Sơ lược phương pháp phân tích kích hoạt neutron

S lc v phng php phn tch kch hot neutron

ng Nguyn [email protected]

Ngy 15 thng 5 nm 2014

Mc lc

1 M u 2

2 Cc phng php phn tch NAA 32.1 Theo nng lng neutron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Theo tia gamma pht ra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.3 Theo k thut chiu x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.4 Gii hn pht hin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3 Ngun neutron v h o s dng trong NAA 53.1 Ngun neutron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.2 H o . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4 Chun b mu 84.1 Mu rn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.2 Mu lng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94.3 Mu kh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

5 Nguyn tc ca NAA 105.1 Phn ng kch hot neutron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105.2 Thng lng neutron ca l phn ng . . . . . . . . . . . . . . . . . . . . . . . . 115.3 Quy c Hogdahl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125.4 H s Westcott . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135.5 Phng trnh kch hot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

6 Cc phng php chun ha trong phn tch kch hot neutron 156.1 Phng php tuyt i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156.2 Phng php tng i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166.3 Phng php chun n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166.4 Phng php k0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176.5 Phng php k1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186.6 Phng php ki . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

7 Hiu chnh nhiu trong phn tch kch hot neutron 197.1 Hiu ng t che chn neutron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207.2 Hiu ng t chy (burn-up) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217.3 Phn ng nhiu gy bi neutron nhanh . . . . . . . . . . . . . . . . . . . . . . . 227.4 Hiu ng nh hng ph gamma . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Ti liu tham kho 22

1

ng Nguyn Phng Ti liu ni b NMTP

1 M u

Phn tch kch hot neutron (Neutron Activation Analysis NAA) c Georg von Henvesyv Hilde Levi gii thiu ln u nm 1936 nh l mt phng php dng nh tnh v nhlng a nguyn t (multi-element). Phng php ny da trn phn ng gia neutron v htnhn bia, neutron ti s b nhn bia bt v to thnh nhn hp phn, nhn hp phn ny sau phn r pht ra cc tia gamma c trng (Hnh 1). Da vo hot cc tia gamma ny, tac th bit c hm lng ca cc thnh phn nguyn t cha trong mu.

Hnh 1: Minh ha phn ng kch hot neutron

NAA l mt phng php phn tch c nhy cao m cc phng php phn tch khc khc th t c. Thm vo , vi chnh xc v tin cy ca n, NAA c cng nhn nh lmt phng php chun kim tra chnh xc ca cc phng php khc. NAA c ngdng rng ri trn ton th gii trong rt nhiu lnh vc, chng hn nh trong a cht, mitrng, sinh hc,...

Nhng yu t cn thit c bn c th thc hin phn tch thnh phn mu bng phngphp NAA l

Ngun neutron (l phn ng, my gia tc, cc ng v pht neutron,... ).

Dng c thch hp o tia gamma (h ph k o gamma, chng trnh x l ph,...).

S hiu bit v cc phng trnh phn ng xy ra khi nhn neutron tng tc vi nhnbia.

Hm lng nguyn t trong mu phn tch c tnh da theo phng trnh kch hot. u imca phng php ny l vic khng cn phi ph hy mu trong qu trnh phn tch, do nc s dng nhiu trong phn tch cc mu c vt hoc ngh thut. Ngoi ra, NAA cn c thc s dng xc nh hot ca cc mu phng x thnh phn. Cc lnh vc ng dngca NAA gm c

Kho c: phn loi v tm ngun gc cc mu vt kho c (mu t st, gm, thutinh, kim loi, , xng,...).

iu tra php l: phn tch cc vt chng (thuc sng, n, mng tay, tc, thuc,...).

Khoa hc a cht: nghin cu qu trnh hnh thnh cc loi khc nhau, xc nhhm lng cc nguyn t vt trong mu du th, t .

Vt liu bn dn: xc nh hm lng tp cht trong vt liu bn dn, phn tch vtliu.

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Cng nghip: phn tch nguyn t, kim tra qu trnh (bng chuyn, ng kn,...), thmd qung,...

Nng nghip: nghin cu cc qu trnh nng nghip v cy trng, xc nh cc nguynt vt trong cc loi cy.

Mi trng: xc nh cc nguyn t nhim trong mi trng, phn tch cc mu bikh,...

. . .

Ti liu ny c vit nhm mc ch cung cp cho cc bn mt ci nhn tng qut v phngphp kch hot neutron (NAA), trong tp trung trnh by ch yu v phng php kch hotneutron dng c (INAA) s dng neutron nhit v trn nhit l phng php c s dng phbin nht hin nay trong phn tch kch hot neutron.

2 Cc phng php phn tch NAA

Vic phn loi cc phng php NAA ch yu l da vo cch thc tin hnh th nghim chnghn nh s dng khong nng lng ca neutron, cch thc o c gamma phn r, x lmu,... Di y l mt s cch phn loi NAA chnh

2.1 Theo nng lng neutron

Kch hot neutron nhit v trn nhit: ph nng lng ca neutron c chia lm 3 vngchnh: vng nhit (thermal region), vng trn nhit (epithermal region) hay cn gi l vngtrung gian (intermediate region) hoc vng cng hng (resonance region), v nhanh (fastregion)1. Thng thng trong kch hot NAA, cc neutron tham gia phn ng (n,) cnng lng nm trong vng nhit v trn nhit.

Kch hot neutron trn nhit (Epithermal Neutron Activation Analysis ENAA): ch sdng neutron nm trong vng trn nhit (c ng nng t 0.5eV n 0.1MeV ).

Kch hot neutron nhanh (Fast Neutron Activation Analysis FNAA): ch s dng neu-tron nm trong vng nhanh (c ng nng trn 0.1MeV ).

2.2 Theo tia gamma pht ra

o gamma tc thi (Prompt Gamma Neutron Activation Analysis PGNAA): o cc tiagamma phn r ngay trong qu trnh chiu x neutron. Phng php ny thng c pdng cho cc nguyn t c tit din bt neutron cao, cc nguyn t c thi gian phn rrt ngn hay xc sut phn r pht gamma rt thp.

