α锆中螺形位错与空位盘的相互作用模拟
|
摘要
金属锆及其合金是一种重要的核工业材料,由于其较小的中子吸收截面,常被用于制作燃料包壳管。因此,这种材料在辐射条件下的稳定性对核反应堆的正常安全运转起到至关重要的作用,研究锆在辐射作用下金属内部缺陷的产生与变化方式具有重要意义。近来随着材料科学与计算机技术的发展,分子设计和分子模拟技术得到了迅速发展,其应用前景广泛,己受到很多研究者特别是材料研究者的重视。基于位错和缺陷簇理论的计算机模拟缺陷间的相互影响是当今较流行的材料研究课题。
本文使用了修正共轭梯度法和修正格林方程自由边界条件研究α-锆中双层盘状空位簇的临界坍塌压应变与空位盘尺寸和螺形位错之间的关系。模拟过程中通过改变空位盘半径大小,改变引入的螺形位错与空位盘心间的距离,得出不同情况下的临界坍塌压应变值,并对坍塌的原子晶体结构进行分析。计算结果显示:空位盘尺寸越大,所需的临界坍塌压应变越大。螺形位错的存在会显著减小临界坍塌压应变值,使得空位盘更易坍塌,这种影响在小尺寸空位盘中表现更明显。坍塌结构中出现了正弗兰克不全位错环和负弗兰克全位错环,但没有出现堆垛层错。螺形位错致使中间层位错环发生伯氏矢量为[0001]的错位,形成不闭合的位错环,而且这种错位会随空位盘尺寸增大而在外层原子结构中表现出来。
空位盘的坍塌对金属的宏观塑性变形具有深远影响,因此金属的机械性能在很大程度上取决于这种微观结构的改变,本实验对锆金属的工作寿命和机械性能变化预估有重要参考作用。
Zirconium is an important nuclear industry material used as fuel cladding tube due to its low thermal neutron capture cross section. Hence the stability of this material under irradiation condition is crucial to the safety of nuclear reactors. It is of great significance to study the mode of generation and evolution defects. Molecular design and simulation is developing quickly with the development of material science and computer technology which has bright future for application. Many researchers, especially working in material science, have been paying great attention to this technique. Computer simulation of defects cluster and dislocation interaction is a popular subject based on defect theories.
In this thesis, a compressive strain is applied to a double-layer vacancy cluster platelet which lies in (0001) plane ofα-zirconium. The critical collapse compressive strain under the influence of platelet size and screw dislocation are obtained by using a combination of modified conjugate gradient method and modified Green’s function flexible boundary condition. In this simulation, the radius of platelets and the distance between the screw dislocation and the platelet are changed to get corresponding critical collapse strains. Besides, the collapse atomic-level configurations are analyzed. The results indicate: critical collapse strain becomes larger as the vacancy cluster platelet size increases when screw dislocation is absent. However, it decreases obviously when the screw dislocation is introduced in the simulation box. The influence of the screw dislocation on small vacancy cluster platelets is stronger than on the big ones, which causes the collapse of small vacancy platelet more easily. There are two kinds of dislocation loops including positive Frank partial dislocation loop and negative Frank partial dislocation loop in collapsing atomic-level configuration but no stacking fault loops. A relative slip in middle layers with displacement of Burgers vector [0001] emerges under the impact of the screw dislocation. This kind of slip also appears in outer layers when platelet size is large and leads to dislocation loops unclosed.
The macroscopic plastic deformation due to microscopic configuration evolution plays an important role on mechanical properties of metals. Therefore, our study can help us predict the serve life and the changes of mechanical properties of zirconium.
