron t tng cng cao. Trong hnh 1.10, nng lng ti thiu ca

photon X ti gii phng electron tng K ln hn nng lng gii phng electron tng L,ngha l nng lng cnh hp th ca tng K ln hn tng L.

Qu trnh quang in dn n trng thi electron khng bn v pht x tia X ctrng c minh ha trong hnh 1.10.

Hnh 1.10(a) biu din s hp th theo nng lng i vi photon c nng lngthp hn vng nng lng tia X. Trong trng hp ny, nng lng photon c dng dch chuyn electron t qu o thp ln qu o cao hn v do to nn s dch chuynt trng thi lng t bn n trng thi lng t khng bn. S khc bit v nng lng(gia trng thi bn v khng bn) c xc nh bi nguyn t lm bia. Ch nhng photonc nng lng rt gn vi nng lng khc bit ny mi b hp th bi mu. Hnh 1.10b l

trng hp bc x nm trong vng nng lng tia X. Electron nm qu o thp vi mcnng lng bit trc, c gii phng t trng thi bn ti min lin tc (trng thi kchthch cao nht) khi ri khi nguyn t. Bt k mt nng lng d tha no ca tia X u

bin i thnh ng nng ca electron c gii phng. V vy, khi nng lng tia X pht quang electron thay v c nh hp th nh trong hnh 1.10(a), ta c cnh hp th nhtrong hnh 1.10(b). Vic chn la nng lng kch thch cc nguyn t trong mu sc xem xt da vo cc gi tr nng lng cnh hp th ca cc nguyn t .

10

Hnh 1.9: Minh ha s pht quang electron tng K bi photon tic nng lng cao hn, v pht quang electron tng L bi photon ti

nng lng thp hn.


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1.2.3.2. Nguyn l cnh hp thXt mt chm tia X n sc, c nng lng E, chiu ln mu a nguyn t. Ty

theo nng lng ca tia X ti v nng lng cnh hp th ca cc nguyn t cha trongmu, trn ph ghi nhn c c hoc khng xut hin nh c trng:

* i vi cc nguyn t c nng lng cnh hp th Kht > E, chm tia X ti khng nng lng lm bt nhng electron lp K ca nguyn t nn trn ph khng ccc vch K ca n. Nu E ln hn LIht hoc ln hn LIIht, LIIIht th trn ph ta c th quan st

thy cc vch L tng ng ca nguyn t ny.* Khi tng nng lng E ca chm tia X ti, s dn n h s suy gim khi gim,n khi E = Kht, nng lng tia X ti lm bt cc electron lp K v h s suy gim khitng t ngt, (hnh 1.8). y l hin tng hp th quang in v trn ph s xut hinvch K ca nguyn t ny.

* Khi E >> Kht chm tia X ti c nng lng ln hn rt nhiu nng lng cn thit lm bt cc electron lp K. Khi hiu ng Compton xy ra vi xc sut ln i vicc electron cc lp ngoi, ngha l nhng tia X ny khng b hp th quang in lp K(hay l xc sut hp th rt nh). Trn ph ta khng quan st c cc vch K.

Tm li, khi hp th nng lng th electron s tr nn t do hay chuyn ln vngdn, cn khi pht tia X c trng th electron ch chuyn di trong ni b nguyn t

(chuyn ti lp l trng). Khng c vch no trong mt dy (dy K , dy L 1 , dy L2, dy L3

11

Hnh 1.10: S kch thch cc mc nng lng in t(a) Dch chuyn gia hai mc nng lng(b) S pht quang electron bi photon X ti.


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) c th c nng lng ln hn nng lng cnh hp th ng vi dy . Nh vy khi tia Xs cp dng kch thch c nng lng ln hn nng lng cnh hp th ng vi dy no ca nguyn t phn tch, th tt c cc vch c trng trong dy u xut hin trn

ph. Th d trn ph ghi nhn c, nu c vch K ca mt nguyn t th chc chn phic vch K ca nguyn t .

1.2.3.3. Hiu ng quang inMt trong nhng qu trnh dn n s hp th tia X khi chng xuyn qua vt cht

l hiu ng quang in. Qu trnh ny ng gp ch yu vo s hp th tia X, v l mhnh kch thch cc nguyn t trong mu pht ph tia X c trng.

(a) Trc khi tng tc, mt photon nng lng E p vo nguyn t. (b) Mtelectron tng K hp th ton b nng lng ca photon v thot ra ngoi. (c) v (d) Ltrng tng K c lp y bi mt electron t tng L chuyn v, km theo vic phngthch: hoc (c), tia X c trng; hoc (d), eclectron t tng L chuyn v, km theo vic

phng thch; hoc (d), gii phng electron Auger.

12

Hnh 1.11: Hin tng tng tc quang in


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Khi chm tia X p vo mt electron lin kt trong h nguyn t mi trng, nunng lng E ca chm tia X ti ln hn nng lng lin kt ca electron tng tngng th hiu ng quang in s xy ra: tia X bin mt, nng lng ca n c trao ton b

cho electron lin kt. Electron ny (c gi l quang in t) bc ra khi h nguyn tvi nng lng E -.

Trn hnh 1.11(a) tia X p vo mt electron tng K, quang-electron ny thot rangoi li l trng tng K, nh trong hnh 1.11 (b), do nguyn t trng thi kchthch. Cc electron t cc tng ngoi, ni c nng lng lin kt thp hn (tng L, M,v.v), s dch chuyn ti lp l trng, v mt tia X c trng xut hin vi nng lng

bng hiu nng lng lin kt ca tng nh trong hnh 1.11 (c).Xc sut xy ra hiu ng quang in mt tng no ca v nguyn t c gi

l tit din xy ra hiu ng quang in hay cn gi l h s hp th quang in. Phngtrnh thc nghim din t mi ph thuc gia h s hp th quang in k ca lp K vi

bc s nguyn t Z v nng lng E nh sau:

27

56k )

E

61,13(Z1009,1 = (cm2/ng.t) (1.14)

Hiu ng quang in hu nh khng xy ra i vi cc electron c lin kt yu,nht l cc electron c nng lng lin kt nh hn rt nhiu so vi nng lng ca tia Xti. V vy vic phn tch hunh quang tia X s gp kh khn i vi cc nguyn t nh.

Ni chung, hiu ng thng xy ra ti cc lp electron trong cng (lin kt bn vng), l cc lp K, L.

1.2.3.4. Hiu ng AugerHiu ng quang in xy ra thng km theo hiu ng Auger hay gi l s bin

hon trong (hp th quang in ni ti). Trong trng hp ny, tia X c trng va pht rab hp th ngay bi mt electron tng pha ngoi hn trong cng mt nguyn t, nhtrong hnh 1.11 (d). Khi khng c tia X c trng c phng thch m l mt electronAuger. Hiu ng ny lm gim cng ca vch ph v thng xy ra i vi nhngnguyn t nh.

- H s bin ha trongGi Ne l s electron Auger, Nx l s tia X phng thch cng thi gian t trong cng

mt mu.H s bin hon trong ton phn l:

.......N

NMLK

x

e +++== (1.15)

Vi K: h s bin hon trong i vi cc electron tng K,L : h s bin hontrong i vi cc electron tng L, v.v

Cc electron sau khi bt ra li cc l trng lp v nguyn t. Do km theohin tng bin hon trong lun lun c s pht x ca cc tia X c trng hoc ccelectron Auger.

- Hiu sut hunh quangKhi electron c gii phng t nguyn t do qu trnh quang in, c hai kh

nng xy ra: hoc pht x tia X hoc pht electron-Auger, hai qu trnh ny cnh tranhnhau. Hiu sut hunh quang K ca lp K, l dy t s gia tng s photon i(n)i ca tt

13


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c cc vch trong dy K pht ra vi s l trng NK ca lp K c to ra trong cng thigian y.

)nnn(N

1

N

)n(K2K1K

KK

i iK

K ++=

= (1.16)Thng hiu sut hunh quang khc nhau i vi cc nguyn t khc nhau, v

trong cng mt nguyn t th hiu sut hunh quang cng khc nhau i vi cc lp khcnhau, Eugene P. Berlin a ra cng thc:

4

4

KZA

Z

+= (1.17)

A=1,08 x 106 (i vi lp K), v A ~ 108 (i vi lp L)Mt cch tng qut, hiu sut hunh quang i vi mt lp cho trc c xc

nh theo phng trnh:

241

cZbZa1

++=

(1.18)

Vi a, b, c l nhng hng s cho trong bng 1.1

Bng 1.1: Cc h s tng ng vi cc lp v nguyn tH s K L M

a -0,03795 -0,11107 -0,00036b 0,03426 0,01368 0,00386c -0,1163x10-5 0,2177x10-6 0,201101x10-6

1.3. Cng hunh quang th cp1.3.1 Biu thc tng qut

thit lp mi quan h gia hm lng ca nguyn t c trong mu vi cng tia X c trng pht ra t mu, ta xt mt chm tia X c nng lng trong khong E0 nE0+dE0 pht ra t my pht tia Xhoc mt ngun ng v ( ngin ta xem nh ngun im)trong mt gc khi d1 p ln

b mt ca mu c b dy T dimt gc 1. S photon ti b mtca mu trong mt n v thigian s l I0(E0)dE0d1.

i ti th tch vi cpc b dy dx su x (ni xyra tng tc quang in) chm tia X s cp phi truyn qua mt on ng x/sin 1. Khi

cng tia X s cp ti lp dx ny s l:

14

Hnh 1.13: B tr hnh hc php o


15/137

=1

010001sin

x)E(expddE)E(II (1.19)

y

(E0) l h s suy gim khi tng cng (cm2/g) nng lng E0, i vi muc mt nguyn t .

Khi xuyn qua b dy vi phn ny, tia X di chuyn mt on dx/sin1. Do , s tiaX gy nn tng tc quang in trong qu trnh ny (tnh trn mt n v thi gian) l:

1

012sin

dx)E(II

= (1.20)

y (E0) l h s hp th khi quang in tng cng, c n v cm2/g v ctnh theo cng thc:

)E(w)E(0mmm0

= (1.21)wm l hm lng ca nguyn t th m,

m(E0) l h s hp th khi quang in tng cng ca nguyn t th m.

