ˆ.. ³ Ì μ,.. Ò±,.. ŒÊ Ë μ, ˆ.. Ê Ò,.. Ê Ò,.. ±, ˆ. Ì μ,.. μ
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1 P ˆ.. ³ Ì μ,.. Ò±,.. ŒÊ Ë μ, ˆ.. Ê Ò,.. Ê Ò,.. ±, ˆ. Ì μ,.. μ Œ ˆ ˆ ˆ Ÿ Œ œ ƒ ˆŠ Œ ˆ ˆ ˆˆ Ÿ Œˆ ˆ Œˆ Šˆ ƒˆ Š ˆ ˆ ˆŠ, ˆ Ÿ Š ˆ ˆ ² μ μ ±μ³ É É ±μ Ë Í - ˆŠ-2009, Œμ ±, 16Ä21 μö Ö 2009.
2 ³ Ì μ ˆ... P Œμ Ë Í μ Ö ³μ ²Ó É ²μ μ μ ± ³ É ² Ì μ ²ÊÎ ÉÖ ²Ò³ μ ³ Ò μ± Ì Ô ËÊ ±Í ÉμÎ ±, ÖÐ μé ±μ μ É μ μìμ ÉÖ ²ÒÌ μ μ Î ±μ μ Ò Ò Ì μé Ô μ μ μ³ Ìμ ÊÕÉ Ö Ê Ê μ Ê Ê μ ³μ É Ö. Šμ³- ÓÕÉ Ö μ ³³ SRIM-2008 μ μ²ö É ÒÎ ²ÖÉÓ μé Ô ÉÖ ²ÒÌ μ μ Ì μìμ Î ±μ μ Ò Ò. ²Ö ² μ Ö μ²óïμ Î ³ É ³Ö μé ³μ³ É μ Ö μ ³ Ï Ó μ μ μ² μ μ É μ ±. μ Ò Î ÉÒ ( μ²ó μ ³ ʲÓÉ Éμ μ ³³Ò SRIM-2008) μ± ², ÎÉμ ³Ö μìμ Ö μ μ Ê Ô 700 ŒÔ ± ² μ ³ Ï μ É ²Ö É t μ c. Ò ÊÐ Ì μé Ì ÊÎ ÉÒ ²μ Ó μ ÊÉ ³ É ² Ò ² Ö ÉμÎ ± μ ³ ³ É Ö t μ c. μ μé ² É Ö ³μ ²Ó É ³ Î ±μ μ ± μ Ò³ ÉμÎ ±μ³, ÊÎ ÉÒ ÕÐ ³ μ ÊÉ ³ É ². μé Ò μ² μ Éμ Ëμ ³ Í μ ÒÌ É Ì μ²μ ˆŸˆ. É Ñ μ μ É ÉÊÉ Ö ÒÌ ² μ. Ê, 2009 Amirkhanov I. V. et al. P The Modiˇed Thermal Spike Model in Materials at Irradiation with High Energy Heavy Ions with the Radiant Function Depending on the Ion Velocity At passage of heavy ions through condensed media, their energy losses are generally spent for elastic and inelastic interactions. The SRIM-2008 computer program allows calculating the energy losses of heavy ions at their passage through condensed media. Of great importance for the investigation is the time from the moment of ion's hitting the target to its full stopping. The performed calculations (using the results of the SRIM-2008 program) have shown that the time of passage by a uranium ion with the energy 700 MeV in a nickel target is t ion s. In the previous investigations, the motion of an ion