本文使用了修正共轭梯度法和修正格林方程自由边界条件研究α-锆中双层盘状空位簇的临界坍塌压应变与空位盘尺寸和螺形位错之间的关系。模拟过程中通过改变空位盘半径大小,改变引入的螺形位错与空位盘心间的距离,得出不同情况下的临界坍塌压应变值,并对坍塌的原子晶体结构进行分析。计算结果显示:空位盘尺寸越大,所需的临界坍塌压应变越大。螺形位错的存在会显著减小临界坍塌压应变值,使得空位盘更易坍塌,这种影响在小尺寸空位盘中表现更明显。坍塌结构中出现了正弗兰克不全位错环和负弗兰克全位错环,但没有出现堆垛层错。螺形位错致使中间层位错环发生伯氏矢量为[0001]的错位,形成不闭合的位错环,而且这种错位会随空位盘尺寸增大而在外层原子结构中表现出来。
空位盘的坍塌对金属的宏观塑性变形具有深远影响,因此金属的机械性能在很大程度上取决于这种微观结构的改变,本实验对锆金属的工作寿命和机械性能变化预估有重要参考作用。
Zirconium is an important nuclear industry material used as fuel cladding tube due to its low thermal neutron capture cross section. Hence the stability of this material under irradiation condition is crucial to the safety of nuclear reactors. It is of great significance to study the mode of generation and evolution defects. Molecular design and simulation is developing quickly with the development of material science and computer technology which has bright future for application. Many researchers, especially working in material science, have been paying great attention to this technique. Computer simulation of defects cluster and dislocation interaction is a popular subject based on defect theories.
In this thesis, a compressive strain is applied to a double-layer vacancy cluster platelet which lies in (0001) plane ofα-zirconium. The critical collapse compressive strain under the influence of platelet size and screw dislocation are obtained by using a combination of modified conjugate gradient method and modified Green’s function flexible boundary condition. In this simulation, the radius of platelets and the distance between the screw dislocation and the platelet are changed to get corresponding critical collapse strains. Besides, the collapse atomic-level configurations are analyzed. The results indicate: critical collapse strain becomes larger as the vacancy cluster platelet size increases when screw dislocation is absent. However, it decreases obviously when the screw dislocation is introduced in the simulation box. The influence of the screw dislocation on small vacancy cluster platelets is stronger than on the big ones, which causes the collapse of small vacancy platelet more easily. There are two kinds of dislocation loops including positive Frank partial dislocation loop and negative Frank partial dislocation loop in collapsing atomic-level configuration but no stacking fault loops. A relative slip in middle layers with displacement of Burgers vector [0001] emerges under the impact of the screw dislocation. This kind of slip also appears in outer layers when platelet size is large and leads to dislocation loops unclosed.
The macroscopic plastic deformation due to microscopic configuration evolution plays an important role on mechanical properties of metals. Therefore, our study can help us predict the serve life and the changes of mechanical properties of zirconium.
引文
1. Alder, B. J. and Wainwright, T. E. Phase transition for a hard sphere system. Journal of Chemical physics, 27:1208, 1957.
2. Gibson, J. B., Goland, A. N., Milgram, M., and Vineyard, G. H. Dynamics of radiation damage. Physics Review, 120:1229, 1960.
3. Rahman, A. Correlation of motion of atoms in liquid argon. Physics Review, 136A:405, 1964.
4. Allen, M. P. and Tildesley, D. J. Computer simulation of liquids. Oxford University Press, Oxford, 1987.
5. Landau, D. P. and Binder, K., A Guide to Monte Carlo simulations in statistical Physics, Cambridge University Press, Cambridge, 2000.
6. Schmidt, K. E. and Ceperley, D. Monte Carlo techniques for quantum fluids. Solids and Droplets, 205, 1998.
7. Doolen, G. D., ed. Lattice gas methods for PDEs. North-Holland Amsterdam, 1991.
8. M. Griffiths. A review of microstructure evolution in zirconium alloys during irradiation. Journal of Nuclear Material, 159:190–218, 1988.
9. Osetsky, Y. N., Bacon, D. J., Serra, A., Singh, B. N. and Golubov. Philosophical Magazine, 83:61, 2003.
10. De Diego, N. Osetsky, Y. N. and Bacon, D. J. Metallurgical Transactions A, 33:783-790, 2002.
11. Osetsky, Y. N., Bacon, D. J. and Serra. A. Philosophical Magazine Letters, 79:273-286,1999.
12. Lustman, B., Kerze, F. The metallurgy of Zr. McGraw Hill, 15:156-164, 1955.
13. I. G. Ritchi, Waterside corrosion of zirconium alloys in nuclear power plants. International Atomic Energy Agency, 142:202-211, 1998.