Vy vi nguyn t th i, s tia X gy nn tng tc quang in s l:

1

0ii12

0

0ii3

sin

dx)E(wII

)E(

)E(wI

=

= (1.22)

Trong phng trnh (1.22), s hng i(E0) l do s ion ha ca cc tng ca vnguyn t nng lng lin kt electron nh hn nng lng E 0 ca photon kch thch. Vd ta ch xt tng K, khi ta c:

[ ]

10ki11

30i0ki4

sin

dx

)E(wI

I)E(/)E(I

=

=

(1.23)

ki: h s hp th khi quang in ca nguyn t th i, ng vi tng K xc nh. T s thayi t ngt cnh hp th c xc nh:

)(

)(r

k

kk

=

+ (1.24)

)( k+ v )( k l gi tr cao nht v thp nht ca h s hp th khi quangin ti nng lng cnh hp th k(s bt lin tc ti cnh K).

i vi nng lng gn nng lng cnh hp th, th cc on th ca i(E) vhai pha E < k v E > k gn nh song song. T ta c biu thc gn ng nnglng E

0nh sau:

kk

k

0ki0i

0i r)(

)(

)E()E(

)E(=

+ (1.25)

Hay

k

k0i0ki

r

1r)E()E(

(1.26)

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Hnh 1.14: M hnh suy din gi tr ca ki (E0)

Phng trnh (1.23) cho bit cng ion ha tng K ca nguyn t th i. Sauion ha, cc l trng tng K c lp y bi cc electron chuyn dch t cc tng cnng lng lin kt thp hn. Mt trong s dch chuyn ny c cc electron Auger c

phng thch. Hin tng phng thch electron Auger khng ng gp vo vic pht tia X

th cp, nn ta phi loi b, ngha l ch tnh n s pht hunh quang. Vi hiu sut phthunh quang t tng K ca nguyn t th i l ki, cng tia X pht t tng K canguyn t th i l:

I5 = ki x I4 (1.27)

Mt cch tng qut, ch mt vch trong chui K l c o. Nng lng ca vchny c xc nh l Ei. Nu vch ny chim t lng f trong tng s cc vch trong chuiK, th cng tia X pht ra ng vi vch ny l:

I6 = f x I5 (1.28)

Do tnh ng hng ca chm ra, I6 l tnh cho ton b gc khi . Vy s tia Xth cp hng ti detectoe theo gc khi d2 l:

I7 = I6 x

42d (1.29)

Sau khi pht ra t nguyn t th i trong mu, tia X c trng c th b hp th trnqung ng x / sin2 trong mu. V vy khi l ra khi mu, cng tia X c trng sl:

=2

i78sin

x)E(expII (1.30)

16


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y (Ei) l h s suy gim khi tng cng khi tia X c trng vi nng lng E itruyn trong mu. Nu hiu sut ghi ca detector i vi nng lng E i l (Ei) th cng tia X ghi nhn c trong detector s l

I dx dE0 = (Ei) x I8 (1.31)

Trong thc t, ngun kch thch khng l ngun im. Nh vy cng ca vchi pht ra t dy K do cc nguyn t i thuc lp vi phn dx ca mu, kch thch bi mt nv din tch ds ca ngun kch l:

dI = I ds dx E0=

21

2

i

1

01kiki0

1

i ddxdsin

)E(

sin

)E(xexpfwI

sin4

)E(

+

(1.32)

Trn y ta mi kho st qu trnh quang in xy ra trong phn t th tch vi phnc b dy dx (trong khong x n x+dx), i vi phn nng lng kch thch trong khongE n E+dE. Vy tnh cng ca mt vch ph c trng cho nguyn t trong muth phi ly tch phn phng trnh (1.31), trn ton din tch hiu dng ca ngun kchthch, trn cc gc c gii hn,v trn b dy mu, trong khong nng lng t nnglng t nng lng cnh hp th k n nng lng cc i Emax trong ph kch thch.Trong qu trnh thc hin tch phn, ta xem 1, 2 nh khng i; iu ny c th tc nu khong cch t ngun n mu v t mu n detector rt ln so vi b dy mu,ta c:

== =

max

k0

E

E

T

0x021ii IdxdEddsd)E(I

000

2

i

1

0

2

i

1

0

E

E0ifi0ii dE)E(I

sin

)E(

sin

)E(

sin

)E(

sin

)E(Texp1

)E(QwG)E(Imax

K0

+

+

==

(1.33)

y: f

r

1r

4

)E(f

4

)E(Q kii

k

kikiki

iif

= (1.34)

=

1

210sin

1ddsdG (1.35)

G0 ch ph thuc vo b tr hnh hc ca ngun kch thch.

Trong trng hp ngun kch l n nng, ta c:

2

i

1

0

2

i

1

0

i00ifii

sin

)E(

sinh

)E(

sin

)E(

sinh

)E(Texp1

wIGQ)E(I

+

+

= (1.36)

17


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1.3.2. Trng hp mu dy v hni vi mu dy v hn (hp th 99% khi chiu tia X vo), th ta c th b cc s

hng hm m trong cc phng trnh (1.33) v (1.36). Nh vy i vi mu dy v hn,cng hunh quang th cp l:- Trng hp ngun kch a nng:

0

E

E

2

i

1

0

00if

i0ii dE

sin

)E(

sin

)E(

)E(I)E(QwG)E(I

max

K0

+

=

= (1.37)

- Trng hp ngun kch n nng:

2

i

1

0

i00ifii

sin

)E(

sin

)E(

wIGQ)E(I

+

=

(1.38)

1.3.3. Trng hp mu mng

i vi mu mng (cc lp sn, m, mu, phim v.v), ta c:

+

+

2

i

1

0

2

i

1

0

sin

)E(

sin

)E(T1

sin

)E(

sin

)E(Texp

Do cng tia X hunh quang th cp i vi mu mng l:

- Trng hp ngun a nng:

= =

max

K0

E

E0000ifi0ii dE)E(I)E(QTwG)E(I (1.39)

- Trng hp ngun a nng:

Ii(Ei) = QifG0I0wiT (1.40)

18


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Chng 2

CC PHNG PHP PHN TCH HUNH QUANG TIA X

2.1. Phng php phn tch nh tnhKhi nguyn t nhn mt nng lng t bn ngoi, th s c electron no ca

nguyn t c th nhn c nng lng ny, nu nng lng nhn c ln hn nnglng lin kt ca electron trong nguyn t th n b bc khi nguyn t v lp vnguyn t hnh thnh mt l trng. Nguyn t by gi trng thi kch thch, trng thiny khng bn, ngay sau cc electron cc tng ngoi nhy v lp l trng mi v lixy ra nhng dch chuyn tip theo ca cc electron t cc tng ngoi.

S dch chuyn electron t cc tng ngoi v lp l trng tun theo qui tc la chntrong c hc lng t.

n > 0l = 1j = 1 ; 0

n l s lng t chnh, l l momen gc, v j = l + s l momen spin, s l spin ring.Mi ln c s dch chuyn ca electron t tng ngoi (nng lng kch thch cao

hn) v tng thp th c mt nng lng c gii phng. Nu nng lng pht ra didng photon th hin tng ny c gi l hin tng hunh quang. Bc x pht ra cgi l bc x hunh quang tia X c trng. Nhng thng tin nh tnh t ph tia X l nnglng ca tia X c trng pht ra t mu xut hin trn ph. C s cho s phn tch nhtnh l ph c trng hunh quang tia X cho tt c cc nguyn t u c dng ging nhau,nhng bc sng cc vch c trng cho mi nguyn t ph thuc vo bc s nguyn tZ theo nh lut Moseley:

( )2

bZKR1

v =

= (2.1)

Trong , R l hng s Ryberg,K, b l hng s tng ng vi tng dy vch ph.

2.1.1. Cc vch KMt khi l trng c to thnh trong lp K bi hiu ng quang in, cc electron

t cc tng L, M, v.v... vn chuyn v lp l trng tng K v km theo s pht x cc tiaX c trng dy K : K1 , K2 , K.Qu trnh kch thch v pht quang electron tng K ca Cu c biu din trn hnh

2.1. Hnh 2.1 (a) biu din h s hp th ca Cu theo nng lng tia X t 0 ti 20 keV,trong 8,98 keV l nng lng cnh hp th Kht ca Cu. Hnh 2.1(b) biu th cc mcnng lng electron ca Cu. Tia X c nng lng ln hn 8,98 keV kch nguyn t Cu

pht quang electron tng K.

19


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Bng 2.1: Cc mc dch chuyn v cng tng i ca CuVch Dch chuyn Cng tng i E(keV)K1 LIIIK(2p3/21s1/2) 63 8,047K2 LIIK(2p1/21s1/2) 32 8,027K1 MIIIK(3p3/21s1/2)

58,903

K3 MIIK(3p1/21s1/2) 8,973

K5 MVK(3d5/21s1/2) < 1 (cm) 8,970

Hnh 2.1(b) biu th s chuyn mc vch K ca Cu. Nghin cu bng s liu (Bng2.1), ta thy c s tng quan gia cng tng i ca cc vch K. Vch K1 sinh rado s chuyn mc t LIII(2p3/2) v K(s1/2) v vch K2 sinh ra do s chuyn mc t L-II(2p1/2) v K(1s1/2). Qu o LIII(2p3/2) cha bn electron, qu o L II(2p1/2) cha haielectron. V vy, t s cng quan st l 2 : 1 i vi vch K1 v K2 l kt qu ca xcsut thng k ca s chuyn mc. Mc du hai vch ny sinh ra t s chuyn mc khcnhau nhng nng lng ca chng rt gn nhau n ni kh phn bit c. Thng thngnng lng trung bnh ca nhng vch ny c cho bi phng trnh:

3

EE2E 2K1KK

+= (2.2)

Vch K xut hin nng lng cao hn vch K, do s dch chuyn electron ttng M v lp l trng tng K. Cng tng i ca vch K v K l mt hm phctp do s khc nhau gia nhng mc nng lng ca cc tng L v M. Tuy nhin thcnghim cho thy cng vch ph K ca cc nguyn t c bc s nguyn t Z t 24 n30 th xp x bng 10% ti 13% cng tng cng ca K v K.

2.1.2. Cc vch LKhi nng lng ca photon ti khng ln hn nng lng cnh hp th E K ca

nguyn t cn phn tch, th trn ph ghi nhn c s khng c cc vch K c trng.

20

Hnh 2.1: Cc mc nng lng electronDch chuyn gia hai mc nng lng.Pht quang electron bi bc x tia X.


21/137

Trong trng hp ny ta quan st cc vch L, M. Do c ba s lng t momen gc i vielectron tng L ng vi cc qu o 2s1/2, 2p1/2, 2p3/2 nn c ba cnh hp th l L Iht, LIIht,LIIIht. kch thch tt c ba dy vch L, nng lng photon ti phi c gi tr ln hn E-

LIht. Nu dng ngun ng v kch, bng ngun tia X ng v cho thy nng lng cdng ln nht khong 22 keV (ngun Cd 109, Am241) th vch L c gi tr i vi nguyn tc bc s nguyn t Z ln hn 45 (Rh).

2.1.3 Cc vch MVch M t s dng trong ph tia X. Khng quan st thy i vi nguyn t c bc s

nguyn t Z < 57. Trong thc t ch dng cho ba nguyn t Th, U, Pa. Chng c dngtrong trng hp trnh s giao thoa vi vch L ca nhng nguyn t khc trong mu.

2.2. Cc phng php phn tch nh lng2.2.1. Phng php chun ngoi tuyn tnh

T phng trnh (1.38), ta c:- i vi mu phn tch:

2

i

1

0

iii

sin

)E(

sin

)E(

wK)E(I

+

=

(2.3)

- i vi mu so snh:

2

i

*

1

0

*

*

ii

*

i

sin

)E(

sin

)E(

wK)E(I

+

=

(2.4)

y:)E()w1()E(w)E( iiii +=

)E()w1()E(w)E( *i*i

*i

*i

* += (2.5)Vi: )E( 0i v )E(i l h s suy gim khi ca nguyn t i cn xc nh tng ngvi bc x th cp. )E( 0 v )E( l h s suy gim khi ca mu (c n nguyn t i, j, k, ..l, ...) tngng vi bc x s cp v bc x th cp.