1Trong thc t c rt nhiu cch chia vng nng lng neutron khc nhau ty vo mc ch s dng. V dnh ta c th chia nh sau:

Neutron lnh (Cold neutron) 0.0 0.025eV Neutron nhit (Thermal neutron) 0.025eV Neutron trn nhit (Epithermal neutron) 0.025 0.4eV Neutron trong vng hp th Cadmium (Cadmium neutron) 0.4 0.6eV Neutron trn vng hp th Cadmium (EpiCadmium neutron) 0.6 1eV Neutron chm (Slow neutron) 1 10eV Neutron cng hng (Resonance neutron) 10 300eV Neutron trung gian (Intermediate neutron) 300eV 0.5MeV Neutron nhanh (Fast neutron) 0.5 20MeV Neutron tng i tnh (Relativistic neutron) > 20MeV

3


o gamma tr (Delay Gamma Neutron Activation Analysis DGNAA): o cc tia gammaphn r sau khi qu trnh chiu x neutron kt thc. u im ca phng php ny l cth tng nhy trong vic xc nh cc nguyn t c chu k bn r di, do ta c th mu kch hot ch mt thi gian trc khi o loi cc ng v c thi gian sng ngn.

2.3 Theo k thut chiu x

Kch hot dng c (Instrumental Neutron Activation Analysis INAA): chiu x trctip mu khng qua x l ha hc.

Kch hot ho phng x (Radiochemical Neutron Activation Analysis RNAA): c sdng cc phng php x l ha hc loi b cc thnh phn gy nhiu hay tng tp trung ca cc nguyn t cn quan tm trc khi chiu x.

2.4 Gii hn pht hin

Cc loi nguyn t m phng php NAA c th c s dng xc nh hm lng gm c

Cc nguyn t chnh (major elements): cc nguyn t c hm lng ln (vo c %) trnb mt tri t.

Cc nguyn t ph (minor elements): cc nguyn t c hm lng tng i nh (khongt 0.1% n 1%) trn b mt tri t.

Cc nguyn t vt (trace elements): cc nguyn t c hm lng vo c phn triu (partper million ppm). Thng thng hm lng ny l di 100ppm (hay 0.01%), tuy nhini vi cc mu a cht th i khi hm lng l di 1000ppm (hay 0.1%).

Cc nguyn t t him (rare earth elements REE ): c 17 nguyn t bao gm ccnguyn t thuc h lathanides (Z t 57 n 71) v hai nguyn t scandium v yttrium,thng thng c hm lng vo c phn triu n phn nghn (mg/g).

Hnh 2: Gii hn pht hin ca cc ng v trong phng php NAA

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3 Ngun neutron v h o s dng trong NAA

3.1 Ngun neutron

Cc ngun neutron thng c s dng trong phn tch kch hot NAA bao gm nhiu loikhc nhau, t cc l phn ng c kch thc ln n cc ngun ng v c kch thc nh cth d dng c s dng trong cc phng th nghim.

Thit b kch thc ln

L phn ng phn hch (nuclear fission reactor): cc phn ng phn hch bn trong lphn ng ht nhn cung cp mt lng ln neutron vi nhiu mc nng lng khc nhau(Hnh 3). Thng lng neutron t cc l phn ng vo khong 1015n/(cm2s).

Hnh 3: Mt ct ngang ca mt li l phn ng cung cp ngun neutron

H thng nhit hch (nuclear fusion system): s dng cc phn ng nhit hch kt hpcc ng v nng ca hydrogen to ra neutron, v d nh cc phn ng d(d,n)3He hayt(d,n)4He. Cc thit b nhit hch (fusor) thng mi c th cung cp thng lng neutronln ti 109n/s, tng ng vi khong 105n/(cm2s).

My gia tc ht nng lng cao (high energy particle accelerator): s dng chm protonc nng lng cao t cc my gia tc ht ph v ht nhn nguyn t v gii phngneutron (Hnh 4). Thng lng neutron t c c th ln ti 1017n/(cm2s).

Thit b kch thc trung bnh

Thit b to plasma (plasma focus device hay Farnsworth-Hirsch fusor): l cc thit bdng gia tc in t v nn cc kh deuterium hay tritium, to thnh mt chm plasmabc x tia X v neutron.

My gia tc ion nh (light ion accelerator): dng gia tc cc ht nh nh hydrogen,deuterium, tritium, lithium, beryllium hay cc ng v c Z nh khc ln mc nng lngkhong vi MeV v cho p vo bia ht nhn nh to ra cc phn ng pht neutronnh (p,n), (d,n), (t,n).

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Hnh 4: S to chm neutron t my gia tc proton

H thng to bc x quang neutron hay quang phn hch (high energy bremsstrahlungphotoneutron/photofission system): cc neutron c to ra thng qua phn ng cnghng ln (giant dipole resonance) khi nng lng photon ti ln hn nng lng lin ktca cc nucleon trong ht nhn (khong t 7 n 40MeV ), khi ht nhn s hp thphoton v pht ra neutron (photoneutron) hay phn hch (photofission).

