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Ultra-high local plasticity in high-strength nanocomposites

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Abstract

We subjected an aged Cu-24wt%Ag ingot to cold drawing to create a high-strength nanostructured composite wire with both Cu-rich proeutectic and Ag-rich eutectic components. During the drawing, a fine lamellar structure (average spacing 20 ± 6 nm) developed in the proeutectic component, which contained a high density of Ag fibers (average width below 5 nm) embedded in the matrix. In the eutectic component, a relatively coarse structure developed, with an average Ag grain size around 100 nm. The result of such a bimodal size of Ag fibers was ultra-high bending plasticity, i.e., the drawn wire tolerated 59% bending strain at the outermost edge, 15 times its tensile elongation (3.6%). During our bending test, dynamic recovery and partial recrystallization occurred more near the inner edge than near the outer edge and primarily in the eutectic component. High bending strain caused some of the thicker Ag fibers to become discontinuous and lose their original alignment. This structural evolution increased local plasticity, resulting in an unexpectedly high achievable bending strain, which is unusual in nano-sized, Ag-fiber-reinforced high-strength composites.

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References

  1. Bacon JL, Ammerman CN, Coe H, Ellis GW, Lesch BL, Sims JR, Schillig JB, Swenson CA (2002) The U.S. NHMFL 100 Tesla multi-shot magnet. IEEE Trans Appl Supercond 12(1):695–698. https://doi.org/10.1109/TASC.2002.1018496

    Article  Google Scholar 

  2. Marshall WS, Swenson CA, Gavrilin A, Schneider-Muntau HJ (2004) Development of “Fast Cool” pulse magnet coil technology at NHMFL. Phys. B 346–347:594–598. https://doi.org/10.1016/j.physb.2004.01.156

    Article  CAS  Google Scholar 

  3. Marshall WS, Swenson CA, Gavrilin AV, Rickel DG, Schneider-Muntau HJ (2004) Development of 'poly-layer' assembly technology for pulsed magnets. IEEE Trans Appl Supercond 14(2):1241–1244. https://doi.org/10.1109/TASC.2004.830542

    Article  Google Scholar 

  4. Schneider-Muntau HJ, Ke H, Bednar NA, Swenson CA, Walsh R (2004) Materials for 100 T monocoil magnets. IEEE Trans Appl Supercond 14(2):1153–1156. https://doi.org/10.1109/TASC.2004.830461

    Article  CAS  Google Scholar 

  5. Swenson CA, Marshall WS, Gavrilin AV, Han K, Schillig J, Sims JR, Schneider-Muntau HJ (2004) Progress of the insert coil for the US-NHMFL 100T multi-shot pulse magnet. Phys B 346–347:561–565. https://doi.org/10.1016/j.physb.2004.01.082

    Article  CAS  Google Scholar 

  6. Swenson CA, Marshall WS, Miller EL, Pickard KW, Gavrilin AV, Han K, Schneider-Muntau HJ (2004) Pulse magnet development program at NHMFL. IEEE Trans Appl Supercond 14(2):1233–1236. https://doi.org/10.1109/TASC.2004.830538

    Article  Google Scholar 

  7. Embury J, Han K (2004) A survey of processing methods for high strength-high conductivity wires for high field magnet applications. In: megagauss magnetic field generation, its application to science and ultra-high pulsed-power technology. pp 147-153. https://doi.org/10.1142/9789812702517_0026

  8. Embury J, Han K, Sims J, Coulter J, Pantsyrnyi V, Shikov A, Bochvar A (2004) Fabrication routes for high strength-high conductivity wires. In: megagauss magnetic field generation, its application to science and ultra-high pulsed-power technology. pp 158–160. https://doi.org/10.1109/TASC.2004.830538

  9. Embury JD, Han K (1998) Conductor materials for high field magnets. Curr Opin Solid State Mater Sci 3(3):304–308. https://doi.org/10.1016/S1359-0286(98)80106-X

    Article  CAS  Google Scholar 

  10. Han K, Vasquez AA, Xin Y, Kalu PN (2003) Microstructure and tensile properties of nanostructured Cu-25wt%Ag. Acta Mater 51(3):767–780. https://doi.org/10.1016/S1359-6454(02)00468-8

    Article  CAS  Google Scholar 

  11. Sakai Y, Schneider-Muntau HJ (1997) Ultra-high strength, high conductivity Cu-Ag alloy wires. Acta Mater 45(3):1017–1023. https://doi.org/10.1016/S1359-6454(96)00248-0

