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Measurement of the thickness of thin foils
NUCLEAR
1N57RUMEN75
AND
35
ME7H0D5
MEA5UREMEN7
(1965) 2 1 0 - - 2 1 2 ;
0F 7HE 7H1CKNE55
(~ N 0 R 7 H - H 0 L L A N D
PU8L15H1N6
C0.
0F 7H1N F01L5
M. A. FAR0UK, M. H. NA55EF, A. 2. EL-8EHAY and 1. 1. 2AL0U80V5KY At0m1c Ener9y E5ta6115hment, Ca1r0, E~,ypt, UA R
Rece1ved 7 Decem6er 1964 A meth0d f0r mea5ur1n9 the th1ckne55 0f th1n f0115 15 de5cr16ed. 7he cham6er wa5 de519ned 50 that f011 th1ckne55e5 fr0m 5.0 t0 0.5 m9/cm 2 c0u1d 6e determ1ned 6y mea5ur1n9 the ener9y 1055 0f P0210 ~-part1c1e5 pa551n9 thr0u9h matter. 7h1ckne55e5 fr0m
0.5 m9/cm 2 t0 5.01t9/cm 2 0r 1e55 c0u1d 6e determ1ned 6y c0mpar1n9 the e4u1va1ent th1ckne55e5 0f a1r and f011 mater1a1. Ca116rat10n curve5 are 91ven f0r A1, Cr, N1 and 5n. 7he accuracy 0f mea5urement5 15 6etter than 10%.
1.1ntr0duct10n A c c u r a t e determ1nat10n 0f th1n tar9et th1ckne55 15 4u1te 1mp0rtant 1n nuc1ear phy51c5 exper1ment5. 1n pr1nc1p1e there are m a n y meth0d5 f0r the mea5urement5 0f the f011 th1ckne55 ~). H 0wever, m05t 0f the5e meth0d5 are n0t 4u1te 5u1ta61e 1n the n0rma1 c0nd1t10n5 0 f nuc1ear 1a60rat0r1e5. F 0 r 1n5tance, we19h1n9 d0e5 n0t 91ve the re4u1red accuracy 51nce the f0115 u5ua11y are f1xed 0n h01der5 f r 0 m wh1ch they c a n n 0 t 6e 5eparated and the d1fference 6etween the1r we19ht5 15 very 1ar9e. Chem1ca1 ana1y515 m e t h 0 d 15, h0wever, a c0mp11cated pr0ce55.1t c a n n 0 t a1way5 6e u5ed 6ecau5e 1t 1ead5 t0 the de5truct10n 0 f the tar9et. 0 t h e r meth0d5 5uch a5 X a n d 6 e t a - r a y a650rpt10n, rad10-act1vat10n a n d e1ectr1ca1 c0nduct1v1ty re4u1re 5pec1a1 arran9ement5 and 50 cann0t 6e w1de1y u5ed. A 51mp1e a r r a n 9 e m e n t 15 5u99e5ted 1n the pre5ent w0rk. 1t a110w5 4u1ck and 51mp1e determ1nat10n 0 f the f011 th1ckne55. 50Urx:e D1aphra9m
1•ar9et
-
3---
$~rn1 C0ndUet0r
Pre Arnpt1f1er
2
Amp11f1er
11 111
F~H.A.
F19. 1. 810ck d1a9ram 0f the exper1ment. 2. De5cr1pt10n 0f.the 1n5trument and m e t h 0 d 0 f mea5urement
2
0•
7 h e m e t h 0 d u5ed 1n the pre5ent w 0 r k 15 6a5ed 0n the fact t h a t the ener9y 1055 0 f a1pha-part1c1e5 (0r any 0ther char9ed part1c1e5) wh11e pa551n9 t h r 0 u 9 h a f011, 15 210
1
0
F19. 2. Vacuum cham6er u5ed f0r mea5ur1n9 f011 th1ckne55e5.