Thit b kch thc nh

ng v phn hch t pht (spontaneous fission isotope): ngun ng v phn hch tpht ph bin nht l californium (252Cf) c chi k bn r 2.645 nm, thng lng neutronpht ra thng thng vo khong t 107 n 109n/s. Ngoi ra cn c cc ng v phnhch t pht khc nh cc ng v ca uranium (235U, 238U), plutonium (239Pu, 240Pu),curium (250Cm).

ng v phn r alpha cng vi ht nhn c Z thp: c to ra bng cch kt hp mtng v phn r alpha vi mt ng v c kh nng tham gia phn ng (,n), neutron cto ra c thng lng vo khong 106 n 108n/s. Cc ngun thng dng l plutonium-beryllium (Pu-Be), americium-beryllium (Am-Be) v americium-lithium (Am-Li).

ng v phn r pht photon nng lng cao vi beryllium hay deterium: s dng cc bcx gamma c nng lng ln hn nng lng ln kt ca neutron trong ht nhn btneutron ra khi ht nhn, cc phn ng ph bin nh

9Be+ (1.7MeV ) n+ 2 4He2H + (2.26MeV ) n+ 2 1H

3.2 H o

Phn ln cc h o s dng trong phn tch kch hot neutron l cc h o gamma. Hnh 6 trnhby s ca mt h o kch hot neutron v Hnh 7 cho v d mt ph gamma thu c bih o ny. Ngoi ra, trong mt s trng hp cc h o alpha v beta cng c s dng ghinhn cc ht v phn r t ht nhn kch thch, tuy nhin vic o c ny khng ph binlm do cc ht v d dng b hp th trong mu.

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Hnh 5: Cu trc ngun ng v 252Cf (tri) v Pu-Be (phi)

Hnh 6: S h phn tch kch hot neutron

Cc loi detector thng c s dng trong phn tch kch hot gm c

Detector kh ion ho (gas ionization detector) t c s dng.

Detector nhp nhy (scintillation detector) ch yu l detector sodium iodide (NaI(Tl)).

Detector bn dn (semiconductor detector) c hai loi l silicon v germanium, tuy nhinloi germanium thng c a chung hn do kh nng ghi nhn gamma tt hn. Ccloi detector germanium c s dng ph bin l Ge(Li) v HPGe. Cu hnh ca detectorcng l mt trong nhng yu t c xem xt khi tin hnh xy dng h o cho phn tchkch hot neutron:

Dng phng (planar type) b mt tip xc ln, c th d dng t gn mu trongqu trnh chiu x cho nn thng c s dng cho PGNAA.

Dng ging (well type) c dng hnh hc o bao quanh mu, b mt tip xc ln nndng tt cho DGNAA.

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Hnh 7: V d ph gamma thu nhn c t phn tch kch hot neutron

Cc loi detector ghi nhn , i km vi gamma (t c s dng).

4 Chun b mu

4.1 Mu rn

Cc mu rn thng thng tn ti dng khi hoc dng bt. Cch thc x l cc mu dngny nh sau:

Dng khi

C th c bc trong l nhm hoc b trong hp nhm chiu x.

Cc mu qu ln c th c gim kch thc bng cch nghin, ct, khoan,... trc khichiu x (Hnh 8).

Cc mu rn c th c gia cng thnh cc dng a, dy, ng tr,... trc khi em ichiu x c hoc khng c hp cha (Hnh 9).

Hnh 8: Mt mu c ct ra t mt tm g tm du vt ca vng

Dng bt

Mu bt thng c cha trong cc hp hoc ng thch hp v c chiu x trc tipt l hay my gia tc (Hnh 10).

8


Hnh 9: Mu Rhemium dng dy di 1 cm (hnh tri) v l vng (hnh phi)

C th gim kch thc mu bt bng cch nn li di dng vin hoc a c cdng hnh hc chiu v o nh nht (Hnh 11).

Hnh 10: ng dng mu dng tr

Hnh 11: Mu bt dng a trn

4.2 Mu lng

Cc mu lng c th dng cht lng hon hon hoc dng keo. Cch thc x l cc mu dngny nh sau:

Dng lng

Mu dng ny phn ln c ng trong nhng ng lm bng thch anh (SiO2) haypolyethylene khi chiu x.

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trnh s nhim bn t vt cha ngi ta c th lm ng lnh mu trong sut thigian chiu x v b lp bn ngoi trc khi o.

Cc mu dng lng c th tp trung li bng cch lm cho bc hi.

Dng keo

Cc mu sinh hc thng c dng ny, do vy n c th ct c. trnh nhim bn,c th dng dao thch anh hay plastic.

Nu khng th chiu x mt cch trc tip, c th lm kh mu trc khi chiu.

Mu dng ny thng c cha trong nhng hp polypropylene.

4.3 Mu kh

Cch thc x l cc mu dng kh nh sau:

Mu kh thng c ng trong nhng ng thch anh.

Chiu x trc tip mu kh ch c s dng cho cc kh him. Cc kh cn li thngc chuyn thnh dng rn.

Hnh 12: ng thch anh ng mu dng lng hoc kh

5 Nguyn tc ca NAA

5.1 Phn ng kch hot neutron

Phng php NAA da trn phn ng ca neutron vi ht nhn nguyn t, c bit l phnng (n,). Tc phn ng (reaction rate) c tnh bng cng thc

R =

0

(v)(v)dv = 0

(E)(E)dE (1)

Trong (v) tit din phn ng (n,) vn tc neutron v(E) tit din phn ng (n,) nng lng E(v) thng lng neutron vn tc v(E) thng lng neutron nng lng E

Hm tit din t l nghch vi vn tc hay cn bc hai ca nng lng

(v) 1/v hay (E) 1/E

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5.2 Thng lng neutron ca l phn ng

Phn ln cc phn tch NAA hin nay u c thc hin trn l phn ng ht nhn, do trong phn ny ta s xem xt phn b thng lng ca neutron trong l phn ng. Phn bny c th c chia lm 3 phn chnh (Hnh 13)

Neutron nhit (0 < E 0.1eV ): tun theo phn b Maxwell - Boltzmann. Neutron trn nhit (0.1eV < E 100keV ): tun theo phn b 1/E. Neutron nhanh (100keV < E 20MeV ): tun theo phn b Watt.

Hnh 13: Phn b thng lng neutron ca l phn ng

Neutron nhit cc neutron chuyn ng nhit c vn tc trung bnh v0 = 2200m/s v nnglng trung bnh E0 = 0.0253eV . Mt phn b ca cc neutron nhit tun theo phn bMaxwell Boltzmann

n(E) =2pin

(pikT )3/2eE/kT

E (2)

vi n =0 n(E)dE l mt neutron ton phn.

Thng lng neutron nhit c tnh theo cng thc

th = n(E)E = n(v)v (3)

Neutron trn nhit Thng lng phn b theo 1/E

e(E) =eE

(4)

Trong thc t th thng lng phn b gn ng theo dng

e(E) =eE1+

(5)

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Neutron nhanh Thng lng phn b theo Watt

f (E) = 0.484feE sinh

2E (6)

Ngng ct Cadmium trong phn tch NAA s dng neutron trn nhit (ENAA), ngi tathng chiu x mu c bc trong mt lp Cadmium c b dy thng thng t 7 1.5mm(Hnh 14). Lp Cadmium ny s hp th hu ht cc neutron nhit (c nng lng di mc0.4 0.6eV ) chiu x t l, t s neutron nhit i qua c lp Cadmium l 1/2000 i vi bdy 7mm v 105 i vi b dy 1.5mm.

Hnh 14: Ngng ct Cadmium i vi thng lng neutron t l phn ng

5.3 Quy c Hogdahl

Quy c Hogdahl (Hogdahl convention) l phng php tnh tc phn ng ca hn hpneutron nhit trn nhit (c th p dng i vi nng lng neutron ln ti c 1.5eV ).Phng php ny gi s rng tit din kch hot neutron tun theo quy lut 1/v (hay 1/

E)

(vn) =0v0vn

(7)

Trong tit din phn ng kch hot neutronvn vn tc neutronv0 vn tc trung bnh ca neutron 20C (2200m/s)0 tit din phn ng kch hot neutron vn tc v0

Cng thc tnh tc phn ng (1) c vit li nh sau

R =

ECd0

(E)(E)dE + ECd

(E)(E)dE (8)

Trong ECd = 0.55eV l nng lng ct Cadmium (Cadmium cut-off energy), chia ph phnb neutron thnh hai thnh phn neutron nhit (di 0.55eV ) v trn nhit vi thng lngth v e tng ng.

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T (7) v (8) ta cR = th0 + eI0() (9)

vi

I0() =

[(I0 0.4290)E +

0.4290

ECd(2+ 1)

](1eV ) (10)

E nng lng cng hng hiu dngI0 tch phn cng hng trn trong trng hp = 0

I0 =

ECd

(E)dE

E(11)

Cng thc (9) c th vit li nh sau

R = th0 (1 +Q0()/f) (12)

Trong , h s f l t s gia thng lng neutron nhit v thng lng neutron trn nhit

f =the

(13)

H s Q0 c nh ngha

Q0() =I0()

0(14)

5.4 H s Westcott

Gi thit tit din phn ng (n,) trong vng neutron nhit v trn nhit tun theo quy lut1/v ng cho phn ln cc ht nhn. Tuy nhin, n khng ng trong mt s trng hp nhphn ng 176Lu(n,)177Lu hay 151Eu(n,)152Eu. hiu chnh cho cc trng hp ny, ta cth s dng hnh thc lun Westcott (Westcott formalism).

Hnh thc lun ny p dng cho cc tit din khng tun theo quy lut 1/v thng qua vic ara mt h s Westcott g(Tn) ph thuc vo nhit neutron Tn. H s ny biu th lch catit din hiu dng ra khi quy lut 1/v.

Vi vic hiu chnh da trn hnh thc lun Westcott, h s Q0() c thay th bng h ss0() v h s 1/f c thay th bng r()

Tn/T0, cng thc tnh tc phn ng (12) tr

thnhR = nv00

[g(Tn) + r()

Tn/T0s0()

](15)

Trong nv0 thng lng Westcottn mt neutron ton phng(Tn) h s Westcotts0() t s ca tch phn cng hng suy gim

5.5 Phng trnh kch hot

Trong phn tch kch hot neutron, ta c th thit lp mi quan h gia tc phn ng R vs m Np ca nh ghi c

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Trong tng hp chiu trn

R =Np/tc

S.D.C.N..p(16)

Trong trng hp chiu bc Cd

Re =

(Np/tc

S.D.C.N..p

)Cd

(16)

Trong tc thi gian o

N =.w

M.NA s Avogadro

ph cp ca ng v biaw khi lng nguyn t c chiu x (g)M khi lng nguyn t ca nguyn t biaS = 1 eti h s bo ha (ti l thi gian chiu)D = etd h s r (td l thi gian r)

C =1 etctc

h s o (hiu chnh cho s phn r trc khi o)

cng tuyt i ca tia c op hiu sut ghi ti nh nng lng tia

Thay cng thc tnh ca N vo (16) ta c

R =Np/tcS.D.C.w

.M

NA..p.(17)

Trong khi , R cn c tnh theo cng thc (9), trong trng hp c tnh n s t che chnneutron (neutron self-shielding) ta nhn thm cc h s hiu chnh Gth v Ge tng ng

R = Gthth0 +GeeI0() (18)

Cc h s hiu chnh s t che chn i vi neutron nhit Gth v trn nhit Ge c gi tr gnbng 1 trong hu ht cc trng hp, c bit l i vi cc mu sinh hc. H s ny c gi trkhc 1 trong trng hp mu kch hot c cha mt lng ln cc ng v c tit din hp thneutron cao. Phn 7.1 s trnh by cng thc tnh cc h s hiu chnh ny trong mt s hnhhc mu c bit.

T (17) v (18) ta suy ra

Np/tcS.D.C.w

.M

NA..p.= Gthth0 +GeeI0() (19)

hayNp/tcS.D.C.w

.M

NA..= [Gthth0 +GeeI0()] p (19)

Ta t Asp =Np/tc

S.D.C.wl tc m ring trong trng hp chiu trn.

T (19) ta c

Asp =NA..

M[Gthth0 +GeeI0()] p (20)

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Trong trng hp chiu bc Cd

(Asp)Cd =NA..

MGeFCdeI0()p (20)

T ta suy ra hm lng nguyn t c tnh theo cng thc

w(g) =Np/tcS.D.C

.M

NA...