14. D. J. Bacon and T. Diaz de la Rubia. Journal of Nuclear Material, 216:275-284, 1994.
15. R. S. Averback and T. Diaz de la Rubia, Solid State Physics, 51:281-294, 1998
16. D. J. Bacon et al. Nuclear Instrument and Methods, B102:37-43, 1995.
17. D. J. Bacon, F. Gao, and Yu. N. Osetsky. Journal Computer-Aided Material, 6:225, 2000.
18. Yu. N. Osetsky et al., Philosophical Magazine, 83:61-70, 2003.
19. N. de Diego, Yu. N. Osetsky, and D. J. Bacon. Metallurgical and Materials Transactions A, 33:783-797, 2002.
20. Yu. N. Osetsky, D. J. Bacon, and A. Serra. Philosophical Magazine Letter, 79:273-283, 1999.
21. Kenji Yamaura, Akiyuki Takahashi, and Masanori Kikuchi. Molecular Dynamics Study on Interaction of C-Component Dislocation Loop and Edge Dislocation inα-Zirconium. Springer Berlin Heidelberg, 3:247-251, 2007.
22. Xiangli Liu, S. I. Golubov, C. H. Woo, and Hanchen Huang. Atomistic Simulations of Dislocation-Void Interactions using Green’s Function Boundary Relaxation. Computer Modeling in Engineering and Sciences, 5:527-539, 2004.
23. Jae-Hyeok Shima and Young Whan Cho, Sang Chul Kwon and Whung Whoe Kim. Screw dislocation assisted martensitic transformation of a bcc Cu precipitate in bcc Fe. Applied Physics Letters, 90:021906, 2007.
24. R. E. Voskoboynikov, Yu. N. Osetsky, D. J. Bacon. Self-interstitial atom clusters as obstacles to glide of 1/3[11 2 0](1100) edge dislocations inα-zirconium. Materials Science and Engineering A, 400:54–58, 2005.
25. D. Kulikov, M. Hou. Vacancy dislocation loops in zirconium and their interaction with self-interstitial atoms. Journal of Nuclear Materials, 342:131–140, 2005.
26. XiangLi Liu, Nano-plasticity in BCC and HCP Metals. Thesis for Degree of Doctor of Philosophy, 5-6, 41-50, 144-160, 2004.
27. R.A, Holt, A. R. Causey, N. Christodoulou, M. Griffith, E.T.C Ho and C.H. Woo. American Society for Testing Material Special Technical Publications, 1295:623, 1996.
28. C. H. Woo. Defect accumulation behavior in hcp metals and alloys. Journal of Nuclear Materials, 276:90-103, 2000.
29. R. A. Holt, In-reactor deformation of cold-worked Zr–2.5Nb pressure tubes. Journal of Nuclear Materials, 372(2-3):182-214, 2008.
30. R. A. Holta. Mechanisms of irradiation growth of alpha-zirconium alloys. Journal of Nuclear Materials, 159:310-338, 1988.
31. C. H. Woo, R. A. Holt and M. Griffiths, Materials Modeling:from theory to technology. Institute of Physics Publishing, 124:55-60, 1992.
32. J. P. Hirth and J. Lothe. Theory of Dislocations. McGraw-Hill New York, 1968.
33. V. Vitek, M. S. Duesbery. Mechanical Properties of BCC Metals. M. Meshii, 3-15, 1982.
34. A. H. Cottrell. Dislocations and plastic flow in crystals. Oxford university Press, 1953.
35. J. Friedel. Les Dialocations. Gauthier Villars, Paris, 1958.
36. A. C. Damask and G. J., Dienes. Point defects in metals. Gordon and breach science publishers, 1971.
37. F. Gao, D. J. Bacon, L. M. Howe and C. B. So. Temperature-dependence of defect creation and clustering by displacement cascades inα-zirconium. Journal of Nuclear Materials, 294(3):288-298, 2001.
38. D. J. Bacon, Osetsky YuN, R. E. Stoller, R. E. Voskoboinikov. Journal of Nuclear Materials, 323:152–162, 2003.
39. After Seeger. Dislocations and Mechanical Properties of Crystals, 243, 1957
40. After Read. Dislocation in Crystals, McGraw-Hill, 1953.
41. D. Hull and D. J. Bacon. Introduction to Dislocations Fourth Edition. Butterworth Heinemann Press, 2001.
42. Gary S. Was. Fundamentals of Radiation Materials Science. Springer Berlin Heidelberg New York, 2007.
43. J. F .Justo, M. D. Koning, W. Cai, V. V. Bulatov, Point defect interaction with dislocations in silicon. Materials Science and Engineering A, 309:129-135, 2001.