MEA5UREMEN7 0F 7HE 7H1CKNE55 0F 7H1N F01L5 pr0p0rt10na1 t0 1t5 th1ckne55. 1f the ener9y 0f c~part1c1e5 enter1n9 and 1eav1n9 the f011 15 kn0wn, 1t5 th1ckne55 can 6e determ1ned acc0rd1n9 t0 the f0110w1n9 expre5510n :
211
~ mc ~ m 2 Et~0:53
MeV
5
4
/ d E ( MeV 1(rn9/cm 2) = (E 0 -- E,) d.~ •m9/cm2•
•
1
/
(1) 3
where E 0 15 the ener9y 0f c~-part1c1e5 enter1n9 the f011. 1n the pre5ent ca5e E 0 = E(P0 21°) = 5.3 MeV, E 1 15 the ener9y 0f a-part1c1e5 1eav1n9 the f011, (dE/dx) 15 the rate 0f ener9y 1055 f0r a-part1c1e5 at an avera9e ener9y ~(E0 + E1). 7he rate 0f ener9y 1055 f0r ~ part1c1e5 at d1fferent ener91e5 and f0r many e1ement5 15 91ven 1n re1", 2). 7he 610ck d1a9ram f0r mea5ur1n9 the ener9y 1055 AE = E0 -- E~ 15 5h0wn 1n f19. 1.7he vacuum cham6er u5ed 15 5h0wn 1n f19. 2. 5em1c0nduct0r detect0r wa5 f1xed 1n the h01der AA. Pu15e5 fr0m the detect0r were fed t0 a preamp11f1er thr0u9h a 91a55 t0 meta1 5ea1.7he
u1
t~
c ~J
2~
•1--1
J
10
20
t
1
1
30
40
50
-1P
Num6er 0f 6hanne15
F19. 3. 7yp1ca1 5pectrum 0f the a1pha-part1c1e5 6ef0re and after the f011. f011 wa5 f1xed 1n C0nta1ner 88, Wh1Ch C0U1d 6e p1aCed 1n tW0 p051t10n5.0ne 11e5 6etWeen the a-50UrCe and the detect0r Wh11e the 0ther 15 a51de fr0m the path 0f the ct-part1C1e5. 7he p051t10n 0f th15 C0nta1ner C0u1d 6e Chan9ed fr0m 0Ut51de W1th0ut d15tur61n9 the VaCUUm 1n the Cham6er. 7he c¢-part1C1e 50UrCe Wa5 p1aCed 1n the h01der DD, Wh1ch C0U1d 6e f1Xed at any d15tance away fr0m the detect0r W1th the he1p 0f the 5Crew 6 . 7he d15tance 6etWeen tW0 C0n5eCUt1Ve thread5 0f the 5Crew 6 15 e4ua1 t0 1 mm. 7h15 d15tance 0f 1 m m 15 d1V1ded 1nt0 100 d1v1510n5 0n the d15k FF. 7hU5 the d15tance 6etWeen the detect0r and the 50UrCe C0U1d 6e determ1ned w1th an accuracy 0f 10 p. D1fferent d1aphra9m5 c0u1d 6e f1xed 1n the c0nta1ner CC.
2
1
02
02.
06
08
10
1.2
14
1.6
2•F (MeV)
F19.4. Ca116rat10n curve5 f0r A1, Cr, N1 and 5n.
Pu15e5 fr0m t11e detect0r after pa551n9 thr0u9h a char9e amp11f1er were fed 10 a 400-channe1 pu15e he19ht ana1y5er. 7yp1ca15pectrum 0fthe a-part1c1e5 fr0m P021° 6ef0re and after pa551n9 thr0u9h an a1um1n1um f011 15 5h0wn 1n f19. 3. Kn0w1n9 the ener9y 1055 AE, 0ne can 06ta1n the f011 th1ckne55 u51n9 re1at10n (1). 1f the ener9y 1055 AE 15 1ar9e, the va1ue (dE/dx) at •(E0 + E1) c0u1d n0t 6e u5ed 51nce the rate 0fener9y 1055 15 n0t a 11near funct10n 0f the ener9y. 1n th15 ca5e the 1nterva1 AE mu5t 6e d1v1ded 1nt0 5ma11 5u61nterva15, thr0u9h wh1ch the 5t0pp1n9 p0wer may 6e taken a5 a 11near funct10n 0f ener9y. 7he t0ta1 th1ckne55 0f the f011 15 then 06ta1ned 6y 5umm1n9 the c0rre5p0nd1n9 th1ckne55e5 f0r the5e 5ma11 ener9y 5u61nterva15. Ca116rat10n curve5 were p10tted f0r A1, Cr, N1 and 5n a5 5h0wn 1n f19. 4. U51n9 the5e curve5 1t 15 ea5y t0 determ1ne any f011 th1ckne55, f0r the5e meta15, 6y mea5ur1n9 the ener9y 1055 A E 0f the a-part1c1e5 (P0 2~°) thr0u9h them. 7a61e 1 91ve5 the f011 th1ckne55e5 06ta1ned 6y the 7A8LE
E1ement
A1 A1 Cr Cr Cr N1 N1 N1 5n 5n•• 5n
1
.1E (MeV)
1(m9/cm2) (a1pha-part1c1e 5t0pp1n9 p0wer)
1(m9/cm2) (we19h1n9)
1.55 0.95 0.43 0.65 1.08 0.60 0.95
2.46 1.60 0.94 1.36 2.27 1.35 2.13
2.44
1.40
3.15
2.10 3.12
1.53 1.15 0.76
1.17 0.74
0.50 0.38 0.28
1 •
1
1.59 1.06 1.34
2.21 1.34
1.61
212
M.a. F A R 0 u K et a1.