Ta lp t l:

2

i

1

0

2

i

*

1

0

*

*

i

i

i

*

i

ii

sin

)E(

sin

)E(

sin

)E(

sin

)E(

w

w

)E(I

)E(I

+

+

= (2.6)

Nu cht n ca mu phn tch v mu so snh c thnh phn ha hc nh nhau vhm lng ca nguyn t cn xc nh trong mu thay i nh, th ta c th xem h s suygim khi khng i, ngha l * . Khi t phng trnh (2.6) ta c phng trnhgn ng:

** wII

w = (2.7)

y l trng hp n gin nht, ta ch dng mt mu so snh. Tuy nhin, nu hmlng ca nguyn t cn xc nh thay i trong mt khong gii hn ln, th phng trnh

21


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(2.7) khng p dng c. Trng hp ny ta phi dng nhiu mu so snh v lp thI = f(w). Thng thng th ny c dng tuyn tnh:

w = aI + b (2.8)

i vi mi min ca th ta c th dng phng php bnh phng ti thiu tnh cc gi tr a v b. chnh xc, i khi ng chun phi l mt a thc bc hai hayln hn. Tuy nhin, kt qu phn tch cn chu nh hng ca cc yu t bn ngoi vcng ngun kch lun thay i theo thi gian dn n hin tng tri ph v ngchun lp trc y khng cn dng c, chnh v vy vic xc nh ng chun philm hng ngy, hng tun. trnh tnh trng ny ngi ta dng t s cng tng iI/IC. Trong IC l cng ca vch tn x kt hp hoc vch tn x khng kt hp.Phng trnh (2.8) tr thnh:

bII

aw C += (2.9) phng trnh ny, ngi ta pha ch cc mu so snh gn ging mu phn tch.

Cc mu ny c hm lng nguyn t cn xc nh bit. Do o cng bc x ctrng pht ra t chng, ngi ta xy dng ng cong biu din mi quan h gia cng v hm lng. vi ng chun ny, khi bit cng ta c th tnh c hm lngnguyn t cn phn tch.

Trong trng hp vt liu c thnh phn ha hc a dng, ngha l * , ta c:

)E(

)E(

w

w

)E(I

)E(I

i

i

*

*

i

i

i

*

i

ii

= (2.10)

Khi xc nh hm lng nguyn t w i trong mu ta ch cn bit h s suy

gim khi i vi tia X c trng pht ra t mu. iu ny c tm thy t thc nghimbng cch xy dng ng cong hp th biu din mi lin h ph thuc ca h s suygim khi vo nng lng. Phng php thc nghim nh sau:

- o cng I0(E) khi cha c mu v cng I(E) khi c mu.- T phng trnh (1.2) cho php ta tnh h s suy gim khi )E( :

=

=)E(I

)E(ILn

P

S

)E(I

)E(ILn

T

1)E( 00 (2.11)

Nh vy s dng cc ngun chun tia X, th d cc ngun chun Fe 55, Zn69, Cd109 vAm241 m nng lng cc bc x c s dng trong bng 2.2

Bng 2.2: Cc ngun kch thch hunh quang tia XNgun Fe55 Zn65 Am241 Am241 Cd109

E(eV) 5898(MnK)

8047(CuK)

13945(NpL)

17740(NpL)

22162(AgK)

T bng trn cho php ta xy dng c ng cong suy gim khi )E(= . Khi vi gi tr Ei ta suy ra c cc gi tr tng ng )E( i v )E( i

* . T phng trnh(2.10) ta c biu thc xc nh c hm lng wi:

*

i

i*

i

i*i

iii w

)E(

)E(

)E(I

)E(Iw

= (2.12)

22


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Nu trong vt liu phn tch c cha nguyn t k, m nng lng cnh hp th E k(ht)ca n nm gia nng lng cnh hp th E i(ht) v nng lng Ei ca tia X c trngnguyn t i cn phn tch: Ei < Ek(ht) < E i(ht), th s thay i hm lng ca nguyn t k s

dn n sai s h thng trong kt qu phn tch. Trong trng hp ny ta phi tnh ton nhhng ca nguyn t k ln cng tia X c trng ca nguyn t i cn phn tch. Khi hm lng ca nguyn t i c tnh theo phng trnh sau:

)m(F)E()E(I

w)E()E(Iw

i*

i*

*iii

i

= (2.13)

y F(m) l hm ca m (vi m = ))E(/)E( ki

)E(

)E(

)E(

)E(

sin

sin)m(F

k

i

k

i

2

13

k

=

= (2.14)

l h s khng i cho tng iu kin phn tch chn.Gi tr F(m) xc nh theo th m c xy dng bng cch s dng nhm mu so

snh vi hm lng ca nguyn t i bit v thay i trong mt khong gii hn quanhgi tr wi ca mu phn tch, sao cho gi tr h s suy gim khi (Ei) i vi ton b nhmmu so snh c gi nguyn khng i. Khi t phng trnh (2.14) ta c:

*ji

*a

i

i*a

i

*j

w

w

)E(I

)E(I)m(F = (2.15)

Trong Ia*(Ei) v Ij*(Ei) l cng tia X c trng pht ra t nguyn t i trong mtmu so snh c nh A v trong mt mu j a thuc nhm mu so snh. Vi mu j ta c

mt gi tr Fj(m) tng ng vi mt gi tr)E(

)E(m

k

i

= . Cc h s (Ej) v (Ek) c xc

nh theo phng trnh (2.11).Nh vy, o cng cc vch c trng ca cc nguyn t i v nguyn t k trong

mu phn tch v trong cc mu so snh ta xc nh c cc h s lm yu khi, xy dngc hm Fj(m). T ta tnh c gi tr F(m) ca mu phn tch. Dng phng trnh(2.13) ta tnh c wi.

2.2.2. Phng php phn tch vi mu mngNu b dy mu phn tch T 0 th t phng trnh (1.40), ta c th vit:

TKw)E(I iii = (2.16)Phng trnh trn cho thy cng hunh quang pht ra t mu mng khng ph thucthnh phn ha hc ca mu, ngha l khng c s hin din ca cc h s hp th hay hs tng cng. Do vi mu mng ta loi c nh hng ca hiu ng matrix. xcnh nh th no l mu mng ta c biu thc sau:

23


24/137

Sai s phn tch %100)].Texp().T1(1[(%) = (2.17)Trong ,

2

i

1

0

sin)E(

sin)E(

+

= (2.18)

Th d: vi = 100 500 cm2/g = 2 5 g/cm3

T = 1 10m

th sai s phn tch mu mng c tnh trong bng 2.3.

Bng 2.3: Sai s phn tch vi mu mngT Sai s (%) phng php mng mng

0,0100,1000,1350,2000,5000,7501,000

0,0050,5351,0002,290

17,60047,100

100,000

Nu t T = s (mt b mt ca mu), th ta c tiu chun v mng cn c quinh theo chnh xc nh sau:

* i vi s gn ng 1%

)w1(w

022,0

inii

s + (2.19)

* i vi s gn ng 10%

)w1(w

195,0

inii

s + (2.20)

Trong :2

i

1

i

i

sinsin

+

= (2.21)

2

n

1

nn

sinsin

+

= (2.22)

Sau khi xc nh s theo cc phng trnh trn, o cng ph, hm lng ctnh theo phng trnh:

s

ii

K

Iw

= (2.23)

y K l h s khng i, c th xc nh bng thc nghim bi mt mu c hmlng bit trc.

24


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Cn c phng trnh (2.23) ta thy rng nu s khng i th hm lng w i t ltuyn tnh vi cng Ii. Vy nu chun b cc mu so snh v mu phn tch c cngkhi lng P v din tch b mt S, th xc nh hm lng w i ta xy dng th phn

tch Ii = f(wi) vi b mu so snh c hm lng nguyn t phn tch bit. chnh xc ca phng php mu mng ty thuc vo ng u ca cc

nguyn t trn b mt mu, chnh xc ca php o v s thc hin iu kin v mng. i khi t n mng ca lp mu, ngi ta pha long bng cht hp thkm. Trong trng hp ny b dy ca lp mu c th t n 12 mm m vn tha mniu kin mng ca mu.

Phng php phn tch mu mng gim thiu c nh hng hiu ng matrix, tuynhin khuyt im ca n l s phc tp giai on chun b mu mng v nht l nhy rt thp.

2.2.3. Phng php chun nia vo mu phn tch mt lng nguyn t B no c bc s nguyn t khc

bc s nguyn t ca nguyn t A cn phn tch mt n v (nhiu lm l hai n v).Nguyn t ny c hm lng bit trc, c gi l nguyn t chun ni hay nguyn tso snh. Ta s so snh cng bc x c trng ca hai nguyn t ny. Ta c biu thclin h sau:

B

ABA

I

Iww = (2.24)

WB l hm lng nguyn t so snh trong mu, l h s cng , c xc nh bng thc nghim nh sau:

- Dng mu so snh c hm lng nguyn t A v nguyn t B xc nh, ta c:

B

A

A

B

w

w

I

I= (2.25)

Phng trnh (2.24) v (2.25) c s dng tnh wA khi hm lng nguyn t A cc mu cn phn tch thay i trong mt khong gii hn khng ln. Trong trng hpngc li th phi to b mu so snh c hm lng ca cc nguyn t A v B xc nh,trong hm lng ca nguyn t B nh nhau trong cc mu so snh. Lp th phn

tch: )w(fI

IA

B

A = . nghing ca ng phn tch c trng cho h s cng .

2.2.4. Phng php chun nhyT phng trnh (1.36) ta c:

=)Texp(1

Sw)E(I iii

(2.26)S = QifG0 I0: nhy ca h thng thit b phn tch i vi vch phn tch,: kh nng hp th ca mu i vi bc x s cp v th cp,

2

is

1

0s

sin

)E(

sin

)E(

+

=

Sau khi o cng Ii, t phng trnh (2.26) ta tnh c hm lng ca nguynt phn tch l:

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)Texp(1(S

Iw i

i

= (2.27)

T biu thc S = Qif G0 I0 ta thy rng S ph thuc vo nguyn t cn phn tch, btr hnh hc v ngun kch thch, m khng ph thuc vo dng thc v thnh phn cu tonn mu. V vy c th dung cc mu chun dy v hn c cha nguyn t phn tch i tnh Si.

i vi mu dy v hn, ta c:

=

= ii00ifi

wS

wIGQI (2.28)

Nh vy v mt thc nghim ta tin hnh cc php o nh sau:- Chun b mu phn tch di dng mu mng.

- To mt mu dy v hn, c cha nguyn t cn phn tch vi cc thnh phn bit, dng o nhy v lm chun hp th.- o cng )E(I i

*

i ca vch c trng nguyn t phn tch i pht ra t mudy v hn. Khi nhy Si c xc nh bi h thc:

*i

i*i

iw

)E(IS

= (2.29)

Trong , tnh ta phi xc nh cc h s hp th khi )E( 0s , )E( is bngcch tra bng hoc xc nh bng thc nghim theo cng thc (2.11).

xc nh T, ta t mu phn tch vo gia mu chun hp th v detector, rio cng I2:

)E(I]Texp[)E(I)E(I ii*ii2 +=Do gi tr T c xc nh bi phng trnh sau:

=II

ILnT

2

*

i (2.30)

Trong I l cng vch c trng pht ra t mu phn tch. Tt c cc php ou c thc hin trong cng iu kin hnh hc.

Vi cc gi tr Si v T tnh c bng thc nghim, thay vo phng trnh (2.27)ta tnh c wi.

2.2.5. Phng php hm kch thchT phng trnh tnh cng bc x hunh quang th cp (1.36):

2

i

1

0

2

i

1

0

i00ifii

sin

)E(

sin

)E(

sin

)E(

sin

)E(Texp1

wIGQ)E(I

+

+

=

Trong : f4

)Ei(Q

kikiif

=

M ki l h s hp th khi quang in ca bc x c trng nguyn t I, nn n l mt

hm ca Zi. Do ta c th t:Qif G0 I0 = F(Zi) (2.31)

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F(Zi) c gi l hm kch thch.