44. S. T. Zhou, Preston D. L., Lomdahl, P. S., Beazley, D. M., Science, 279:1525 1998.
45. D. Rodney, and R. Phillips. Structure and strength of dislocation junction: an atomistic level analysis. Physics Review Letter, 82:1704, 1999.
46. D. Rodney and G. Martin. Dislocation pinning by glissile interstitial loops in a nickel crystal: a molecular-dynamics study. Physics Review B, 61:8714, 2000.
47. D. Rodney and G. Martin. Dislocation pinning by small interstitial loops: a molecular-dynamics study. Physics Review Letter, 82:3272, 1999.
48. Q. Yue, A. Strachan, T. Cagin, W. A. Goddard III. Large scale atom simulations of screw dislocation structure, annihilation and cross-slip in fcc Ni. Material. Science and Engineering A, 309-3l0:156, 2001.
49. C. H. Woo, B. N. Singh. The concept of production bias and its possible role in defect accumulation under cascade damage conditions. Physica Status Solidi B, 159: 609-618, 1990.
50. C. H. Woo, B. N. Singh. Production bias due to clustering of point defects in irradiation-induced cascades. Philosophical Magazine A, 65:889-899, 1992.
51. B. N. Singh, S. I. Golubov, H. Trinkaus, A. Serra, Yu. N., Osetsky, A.V. Barashev. Aspects of microstructure evolution under cascade damage conditions. Journal of Nuclear Materials, 251:107-119, 1997.
52. Yu. N. Osetsky, D.J. Bacon, A. Serra, B.N. Singh, S.I. Golubov. Stability and mobility of defect clusters and dislocation loops in metals. Journal of Nuclear Materials, 276:65-78, 2000.
53. Yu N., Osetsky, A. Serra, B.N. Singly S.I. Golubov. Structure and properties of clusters of self-interstitial atoms in fcc copper and bcc iron. Philosophical Magazine A, 80:2131-2145, 2000.
54. B. N. Singh and J. H. Evans. Significant differences in defect accumulation behavior between fcc and bcc crystals under cascade damage conditions. Journal of Nuclear Materials, 226:277-288, 1995.
55. S. Amelinckx, W. Bontinck, W. Dekeyser, and F. Seitz. On the formation and properties of helical dislocations. Philosophical Magazine, 2:355-368, 1957.
56. K. S. Cheung, S. Yip. Brittle-ductile transition in intrinsic fracture-behavior of crystals. Physical Review Letters, 65:2804-2816, 1990.
57. B. L. Holian, R. Ravelo. Fracture simulations using large-scale molecular-dynamics. Physical Review Letters B, 51:11275, 1995.
58. J. E. Sinclair R. Fletcher. New method of saddle-point location for calculation of defect migration energies. Journal of physics C, 7:864-867, 1974
59. B. J. AIder and T. E. Wainwright. Phase transition for a hard sphere system. Journal of Chemical physics, 27:1208, 1957.
60. L. Verlet. Computer experiments on classical fluids. I. thermodynamical properties of Lennard Jones molecules. Physical Review Letters, 165:201-215, 1967.
61. M. Parrinello and A. Rahman. Polymorphic transitions in single crystals: A New Molecular Dynamics Metros. Journal of Applied Physics, 52:7182-7197, 1981.
62. C. Kittle. Introduction to Solid State Physics, 5th edition. Wi1ey, New York, 1976.
63. M. W. Finnis, J. E. Sinclair. A simple empirical n-body potential for transition-matter structure defects and mechanical properties. Philosophical Magazine A, 50:45-56, 1984.
64. G. J. Ackland, R. Thetford. An improved n-body semiempirical model for body-centered cubic transition-metals. Philosophical Magazine A, 56: 15-22, 1987.
65. http://trond.hjorteland.com/thesis/node27.html
66. E. M. Beale. A derivation of conjugate gradients, Numerical methods for Non-linear Optimization, ed. F. A. Lootsma, London, Academic Press, 1972.
67. D. C. Rapaport.The art of molecular dynamics simulation, Second Edition. Cambridge University Press, 32, 2004
68. J. E. Sinclair. Improved atomistic model of a bcc dislocation core. Journal of Applied Physics. 42: 5321-5334, 1971.
69. J. E. Sinclair. Influence of interatomic force law and of kinks on propagation of brittle cracks. Philosophical Magazine. 31:647-656, 1975.