    Article  CAS  Google Scholar 

  12. Thilly L, Lecouturier F, Coffe G, Peyrade JP, Askenazy S (2000) Ultra high strength nanocomposite conductors for pulsed magnet windings. IEEE Trans Appl Supercond 10(1):1269–1272. https://doi.org/10.1109/77.828466

    Article  Google Scholar 

  13. Han K, Embury JD, Sims JR, Campbell LJ, Schneider-Muntau HJ, Pantsyrnyi VI, Shikov A, Nikulin A, Vorobieva A (1999) The fabrication, properties and microstructure of Cu–Ag and Cu–Nb composite conductors. Mater Sci Eng, A 267(1):99–114. https://doi.org/10.1016/S0921-5093(99)00025-8

    Article  Google Scholar 

  14. Mara NA, Beyerlein IJ (2015) Interface-dominant multilayers fabricated by severe plastic deformation: Stability under extreme conditions. Curr Opin Solid State Mater Sci 19(5):265–276. https://doi.org/10.1016/j.cossms.2015.04.002

    Article  CAS  Google Scholar 

  15. Mara NA, Beyerlein IJ (2014) Review: effect of bimetal interface structure on the mechanical behavior of Cu–Nb fcc–bcc nanolayered composites. J Mater Sci 49(19):6497–6516. https://doi.org/10.1007/s10853-014-8342-9

    Article  CAS  Google Scholar 

  16. Mara NA, Bhattacharyya D, Dickerson PO, Hoagland RG, Misra A (2010) Ultrahigh strength and ductility of Cu-Nb nanolayered composites. Mater Sci Forum 633–634:647–653. https://doi.org/10.4028/www.scientific.net/MSF.633-634.647

    Article  CAS  Google Scholar 

  17. Tian YZ, Zhang ZF (2009) Microstructures and tensile deformation behavior of Cu–16wt.%Ag binary alloy. Mater Sci Eng A 508(1):209–213. https://doi.org/10.1016/j.msea.2008.12.050

    Article  CAS  Google Scholar 

  18. Tian YZ, Zhang ZF, Wang ZG (2009) Cyclic deformation and fatigue cracking behaviors of Cu–28wt%Ag binary alloy. Phil Mag 89(21):1715–1730. https://doi.org/10.1080/14786430903032548

    Article  CAS  Google Scholar 

  19. Wang CJ, Ning YT, Zhang KH, Geng YH, Bi J, Zhang JM (2009) Thermal stability of heavily deformed Ag–10wt.%Cu microcomposite wires. Mater Sci Eng A 517(1):219–224. https://doi.org/10.1016/j.msea.2009.03.065

    Article  CAS  Google Scholar 

  20. Wu ZW, Liu JJ, Chen Y, Meng L (2009) Microstructure, mechanical properties and electrical conductivity of Cu–12wt.% Fe microcomposite annealed at different temperatures. J Alloys Compd 467(1):213–218. https://doi.org/10.1016/j.jallcom.2007.12.020

    Article  CAS  Google Scholar 

  21. Zhang L, Meng L (2004) Microstructure, mechanical properties and electrical conductivity of Cu–12 wt.% Ag wires annealed at different temperature. Mater Lett 58(30):3888–3892. https://doi.org/10.1016/j.matlet.2004.08.014

    Article  CAS  Google Scholar 

  22. Zhang L, Meng L (2005) Evolution of microstructure and electrical resistivity of Cu–12wt.%Ag filamentary microcomposite with drawing deformation. Scripta Mater 52(12):1187–1191. https://doi.org/10.1016/j.scriptamat.2005.03.016

    Article  CAS  Google Scholar 

  23. Han K, Embury J, Sims J, Pantsyrnyi V, Shikov A, Bochvar A (1998) Fabrication routes for high strength high conductivity wires. Los Alamos National Lab., NM. https://doi.org/10.1016/S0921-5093(99)00025-8

    Book  Google Scholar 

  24. Sakai Y, Inoue K, Maeda H (1994) High-strength and high-conductivity Cu-Ag alloy sheets: new promising conductor for high-fieId Bitter coils. IEEE Trans Magn 30(4):2114–2117. https://doi.org/10.1109/20.305687

    Article  CAS  Google Scholar 

  25. Sakai Y, Inoue K, Asano T, Maeda H (1992) Development of a high strength, high conductivity copper-silver alloy for pulsed magnets. IEEE Trans Magn 28(1):888–891. https://doi.org/10.1109/20.120021