in a material was not considered and a source with the action time t ion s was used. In this paper the thermal spike model with a new source considering the motion of an ion within a material is proposed. The investigation has been performed at the Laboratory of Information Technologies, JINR. Preprint of the Joint Institute for Nuclear Research. Dubna, 2009
3 ˆ μ ² μ Ò μ É ÕÐ ³ É μ³ μ μ ÖÉ Ö Ô± ³ - É ²Ó Ò ² μ Ö ²Ö ÊÎ Ö μ É ÉÖ ²ÒÌ Ö ÒÌ Î É Í ³ É ²Ò. Š É ± ³ ² μ Ö³ μé μ ÖÉ Ö, Î É μ É, ÊÎ μ μ μ É Í μ μ μ Ò² Ö, μ μ É ±μ ³ - ³ Ì Î ± Ì μ É ³ É ²μ μ ²ÊÎ Ì ÉÖ ²Ò³ μ ³ Ò μ± Ì Ô. ³ É ³, ÎÉμ, ³μÉ Ö μ μ²ó μ ² É ²Ó Ò μ - ² μ, Ê ²μ Ö μ μ Ö É ±μ É ÒÌ É ² Ì Ö Ò É ²ÖÌ μ Ì μ. ±μ²μ ÖÉ ÖÉ ² É Ò² ²μ Ò ³μ ², μ Ñ- Ö ÖÕÐ Î Ò μ ± μ Ö É ± Ô² ±É ± Ì, ³ μ ³μ ²Ó É ³ Î ±μ μ ± [1Ä3] ³ Ì ³ ±Ê²μ μ ±μ μ Ò [4, 5]. Œμ ²Ó É - ³ Î ±μ μ ± μ Ò É Ö É ³μ ÊÌ Ö ÒÌ Ê Î É ÒÌ μ μ ÒÌ ²Ö É ³ ÉÊ Ò Ô² ±É μ μ T e Ï É± T i. μ μé ² É Ö ³μ Ë Í μ Ö ³μ ²Ó É ³ Î ±μ μ ±, ÊÎ ÉÒ ÕÐ Ö μ ÊÉ ³ É ². Šμ³ ÓÕÉ Ö μ- ³³ SRIM-2008 [6] μ μ²ö É ÒÎ ² ÉÓ μé Ô ÉÖ ²ÒÌ μ μ Ì μìμ Î ±μ μ Ò Ò. μ²óïμ Î ²Ö μ ³ Ö ³ É ³Ö μé ³μ³ É μ Ö μ ³ Ï Ó μ μ μ² μ μ É μ ±. μ Ò Î ÉÒ ( μ²ó μ ³ ʲÓÉ Éμ μ- ³³Ò SRIM-2008) μ± ², ÎÉμ ³Ö μìμ Ö μ μ Ê Ô 700 ŒÔ ± ² μ ³ Ï μ É ²Ö É t μ c. Ò ÊÐ Ì ² μ ÖÌ [7, 9] ÊÎ ÉÒ ²μ Ó μ ÊÉ ³ É ² - ² ² Ö ÉμÎ ± μ ³ ³ É Ö t μ c. ²ÓÕ ÉμÖÐ μéò Ö ²Ö É Ö ³ ³μ Ë Í μ μ ³μ- ² É ³ Î ±μ μ ± ²Ö ² μ Ö É ²μ ÒÌ μí μ ± ² μ ³ Ï μ ²ÊÎ μ ³ Ê Ô E0 μ = 700 ŒÔ ÉμÎ - ±μ³, ÊÎ ÉÒ ÕÐ ³ μ ÊÉ ³ É ². 1. ˆ ˆ Šˆ Š ˆ ˆŠˆ ˆ ˆˆ Ÿ ƒ ˆ ƒˆ E 0 μ = 700 ŒÔ ˆŠ Œˆ œ Šμ³ ÓÕÉ Ö μ ³³ SRIM-2008 μ μ²ö É ÒÎ ²ÖÉÓ ² ÊÕÐ μé Ô ÉÖ ²ÒÌ μ μ Ì μìμ Î ±μ μ Ò Ò: 1