1

[Gthth0 +GeeI0()].

1

p(21)

V trong trng hp chiu bc Cd

(w)Cd (g) =Np/tcS.D.C

.M

NA...

1

GeFCdeI0().

1

p(21)

Hai phng trnh (21) v (21) chnh l nhng phng trnh c bn trong phn tch kch hotneutron.

6 Cc phng php chun ha trong phn tch kch hot neutron

Cc phng php chun ho trong phn tch kch hot neutron gip cho quy trnh phn tchc thc hin mt cch nhanh chng v hiu qu hn. Do neutron c kh nng m xuyn caov bc xa tia gamma, hm lng nguyn t phn tch c khng b nh hng bi cht nnnn cc phng php chun ho c th c p dng mt cch d dng v chnh xc. Trongphn tch kch hot neutron, ngi ta a ra mt s phng php chun ho nh

Phng php tuyt i

Phng php tng i

Phng php so snh n

Phng php k0

Phng php k1

Phng php ki

6.1 Phng php tuyt i

y l phng php chun ho c p dng sm nht. Trong phng php ny, hm lngnguyn t c tnh mt cch trc tip thng qua cc thng s ht nhn, trng neutron vcc s liu o c c bi h ph k gamma.

Hm lng nguyn t c th c tnh bng vic chiu km mu cn phn tch vi mt monitorchun (c k hiu l *). Theo phng trnh (21), khi lng monitor chun c tnh nh sau

w(g) =(Np/tcS.D.C

).

M

NA...

1[Gthth

0 +G

eeI

0 ()

] . 1p

(22)

Chia (22) cho (21) v thay w = W , vi l hm lng (g/g) v W l khi lng mu (g), saukhi sp xp li ta c

(g/g) =

Np/tc

W.S.D.CAsp

.M..

M...[Gthth

0 +G

eeI

0 ()]

[Gthth0 +GeeI0()].pp

(23)

15


Nhn (23) vi 0/0 v e/e th phng trnh khng thay i v sp xp li ta c

(g/g) =

Np/tc

W.S.D.CAsp

.M...0M...0

.[Gthf +G

eQ0()]

[Gthf +GeQ0()].pp

(24)

vi f =th

e; Q0() =

I0()

0v I0() =

[(I0 0.4290)E +

0.4290

(2+ 1)(0.55)

](1eV ).

Phng php ny c mt nhc im, ta thy rng trong cng thc c bn ca phng phptuyt i, cc s liu ht nhn (M , , 0, ) c xc nh mt cch c lp, do sai s cacc phng php ny s ng gp vo hm lng c tnh v dn n kt qu l sai s ln.Ngoi ra, trong nhiu phn ng kch hot (n,) quan tm, cc thng s 0 v khng c bitmt cch chnh xc do khng th xc nh hm lng da vo cc tia gamma trong phnng ny.

6.2 Phng php tng i

Trong phng php, mt mu chun c hm lng nguyn t cn phn tch bit c chiukm vi mu phn tch. Do xem nh thng lng neutron, tit din, thi gian chiu v ccthng s khc ca php o l nh nhau i vi chun v mu hnh hc o xc nh. T t sdin tch nh ca cc nguyn t ta tnh c hm lng ca nguyn t cn phn tch

(g/g) =

(Np/tc

D.C.W

)x(

Np/tc

D.C.w

)s

(25)

Trong W (g) khi lng muw(g) khi lng ca nguyn t quan tm trong mu chun,

= hm lng khi lng mu chunx k hiu ch mus k hiu ch mu chun

Phng php ny l chnh xc nu thnh phn mu chun tng t nh thnh phn mu cnphn tch. Nu n c p dng cho phn tch a nguyn t th s c mt s bt li do vicchun b mt mu chun c thnh phn tng t mu cn phn tch thng l rt kh khn.

iu cn lu trong phng php ny l mu v chun phi c hiu chnh hiu ng t chechn neutron trong khi chiu v s suy gim gamma trong khi o.

6.3 Phng php chun n

Mt phng php so snh, c gng kt hp hai u im v phng php lun ca phng phptuyt i v chnh xc ca phng php tng i. Phng php ny c a ra ln utin bi Girardi v cng s (1965). Trong phng php ny mu v mt cht so snh bt k(thng chn Au, Zr, Co) c chiu ng thi v cc thng s ht nhn, iu kin chiu v oc gp vo h s k

k =M..0.

M..0..[Gthf +G

eQ0()]

[Gthf +GeQ0()].pp

(26)

16


H s k ca nguyn t chn lm chun i vi tng nguyn t quan tm c xc nh bngthc nghim sau lp thnh bng khi phn tch ngi ta ch cn chiu km mu v nguynt chun chn v dng h s k tnh hm lng ca nguyn t cn quan tm

(g/g) =

Np/tc

S.D.C.WAsp

.1

k(27)

H s k ca phng php ny ph thuc vo dng ph neutron v hiu sut ghi ca detector do hn ch ca phng php ny l khng linh hot cho vic chiu v o bc x.

6.4 Phng php k0

Phng php k0 c A. Simonits v F. De Corte gii thiu vo nm 1975. y l phng phpc s dng khc phc nhc im ca phng php tuyt i v phng php chun n.Ngha l n linh hot hn phng php chun n trong vic thay i iu kin chiu v ong thi chnh xc hn phng php tuyt i.

Trong phng php ny h s k0 c lm cho c lp vi cc h s m t iu kin chiuv o

k0,c(s) =Mc.s.s.0,sMs.c.c.0,c

(28)

c k hiu ch nguyn t so snhs k hiu ch nguyn t phn tch

Phng trnh c bn ca phng php k0 Hm lng ca nguyn t trong mu ctnh bng cng thc

(g/g) =

(Np/tc

W.S.D.C

)a

Asp,m.