Vy phng trnh (1.36) c th trnh by nh sau:

2

i

1

0

2

i

1

0

iiii

sin

)E(

sin

)E(

sin

)E(

sin

)E(Texp1

w)Z(F)E(I

+

+

= (2.32)

Th nghim c b tr sao cho cc gc 1, 2 gn bng 900. Khi ta c:

{ }[ ]

)E()E(

)E()E(Texp1w)Z(F)E(I

i0

i0

iiii ++

= (2.33)

i vi mu mng ta c:Tw)Z(F)E(I

iiii=

(2.34)

S dng cc mu chun mng n nguyn t tng ng vi cc gi tr Z khc nhaubao quanh gi tr Zi ca nguyn t cn phn tch, bng thc nghim ta o cc cng Ica bc x c trng cc nguyn t theo nng lng vch K, L, M, trong cc mumng ni trn. Vi cc gi tr , T bit ca cc mu mng ta tnh c cc gi tr F(Z)tng ng t phng trnh.

Tw

I)Z(F

= (2.35)Dng phng php bnh thng ti thiu thit lp hm kch thch F(Z) ng vi

vch K, L, M, Do , vi gi tr Z i ca nguyn t cn phn tch ta c c gi tr F(Z i)tng ng. i vi mu phn tch (mu mng), ta o cng I i, cn gi tr T tnh t

biu thc: T =S

P

Thay cc gi tr o c vo phng trnh (2.34), ta c:

S

P)Z(F

)E(Iw

i

iii =

(2.36)Trng hp khng to c mu mng, th ta phi xc nh cc h s hp th khi

)E( 0 , )E( i bng cch tra bng hoc xc nh bng thc nghim theo cng thc(2.11). Thay cc gi tr c c vo phng trnh (2.33) ta tnh c w i.

2.2.6. Phng php dung t s cng nh

Gi s mu c n thnh thnh (I, j, k, l, ) sao cho 1Cn

ii = , lp t s hm lng

nguyn t tng ng ta c h thng phng trnh tuyn tnh sau:

=+++++

n

l,k,j,imii

m

i

l

i

k

i

j

C

1

C

C.......

C

C

C

C

C

C1

27


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=+++++

n

l,k,j,im jj

m

j

l

j

k

j

i

C

1

C

C.......

C

C

C

C1

C

C(2.37)

=+++++ n

l,k,j,imkk

m

k

l

k

j

k

i

C1

CC.......

CC1

C

C

CC

. . . . . . . . . . . . . . . .Xy dng ng chun t s cng nh nng lng hunh quang theo t s hm

lng nguyn t tng ng theo biu thc sau:

0

1n

j

i

1n

n

j

i

n

j

i a.......C

Ca

C

Ca

I

I++

+

=

(2.38)

Nh vy vi mu c ba thnh phn ta c su ng chun tng ng. xc nhhm lng mu phn tch, ta o cng nh hunh quang tng ng sau thay vocc phng trnh ng chun ngoi suy cc t s hm lng; sau thay cc gi tr

ny vo h phng trnh trn v dng phng php lp tnh hm lng.

28


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Chng 3

HIU NG MATRIX V CC PHNG PHP HIU CHNH

Trong nhiu loi mu thch hp cho vic phn tch bng phng php hunh quangtia X nh mu hp kim, khong qung v.v... l nhng vt liu nhiu thnh phn. V vy khi

phn tch mt nguyn t cha trong mu, ngi ta phi quan tm n nhng hiu ng xuthin do s c mt ca cc nguyn t thnh phn. Cc hiu ng dn n s hp th haytng cng bc x c trng nguyn t phn tch v ta gi l hiu ng matrix. V vyhiu ng matrix lm nh hng n chnh xc ca phng php phn tch hunh quangtia X. C hai loi hiu ng matrix chnh: s hp th bc x hunh quang ca nguyn tmun o bi cc nguyn t nng trong mu (hiu ng hp th) v s gia tng bc x hunh

quang ca nguyn t ny do bc x hunh quang c nng lng cao hn t nhng nguynt khc cha trong mu kch thch (hiu ng tng cng).

3.1. Cc hiu ng hp th v tng cngCc nguyn t matrix khng ch hp th cc bc x c trng pht ra t nguyn t

phn tch khi nng lng cnh hp th ca n nh hn nng lng bc x c trng (hpth th cp) m cc nguyn t matrix cng hp th c ph kch thch s cp (hp th scp). iu ny lm cho vic phn tch nh hnh lng thm kh khn.

3.1.1. Hiu ng hp th s cpHiu ng hp th s cp c miu t trong hnh 3.1. Trong hiu ng ny mt phn

nh ca ph nng lng kch thch s cp l kh dng kch thch mt vi nguyn t trongmu. Nu nng lng kch thch qu ln so vi nng lng cnh hp th ca nguyn t thhiu sut kch thch khng ng k.

29


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Hnh 3.1: Ph s cp c th dng kch thch cc nguyn t A v B(phn din tch gch cho biu th phn b photon c th dng kch thch)

Trong hnh 3.1 nguyn t A v B u chu s kch thch ca mt min nh trongvng lin tc ca ph nng lng kch thch (ph hm). Cc bc sng tng ng vi cccnh hp th ca A v B khc nhau, nn ty vo cc cnh hp th ng vi hai nguyn t Av B m dy ph nng lng kch thch s cp kh dng hn i vi mt trong hai nguynt . Nh vy i vi mt nguyn t cho trc, hiu sut kch thch ca bc x s cpkhng ch ph thuc vo cnh hp th ca nguyn t phn tch m cn ph thuc vo cccnh hp th ca cc nguyn t matrix. iu c ngha l tn ti mt hiu ng do ccnguyn t matrix nh hng n s kch thch s cp ca mt nguyn t cho trc. Hiung ny c gi l hiu ng hp th s cp.

3.1.2. Hiu ng hp th th cp

Khi tia X hunh quang c trng nguyn t phn tch c nng lng ln hn nnglng hp th ca mt vi nguyn t matrix, mt phn nng lng b hp th bi ccnguyn t matrix ny nn cng bc x c trng b gim. Hiu ng ny gi l hiung hp th th cp. Trong cc phng trnh din t mi quan h gia cng v hmlng chng 2, s hng (Ei)/sin2 l hp th khi ton phn th cp i vi mt tiaX ring bit c nng lng Ei pht ra t nguyn t phn tch i.

T phng trnh (2.3), ta c:

=

2

ij

jj

2

i

sin

)E(w

sin

)E((5.1)

Vi wj l hm lng ca nguyn t j (j biu din tt c cc loi nguyn t cha

trong mu). hp th khi ton phn cho c hai s hng hp th s cp v th cp l:

+

=2

ij

1

0j

jjiT

sin

)E(

sin

)E(w)E( (5.2)

Trong phng trnh trn, (E0) biu din hp th ca nguyn t j i vi tia Xs cp c nng lng E0.

3.1.3. Hiu ng tng cngQu trnh cn bn dn n hiu ng matrix l tia X c trng pht ra t cc nguyn

t j no , c nng lng ln hn cnh hp th ca nguyn t i trong cng mu, th s gpphn kch thch nguyn t i pht quang. Do cng tia X c trng o c canguyn t i s tng theo hm lng ca nguyn t j (ta ni nguyn t j tng cng nguynt i). Ngc li cng tia X c trng nguyn t j s gim khi hm lng nguyn t itng. Hnh 3.2 cho thy rng khng ch vng lin tc ca ph kch thch s cp m c tia X

pht ra t cc nguyn t A v B u c kh nng kch thch nguyn t i pht hunh quang.

30

Hnh 3.2: Cc hiu ng hp th gia cc nguyn t


31/137

Mt qu trnh phc tp hn, l trng hp nguyn t j li c mt nguyn t k(nguyn t th ba) kch thch v nguyn t k ny cng kch thch nguyn t i pht quang.Qu trnh ny gi l hiu ng nguyn t th ba.

Hnh 3.3: S tng cng v hiu ng nguyn t th ba

3.2. Cc biu thc c bn3.2.1. Hunh quang cp 1

Hunh quang cp mt l mt phn tia X pht ra t nguyn t do s kch thch cangun s cp. T phng trnh (1.38) ta c biu thc cng hunh quang cp mt ivi trng hp kch thch bi ngun n nng.

)E(sin

sin)E(

w

sin

IGQ)E(A

i

2

10

i

1

00if

ii

+= (3.3)

Trong i l nguyn t hunh quang, wi l hm lng ca nguyn t i

t Ki = QifG0 I0 / sin 1 ;2

1

sin

sinS

=

)E(S)E(

wKA

i0

iii +

= (3.4)

)E(S)E( is0)hd( += : h s suy gim khi hiu dng ca mu cho c bc x ti E 0 vbc x hunh quang Ei.

3.2.2. Hunh quang cp 2Hunh quang cp hai l phn tia X pht ra t mt nguyn t do s kch thch ca

bc x hunh quang cp mt pht ra t nguyn t khc.Guilliam v Heal tm ra hunh quang cp hai hay cn gi l hunh quang tng

cng, ngha l nguyn t i b kch thch bng bc x c lc la ca mt vi nguyn t j.Do phn cng tng cng cho mt vch Ei l:

ijijijAwaB = (3.5)

Vi L)E()E(

)E(

2

1a ji

0i

0j

jij

= (3.6)

Trong , )E( ji l h s hp th khi ca nguyn t i i vi bc x nng lng Ej.

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)E( 0i , )E( 0j l h s hp th khi ca cc nguyn t i, j i vi bc x cnng lng E0.

2

i

j

2

i

1

0

j

1

0

sin

)E(

)E(

sin

)E(

1Ln

sin

)E(

)E(

sin

)E(

1Ln

L

+

+

+

=(3.7)

j : l h s kch thch ca nguyn t i cho mt vch ph cho trc.V d, j cho vch K l:

= kkk

kj f

r

1r(3.8)

k

k

r1r l xc sut kch thch nguyn t j pht quang electron tng K; k l hiu

sut hunh quang tng K khi bc x kch thch c nng lng E i; fk xc sut bc x vchK (so vi cc vch K khc).

Nu cng vch c trng nguyn t i c tng cng bi nhiu vch (bc xc trng) ca mt nguyn t j th S ij c thay bng mt tng S

T

ij tng ng. Trng hp

nhiu nguyn t j (i), th ta c:=ij

Tiji BB (3.9)

Cui cng cng tng cng ca nguyn t i l:iii BAI += (3.10)

Trng hp ngun kch a nng, ta c:- Cng hunh quang cp mt l:

+

==

max

K0

E

E i0

000i

iii)E(S)E(

dE)E(I)E(wS

4

dA (3.11)

- Cng hunh quang cp hai l:

+

==

max

K0

E

Ejj

i0

000i

iiji w)E(S)E(

dE)E(I)E(wS

4

d

2

1B (3.12)

3.2.3. Hunh quang cp 3Hunh quang cp ba l phn tia X pht ra t nguyn t phn tch do s kch thch

ca bc x hunh quang cp hai pht ra t mt nguyn t matrix. Cn hiu ng nguyn tth ba xy ra khi c s kch thch cho nh ni trn, ngha l khi yu t th ba k va kchthch nguyn t j pht hunh quang cp hai va kch thch nguyn t phn tch i phtquang.

Trong thc t hung quang cp ba khng ng k, nn ta khng lp biu thc chotrng hp ny. Nh vy vi cc cng thc trn cho php ta tnh c cng hunhquang trong trng hp phi tnh n hiu ng matrix.