70. J. D. Eshelby, W. T. Read and W. Shockley. Anisotropic elasticity with applications to dislocation theory. Acta MetalL. 1:251-267, 1953.
71. J. E. Sinclair, P. C. Gehlen, R. G Hoagland, J. P. Hirth. Flexible boundary conditions and non-linear geometric effects in atomic dislocation modelling. Journal of Applied Physics. 49: 3890-3908, 1978.
72. R. G. Hoagland, J .P. Hirth, P. C. Gehlen. Atomic simulation of dislocation core structure and Peierls stress in alkali-halide. Philosophical Magazine. 34:p413-422, 1976.
73. C. H. Woo, M. P. Puls. Improved method of calculating lattice friction stress using an atomistic model. Journal of physics C, Solid State Physics, 9:L27-L35, 1976.
74. S. Rao, C. Hernandez, J. P. Simrnons, T. A. Parthasarathy, C. Woodward. Green’s function boundary conditions in two-dimensional and three-dimensional atomistic simulations of dislocations. Philosophical Magazine A, 77:231-245, 1998.
75. J. W. Deutz and H. R. Schrober. Program to calculate elastic Green’s functions, displacement fields and interaction energies in cubic materials. Computer Physics Communications, 30:87-99, 1983.
76. S. I. Golubov, X. L. Liu, H. Huang, C. H. Woo. GFCUBHEX: Program to calculate elastic Green’s functions and displacement fields for applications in atomistic simulations of defects in cubic and HCP crystals. Computer Physics Communications, 137:312-322, 2001.
77. K. Ohsawa, E. Kuramoto. Flexible boundary condition for a moving dislocation. Journal of Applied Physics, 86:179-194, 1999.
78. S. J. Zhou, D. L. Preston, P. S. Lomdahl, and D. M. Beazley. Large-scale molecular dynamics simulations of dislocation intersection in copper. Science, 279:1525-1527, 1998.
79. G. J. Ackland, S. J. Wooding, D. J. Bacon. Defect, surface and displacement-threshhold properties of alpha-zirconium simulated with a many-body potential. Philosophical Magazine A, 71:553-566, 1995.
80. A. N. Stroh. Dislocation and cracks in anisotropic elasticity. Philosophical Magazine, 3:625-638, 1958.
81. D. Kulikov, L. Malerba, M. Hou, Philosophical Magazine, 86(2):141-172, 2006.
82. D. Kulikov, L. Malerba, M. Hou, Nuclear Instrument Methods B, 228:245-255, 2005.
83. D. Kulikov M. Hou, L. Malerba. Calculations of the formation and binding energies for point defect clusters in the Fe-Cu system and Zr. ITEM meeting, 2003.
84. Berghezan, Fourdeux and Amelinckx. Transmission electron microscopy studies of dislocations and stacking faults in a hexagonal metal:Zinc. Acta Metallurgica, 9:464-490, 1961.
85. Vikram Gavini, Kaushik Bhattacharya and Michael Ortiz. Vacancy clustering and prismatic dislocation loop formation in aluminum. Physical Review B, 76(18):01011-01014, 2007.
86. C. H. Woo, R.A. Holt and M. Griffith. Anisotropic diffusion of point defects: effects on irradiation-induced deformation and microstructure, materials modelling: from theory to technology. Institute of Physics Publishing, Bristol and Philadelphia, 20:55-60, 1991.
2. Gibson, J. B., Goland, A. N., Milgram, M., and Vineyard, G. H. Dynamics of radiation damage. Physics Review, 120:1229, 1960.
3. Rahman, A. Correlation of motion of atoms in liquid argon. Physics Review, 136A:405, 1964.
4. Allen, M. P. and Tildesley, D. J. Computer simulation of liquids. Oxford University Press, Oxford, 1987.
5. Landau, D. P. and Binder, K., A Guide to Monte Carlo simulations in statistical Physics, Cambridge University Press, Cambridge, 2000.
6. Schmidt, K. E. and Ceperley, D. Monte Carlo techniques for quantum fluids. Solids and Droplets, 205, 1998.
7. Doolen, G. D., ed. Lattice gas methods for PDEs. North-Holland Amsterdam, 1991.
8. M. Griffiths. A review of microstructure evolution in zirconium alloys during irradiation. Journal of Nuclear Material, 159:190–218, 1988.