a60ve ment10ned meth0d and 6y we19h1n9. 6 0 0 d a9reement 6etween the5e tw0 meth0d5 wa5 06ta1ned. 7 h e err0r 1n th15 meth0d d1d n0t exceed 10~0.7he ma1n err0r may 6e 1n the va1ue5 0f the 5t0pp1n9 p0wer 51nce they are 06ta1ned w1th an accuracy 0f 8 ~ , ref. 2). 7h1ckne55e5 fr0m 0.5 m9/cm 2 0r 1e55 may 6e mea5ured 6y c0mpar1n9 the e4u1va1ent th1ckne55e5 0f a1r and f011 mater1a1. F0r th15 purp05e the num6er-d15tance curve5 d N / d R w1th and w1th0ut f0115 are mea5ured 1n a1r. 7 h e
deta11ed de5cr1pt10n 0f th15 meth0d 15 n0t 91ven here 51nce 1t 15 91ven 1n ref. 3).
Reference5 1) p. C0tt0n and P. R0uard, J. Phy5. Rad. 11 (1950) 461. K. M. 6reen1and, Vacuum 2 (1952) 216. L. H011and, Vacuum Dep051t10n 0f 7h1n F1hn5 (Chapman and Ha11 Ltd., L0nd0n, 1956). 2) Hand6uch der Phy51k 34 (1958) p. 193. 3) K. Ramavat0ram and D. 1. P0rat, Nuc1. 1n5tr. and Meth. 4 (1959) 239.
1N57RUMEN75
AND
35
ME7H0D5
MEA5UREMEN7
(1965) 2 1 0 - - 2 1 2 ;
0F 7HE 7H1CKNE55
(~ N 0 R 7 H - H 0 L L A N D
PU8L15H1N6
C0.
0F 7H1N F01L5
M. A. FAR0UK, M. H. NA55EF, A. 2. EL-8EHAY and 1. 1. 2AL0U80V5KY At0m1c Ener9y E5ta6115hment, Ca1r0, E~,ypt, UA R
Rece1ved 7 Decem6er 1964 A meth0d f0r mea5ur1n9 the th1ckne55 0f th1n f0115 15 de5cr16ed. 7he cham6er wa5 de519ned 50 that f011 th1ckne55e5 fr0m 5.0 t0 0.5 m9/cm 2 c0u1d 6e determ1ned 6y mea5ur1n9 the ener9y 1055 0f P0210 ~-part1c1e5 pa551n9 thr0u9h matter. 7h1ckne55e5 fr0m
0.5 m9/cm 2 t0 5.01t9/cm 2 0r 1e55 c0u1d 6e determ1ned 6y c0mpar1n9 the e4u1va1ent th1ckne55e5 0f a1r and f011 mater1a1. Ca116rat10n curve5 are 91ven f0r A1, Cr, N1 and 5n. 7he accuracy 0f mea5urement5 15 6etter than 10%.