3.3. Cc h s c bn3.3.1 H s alpha Phng trnh Lachance v Traill

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Beattie v Brissey a ra cc phng trnh i vi mu ba thnh phn nh sau:)wKwKw(Rw kikjijiii ++=

)wKwKw(Rw ijikjkjjj ++= (3.13))wKwKw(Rw jkiikikkk ++=

1www kji =++

Ri, Rj, Rk l cc t s cng ng o c t mu phn tch trn cng o ct mu tinh khit tng ng.

Kij, Kjk, Kki l cc h s hiu chnh.

Vi gi thit ngun kch thch n nng E0, Beattie v Brissey a ra cc h sK cho trng hp ch n thun hiu ng hp th nh sau:

)E(S)E(

)E(S)E(K

ii0i

ij0j

ij ++

= (3.14)

Cc h s ny cng c th xc nh bng thc nghim bng cch dng b mu sosnh.

Trn c s tng qut hn, Lanchance v Traill a ra h phng trnh sau:)waw1(Rw kikjijii ++=

)waw1(Rw ijikjkjj ++= (3.15))waw1(Rw jkiikikk ++=

So snh (3.13) v (3.15), ta c:1K

ijij= ; 1Kjkjk = ; 1Kkiki =

Do : 1)E(S)E(

)E(S)E(

ii0i

ij0j

ij

+

+= (3.16)

2.2

2.0

1.8

1.6

1.4

0 0.2 0.4 0.6

2

4

3

1

CFe

0.8

33

FeCr

1.0

Hnh 3.4: Trng hp ch c hp th (H Fe-Cr)

(1): bia W, 50 KV, gc hnh hc 600

/ 300

(2): bia W, 45 KV, gc hnh hc 450 / 450

(3): bia Cr, 45 KV, gc hnh hc 450 / 450

(4): kch thch n nng = 1,14 A


34/137

Trong biu thc trn, E0 l nng lng bc x ti, nu bc x a nng th E0 l gitr hiu dng. R rng i vi s kch thch n sc h s ij l hng s. Trong hnh 3.4,kho st h Fe-Cr, nguyn t phn tch Fe ch chu s hp th bi nguyn t Cr, th (4)

cho thy vi trng hp kch thch n nng h s Fe-Crl hng s.

3.3.2. Mu hai thnh phn Hp th v tng cngTrong phng trnh Lanchance v Traill, cc h s alpha tnh theo biu thc (3.16)

ch ng cho trng hp n thun hiu ng hp th. Tht ra cc s alpha cng biu th stng cng, v khi h s ij khng tnh theo biu thc (3.16) trn na. Nu hp thchim u th th ij > 0, ngc li nu tng cng chim u th th ij < 0, cng c trnghp ij = 0.

Xt trng hp n gin: kch thch bng ngun n nng. T cc phng trnh(3.4), (3.5) v (3.10) ta c:

)wa1(wI jiji0i += (3.17)

Vi)E(S)E(

K

i0

i0 +

= (3.18)

H s ij c tnh mt cch nh lng nh sau:Gi 'iR l t s cng ton phn, Ri l t s cng ch ph thuc vo hunh

quang s cp, ta c:)wa1(RR jiji

'

i += (3.19)i vi mu hai thnh phn, phng trnh Lanchance Traill nh sau:

)w1(Rw jijii += (3.20)

Trong h s ij ng vi trng hp ch xt n thun hp th. Nu xt c hpth ln tng cng th cng Ri c thay bi 'iR , v h s ij c thay bi h s'

ij ng vi trng hp c xt ti s tng cng. Khi ta c:

)w1(Rw j'ij

'ii += (3.21)

T (3.19), (3.20) v (3.21), ta c:)w1(R)w1)(wa1(R jijij

'

ijjiji +=++

Suy ra:( )

jij

jij

'

ij

jij

jij

j

'

ijwa1

wa1

wa1

w1w

+

=

+

+=

jij

ijij'

ij

wa1

a

+

= (3.22)

Hnh 3.5 cho thy mt v d in hnh: H Fe-Ni

34


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0.2

0

-0.2

-0.4

-0.8

0 0.2 0.4 0.6

CF

0.8 1.0

0.4

0.6

0.8

1.0

1.5

Hnh 3.5: S bin thin ca h s 'ij trong trng hp c tng cngH Fe-Ni. Nguyn t phn tch l FeKch thch n nng 02,1= ; 450 / 450

Nhng bin thin tng t cng c tm thy trong cc h Cr-Fe, , Mn-Co, Co-Cu

v Ni-Zn.

Mt cch tng qut, s bin thin ca h s 'ij ca hm lng c biu dintrong th trn hnh 3.6 nh sau:

-0.6

0 0.2 0.4 0.6 0.8 1.0

-0.4

-0.2

0

Hnh 3.6: S bin thin ca h s 'ij theo hm lng wi trong trng hp tng cng

35

'FeNi

FeNi

'FeNi

FeNi

'lj

'lj

wi

1

0


36/137

T th trn ta c:)(wtgw 01i0i0

'

ij +=+=

Do dng th l ng cong nn chnh xc hn ta a vo h s iu chnh cho h hp phn bc hai. Ta c phng trnh chnh xc:

( )

)1(

01

0

'

ii

i

ijww

w

+

+=

(3.23)

Vi: 0, 1 l gi tr gii hn ca 'ij ti wi = 0 v wi = 1.Phng trnh ny cng ba tham s 0, 1, cho php biu din tt c cc ng

cong bin thin ca 'ij theo hm lng wi vi chnh xc cao.T phng trnh (3.22) ta c:

ijijjij'ij a)wa1( =+

( ) 'ii

ijijj

'

ijijij

'

ijR

w

aw1a =+= (3.24)

3.3.3. Mu ba thnh phn Hiu ng nguyn t th baKhi c t nht ba nguyn t cng tn ti trong mt hp phn v chng t nhiu lm

mt hiu qu cc h s Lachance Traill bc hai tnh phng trnh (3.16). Chng taxem xt bn cht ca hiu ng nguyn t th ba v c tnh nh hng ca chng.

Hiu ng ny khc hn hunh quang cp ba. Hunh quang cp ba c xem nhbc x hunh quang thm vo. V d trong h Cr-Fe-Ni, hunh quang cp ba (Cr) l gialng lin quan n s kch thch do hunh quang cp hai (Fe), hunh quang cp hai (Fe)l c gia tng bi hunh quang cp mt (Ni). Cn hiu ng nguyn t th ba li khc, n

cn c gi l hiu ng hunh quang bt cho, bt ngun t s bin i hp th trongmu v s tc ng tr li ca chng trong hiu sut tng cng. Do hunh quang cp bakhng ng k nn trong qu trnh kho st hiu ng nguyn t th ba ta ch xt ti hunhquang cp hai.

Xt trng hp ngun kch n nng, nguyn t phn tch l w i.- i vi trng hp hai thnh phn: wi + wj = 1 (3.25)- i vi trng hp ba thnh phn:

wi + wjT + wkT = 1 (3.26)wi l hm lng nguyn t phn tch trong mu hai thnh phn cng nh trong mu

ba thnh phn.wj v wjT l hm lng ca nguyn t j trong mu hai thnh phn v trong mu ba

thnh phn.wkT l hm lng ca nguyn t k trong mu ba thnh phn.

j l nguyn t tng cng cho i, cn k l nguyn t th ba.T phng trnh (3.24) ta c h s 'ij i vi mu hai thnh phn (k hiu H) v

i vi mu ba thnh phn (k hiu B) l:

( ) ( )H

'

i

i

HijijH

'

ijR

wa

= (3.27)

( ) ( )B

'

i

i

BijijB

'

ijR

wa

= (3.28)

36


37/137

Trong ij cho bi biu thc (3.16) cn (a ij)H v (aij)B c ly t biu thc (3.6)cho mu hai thnh phn v mu ba thnh phn nh sau:

( )

( )

( ) ( )( )Hji

0i

0j

jHij LEE

E

2

1

a

= (3.29)

( )( )

( )( )( )

Bji

0i

0j

jBijLE

E

E

2

1a

= (3.30)

Vi L ly t biu thc (3.7)

Ta c th kho st hiu ng nguyn t th ba bng cch khc nh sau:Trc ht ta cha xt n hiu ng nguyn t th ba, ngha l trong mu ba thnh

phn, cc nguyn t j v k khng nh hng ln nhau.i vi mu hai thnh phn Hij (wi + wj = 1), ta c:

( )j

'

ij

'

iji w1Rw += (3.31)i vi mu hai thnh phn Hik(wi + wk= 1), ta c:

)k'

ik

'

iki w1Rw += (3.32)

i vi mu ba thnh phn Bijk(wi + wjB + wkB = 1), ta c:( )Bk

'

ik

B

j

'

ij

'

ijki ww1Rw ++= (3.33)

+

+= Bkk

'

ik

i

B

j

j

'

ij

i

'

ijk ww

1R

w

ww

1R

w

1R

++=

k

B

k

k

'

ik

B

ki

j

B

j

j

'

ij

B

ji'ijk

ww

wRww

ww

wRww1R

( ) ( )

+

+

+=

i

B

k

B

j

i

'

ik

B

ki

i

'

ij

B

ji'

ijkw1

ww

w1R

ww

w1R

ww1R

Lu : wj = 1 wi (i vi mu hai thnh phn i v j)wk= 1 wi (i vi mu hai thnh phn i v k)wjB + wkB = 1 wi (i vi mu ba thnh phn i, j v k)

Do :( ) ( )Bk

B

j

'

ik

B

k

B

k

B

j

'

ij

B

j'

ijkiwwR

w

wwR

wRw

++

+=

Vy: 'ik

B

k

'

ij

B

j

'

ijk

B

k

B

j

R

w

R

w

R

ww+=

+(3.34)

Nh trn ni phng trnh (3.33) ng vi trng hp b qua hiu ng nguynt th ba. V vy khi xt n hiu ng nguyn t th ba th cng t i 'ijkR phi hiu

chnh, ngha l thay 'ijkR o c bib

ijkR :

'

ijk

B

k

'

ijk

B

j

B

k

B

j'

ijk

'

ijk

R

w

R

w

wwRR

+

+=

Khi phng trnh (3.34) tr thnh

37


38/137

( )Bk'

ik

B

j

'

ij

i

'

ijk

i ww11

Rw ++

+= (3.35)

l h s dng hiu chnh khi dng cc h s cp hai.y l biu thc tng qut cho mt hp phn bt k. Hnh 3.7 sau y cho thy

mc nh hng ca Fe i vi nguyn t Fe trong h Ni-Fe-Cr:

Hnh 3.7: Hiu ng nguyn t th ba i vi nguyn t Fe trong h Ni-Fe-CrFe ti cc gi tr hm lng wFe nh l mt hm ca wNi v wCr

Hnh bn tri: ngun kch n nng, = 1,02 A0

Hnh bn phi: ngun kch a nng, bia Cr, 50 KV.

3.4. Cc phng php hiu chnh hiu ng matrix chnh xc ca phng php phn tch hunh quang tia X c th b nh hng do

s hin din ca nhng nguyn t khc trong mu. Nhng hiu ng ny ni chung cxem nh hiu ng matrix ni trn.

Mt vi k thut khc phc hiu ng matrix m ta cp trong cc phngphp phn tch nh lng c th tm tt nh sau:

- S dng phng php tnh da trn cc th ly t hai hay nhiu php o ring

trn cng mt mu.- Nhng k thut khc da trn cc phng php chun b mu c bit c s phalong kt hp vi acid boric hoc pha thm nhng cht ni.