9. Osetsky, Y. N., Bacon, D. J., Serra, A., Singh, B. N. and Golubov. Philosophical Magazine, 83:61, 2003.
10. De Diego, N. Osetsky, Y. N. and Bacon, D. J. Metallurgical Transactions A, 33:783-790, 2002.
11. Osetsky, Y. N., Bacon, D. J. and Serra. A. Philosophical Magazine Letters, 79:273-286,1999.
12. Lustman, B., Kerze, F. The metallurgy of Zr. McGraw Hill, 15:156-164, 1955.
13. I. G. Ritchi, Waterside corrosion of zirconium alloys in nuclear power plants. International Atomic Energy Agency, 142:202-211, 1998.
14. D. J. Bacon and T. Diaz de la Rubia. Journal of Nuclear Material, 216:275-284, 1994.
15. R. S. Averback and T. Diaz de la Rubia, Solid State Physics, 51:281-294, 1998
16. D. J. Bacon et al. Nuclear Instrument and Methods, B102:37-43, 1995.
17. D. J. Bacon, F. Gao, and Yu. N. Osetsky. Journal Computer-Aided Material, 6:225, 2000.
18. Yu. N. Osetsky et al., Philosophical Magazine, 83:61-70, 2003.
19. N. de Diego, Yu. N. Osetsky, and D. J. Bacon. Metallurgical and Materials Transactions A, 33:783-797, 2002.
20. Yu. N. Osetsky, D. J. Bacon, and A. Serra. Philosophical Magazine Letter, 79:273-283, 1999.
21. Kenji Yamaura, Akiyuki Takahashi, and Masanori Kikuchi. Molecular Dynamics Study on Interaction of C-Component Dislocation Loop and Edge Dislocation inα-Zirconium. Springer Berlin Heidelberg, 3:247-251, 2007.
22. Xiangli Liu, S. I. Golubov, C. H. Woo, and Hanchen Huang. Atomistic Simulations of Dislocation-Void Interactions using Green’s Function Boundary Relaxation. Computer Modeling in Engineering and Sciences, 5:527-539, 2004.
23. Jae-Hyeok Shima and Young Whan Cho, Sang Chul Kwon and Whung Whoe Kim. Screw dislocation assisted martensitic transformation of a bcc Cu precipitate in bcc Fe. Applied Physics Letters, 90:021906, 2007.
24. R. E. Voskoboynikov, Yu. N. Osetsky, D. J. Bacon. Self-interstitial atom clusters as obstacles to glide of 1/3[11 2 0](1100) edge dislocations inα-zirconium. Materials Science and Engineering A, 400:54–58, 2005.
25. D. Kulikov, M. Hou. Vacancy dislocation loops in zirconium and their interaction with self-interstitial atoms. Journal of Nuclear Materials, 342:131–140, 2005.
26. XiangLi Liu, Nano-plasticity in BCC and HCP Metals. Thesis for Degree of Doctor of Philosophy, 5-6, 41-50, 144-160, 2004.
27. R.A, Holt, A. R. Causey, N. Christodoulou, M. Griffith, E.T.C Ho and C.H. Woo. American Society for Testing Material Special Technical Publications, 1295:623, 1996.
28. C. H. Woo. Defect accumulation behavior in hcp metals and alloys. Journal of Nuclear Materials, 276:90-103, 2000.
29. R. A. Holt, In-reactor deformation of cold-worked Zr–2.5Nb pressure tubes. Journal of Nuclear Materials, 372(2-3):182-214, 2008.
30. R. A. Holta. Mechanisms of irradiation growth of alpha-zirconium alloys. Journal of Nuclear Materials, 159:310-338, 1988.
31. C. H. Woo, R. A. Holt and M. Griffiths, Materials Modeling:from theory to technology. Institute of Physics Publishing, 124:55-60, 1992.
32. J. P. Hirth and J. Lothe. Theory of Dislocations. McGraw-Hill New York, 1968.
33. V. Vitek, M. S. Duesbery. Mechanical Properties of BCC Metals. M. Meshii, 3-15, 1982.
34. A. H. Cottrell. Dislocations and plastic flow in crystals. Oxford university Press, 1953.
35. J. Friedel. Les Dialocations. Gauthier Villars, Paris, 1958.
36. A. C. Damask and G. J., Dienes. Point defects in metals. Gordon and breach science publishers, 1971.
37. F. Gao, D. J. Bacon, L. M. Howe and C. B. So. Temperature-dependence of defect creation and clustering by displacement cascades inα-zirconium. Journal of Nuclear Materials, 294(3):288-298, 2001.