1.1ntr0duct10n A c c u r a t e determ1nat10n 0f th1n tar9et th1ckne55 15 4u1te 1mp0rtant 1n nuc1ear phy51c5 exper1ment5. 1n pr1nc1p1e there are m a n y meth0d5 f0r the mea5urement5 0f the f011 th1ckne55 ~). H 0wever, m05t 0f the5e meth0d5 are n0t 4u1te 5u1ta61e 1n the n0rma1 c0nd1t10n5 0 f nuc1ear 1a60rat0r1e5. F 0 r 1n5tance, we19h1n9 d0e5 n0t 91ve the re4u1red accuracy 51nce the f0115 u5ua11y are f1xed 0n h01der5 f r 0 m wh1ch they c a n n 0 t 6e 5eparated and the d1fference 6etween the1r we19ht5 15 very 1ar9e. Chem1ca1 ana1y515 m e t h 0 d 15, h0wever, a c0mp11cated pr0ce55.1t c a n n 0 t a1way5 6e u5ed 6ecau5e 1t 1ead5 t0 the de5truct10n 0 f the tar9et. 0 t h e r meth0d5 5uch a5 X a n d 6 e t a - r a y a650rpt10n, rad10-act1vat10n a n d e1ectr1ca1 c0nduct1v1ty re4u1re 5pec1a1 arran9ement5 and 50 cann0t 6e w1de1y u5ed. A 51mp1e a r r a n 9 e m e n t 15 5u99e5ted 1n the pre5ent w0rk. 1t a110w5 4u1ck and 51mp1e determ1nat10n 0 f the f011 th1ckne55. 50Urx:e D1aphra9m
1•ar9et
-
3---
$~rn1 C0ndUet0r
Pre Arnpt1f1er
2
Amp11f1er
11 111
F~H.A.
F19. 1. 810ck d1a9ram 0f the exper1ment. 2. De5cr1pt10n 0f.the 1n5trument and m e t h 0 d 0 f mea5urement
2
0•
7 h e m e t h 0 d u5ed 1n the pre5ent w 0 r k 15 6a5ed 0n the fact t h a t the ener9y 1055 0 f a1pha-part1c1e5 (0r any 0ther char9ed part1c1e5) wh11e pa551n9 t h r 0 u 9 h a f011, 15 210
1
0
F19. 2. Vacuum cham6er u5ed f0r mea5ur1n9 f011 th1ckne55e5.
MEA5UREMEN7 0F 7HE 7H1CKNE55 0F 7H1N F01L5 pr0p0rt10na1 t0 1t5 th1ckne55. 1f the ener9y 0f c~part1c1e5 enter1n9 and 1eav1n9 the f011 15 kn0wn, 1t5 th1ckne55 can 6e determ1ned acc0rd1n9 t0 the f0110w1n9 expre5510n :
211
~ mc ~ m 2 Et~0:53
MeV
5
4
/ d E ( MeV 1(rn9/cm 2) = (E 0 -- E,) d.~ •m9/cm2•
•
1
/
(1) 3
where E 0 15 the ener9y 0f c~-part1c1e5 enter1n9 the f011. 1n the pre5ent ca5e E 0 = E(P0 21°) = 5.3 MeV, E 1 15 the ener9y 0f a-part1c1e5 1eav1n9 the f011, (dE/dx) 15 the rate 0f ener9y 1055 f0r a-part1c1e5 at an avera9e ener9y ~(E0 + E1). 7he rate 0f ener9y 1055 f0r ~ part1c1e5 at d1fferent ener91e5 and f0r many e1ement5 15 91ven 1n re1", 2). 7he 610ck d1a9ram f0r mea5ur1n9 the ener9y 1055 AE = E0 -- E~ 15 5h0wn 1n f19. 1.7he vacuum cham6er u5ed 15 5h0wn 1n f19. 2. 5em1c0nduct0r detect0r wa5 f1xed 1n the h01der AA. Pu15e5 fr0m the detect0r were fed t0 a preamp11f1er thr0u9h a 91a55 t0 meta1 5ea1.7he
u1
t~
c ~J
2~
•1--1
J
10
20
t
1
1
30
40
50
-1P
Num6er 0f 6hanne15
F19. 3. 7yp1ca1 5pectrum 0f the a1pha-part1c1e5 6ef0re and after the f011. f011 wa5 f1xed 1n C0nta1ner 88, Wh1Ch C0U1d 6e p1aCed 1n tW0 p051t10n5.0ne 11e5 6etWeen the a-50UrCe and the detect0r Wh11e the 0ther 15 a51de fr0m the path 0f the ct-part1C1e5. 7he p051t10n 0f th15 C0nta1ner C0u1d 6e Chan9ed fr0m 0Ut51de W1th0ut d15tur61n9 the VaCUUm 1n the Cham6er. 7he c¢-part1C1e 50UrCe Wa5 p1aCed 1n the h01der DD, Wh1ch C0U1d 6e f1Xed at any d15tance away fr0m the detect0r W1th the he1p 0f the 5Crew 6 . 7he d15tance 6etWeen tW0 C0n5eCUt1Ve thread5 0f the 5Crew 6 15 e4ua1 t0 1 mm. 7h15 d15tance 0f 1 m m 15 d1V1ded 1nt0 100 d1v1510n5 0n the d15k FF. 7hU5 the d15tance 6etWeen the detect0r and the 50UrCe C0U1d 6e determ1ned w1th an accuracy 0f 10 p. D1fferent d1aphra9m5 c0u1d 6e f1xed 1n the c0nta1ner CC.