3.4.1. Phng php nh cGi s mu phn tch gm cc nguyn t a, b, c, d, . . . . p, . . m vi nng tng

ng l wa, wb, wc, wd, . . . . . wj, . . wm . . Cc nguyn t ca mu c nh hng n cng dy ph phn tch. V vy nu hm lng ca chng thay i mt cch ty tin t muny sang mu khc th khi phn tch ta cn phi tnh ton mi quan h (nh hng) ca cc

nguyn t.

38


39/137

Lp t sj

)pure(

j

jI

IN = , y )pure(jI v jI l cng vch c trng nguyn t

j o t mu tinh khit v o t mu a nguyn t.Vi Np 1, ta c h phng trnh:( ) =+

jpp

pjjj 0wqw1N , khi =j j

1w

(3.36) y qjp l i lng khng i.Chi tit phng trnh ny c dng:

( )

( )

( )

=++++++=++

=+++

=++++

1w...............w............wwww

0w1N......................wqwqwq

........................................................................

0wq..................wqw1Nwq

0wq..............wqwqw1N

mpdcba

mmc

c

mb

b

ma

a

b

m

m

bc

c

bbba

a

b

m

m

ac

c

ab

p

aaa

(3.37)Phng trnh cui nhn c mt cch d dng t biu thc cng hunh quang

pht ra khi kch thch bi bc x n sc. Khi (E0) v (Ei) trong mu s phngtrnh (1.36) trnh by di dng:

)E(w......)E(w)E(w)E(w)E( mmccbbaa ++++= (3.38)Gii h phng trnh (3.37) ta c th xc nh hm lng wj, cc tham s qjp c th

tnh bng l thuyt bi cng thcsau:

2

jj

1

0j

2

jp

1

0p

p

j

sin

)E(

sin

)E(

sin

)E(

sin

)E(

q

+

+

= (3.39)

y, )E( 0p v )E( 0j l cc h s suy gim khi i vi bc x s cp E 0;ng vi nguyn t p v nguyn t j.

)E( jp v )E( jj l cc h s suy gim khi i vi bc x th cp Ej;ng vi nguyn t p v nguyn t j.

Tuy nhin nhng h s qjp xc nh bng thc nghim th tt hn bi v cc phng

trnh (3.37) v (3.39) nhn c t gi thit bc x kch thch l n sc, trong thc t nc th l bc x hm hay l a nng.

Nh vy vi phng php ny, trc tin ta xc nh bng thc nghim cc h sqjp, sau gii h phng trnh (3.37) ta c kt qu hm lng wj mun tm.

3.4.2. Phng php tham s c bnCng ng tia c trng nguyn t phn tch i kch thch bi ngun n nng vi

tham s hnh hc ca ph k bit trc c tnh bi phng trnh (1.36) thit lp chng 1:

39


40/137

2

i

1

0

2

i

1

0

i00ifii

sin)E(

sin)E(

sin

)E(

sin

)E(Texp1

wIGQ)E(I

+

+

=

Phng trnh trn v nguyn tc khng dng mu chun. Trong cc h s hnhhc dng c v hiu sut ghi ca detector nh l hm ca nng lng. nh chun thit

b ngi ta thng s dng mt mu chun n nguyn t.T phng trnh trn ta nhn thy rng xc nh hm lng w i, ngoi gi tr Ii

o c, gi tr I0 ca cng ngun kch, gi tr T ca khi lng trn mt n v dintch ta phi xc nh cc tham s c bn sau:

H s hp th khi ca mu: )E( jp , )E( jj xc nh bi cng thc (2.11).H s Qifv G0 c xc nh t mu n nguyn t.

Gc 1 v 2 xc nh bng phng php Monte Carlo.

Phng php ny ch s dng mt mu chun n nguyn t v cc thng s vt lc xc nh trc i vi mt h o c nh, cho kt qu vi chnh xc khng caonn ch l phng php phn tch bn nh lng. Ngoi ra phng php tham s c bns dng nhiu thng s vt l tra cu t cc bng s liu vt l ht nhn, phi tnh tonnhiu nn t c s dng.

3.4.3. Phng php h s c bn tnh cng bc x hunh quang tng cng ca nguyn t i trong mu nhiu

thnh phn (i, j, k, . . .) c kch thch bi ngun n nng c cng I 0, ta c phngtrnh c bn ca Sherman nh sau:

[ ]++

= j ijj0

i0

0iik0 Sw1I

)E(A)E(

)E(wqEI

(3.40)Trong :

=4

d

sin

sinq

2

1

ii

i

i

k fr

1rE

= : h s kch thch

wi: hm lng nguyn t phn tch i trong mu.)E( 0i : h s hp th khi ca nguyn t i ng vi nng lng ngun kch E0.)E( 0 , )E( i : h s hp th khi ca mu ng vi nng lng ngun kch E0

v nng lc bc x hunh quang c trng Ei

2

1

sin

sinA

= : h s hnh hc

I0: cng ngun kch thchSij: h s hp th - tng cng gia cc nguyn t i v jt )E(A)E( i0

* +=)E(A)E( ij0j

*

j +=

Ta c:

40


41/137

=

+=

== 1j

*

jj*

i

*

j

1jj

*

j

*w

1w1

t 1*

i

*

j

ij =

==> =

+=

== 1j

*

jjij1j

j

*

i

* ww1

Phng trnh (3.40) tr thnh

+

+

=

=

=

ij1j

j0

1jijj

*

i

0i

iki Sw1I

w1

)E(wqEI

(3.41)

t )p(i

i

i I

IR

=)p(

iI : cng vch ph c trng nguyn t i trong mu n cht tinh khit.i vi mu tinh khit,

wi = 1 v Sij = 0; ij = 0T phng trnh (3.40) ta c:

0*

i

0ik

)p(

i I)E(

qEI

= (3.42)

Lp t s hai phng trnh (3.41) v (3.42), ta c:

+

+

===

=

ij

1j

j

1jijj

i

)p(

i

i

i Sw1

w1

w

I

IR

Hay+

+=

=

=

1jiji

1jiji

iiSw1

w1

Rw (3.43)

xc nh hm lng wi, ta dng m hnh Lachance-Trail:T phng trnh (3.43), ta t:

==1j

ijjwx

==1j

ijjSwy

y1

x1Rw ii +

+= (3.44)

y1

yx1

y1

x111

y1

x1

R

w

i

i

+

+=++

+=++

=

+

+=

=

==

1jijj

1jijj

1jijj

Sw1

Sww

1

41


42/137

+

+=

=

=

1j

ijj

1jijijj

i

i

Sw1

)S(w

1R

w(3.45)

t +

=

=1jijj

ijij

ijSw1

S

+==1j

ijj

i

i w1R

w(3.46)

ij gi l h s hiu chnh matrix v c tnh t cng thc bn thc nghim ca Tertiannh sau:

)w1(w

)(w

ii

21i

0ij +

+=

Vi:0 : gi tr ca ij trong trng hp wi = 0

1 : gi tr ca ij trong trng hp wi = 1: hng s ph thuc vo h hai thnh phn ca mu v thng ly gi tr

2

10 +=

Hm lng cc nguyn t c tnh theo thut ton ca Lachance Trail nh sau:T phng trnh (3.46) ta c:

+==1j

ijjii w1Rw (3.47)

Bc 1: Cho gi tr u tin cc wj l Ri vo phng trnh (3.47) vi cc gi tr Riv ij bit trc ta tnh c cc gi tr w1(0).

Bc 2: Thay cc gi tr w1(0) vo phng trnh (3.47) tng ng vi wj ta tnh ccc gi tr mi wi(1).

Bc 3: Tip tc thay th cc gi tr w i(1) vo phng trnh (3.47) tng ng vi wjta tnh c cc gi tr mi wi(2).

. . . . . . . .

cho n khi iu kin hi t =n

ii 1w c tha mn ta dng li vi cc gi tr w i, wj, wk,

. . . mun tm.

3.4.4. Phng php hm deltaS thay i hm lng ca cc thnh phn mu dn n s khng tuyn tnh ca

ng chun cng . Mi lin h gia cng I v hm lng w c vit nh sau:++++= Aj,i

jiijAi

2

iiiAi

iiA0AA1A wwbwbwbawaI (3.48)

Nu cc s liu gi s c tr phng, th cc h s a0 c th b 9i.Vi mu tinh khit: wA(pure) = 1, IA(pure) = a1AT phng trnh trn ta c:

Vy: w=

=

Aj,ijiij

Ai

2

iiiAi

iiA

)pure(A

AwwbwbwbI

I

1w (3.49)

t: )pure(AAA I/IR =

42


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)pure(AiiI/b=

)pure(Aiiii I/b=

)pure(AijijI/b=

Ta c h thc xc nh hm lng ca nguyn t A trong mu ( hiu chnh hiung matrix) l:

+++=

Aj,ijiij

Ai

2

iiiAi

iiAAwwww1Rw (3.50)

Nu trong mu phn tch ch c hai nguyn t A v B gy nn hiu ng hpth/tng cng (hiu ng matrix). Th phng trnh (3.50) c dng n gin:

( )2BBBBBAA ww1Rw ++= (3.51)Vit li phng trnh (3.51) i vi nguyn t B ta c:

( )2AAAAABB ww1Rw ++= (3.52)

tnh cc h s j , jj ta v th biu din phng trnh

jjjj

j

i

i

ww

1R

w

+=

- H s j l tung im ct ca ng biu din vi trc tung.- H s jj l dc ca ng thng.Sau khi tnh c cc h s , ta thay vo cc phng trnh (3.51), (3.52).T cc phng trnh ny ta xc nh c hm lng ca cc nguyn t A v B.

* H s delta:

tng chnh xc ca kt ca phn tch, ta to mt mu chun (*) c hm lngca cc nguyn t A v i rt gn vi mu phn tch.

Thnh phn ca mu c tnh t mu chun (*) theo h thc sau.

i

*

ii www += (3.53)T phng trnh (3.50), ta c th vit:

+ + +=

*

jAj,i

*

iijAi

2*

iiiAi

*

ii

*

A

*

A wwww1Rw (3.54)

Lp t s *A

A

w

wta c:

++ ++= 2

iii

*

ii

i

*

iiiii*

A

A*AA

waw1wwa2w1

IIww (3.55)

Trong phng trnh trn v wi, wj nh nn cc s hng cha (wi)2, wiwj c b i. Trong trng hp hiu ng nguyn t th ba khng ng k cc s hng chah s jj c th b qua.

Cn s hng )I/I(w *AA*

A chnh l hm lng biu kin ca nguyn t A (tnhton t ph ghi nhn c)

*

A

A*

A

)bk(

AI

Iww = (3.56)

Do : ( ) += ii)bk(

AA w1ww (3.57)

43


44/137

Vi: + +

+=

Ai

2*

iiiAi

*

ii

*

BBBB

A

ww1

w2(3.58)

- Dng phng trnh (3.53) tnh wi. Trc ht phng trnh ny p dng vihm lng w(bk) thay cho hm lng wi.

- Dng phng trnh (3.57) tnh hm lng vi gi tr wi va tnh c bctrn.

- Lp li cc bc trn nhiu ln n khi gi tr w bt u n nh.Trong mi ln lp, lun lun s dng cng mt gi tr w(bk).