38. D. J. Bacon, Osetsky YuN, R. E. Stoller, R. E. Voskoboinikov. Journal of Nuclear Materials, 323:152–162, 2003.
39. After Seeger. Dislocations and Mechanical Properties of Crystals, 243, 1957
40. After Read. Dislocation in Crystals, McGraw-Hill, 1953.
41. D. Hull and D. J. Bacon. Introduction to Dislocations Fourth Edition. Butterworth Heinemann Press, 2001.
42. Gary S. Was. Fundamentals of Radiation Materials Science. Springer Berlin Heidelberg New York, 2007.
43. J. F .Justo, M. D. Koning, W. Cai, V. V. Bulatov, Point defect interaction with dislocations in silicon. Materials Science and Engineering A, 309:129-135, 2001.
44. S. T. Zhou, Preston D. L., Lomdahl, P. S., Beazley, D. M., Science, 279:1525 1998.
45. D. Rodney, and R. Phillips. Structure and strength of dislocation junction: an atomistic level analysis. Physics Review Letter, 82:1704, 1999.
46. D. Rodney and G. Martin. Dislocation pinning by glissile interstitial loops in a nickel crystal: a molecular-dynamics study. Physics Review B, 61:8714, 2000.
47. D. Rodney and G. Martin. Dislocation pinning by small interstitial loops: a molecular-dynamics study. Physics Review Letter, 82:3272, 1999.
48. Q. Yue, A. Strachan, T. Cagin, W. A. Goddard III. Large scale atom simulations of screw dislocation structure, annihilation and cross-slip in fcc Ni. Material. Science and Engineering A, 309-3l0:156, 2001.
49. C. H. Woo, B. N. Singh. The concept of production bias and its possible role in defect accumulation under cascade damage conditions. Physica Status Solidi B, 159: 609-618, 1990.
50. C. H. Woo, B. N. Singh. Production bias due to clustering of point defects in irradiation-induced cascades. Philosophical Magazine A, 65:889-899, 1992.
51. B. N. Singh, S. I. Golubov, H. Trinkaus, A. Serra, Yu. N., Osetsky, A.V. Barashev. Aspects of microstructure evolution under cascade damage conditions. Journal of Nuclear Materials, 251:107-119, 1997.
52. Yu. N. Osetsky, D.J. Bacon, A. Serra, B.N. Singh, S.I. Golubov. Stability and mobility of defect clusters and dislocation loops in metals. Journal of Nuclear Materials, 276:65-78, 2000.
53. Yu N., Osetsky, A. Serra, B.N. Singly S.I. Golubov. Structure and properties of clusters of self-interstitial atoms in fcc copper and bcc iron. Philosophical Magazine A, 80:2131-2145, 2000.
54. B. N. Singh and J. H. Evans. Significant differences in defect accumulation behavior between fcc and bcc crystals under cascade damage conditions. Journal of Nuclear Materials, 226:277-288, 1995.
55. S. Amelinckx, W. Bontinck, W. Dekeyser, and F. Seitz. On the formation and properties of helical dislocations. Philosophical Magazine, 2:355-368, 1957.
56. K. S. Cheung, S. Yip. Brittle-ductile transition in intrinsic fracture-behavior of crystals. Physical Review Letters, 65:2804-2816, 1990.
57. B. L. Holian, R. Ravelo. Fracture simulations using large-scale molecular-dynamics. Physical Review Letters B, 51:11275, 1995.
58. J. E. Sinclair R. Fletcher. New method of saddle-point location for calculation of defect migration energies. Journal of physics C, 7:864-867, 1974
59. B. J. AIder and T. E. Wainwright. Phase transition for a hard sphere system. Journal of Chemical physics, 27:1208, 1957.
60. L. Verlet. Computer experiments on classical fluids. I. thermodynamical properties of Lennard Jones molecules. Physical Review Letters, 165:201-215, 1967.
61. M. Parrinello and A. Rahman. Polymorphic transitions in single crystals: A New Molecular Dynamics Metros. Journal of Applied Physics, 52:7182-7197, 1981.