2
1
02
02.
06
08
10
1.2
14
1.6
2•F (MeV)
F19.4. Ca116rat10n curve5 f0r A1, Cr, N1 and 5n.
Pu15e5 fr0m t11e detect0r after pa551n9 thr0u9h a char9e amp11f1er were fed 10 a 400-channe1 pu15e he19ht ana1y5er. 7yp1ca15pectrum 0fthe a-part1c1e5 fr0m P021° 6ef0re and after pa551n9 thr0u9h an a1um1n1um f011 15 5h0wn 1n f19. 3. Kn0w1n9 the ener9y 1055 AE, 0ne can 06ta1n the f011 th1ckne55 u51n9 re1at10n (1). 1f the ener9y 1055 AE 15 1ar9e, the va1ue (dE/dx) at •(E0 + E1) c0u1d n0t 6e u5ed 51nce the rate 0fener9y 1055 15 n0t a 11near funct10n 0f the ener9y. 1n th15 ca5e the 1nterva1 AE mu5t 6e d1v1ded 1nt0 5ma11 5u61nterva15, thr0u9h wh1ch the 5t0pp1n9 p0wer may 6e taken a5 a 11near funct10n 0f ener9y. 7he t0ta1 th1ckne55 0f the f011 15 then 06ta1ned 6y 5umm1n9 the c0rre5p0nd1n9 th1ckne55e5 f0r the5e 5ma11 ener9y 5u61nterva15. Ca116rat10n curve5 were p10tted f0r A1, Cr, N1 and 5n a5 5h0wn 1n f19. 4. U51n9 the5e curve5 1t 15 ea5y t0 determ1ne any f011 th1ckne55, f0r the5e meta15, 6y mea5ur1n9 the ener9y 1055 A E 0f the a-part1c1e5 (P0 2~°) thr0u9h them. 7a61e 1 91ve5 the f011 th1ckne55e5 06ta1ned 6y the 7A8LE
E1ement
A1 A1 Cr Cr Cr N1 N1 N1 5n 5n•• 5n
1
.1E (MeV)
1(m9/cm2) (a1pha-part1c1e 5t0pp1n9 p0wer)
1(m9/cm2) (we19h1n9)
1.55 0.95 0.43 0.65 1.08 0.60 0.95
2.46 1.60 0.94 1.36 2.27 1.35 2.13
2.44
1.40
3.15
2.10 3.12
1.53 1.15 0.76
1.17 0.74
0.50 0.38 0.28
1 •
1
1.59 1.06 1.34
2.21 1.34
1.61
212
M.a. F A R 0 u K et a1.
a60ve ment10ned meth0d and 6y we19h1n9. 6 0 0 d a9reement 6etween the5e tw0 meth0d5 wa5 06ta1ned. 7 h e err0r 1n th15 meth0d d1d n0t exceed 10~0.7he ma1n err0r may 6e 1n the va1ue5 0f the 5t0pp1n9 p0wer 51nce they are 06ta1ned w1th an accuracy 0f 8 ~ , ref. 2). 7h1ckne55e5 fr0m 0.5 m9/cm 2 0r 1e55 may 6e mea5ured 6y c0mpar1n9 the e4u1va1ent th1ckne55e5 0f a1r and f011 mater1a1. F0r th15 purp05e the num6er-d15tance curve5 d N / d R w1th and w1th0ut f0115 are mea5ured 1n a1r. 7 h e
deta11ed de5cr1pt10n 0f th15 meth0d 15 n0t 91ven here 51nce 1t 15 91ven 1n ref. 3).
Reference5 1) p. C0tt0n and P. R0uard, J. Phy5. Rad. 11 (1950) 461. K. M. 6reen1and, Vacuum 2 (1952) 216. L. H011and, Vacuum Dep051t10n 0f 7h1n F1hn5 (Chapman and Ha11 Ltd., L0nd0n, 1956). 2) Hand6uch der Phy51k 34 (1958) p. 193. 3) K. Ramavat0ram and D. 1. P0rat, Nuc1. 1n5tr. and Meth. 4 (1959) 239.