1

k0,m(a).Gth,mf +Ge,mQ0,m()

Gth,af +Ge,aQ0,a().p,mp,a

(29)

a nguyn t phn tchm monitor

H s k0 c nh ngha l k0,c(s) =Mc.s.s.0,s

Ms.c.c.0,c

H s k0 c xem nh mt hng s ht nhn v trong phng php chiu trn k0 c xcnh theo cng thc sau

k0,m(a) =Asp,aAsp,m

.Gth,mf +Ge,mQ0,m()

Gth,af +Ge,aQ0,a().p,mp,a

(30)

Hoc phng php t s Cd theo cng thc

k0,m(a) =

(Asp

p

)a

(

Asp

pFCd

)a,Cd(

Asp

p

)m

(

Asp

pFCd

)m,Cd

.Gth,mGth,a

(31)

17


Trong thc t ngi ta chiu mu vi mt monitor m v i

k0,m(a) =k0,Au(a)

k0,Au(m)(32)

6.5 Phng php k1

Phng php k0 c a ra vo nm 1975, l thi k ca cc detector Ge(Li) c hiusut tng i2 vo khong 20%. Ngy nay, cc detector HPGe vi hiu sut tng i khong100% xut hin trn th trng v cc detector dng ging cng bt u c s dng trongphn tch kch hot neutron. Vic o c bng nhng detector hiu sut cao lm xut hincc nh tng do hiu ng trng phng trong ph gamma, nhng hu ht chng u thch hp o cc ng v sng di, c vi tun hay vi thng sau khi kch hot.

Cc nh tng thng him khi c s dng tnh ton hm lng nguyn t. Tuy nhinchng c th trng vi cc nh t nhin quan trng. V d 82Br c 17 nh vi xc sut phtgamma trong vng 0.1%. Khi o vi detector dng ging c khong 30 nh tng xut hin vicng tng ng, hai trong s chng c th trng vi cc nh 60Co. Lu rng s trngny c th gy ra nhng sai lch trong vic xc nh hm lng Cobalt, trong khi s trngphng mt t cc nh ca 82Br c th khng ng k.

Hng s k0 c cha , xc sut pht ca photon tng ng vi nh quang in cn quan tm.Tuy nhin i vi mt s nh quang in quan st c trong ph gamma, gi tr ny khngtn ti. Nhng nh ny, c gi l nhng nh nhn to, c chia lm hai loi

Nhng nh quang in khng tng ng vi s ghi nhn mt photon n: nh tng gyra bi trng phng thc.

Cc nh tng ng vi s ghi nhn mt photon n nhng khng trc tip nng lngca n; cc nh thot v ng gp vo nh hu ca s to cp ca vt liu xung quanhht nhn.

Phng php k0 khng th x l nhng nh nhn to bi v hng s k0 cha xc sut phtgamma. Hiu ng trng phng c x l qua h s COI, nhng i vi cc nh tng, h strng phng ny khng th xc nh c. H s k1 c gii thiu nm 1991 bi M. Blaauwv P. Bode vi hng s k0 c tnh vo trong hng s k1 v xc sut pht tia

k1,c(s) =Mc.s.0,sMs.c.0,c

=csk0,c(s) (33)

Hng s k1 ch c p dng cho kch hot cn hng s k0 c p dng cho c kch hot lno c. i lng k1 chia k0 thnh hai phn lin quan ti kch hot (k1) v ti h ph k ().Khng c k1 ring r cho mi nh ca ng v phng x.

Trong phng php k0, hm lng c tnh ton t nhng nh n, mt ca mu chun vmt ca mu phn tch. Trong phng php k1, biu thc tng ng l

(g/g) =

(Np/tc

W.S.D.C

)a

Asp,m.

1

k1,m(a).Gth,mf +Ge,mQ0,m()

Gth,af +Ge,aQ0,a().Pp,mPp,a

(34)

2Hiu sut tng i ca mt detector germanium l t s gia hiu sut ghi nhn tia gamma c nng lng1.332MeV ti khong cch 25cm ca n so vi hiu sut ghi nhn ca mt detector NaI(Tl) kch thc 3 3(gi tr hiu sut ny vo khong 1.2 103).

18


vi P l xc sut ghi nhn nh nng lng ton phn trn mt phn r ht nhn. Vi nhbnh thng, P c th c tnh bng

P = ..c (35)

vi c l h s hiu chnh trng phng cho nh, nhng i vi nh tng, gi tr phi c thut s phn r v ng cong hiu sut ca detector mt cch trc tip.

H s k1 khng th c o trc tip nh k0. N phi c tnh t k0, thu c li th gct t nhin thc nghim ca n. Khi hiu chnh trng phng c yu cu, s phn r phic s dng tnh ton gi tr ca P . Khi khng cn phi hiu chnh trng phng, cng c th c kt hp li vi k1 cho ra k0.

Lu rng hiu ng hp th tia v tia X s thay i P ca tt c cc nh chi phi bi strng phng, c hai phng php k0 v k1 u cha cung cp cch thc hiu chnh hiu ngny.

6.6 Phng php ki

Nh trn chng ta nhn thy rng, phng php k0 ch c tc dng cho tng vch ring lv do bt u t cc din tch nh ca ph gamma tnh ton kt qua cui cng. Ngynay ngi ta s dng chng trnh xc nh ng v m tnh ton hot tuyt i c hiuchnh thi gian phn r ca ng v. N c li th hn trong vic tnh ton cc ng v c vchgamma chng chp, do vy cho kt qu chnh xc hn.

Phng php ny c a ra bi H. Petri v G. Kupper nm 2000. y cng l mt phngphp bin th ca k0 vi hm lng nguyn t c tnh t tc phn r tuyt i. Vi mcch ny, h s k0 lin quan n tng nh c chuyn thnh h s ki lin quan ti ng vtng ng vi phng trnh

ki =M

NA...0

j

j

k0,jwj

j wj(36)

trong , j l ch s ca cc nh gamma ca ng v v wj l trng s

wj =104

k2i,j(s2k0,i + s

2i) (37)

vi s l bt nh theo %.