62. C. Kittle. Introduction to Solid State Physics, 5th edition. Wi1ey, New York, 1976.
63. M. W. Finnis, J. E. Sinclair. A simple empirical n-body potential for transition-matter structure defects and mechanical properties. Philosophical Magazine A, 50:45-56, 1984.
64. G. J. Ackland, R. Thetford. An improved n-body semiempirical model for body-centered cubic transition-metals. Philosophical Magazine A, 56: 15-22, 1987.
65. http://trond.hjorteland.com/thesis/node27.html
66. E. M. Beale. A derivation of conjugate gradients, Numerical methods for Non-linear Optimization, ed. F. A. Lootsma, London, Academic Press, 1972.
67. D. C. Rapaport.The art of molecular dynamics simulation, Second Edition. Cambridge University Press, 32, 2004
68. J. E. Sinclair. Improved atomistic model of a bcc dislocation core. Journal of Applied Physics. 42: 5321-5334, 1971.
69. J. E. Sinclair. Influence of interatomic force law and of kinks on propagation of brittle cracks. Philosophical Magazine. 31:647-656, 1975.
70. J. D. Eshelby, W. T. Read and W. Shockley. Anisotropic elasticity with applications to dislocation theory. Acta MetalL. 1:251-267, 1953.
71. J. E. Sinclair, P. C. Gehlen, R. G Hoagland, J. P. Hirth. Flexible boundary conditions and non-linear geometric effects in atomic dislocation modelling. Journal of Applied Physics. 49: 3890-3908, 1978.
72. R. G. Hoagland, J .P. Hirth, P. C. Gehlen. Atomic simulation of dislocation core structure and Peierls stress in alkali-halide. Philosophical Magazine. 34:p413-422, 1976.
73. C. H. Woo, M. P. Puls. Improved method of calculating lattice friction stress using an atomistic model. Journal of physics C, Solid State Physics, 9:L27-L35, 1976.
74. S. Rao, C. Hernandez, J. P. Simrnons, T. A. Parthasarathy, C. Woodward. Green’s function boundary conditions in two-dimensional and three-dimensional atomistic simulations of dislocations. Philosophical Magazine A, 77:231-245, 1998.
75. J. W. Deutz and H. R. Schrober. Program to calculate elastic Green’s functions, displacement fields and interaction energies in cubic materials. Computer Physics Communications, 30:87-99, 1983.
76. S. I. Golubov, X. L. Liu, H. Huang, C. H. Woo. GFCUBHEX: Program to calculate elastic Green’s functions and displacement fields for applications in atomistic simulations of defects in cubic and HCP crystals. Computer Physics Communications, 137:312-322, 2001.
77. K. Ohsawa, E. Kuramoto. Flexible boundary condition for a moving dislocation. Journal of Applied Physics, 86:179-194, 1999.
78. S. J. Zhou, D. L. Preston, P. S. Lomdahl, and D. M. Beazley. Large-scale molecular dynamics simulations of dislocation intersection in copper. Science, 279:1525-1527, 1998.
79. G. J. Ackland, S. J. Wooding, D. J. Bacon. Defect, surface and displacement-threshhold properties of alpha-zirconium simulated with a many-body potential. Philosophical Magazine A, 71:553-566, 1995.
80. A. N. Stroh. Dislocation and cracks in anisotropic elasticity. Philosophical Magazine, 3:625-638, 1958.
81. D. Kulikov, L. Malerba, M. Hou, Philosophical Magazine, 86(2):141-172, 2006.
82. D. Kulikov, L. Malerba, M. Hou, Nuclear Instrument Methods B, 228:245-255, 2005.
83. D. Kulikov M. Hou, L. Malerba. Calculations of the formation and binding energies for point defect clusters in the Fe-Cu system and Zr. ITEM meeting, 2003.
84. Berghezan, Fourdeux and Amelinckx. Transmission electron microscopy studies of dislocations and stacking faults in a hexagonal metal:Zinc. Acta Metallurgica, 9:464-490, 1961.
85. Vikram Gavini, Kaushik Bhattacharya and Michael Ortiz. Vacancy clustering and prismatic dislocation loop formation in aluminum. Physical Review B, 76(18):01011-01014, 2007.
86. C. H. Woo, R.A. Holt and M. Griffith. Anisotropic diffusion of point defects: effects on irradiation-induced deformation and microstructure, materials modelling: from theory to technology. Institute of Physics Publishing, Bristol and Philadelphia, 20:55-60, 1991.