Chng 4

I CNG V PHN TCH KCH HOT NEUTRON

4.1. Cc tnh cht c bn ca php phn tch kch hot neutron4.1.1. Phn tch kch hot

Nm 1936, phn tch kch hot ra i v c Von Hevesy & Levi ln u tin pdng, cho n nay phn tch kch hot l mt phng php phn tch hm lng cc

nguyn t trong mu chnh xc nht v tin li nht so vi cc php phn tch khc. T

44


45/137

1938 n 1940, ngi ta phn tch kch hot bng cc ht mang in nh proton(p),alpha(), deuteron(d),....Vi s pht trin ca l phn ng ht nhn cho php to ranhng neutron c thng lng ln n 1012-1015 n.cm-2.s-1 th khi phn tch kch hot

bng neutron c xem nh l mt k thut phn tch thng dng nht vi tin cy rtcao so vi cc phng php phn tch khc.

Phn tch kch hot l phng php phn tch nguyn t hin i, s dng k thutht nhn da trn cc nguyn tc sau:

- Dng mt chm ht bn vo mu cn phn tch. Cc nguyn t cha trong mucn phn tch cng nh cc ng v ca nguyn t c bin i qua cc phn ng htnhn to thnh cc ng v phng x; nhng ng v phng x ny c th phn bitc da trn cc tnh cht bc x khc nhau ca chng nh: loi bc x phng ra, nnglng bc x, thi gian bn r. T s khc nhau ny, ta s nh tnh c cc nguyn thin din trong mu. Ngoi ra, phng x ca cc ng v sinh ra do phn ng ht nhndi nhng iu kin khng i t l vi hm lng nguyn t cha trong mu, da votnh cht ny ta nh lngcc nguyn t .

- phng x do kch hot khng ch ph thuc vo lng nguyn t cha trongmu m cn vo thng lng chm ht chiu, tit din kch hot ca nhn bia, thi gianchiu v c trng phn r ca nguyn t phng x to thnh.

kch hot, ta c th dng neutron, photon hay cc ht mang in t cc l phnng hay my gia tc: neutron, proton, deuteron, He3, He4,.v.v...Trong , kch hot bngneutron ng vai tr c bit bi v neutron c cc tnh cht c trng sau:

- Neutron trung ha in nn c kh nng i su vo nhn nguyn t.- D dng xuyn vo mi vt cht.- Khng lm thay i thnh phn ha hc ca nguyn t c chiu v c bit l

khng hy mu.Trong phn tch kch hot, cn lu n mt s vn sau: chiu x mu v chundi cng iu kin, m c hai di cng iu kin, t l s m ca mu phn tch vmu chun phi t l vi khi lng ca chng. c hiu qu, ngi phn tch c hiu

bit v ha hc v c kin thc vng v ha ht nhn, v vic o, v thit b o v vngun chiu x. Khi phn tch, mu c th thay i t v tr ny n v tr khc trong l

phn ng cho nn thng lng c th thay i, dn n vic nh hng phn ng ht nhnv nh hng n kt qu o. Vic o bc x cng phc tp v gp nhiu kh khn nh: shp thu bc x, s khng n nh ca thit b, tnh khng tuyn tnh trong detector. Nichung, kt qu thu c trong phn tch kch hot bng neutron c tnh cht thng k. Tuyvy, tnh phc tp trong phn tch v gi thnh cao cho vic chiu x v thit b o cng

khng th ngn cn c tc pht trin nhanh ca phn tch kch hot neutron.

4.1.2. Tnh cht ca phn tch kch hot bng neutronTrong phn tch kch hot bng neutron, iu kin u tin l nguyn t quan tm qua

cc phn ng ht nhn, cho ra cc ng v phng x, cho nn xc sut phn ng (tit dinbt neutron), ph cp ng v ca ht nhn bia v T1/2 ca ng v phng x phi ln ghi nhn c bc x. Loi bc x v nng lng ca bc x cng cn quan tm.

K thut phn tch kch hot bng neutron c th t n mc ppb (10-9g/g) khi chiux trong l phn ng vi thng lng neutron ln. i vi nhng phn ng neutron nhanh

phi la chn mt v tr chiu x trong l phn ng vi mt thng lng thch hp. Trong

hu ht cc trng hp, s nhim x c th tri khp b mt phn ng. V vy, mu cn

45


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phi lm sch trc khi phn tch. Mc d mt s phn tch c th c tin hnh bngmt thit b no nhng trong phn tch vt, vic chun b ha hc i khi tr nn quantrng v khng c php b qua.

4.1.3. Phng php thch hp cho phn tch vtVn t ra y l nhy trong php phn tch. Do , mt s thit b cn phic nhy cao. Trong qu trnh phn tch th s nhim bn cn phi c trnh hay gicho mc nhiu ny cng t cng tt c th thu c kt qu mong mun. Phn tch mucha nhng tp cht trn mc ppm (1ppm = 1g/g) th khng thch hp cho phn tch vt.Trong phn tch vt, kt qu thu c khng lun ng i vi k thut ny, iu l dos phn b khng ng u ca cc nguyn t trong matrix. Tnh chnh xc trong phn tchvt ph thuc hon ton vo mu chun. V vy, trong phn tch phi tnh n nhng kthut nh to mu chun hay so snh vi mt phng php c lp khc. Hm lng mucng cn c cu thnh mt h s xc nh cho vic la chn mt k thut phn tch. Chonn, nhng mu ln ng tnh th thch hp hn.

4.2. Ph neutron trong l phn ng ht nhnCc neutron trong l phn ng c hnh thnh qua phn ng phn hch ht nhn

l nhng neutron nhanh hay neutron phn hch. Do s va chm vi mi trng cht lmchm nn cui cng chng s b nhit ha.

Trn hnh 4.1 cho thy ph thng lng neutron ca l phn ng phn hch htnhn vi ba thnh phn ch yu: (i) ph Maxwell-Boltzmann; (ii) ph 1/E; v (iii) ph

phn hch.4.2.1. Ph neutron theo phn b Maxwell-Boltzmann (vng neutron nhit): l vng

neutron c nng lng t 0 n 0,5 eV. Neutron phn hch sau khi c lm chm trong lphn ng s mt dn nng lng v tr v trng thi cn bng nhit vi mi trng, nngi l neutron nhit. Cc neutron nhit chuyn ng trong trng thi cn bng nhit vi cc

phn t mi trng. Qu trnh gim nng lng ca neutron n vng nhit gi l nhitha. Ph neutron nhit khi phn b theo s phn b Maxwell-Boltzmann:

( )dEEe

kT

2

n

dn 2/1kTE

2/3

n

n

= (4.1)

Trong , dn l s neutron vi nng lng trong khong t E n E + dE, n l s neutrontng cng trong h, k l hng s Boltzmann, v Tn l nhit neutron (hay nhit mitrng).

T cng thc (4.1) ta c th vit li theo s phn b thng lng neutron ti nhit

neutron Tn nh sau:

( ))kT/(E

2

n

mmne

kT

E)E('

= (4.2)

vi k hng s Boltzmann v m thng lng neutron ton phn tun theo phn bMaxwell. Khi , hm phn b thng lng theo vn tc neutron tng ng l :

v).v('n)v(' mm = (4.3)vi nm(v) mt neutron trong phn b Maxwell cho mi khong n v vn tc. Tinhit chun T0 = 293,6 K ( = 20,40C) nng lng tng ng l E0 = k T0 = 0,0253 eV,vn tc tng ng v0 = 2200m.s-1

Nh vy, nng lng ca neutron s ph thuc vo nhit mi trng v trong

vng nng lng ny tit din tng tc ca neutron tun theo lut 1/v.

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4.2.2.Ph neutron phn b theo 1/E (vng neutron trn nhit): l vng neutron angtrong qu trnh chm dn v c nng lng trong khong 0,5 eV < E n < 0,5 Mev. Vng nygi l vng trung gian hay vng cng hng. Mt cch l tng, s phn b neutron trnnhit t l nghch vi nng lng neutron, E :

E)E( e'e

= (4.4)

vi e(E) l thng lng neutron trn nhit thc s cho mi khong logarit nng lng. Docu trc mi trng vt cht trong l phn ng, neutron s b hp th lm cho ph neutrontrn nhit b lch khi quy lut 1/E. Trn thc t th ta c th biu din theo cng thc gnng:

+= )eV1(E

)E(1

e'e

(4.5)vi l hng s c trng cho s lch ph t ph l tng v n c lp vi nng lng( v e lc ny l thng lng neutron trn nhit thc s cho mi khong n v

)eV1(E

).

4.2.3.Ph neutron phn hch (vng neutron nhanh): l vng neutron sinh ra trong phnhch v c nng lng En > 0,5 Mev. Mt vi cng thc bn thc nghim cho vic biudin ph phn hch thng c dng l:

- Ph phn hch ca Watt

47

10-2 10-1 1 10 101 102 103 104 105 106

Neutron trn nhit

Neutron nhit

Neutron phn hch

Ph phn hch

Ph 1/E

PhMaxwell

kTn

kTn

ECd

(E)

(log)

E, eV(log)Hnh 4.1: S ph thng lng neutron ca mt l phn ng

phn hch ht nhn


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E2sinhe484,0)E('E

ff

= (4.6)

- Ph phn hch ca CranbergE29,2sinhe453,0)E(' 965,0/Eff

= (4.7)- Ph phn hch ca Grundl v Usner

E776,0

ff eE77,0)E('=

(4.8)Trong cc cng thc trn, E nng lng neutron (Mev); f(E) thng lng

neutron phn hch cho mi khong n v nng lng ti nng lng E; f(E) thnglng neutron phn hch ton phn.

4.3. Tit din phn ng vi neutron4.3.1. nh ngha

Nu mt bia vi N ht nhn trong mi cm3, mi ht c mt vng hiu dng v cbn knh RA th:

2R= (4.9)c bn vo vi mt chm neutron thng lng (n cm-2 s-1 ). S va chm s cho bi:

S va chm (cm-3s-1)= Ncol = ..N (4.10)(Gi thit rng bia rt mng cho s neutron va chm ht s nguyn t trong bia).

S va chm t l vi thng lng neutron v s nhn bia N trong mi cm3. Hng s tl c xem nh l tit din ca nhn. Tit din va chm c xc nh nh sau:

)cm(N)cm.n(

)s.cm(N

)cm( 32

13

col2

col

= (4.11)

n v ca l cm2 hay barn ( 1b = 10-24 cm2)1mb = 10-3b, 1b = 10-6b

Trong va chm ca neutron vi nhn bia th c vi tn x xy ra, n hi (n, n) haykhng n hi (n, n'), pht photon hay cc ht mang in (n, ), (n, p), (n, ),... Nu brng mc ring phn i vi mi qu trnh xy ra l , p, , n,...th t s tng ng chomi thnh phn phng x x ( x = , p, n, ,...) l x/

vi = + p + + n (4.12)Khi :

(n, x) = cx / (4.13)

(2.7)c gi l xc sut hnh thnh ht nhn hp phn.

4.3.2. Tit din neutron nhit v trn nhit

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Neutron nhit c nng lng 0,025eV (v0 = 2200 m/s). Neutron trn nhit c nnglng t 0,1eV n 1eV, trong vng ny, tit din phn ng t l vi E-1/2 hay v-1.

Neutron nhit hay trn nhit ch yu cho phn ng (n,).

a - Tit din phn ng- L tit din m sau qu trnh phn ng, neutron khng c ti pht x, ngha l

ch c phn ng (n, ), (n, p), (n, ). Thc t tt c tit din phn ng i vi nhn c Z< 88 l phn ng (n,). Tc phn ng thng lng neutron nhit c th tnh t titdin 0 vn tc v0vi iu kin (v) ~ 1/ v.