4 ( E 1) Ê Ê μé Ô S inel (z) z (z) ( ) E 2) Ê Ê μé Ô S el (z) z (z), ) el ), inel ( E 3) Ëμ μ Ò μ Ê Ö S ph (z) z (z). ph É μé Ô μ ²ÊÎ ± ² μ ³ Ï μ ³ Ê Ô E0 μ = 700 ŒÔ ³ ³ ±μ³ ÓÕÉ μ μ ³³Ò SRIM ³ ÕÉ Î Ö R p ΔE inel = S inel (z)dz 688, 59 ŒÔ (98, 37 %), 0 R p ΔE el = S el (z)dz 0, 21 ŒÔ (0, 03 %), 0 R p ΔE ph = S ph (z)dz 11, 20 ŒÔ (1, 60 %) ( ² ) É ² ³μ ÉÓ μ² μ μé Ô S(z) = S inel (z)+s ph (z)+s el (z) μ Ê Ô E 0 μ = 700 ŒÔ μé ²Ê Ò ± ² μ ³ Ï. ˆ μ²ó ÊÖ ÔÉ Ò, ³μ μ ÒÎ ² ÉÓ ² ÊÕÐ : ) ³μ ÉÓ Ô μ μé ²Ê Ò ³ Ï E(z) =E 0 μ Z 0 S inel (z)dz,. 1. ³μ ÉÓ μ² μ μé Ô S(z) ( ² ) Ô E(z) ( ) μ μ Ê Ô E 0 μ = 700 ŒÔ μé ²Ê Ò ± ² μ ³ Ï 2
5 ) ³μ ÉÓ ±μ μ É μ μé ²Ê Ò ³ Ï ( ) 1/2 2E(z) V (z) =, M U Å ³ Éμ³ Ê ( ³³ Ì). ±μ μ ÉÓ μ μ Ê Ìμ ± ² ÊÕ ³ Ï Ó μ É ²Ö É 2E(z =0) V 0 (z =0)= =2, ³/c, M U ) ³μ ÉÓ μé z ³ μé ³μ³ É μ Ö μ ³ Ï Ó μ μ μ² μ μ É μ ± t(z) = M U z 0 dξ V (ξ).. 1 ( ) ³μ ÉÓ Ô μ Ê μé ²Ê Ò ³ Ï,. 2 Å ³μ ÉÓ ±μ μ É ( ² ) ³ t(z) ( ) μ Ê Ô E 0 μ = 700 ŒÔ μé ²Ê Ò ± ² μ ³ Ï. ˆ μ²ó ÊÖ μ ² ÕÕ Ëμ ³Ê²Ê t(z), ³μ μ μí ÉÓ ³Ö μìμ Ö μ ³ Ï μ μ μ² μ μ É μ ± t μ ³μ ÉÓ ±μ μ É V (z) ( ² ) ³ t(z) ( ) μ Ê Ô E 0 μ =700 ŒÔ μé ²Ê Ò ± ² μ ³ Ï 2. Œ œ Œˆ Š ƒ ˆŠ ÊÎ Éμ³ ± ²Ó μ ³³ É É ³ Ê ²Ö μ ² Ö - Ï ÉμÎ μ Ô² ±É μ μ É ³ ÉÊ Í ² Î ±μ É ³ ±μμ É 3
6 ³μ É ÒÉÓ [7Ä9] C e (T e ) T e t = 1 ( rλ e r r (T e) T ) e + ( λ e r z (T e) T ) e z g (T e,i )(T e T i )+A e (r, z, t), (1) C i (T i ) T i t = 1 ( rλ i r r (T i ) T ) i + ( λ i r z (T i) T ) i + g (T e,i )(T e T i ), z (2) Ó C e,i, λ e,i Å É ²μË Î ± ³ É Ò É ³Ò, g Å ±μôëë Í É ³μ É Ö Ô² ±É μ μ Ï ÉμÎ μ μ É ³, ËÊ ±Í Ö A(r, z, t) Å μ Ñ ³ Ö ²μÉ μ ÉÓ μ ³μ μ μ³ ³μÐ μ É ( ÉμÎ ±). É ³ Ê (1), (2) Ï ² Ó μ ² ÊÕÐ ³ Î ²Ó Ò³ - Î Ò³ Ê ²μ Ö³ : T e,i (r, z, 0) = T 0 = 300 K, (3) T e,i (r, z, t) T e,i (r, z, t) r =0, r=0 z =0, (4) z=0 T e,i (R max,z,t)=t e,i (r, Z max,t)=t 0. [7, 9] ÉμÎ ± Ò ² [ ] A e (r, z, t) b e S inel (z)exp (t t e0) 2 ( 2σe0 2 exp r ), (5) r e0 r e0, t e0, σ e0 Å Ë Î ± ±μ É ÉÒ ³μ ². ˆ μ²ó ÊÖ μ²êî ÊÕ ÒÏ ËÊ ±Í Õ t(z), ÉμÎ ± Ô A e (r, z, t), μ ³Ò ² É ÕÐ ³ μ μ³ Ê Ô² ±É μ ÊÕ μ É ³Ê, Ï ³ ² ÊÕÐ ³ : [ ] A e (r, z, t) b e S inel (z)exp (t t e0 t(z)) 2 ( 2σe0 2 exp r ). (6) r e0 ² Ê É ³ É ÉÓ, ÎÉμ Ì ±É μ ³Ö Ëμ μ ÒÌ ±μ² ÊÎ Éμ³ Ì ³μ É μé É ³ ÉÊ Ò ³ É Î ÉμÉÒ ν ph =(1 3) ƒí, μ É μ ³Ö Ëμ μ ÒÌ ±μ² t ph = (0,3 1,0) ³ ÓÏ Ì ±É μ μ ³ μìμ Ö μ. ˆ ÉμÎ ± (5) É Ê É ³ Ï ³Ö 0 <t<10 14 c μé ± 0 z Z max. μé² Î μé μ ÉμÎ ± (6) É Ê É ³ Ï ³Ö 0 <t< ²μ± ²Ó μ μ ² É, Ìμ É Ö μ, ÔÉ μ ² ÉÓ É Ö ³ É μ μ³ μ μ μ É μ ±. 4
7 3. Œ ˆ ƒ ˆŸ ˆ ˆ œ ²Ö Î ² μ μ Ï Ö É ³Ò Ê (1)Ä(4) Ò² μ²ó μ Ò Ö Ö ±μ Î μ- μ É Ö Ì ³ μ Ö ±μ³ μ± ³ Í O(h t + h 2 r + h2 z ) Ì ³ ³ ÒÌ ² É ± ³ μ Ö ±μ³ μ± ³ Í [10].. 3. ³ ÉÊ Ò ³μ É μé ²Ê Ò ³ Ï z Ô² ±É μ μ μ ( ² ) Ï É± ( ) Ò ³μ³ ÉÒ ³ 0 <t< Ï μ³h t = 0, c. 4. ˆ μé ³ Î ± Ö μ Ì μ ÉÓ, μ Î ÕÐ Ö Ò ² Ò μ Ñ ³, ±μéμ μ³ É ³ ÉÊ É ³ ÉÊ ² ² Ö ± ²Ö, ÊÎ É Ö μ ( Ì Ê μ±) ³μ³ ÉÒ ³ t 1 =1, c, t 2 =1, c, t 3 =3, c ÊÎ Éμ³ Ö μ ( Ê μ±) ³μ³ ÉÒ ³ t 1 = c, t 2 = 2, c t 3 = 3, c. ³ Ò Í ² : ³ É μ μ Ö D = 280 A, ²Ê Z =16, A 5
8 . 3 É ² Ò É ³ ÉÊ Ò ³μ É μé ²Ê Ò ³ Ï ²Ö Ô² ±É μ μ μ ( ² ) Ï É± ( ) Ò ³μ³ ÉÒ ³ Ï μ³h t =0, c. ˆ. 3 μ, ÎÉμ ÉμÎ ± Ô - É Ê É Éμ³ ³ É, Ìμ É Ö μ ³Ö ² É ÕÐ ÉÖ ²Ò μ. [9] Ò Ê²ÓÉ ÉÒ ² μ, ±μ μ ÊÉ ³ - É ² ÊÎ ÉÒ É Ö.. 4 ²Ö É ²Ó μ μ ² É ² μé ³ Î ± Ö μ Ì μ ÉÓ, μ Î ÕÐ Ö Ò ² Ò μ Ñ ³, ±μéμ μ³ É ³ ÉÊ É ³ ÉÊ ² ² Ö ± ²Ö, ÊÎ É Ö μ ( Ì Ê μ±) ÊÎ Éμ³ Ö μ ( Ê μ±) ² Î Ò ³μ³ ÉÒ ³. Š ˆ μé ²μ ³μ ²Ó É ³ Î ±μ μ ±, ÊÎ ÉÒ ÕÐ Ö - ² É ÕÐ μ μ ÊÉ ³ É ² μ ²ÊÎ. ³± Ì μ ³μ ² μ²êî Ò Ê²ÓÉ ÉÒ Î ² μ μ ² μ Ö É ³ ÉÊ Ô² ±É μ - μ μ Ï É± ± ²Ö μ ²ÊÎ μ ³ Ê Ô 700 ŒÔ. Ò μ² Î ² Ò ² ÊÌ Ì ³ ÒÎ ². μ ʲÓÉ É ³ ÒÎ ² - É ²Ó ÒÌ Ô± ³ Éμ ³μ μ ² ÉÓ ² ÊÕÐ Ò μ Ò: 1) μ²ó μ ²μ μ μ ³μ ² ËÊ ±Í ÉμÎ- ± (6) μ ³ ³ É Ö Δt = c É ²μ Ò μí Ò μ - Ìμ ÖÉ Î, Î ³ μ²ó μ ËÊ ±Í ÉμÎ ± (5), É.. ÊÎ É Ö μ ÉμÎ ± É Ê É Éμ³ ³ É, Ìμ É Ö μ ³Ö ² É ÕÐ ÉÖ ²Ò μ, 2) ³ μ ² É, É ³ ÉÊ ÒÏ É É ³ ÉÊ Ê ² ² Ö ± ²Ö, ³ ÓÏ μé μ É ²Ó μ ³μ ², ÊÎ ÉÒ É Ö μ : r max 62 A, z =0(. 4 Ê) Å ÊÎ É Ö μ r max 115 A, z =0(. 4 ÌÊ) Å ÊÎ É Ö μ [9]. μé Ò μ² Ë μ μ μ ± ˆ, ÉÒ º º ˆ 1. ËÐ Í ˆ. Œ. É ³ Î ± Ì Òϱ Ì Ì, μ ÊÉÒÌ Ö Ò³ μ ²Ê- Î Ö³ // μ±² , º Ä Š μ Œ. ˆ., ËÏ Í ˆ. Œ., É μ.. μ Ö ² ± Í μ ÒÌ ³ - ³ É ²² Ì // Éμ³ Ö Ô Ö Ä ƒ Ê Ÿ.., Š μ Œ. ˆ., ËÏ Í ˆ. Œ. ² μ μ μ μ μ Ô² ±É μ μ μ É ±Éμ Ö μ Î É ÍÒ ³ É ²² // , º Ä
9 4. Fleisher R. L., Price P. B., Walker R. M. Ion Explosion Spike Mechanism for Formation of Charged-Particle Tracks in Solids // J. Appl. Phys V. 36, No. 11. P. 3645Ä Fleisher R. L., Price P. B., Walker R. M. Nuclear Track in Solids. Los Angeles: Univ. of California, Biersack J. P., Haggmark L. G. A Monte Carlo Computer Program for the Transport of Energetic Ions in Amorphous Targets // Nucl. Instr. Meth. Phys. Res. B V P. 257Ä269 ( 7. ³ Ì μ ˆ.., Ò±.., μë³ A.. Ò² É ÒÌ É ² μ É ³ ÉÖ ²ÒÌ μ μ É ³ ÉÊ Ò ÔËË ±ÉÒ Ô² ±É μ μ Ï ÉμÎ μ μ É ³ Ì // Ÿ , Ò. 6. C. 1592Ä Yavlinskii Yu. N. Track Formation in Amorphous Metals under Swift Heavy Ion Bombardment // Nucl. Instr. Meth. B V Ä ³ Ì μ ˆ.., Ò±.., ³²Ö Ö... ² μ ² μ É ³- ÉÊ ÒÌ ÔËË ±Éμ ³ É ² Ì μ ²ÊÎ Ì ÉÖ ²Ò³ μ ³ Ò μ- ± Ì Ô ³± Ì Ê É ²μ μ μ μ É ²Ö Ô² ±É μ μ Ï É± // Ó³ Ÿ , º 1(130).. 63Ä C ³ ±.. μ Ö μ É ÒÌ Ì ³. Œ.: ʱ, Ä276. μ²êî μ 14 ÉÖ Ö 2009.
10 ±Éμ. ˆ. É μ ± Ö μ μ Î ÉÓ μ ³ É 60 90/16. ʳ μë É Ö. Î ÉÓ μë É Ö. ². Î. ². 0,62. Î.-. ². 0, Ô±. ± º ˆ É ²Ó ± μé ² Ñ μ μ É ÉÊÉ Ö ÒÌ ² μ ,. Ê, Œμ ±μ ± Ö μ ²., ʲ. μ² μ-šõ,
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