Hng s ki l gi tr nghch o ca trung bnh trng s ca tt c cc h s k0 i vi mtng v phng x chia cho cng tia . Trong hu ht trng hp hng s ki c tnh tont h s k0.

N cng c kh nng gii quyt cc bi ton nh chp bng cch tnh tt c nhng vch cang v vi t s phn nhnh ca chng. Cc chng trnh my tnh s dng phng php kitng i n gin tch hp vo h phn tch a knh.

7 Hiu chnh nhiu trong phn tch kch hot neutron

Trong qu trnh kch hot neutron, bnh cnh phn ng (n,) to thnh nhn con pht tiagamma cn c cc hiu ng khc gy nh hng ln kt qu s ng v kch hot c to rahay s gamma pht ra t mu kch hot. Do ta cn phi tin hnh hiu chnh cho cc hiung ny thu c kt qu mt cch chnh xc nht. Cc hiu ng gy nh hng gm c:

19


Hiu ng t che chn neutron (neutron self-shielding): khi chiu x mu c th tch, chmneutron s b suy gim khi i vo bn trong mu, dn n thng lng neutron bn trongmu gim so vi thng lng neutron ti.

Hiu ng t chy (burn-up): cc ng v c hnh thnh trong qu trnh kch hotneutron s b kch hot mt ln na to thnh ng v khc. Hiu ng ny c chiathnh hai loi: t chy nhn bia (kch hot trc tip ng v va c to thnh) v tchy nhn con (ng v va c to thnh phn r thnh nhn con v nhn con ny bkch hot).

Hiu ng nhiu gy bi neutron nhanh: cc neutron nhanh tham gia vo cc phn ng(n,p), (n,), (n,n),... v to ra cc ng v ging nh cc ng v c to ra t phn ng(n,).

Mt s hiu ng nhiu th cp khc nh cc proton c to ra t phn ng (n,p) c ththam gia phn ng (p,n) v to ra cc neutron nhanh, tuy nhin xc sut xy ra cc phnng ny rt nh.

Trong trng hp mu kch hot c ng v 235U, c th xy ra phn ng phn hch (n,f)to ra cc ng v trng vi ng v cn quan tm, v d nh phn ng 94Zr(n,)95Zr v235U(n,f)95Zr.

Bn cnh , sn phm phn r ca mt ng v kch hot ny c th trng vi mt ng

v kch hot khc, chng hn nh 176Lu(n,)177Lu v 176Yb(n,)177Yb 177Lu.

Hiu ng ph gamma (interfering peaks): mt s nh ph gamma ca mt s ng v kchhot c th b chng ln ln nhau, v d nh nh gamma 846.8keV ca 56Mn v 843.8keVca 27Mg.

7.1 Hiu ng t che chn neutron

hiu chnh hiu ng t che chn neutron, ta s dng cc h s hiu chnh Gth v Ge tngng cho cc neutron nhit v trn nhit nh trong cng thc (20). Ngoi ra, ta c th da ra mth s hiu chnh hiu dng (effective self-shielding factor) cho c neutron nhit v trn nhit

Asp = Geff .NA..

M[f +Q0()] p (38)

viGeff =

Gth +GepQ0/f

1 +Q0/f(39)

Ta c th c lng xp x cc h s hiu chnh thng qua hm sigmoid i vi 1 nguyn t nnh sau

Gth =1.00

1 + (m/mth)0.964(40)

Gep =0.94

1 + (m/mep)0.82+ 0.06 (41)

vi m l khi lng nguyn t trong mu, mth v mep l cc tham s ph thuc vo dng hnhhc mu, tit din tng tc vi neutron. i vi mu c dng hnh tr (chiu cao h, bn knhr), cc tham s ny c dng

1

mth=kthNAabsr(r + h)M

(tot/abs)0.15 (42)

20


1

mep=kepNAabsr(r + h)M

abs,ep (43)

Trong tot v abs l cc tit din ton phn v hp th tng ng, kth v kep l cc thams ph thuc vo pha chiu x nh ph neutron v vt liu tn x.

7.2 Hiu ng t chy (burn-up)

ng vi mi loi hiu ng ta c cc cch thc hiu chnh khc nhau:

t chy nhn bia c hnh thnh trc tip s phn ng t chy nhn bia nhsau

AX(A+1X

)(n,)0,1I0,1 2(n,)0,2I0,2

Cc v d ca hiu ng t chy c th k n nh cc phn ng197Au(n,)198Au(n,)199Au181Ta(n,)182Ta(n,)183Ta

Trong trng hp xy ra hiu ng t chy, cc ng v kch hot c to thnh s b mt i to nn nhng ng v mi. iu ny s lm gim s lng cc ng v kch hot thu c,v tt nhin dn n h qu cui cng l hm lng nguyn t c lng c t phng phpNAA s b thp hn so vi thc t.

hiu chnh cho hiu ng t chy ny, ta s dng h s hiu chnh Fburn

Asp,2 =Np,2/tc

S2.D2.C2.w/Fburn (44)

vi

Fburn =2e(1)t1 [1 e(122)ti]

(1 2 2)(1 e2ti) (45)

trong = Gthth0 +GeeI0()

t chy nhn con s phn ng t chy nhn con nh sau

AX A+1X(A+1X

)(n,)0,1,I0,1 F2,2 3(n,)0,3,I0,3

Cc v d ca hiu ng t chy nhn con chng hn nh74Ge(n,)75Ge

75As(n,)76As nh hng n phn ng 75As(n,)76As70Ge(n,)71Ge EC 71Ga(n,)76Ga nh hng n phn ng 71Ga(n,)76Ga

Ngc li vi hiu ng t chy nhn bia, hiu ng t chy nhn con s b sung thm chong v cn quan tm, dn n hm lng nguyn t c lng c s cao hn so vi thc t.