- Tit din hp thu absl tit din phn ng ca nhng ht m c kh nng hp thuneutron. i vi mc ch phn tch kch hot, tit din hp thu l quan trng nht tnhton hiu ng t che chn neutron.

- Tit din kch hot act : i vi neutron nhit ch yu l (n, ), i khi cng cth l (n, p), (n, ) v (n, f).

b - Tit din tn xTit din tn x thng l hng s i vi neutron c nng lng nm trong vng

nhit, iu quan trng i vi cc ht nhn nh. Trong vt l, c vi loi tn x vi cccc tit din tng ng: tit din tn x kt hp (coherent) ( coh), tit din nguyn t t dofa, tit din tn x trung bnh tb v tit din tn x vi phn ( d / d ).

c -Tit din tn x ton phnTit din tn x l tng ca tit din hp thu v tit din tn x trung bnh. c

nh ngha theo cng thc : T = abs + tbs (4.14)

d - Tit din v m Tt c cc tit din c nh ngha trn c gi l tit din vi m, cn tit din

v m c nh ngha nh sau :

A

NN A

== (4.15)

Vi: l mt ht ( g.cm-3);A l khi lng nguyn t;

NA l s Avogadro;N l s nguyn t trong mi cm3; c th nguyn l [ cm-1 ], tnh bng cm2.

Mt cch tng qut, nu trong mu c n ht nhn khc nhau th tit din v m c

tnh bi: =

=

n

1iii

N (4.16)

4.3.3. Tit din tch phn cng hngTrong vng nng lng 1eV < E < 1Mev, tit din neutron khng tun theo lut 1/v

m c nhng ch cng hng ring bit. Tit din ton phn T thay i nhanh theo nnglng neutron v khc nhau ng vi cc ht nhn khc nhau. Gi tr T khng th d onc cho mt nguyn t cho trc. Cc cng hng ch yu do vic bt neutron (n,). Do, trong vng nng lng ny, ta c th cho rng > n > p v , bi v p v rt

49


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nh ng vi vng nng lng ny. Do , cc neutron trung bnh khng nng lngkch thch nhn nn cho php proton v alpha xuyn qua ro Coulomb quanh nhn.

R rng tc phn ng trong vng nng lng neutron cng hng c th tnh

c nu nh phn b nng lng neutron v tit din (E) bit trc. Trong vng nnglng ny tit din neutron khng tun theo lut 1/v m c nhng ch cng hng, titdin cho mt loi phn ng c xc nh

Cd Cd

2Mev

x x x

E E

dE dEI (E) (E)

E E

= (4.17)Ch s x cho bit loi phn ng ht nhn (hp th, tn x,...) v Ixc gi l tch

phn cng hng trn Cadmium.ECd l nng lng ngng khi che tm Cadmium.Tch phn cng hng bao gm s phn b cng hng v ui tun theo lut 1/v.

Do , trong trng hp c mt nh cng hng n trn ng cong (E) th tit dintrong vng cng hng c th chia l hai phn :

Mt phn do s phn b r(E), c cho bi cng thc Breit-Wigner Mt phn do s phn b 1/v(E). Do , khi khng c cng hng th tit din

tun theo s bin i 1/v.Vy, ta c th vit li (4.17) nh sau :

Cd Cd Cd

x 1/ v r

E E E

dE dE dEI (E) (E) (E)

E E E

= = + (4.18)Hay ta c th vit gn li : I = I1/v + I (4.19)

=

cDEv/1v/1 E

dE

)E(I (4.20)

=

cDEr

E

dE)E('I (4.21)

Tr s ca I i vi mt ht nhn c cho trc v sau khi chun ha ngng Cadmiumbng 0,5 eV. Cc gi tr I, I v I1/v ca vi ht nhn cho bng 4.1

Bng 4.1: Cc thng s cng hng ca vi ht nhnHt

nhnT1/2 E0

(eV)I

( barn)I1/v ( barn) I = I + I1/v 0

(barn)a b a b

115

In 54,2 pht 1,457 2000 300 60 68 2060 300 2068300 166 2197Au 250 ngy 4,906 1505 20 38 0,2 44 0,2 1543 20 155120 98,8 0,359Co 5,26 nm 133 50 12 15 17 65 12 67 12 37,2 1,563Cu 12,8 gi 580 2,4 0.5 1,7 2 4,1 0,5 4,4 0,5 4,51 0,23

a: ngng Cadmium 0,68 eV ng vi a dy 1mmb: ngng Cadmium 0,52 eV ng vi a dy 1mm

4.3.4. Tit din phn ng vi neutron nhanh (En > 1Mev )Trong trng hp ny ta ch yu kho st i vi neutron c nng lng 14 Mev.

Trong vng nng lng ny, cc neutron c to ra t my pht neutron da theo phnng T(d,n)

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4.3.4.1. Tit din ton phn T : vi neutron 14 Mev, T c th tnh c d dngcho cc nguyn t cho trc, cn cc neutron nhit v trn nhit th khng tnh c trongvng nng lng ny. Tit din ton phn c nh ngha:

T = 2 R2A (4.22)Vi RA l bn knh ht nhn, RA 1,5x10-13 A1/3 (cm)iu ny c ngha l T1/2 t l vi A1/3 v tt c cc nguyn t theo tnh ton th T

c gi tr t 1,5 barn n 6 barn ng vi nng lng neutron 14 Mev.4.3.4.2. Tit din phn ng (n, ) : Ti nng lng neutron 14 Mev, xc sut xy

ra phn ng (n, ) nh. Hnh 1.2 cho ta thy rng tit din phn ng ny gim rt nhanh khinng lng neutron tng. Do , ti nng lng 14 Mev, tit din phn ng ny xc nhc bng cch ngoi suy tuyn tnh hm Log(T) theo Log En

4.3.4.3. Tit din (n, 2n): Ti neutron 14 Mev, cc phn ng khc c th tnhc tit din, c bit l phn ng (n, 2n). Trong hu ht trng hp, ta thy rng phn

ng (n, 2n) c tit din gn bng 12

tit din ton phn, tc l

12

.T R2 (4.23)

R rng, tit din phn ng (n,2n) ph thuc vo s neutron d trong nhn bia.Neutron th hai c th ri khi ht nhn d dng hn nu nh neutron d ln hn. Php oneutron d ngi ta thng chn (N-Z)/ A.

Theo mi quan h bn thc ngim gia (n,2n) v (N-Z)/A c cho bi: Vi (N-Z)/A 0,07 :

Log (n,2n)14Mev =2,473 + 3,48N Z

A

(mb). (4.24)

Vi (N-Z)/A < 0,07:

Log (n.2n)Mev = -0,341 +42N Z

A

(mb) (4.25)

4.3.4.4. Cc phn ng (n, p), (n, )Cc phn ng (n,p) (n,) cng l phn ng ngng. Trong vng nng lng 14

Mev, tit din phn ng (n, p) v (n, ) thng c tnh theo t s i vi n.e v ccho bi:

51

10210110-110-2

10-1

1

10

E (Mev)

Hnh 4.2 : Tit din (n,) ca Au ti nng lng neutron cao

(

barn)


52/137

max

n.e

(n,p) N Zk exp( 25,2 )

A

=

(4.26)

vi: n.e = (n, 2n) + (n, p) + (n, ) +...... (4.27)

Ti neutron 14 Mev th : n.e (14 Mev) = (0,12 A1/3 + 0,21 )2 barn

vi nhn l-chn k(o-e) = 0,25 v nhn chn chn k(e-e) = 0,47.Ti neutron 14 Mev, tit din phn ng (n, p) cho bi:

n.e

(n,p)(14Mev) N Zk exp( 31,1 )

A

=

(4.28)

Vi vi nhn l-chn k(o-e) = 0,5 v nhn chn chn k(e-e) =0,83.

V d:Gi tr thc nghim ca (n, p) (14 Mev) =13 mb.Gi tr tnh : A=109 , Z=47 , N=62n.e =1,96 b , (n, p) (14 Mev) =11,2 mb.

Tng t, i vi phn ng (n, )

n.e

(n, )max N Zk exp( 37,7 )

A

=

(4.29)

Vi: k(o-e) =0,55 v k(e-e) =0,92

n.e

(n, )(14Mev) N Z

k exp( 37,8 )A

= (4.30)Vi: k(o-e) =0,5 v k(e-e) =0,83

4.4. Tc phn ng vi neutron4.4.1. Tc phn ng vi neutron nhit (lut 1/v)

Tc phn ng R cho mi nhn nguyn t c th tnh c nu nh phn b nnglng neutron (E) v (E) bit trc, tc phn ng khi l :

dR = (E) (E) dE (4.31)Hay dR= (v) v n(v) dv (4.32)Ly tch phn phng trnh (4.32), ta c :

0

R (v)vn(v)dv

= (4.33)Vi n(v)dv l mt neutron c vn tc gia v v v + dv

Khi 1/v th (v) = 0 0v

v

(4.34)

Vi 0 l tit din phn ng ca neutron vn tc v0 = 2200 ms-1

Vy, tc phn ng ca neutron nhit vi nhn bia c tnh bi:

0 0 0 00

R v n(v)dv nv

= = = 0th (4.35)

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vi0

n n (v)dv

= c gi l mt neutron nhit, th gi l thng lng neutron

nhit.

4.4.2. Tc phn ng ca ht nhn khi chiu x trong l phn ngKhi chiu x nhn bia trong l phn ng, tc phn ng ca mi ht nhn nguyn t

c cho bi :

1

1

1

cd

v

0 0 v

v

0 0 e

0 E

th 0 0 e th 0 e

R n(v)v (v)dv n(v)v (v)dv n(v)v (v)dv

(E)v n(v)dv dE

E

n v I I

= = +

= +

= + = +

(4.36)

Trong : I =CdE

(E)dE

E

; (4.37)

nth = mt neutron ng vi nng lng di ngng Cd;v1 = vn tc ng vi nng lng ngng Cadmium ( ECd=0,55eV);v0 = 2200m/s v 0= tit din neutron ti vn tc bng 2200m/s.

( C th vit th = 0)e = thng lng trn Cadmium trong mi khong nng lng trn n v logarit

(

e > ECd).

Trn thc t, ph neutron trong vng trn nhit c th lch khi gi tr ban u ca n,khi tit din tch phn cng hng phi thay i v ph thuc vo v tr chiu x trongl phn ng. Tc phn ng lc ny c tnh theo cng thc:

)(IR e0th += (4.38)trong , l mt hng s ph thuc v tr chiu x trong l phn ng v c gi l h slch ph neutron trn nhit.

Nu thay 0 bng tit din kch hot l reactor, ta c :R = nthv0reactor = threactor (4.39)

vi: )(Ith

e0reactor

+= (4.40)

T phng trnh (4.39) ta c th tnh c tc phn ng nu nh th v e/th chotrc.

4.5.Mt vi ng dng ca phn ng ht nhn vi neutron4.5.1. T s cadmium (CR) v t s thng lng neutron nhit/cng hng

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Nh ta bit, cadmium c tit din hp th rt cao i vi neutron c nng lng 0,4 0,5 eV. Ngng hiu dng ca Cd ph thuc vo b dy ca lp Cd v ph thuc vodng hnh hc ca n.

Nu chiu mu c bao ph lp Cd dy 0,7mm n 1mm th cc neutron nhit honton b hp th, v th m ph

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