一种X射线衍射线形分析中位错衬度因子的计算方法
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摘要
基于Teodosiu各向异性弹性理论计算位错产生的位移场,建立适用于各滑移系中位错衬度因子的计算公式。以立方晶体为实例,对计算过程进行了化简。给出了f.c.c晶体Cu和b.c.c晶体Fe中分布于12个滑移系中位错在8种衍射面指数下的衬度因子,将计算结果同文献进行了对比。对历经不同应变准静态压缩加载的无氧铜开展了X射线衍射实验,阐述了衬度因子在消除衍射谱各向异性展宽中的作用。结合衍射线形分析,获取了样品中的亚晶粒尺寸、螺位错比例和位错密度。
The displacement field produced by dislocations was calculated by using Teodosiu anisotropic elastic theory. The formulas for calculating the dislocation contrast factors of different slip systems were established. Taking the cubic crystal as example,the calculation process was simplified,and the contrast factors of dislocations distributed in 12 slip systems under 8 diffraction indices in f. c. c Cu and b. c. c Fe were given. The calculation results were compared with those in the literature. X-ray diffraction experiments were carried out on oxygen free copper subjected to different quasi-static compression loading strains. The role of the contrast factor in eliminating the anisotropy broadening of the diffraction profiles was described. The subgrain size,screw dislocation ratio and the dislocation density in the sample were obtained by using line profile analysis.
The displacement field produced by dislocations was calculated by using Teodosiu anisotropic elastic theory. The formulas for calculating the dislocation contrast factors of different slip systems were established. Taking the cubic crystal as example,the calculation process was simplified,and the contrast factors of dislocations distributed in 12 slip systems under 8 diffraction indices in f. c. c Cu and b. c. c Fe were given. The calculation results were compared with those in the literature. X-ray diffraction experiments were carried out on oxygen free copper subjected to different quasi-static compression loading strains. The role of the contrast factor in eliminating the anisotropy broadening of the diffraction profiles was described. The subgrain size,screw dislocation ratio and the dislocation density in the sample were obtained by using line profile analysis.
引文
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[4]Krivoglaz M A.X-ray and Neutron Diffraction in Nonideal Crystals[M].Berlin:Springer-Verlag Press,1996.
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[6]Klimanek P,Kuzel R.X-ray diffraction line broadening due to dislocation in non-cubic materials.I.general considerations and the case of elastic isotropy applied to hexagonal crystals[J].Journal of Applied Crystallography,1988,21(1):59-66.
[7]Stroh A N.Dislocations and cracks in anisotropic elasticity[J].Philosophical Magazine,1958,3(30):625-646.
[8]Teodosiu C.Elastic Models of Crystal Defects[M].Berlin:Springer-Verlag Press,1982.
[9]Martinez-Garcia J,Leoni M,Scardi P.Analytical expression for the dislocation contrast factor of the<001>{100}cubic slip-system:application to Cu2O[J].Physical Review B,2007,76:174117.
[10]Ungar T,Dragomir I,Revesz A,et al.The contrast factors of dislocations in cubic crystals:the dislocation model of strain anisotropy in practice[J].Journal of Applied Crystallography,1999,32(5):992-1002.
[11]吴家龙.弹性力学[M].北京:高等教育出版社,2001.
[12]鲍静,冯晓娟,林鸿,等.可变温的固体材料弹性参数测量系统研究[J].计量学报,2015,36(5):449-454.
[13]Dragomir I C,Ungar T.The dislocations contrast factors of cubic crystals in the Zener constant range between zero and unity[J].Powder Diffraction,2002,17(2):104-111.
[14]赖振宇,邹秋林,卢忠远,等.Rietveld全谱拟合方法对磷酸镁水泥水化产物的定量分析研究[J].计量学报,2014,35(4):398-402.
[15]Stokes A R.A numerical Fourier-analysis method for the correction of widths and shapes of lines on X-ray powder photographs[J].Proceedings of the Physical Society,1948,61(4):382-391.
[2]Chen Y Z,Csiszar G,Cizek J,et al.On the formation of vacancies inα-ferrite of a heavily cold-drawn pearlitic steel wire[J].Scripta Materialia,2011,64(5):390-393.
[3]Hu Q S,Zhao F,Fu H,et al.Dislocation density and mechanical threshold stress in OFHC copper subjected to SHPB loading and plate impact[J].Materials Science and Engineering:A,2017,695:230-238.
[4]Krivoglaz M A.X-ray and Neutron Diffraction in Nonideal Crystals[M].Berlin:Springer-Verlag Press,1996.
[5]Groma I,Borbély A.X-ray line broadening due to an inhomogeneous dislocation distribution[J].Physical Review B,1998,57(13):7535-7542.
[6]Klimanek P,Kuzel R.X-ray diffraction line broadening due to dislocation in non-cubic materials.I.general considerations and the case of elastic isotropy applied to hexagonal crystals[J].Journal of Applied Crystallography,1988,21(1):59-66.
[7]Stroh A N.Dislocations and cracks in anisotropic elasticity[J].Philosophical Magazine,1958,3(30):625-646.
[8]Teodosiu C.Elastic Models of Crystal Defects[M].Berlin:Springer-Verlag Press,1982.
[9]Martinez-Garcia J,Leoni M,Scardi P.Analytical expression for the dislocation contrast factor of the<001>{100}cubic slip-system:application to Cu2O[J].Physical Review B,2007,76:174117.
[10]Ungar T,Dragomir I,Revesz A,et al.The contrast factors of dislocations in cubic crystals:the dislocation model of strain anisotropy in practice[J].Journal of Applied Crystallography,1999,32(5):992-1002.
[11]吴家龙.弹性力学[M].北京:高等教育出版社,2001.
[12]鲍静,冯晓娟,林鸿,等.可变温的固体材料弹性参数测量系统研究[J].计量学报,2015,36(5):449-454.
[13]Dragomir I C,Ungar T.The dislocations contrast factors of cubic crystals in the Zener constant range between zero and unity[J].Powder Diffraction,2002,17(2):104-111.
[14]赖振宇,邹秋林,卢忠远,等.Rietveld全谱拟合方法对磷酸镁水泥水化产物的定量分析研究[J].计量学报,2014,35(4):398-402.
[15]Stokes A R.A numerical Fourier-analysis method for the correction of widths and shapes of lines on X-ray powder photographs[J].Proceedings of the Physical Society,1948,61(4):382-391.