21


hiu chnh cho hiu ng ny, ta s dng cng thc sau

Asp,3 =Np,3/tc

(S.D.C)burn.w(46)

vi

(S.D.C)burn =3

3 2S2D2C2 +[3(A3S2 23)

3(A3 2) 3S23 2

]D3C3 (47)

trong = + v = 1 eAti

7.3 Phn ng nhiu gy bi neutron nhanh

Mt s v d v phn ng gy nhiu bi neutron nhanh c cho di dy23Na(n,)24Na nh hng bi 27Al(n,)24Na23Na(n,)24Na 24Mg(n,p)24Na50Cr(n,)51Cr 54Fe(n,)51Cr55Mn(n,)56Mn 56Fe(n,p)56Mn58Fe(n,)59Fe 59Co(n,p)24Fe68Zn(n,)69mZn 69Ga(n,p)69mZn74Ge(n,)75Ge 75As(n,p)75Ge76Sc(n,)77mSc 77Sc(n,n)77mSc86Sr(n,)87mSr 87Sr(n,n)87mSr110Cd(n,)111mCd 111Cd(n,n)111mCd116Sn(n,)117mSn 117Sr(n,n)117mSn v 118Sr(n,2n)117mSn134Ba(n,)135mBa 135Ba(n,n)135mBa v 136Ba(n,2n)135mBa136Ba(n,)137mBa 137Ba(n,n)137mBa v 138Ba(n,2n)137mBa

xc nh nh hng ca cc phn ng nhiu bi neutron nhanh, ta cn phi xc nh thnglng neutron nhanh gy kch hot mu. Thng lng ny c th c xc nh bng cch dngcc monitor Fe hay Ni thng qua cc phn ng 54Fe(n,p)54Mn v 58Ni(n,p)58Co.

7.4 Hiu ng nh hng ph gamma

Hiu ng ny gy ra do mt nguyn t c nh trng vi nh ca nguyn t cn quan tm.

Trong trng hp nguyn t cn quan tm l nguyn t c thi gian sng dai hn nhiu so vithi gian sng ca nguyn t gy nh hng, ta c th cho mt khong thi gian ch trc khio nhm loi b hu ht cc ng v c thi gian sng ngn. Ngoi ra, ta cng c th hiu chnhphn nh hng nh ph theo cch sau:

Gi nh cn quan tm l x, phn n hng l y. Phn nh hng ny cn c mt nh z khngb nh hng bi cc nh khc. Hm lng hiu chnh c tnh nh sau

x = x

(1 y

y

)(48)

x, x hm lng nguyn t X c hiu chnh v khng c hiu chnhy, y hm lng nguyn t Y c hiu chnh v khng c hiu chnh

Ti liu

[1] T. Bereznai, Methods, Problems and Trends of Standardization in Multielement ReactorNeutron Activation Analysis, Frecenius Z. Anal. Chem. 302, 353-363 (1980).

22


[2] F. De Corte, Problems and solutions in the standardization of reactor neutron activationanalysis, J. Radioanal. Chem. 160, 63-75 (1992).

[3] M.L. Verheijke, Instrumental neutron activation analysis developed for silicon integratedcircuit technology, Doctoral thesis at Technische Universiteit Eindhoven (1992).

[4] M. Blaauw, P. Bode, Introduction of the k1-concept for the interpretation of artificial peaksin k0-based NAA, J. Radioanal. Chem. 169, 201-208 (1993).

[5] M.L. Verheijke, Relation between the Hogdahl convention and the modified Westcott formal-ism for (n,) reactions with a pure 1/vn cross-section behaviour, J. Radioanal. Nucl. Chem.183, 293-299 (1994).

[6] H. Petri, G. Kupper, Standardization of NAA using activation equation in isotope-relatedconstants, J. Radioanal. Chem. 245, 163-166 (2000).

[7] B.J.B. Nyarko, E.H.K. Akaho, Y. Serfor-Armah, Application of NAA standardization meth-ods using a low power research reactor, J. Radioanal. Chem. 257, 361-366 (2003).

[8] H Mnh Dng, Nghin cu pht trin phng php k-zero trong phn tch kch hot neutronl phn ng ht nhn cho xc nh a nguyn t, Lun n Tin s Vt l, Trng HKHTNTPHCM (2003).

[9] C. Chilian, J. St-Pierre, G. Kennedy, Dependence of thermal and epithermal neutron self-shielding on sample size and irradiation site, Nucl. Instr. and Meth. A 564, 629-635 (2006).

[10] A. Trkov, G. Zerovnik, L. Snoj, M. Ravnik, On the self-shielding factors in neutron activa-tion analysis, Nucl. Instr. and Meth. A 610, 553-565 (2009).

[11] Robert R. Greenberg, Peter Bode, Elisabete A. De Nadai Fernandes, Neutron activationanalysis: A primary method of measurement, Spectrochimica Acta Part B 66, 193-241(2011).

[12] A. Vrtes et al, Handbook of Nuclear Chemistry, 2nd Edition, Springer Science+BusinessMedia (2011).

[13] http://en.wikipedia.org/wiki/Neutron_activation_analysis

[14] http://en.wikipedia.org/wiki/Neutron_temperature

[15] http://en.wikipedia.org/wiki/Neutron_source

23

M uCc phuong php phn tch NAATheo nang lung neutronTheo tia gamma pht raTheo k thut chiu xaGii han pht hin

Ngun neutron v h o s dung trong NAANgun neutronH o

Chun bi muMu rnMu longMu kh

Nguyn tc cua NAAPhan ng kch hoat neutronThng lung neutron cua l phan ngQuy uc HogdahlH s WestcottPhuong trnh kch hoat

Cc phuong php chun ha trong phn tch kch hoat neutronPhuong php tuyt iPhuong php tuong iPhuong php chun onPhuong php k0Phuong php k1Phuong php ki

Hiu chinh nhiu trong phn tch kch hoat neutronHiu ng t che chn neutronHiu ng t chy (burn-up)Phan ng nhiu gy bi neutron nhanhHiu ng anh hung ph gamma

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