    Article  CAS  Google Scholar 

  26. Davy CA, Han K, Kalu PN, Bole ST (2008) Examinations of Cu-Ag composite conductors in sheet forms. IEEE Trans Appl Supercond 18(2):560–563. https://doi.org/10.1109/Tasc.2008.922510

    Article  CAS  Google Scholar 

  27. Davy C, Kalu P, Shen T, Alexander D, Schwarz R, Han K (2005) Fabrication and Characterization of Nanostructured CuAg (Ag-40at% Cu). Microsc Microanal 11(S02):1718. https://doi.org/10.1017/S1431927605509590

    Article  Google Scholar 

  28. Li GM, Liu Y, Su Y, Wang EG, Han K (2013) Influence of high magnetic field on as-cast structure of Cu-25wt%Ag alloys. China Foundry 10(3):162–166. https://doi.org/10.1016/j.cossms.2015.04.002

    Article  CAS  Google Scholar 

  29. Zuo XW, Guo R, Zhao CC, Zhang L, Wang EG, Han K (2016) Microstructure and properties of Cu-6wt% Ag composite thermomechanical-processed after directionally solidifying with magnetic field. J Alloy Compd 676:46–53. https://doi.org/10.1016/j.jallcom.2016.03.127

    Article  CAS  Google Scholar 

  30. Zuo XW, Han K, Zhao CC, Niu RM, Wang EG (2014) Microstructure and properties of nanostructured Cu28 wt%Ag microcomposite deformed after solidifying under a high magnetic field. Mater Sci Eng Struct Mater Prop Microstruct Process 619:319–327. https://doi.org/10.1016/j.msea.2014.09.070

    Article  CAS  Google Scholar 

  31. Zuo XW, Han K, Zhao CC, Niu RM, Wang EG (2015) Precipitation and dissolution of Ag in ageing hypoeutectic alloys. J Alloy Compd 622:69–72. https://doi.org/10.1016/j.jallcom.2014.10.037

    Article  CAS  Google Scholar 

  32. Zuo XW, Qu L, Zhao CC, An BL, Wang EG, Niu RM, Xin Y, Lu J, Han K (2016) Nucleation and growth of gamma-Fe precipitate in Cu-2% Fe alloy aged under high magnetic field. J Alloy Compd 662:355–360. https://doi.org/10.1016/j.jallcom.2015.12.046

    Article  CAS  Google Scholar 

  33. Zuo XW, Zhao CC, Niu RM, Wang EG, Han K (2015) Microstructural dependence of magnetoresistance in CuAg alloy solidified with high magnetic field. J Mater Process Technol 224:208–212. https://doi.org/10.1016/j.jmatprotec.2015.05.006

    Article  CAS  Google Scholar 

  34. Zuo XW, Zhao CC, Wang EG, Zhang L, Han K, He JC (2013) Microstructure evolution of the proeutectic Cu dendrites in diamagnetic Cu-Ag alloys by electromagnetic suppressing convection. J Low Temp Phys 170(5–6):409–417. https://doi.org/10.1007/s10909-012-0743-z

    Article  CAS  Google Scholar 

  35. Zhao CC, Zuo XW, Wang EG, Han K (2017) Strength of Cu-28 wt%Ag composite solidified under high magnetic field followed by cold drawing. Met Mater Int 23(2):369–377. https://doi.org/10.1007/s12540-017-6417-2

    Article  CAS  Google Scholar 

  36. Zhao CC, Zuo XW, Wang EG, Niu RM, Han K (2016) Simultaneously increasing strength and electrical conductivity in nanostructured Cu-Ag composite. Mater Sci Eng Struct Mater Prop Microstruct Process 652:296–304. https://doi.org/10.1016/j.msea.2015.11.067

    Article  CAS  Google Scholar 

  37. Leprince-Wang Y, Han K, Huang Y, Yu-Zhang K (2003) Microstructure in Cu-Nb microcomposites. Mater Sci Eng Struct Mater Prop Microstruct Process 351(1–2):214–223. https://doi.org/10.1016/s0921-5093(02)00855-9

    Article  Google Scholar 

  38. Yu-Zhang K, Embury JD, Han K, Misra A (2008) Transmission electron microscopy investigation of the atomic structure of interfaces in nanoscale Cu-Nb multilayers. Phil Mag 88(17):2559–2567. https://doi.org/10.1080/14786430802380485

    Article  CAS  Google Scholar 

  39. Beyerlein IJ, Demkowicz MJ, Misra A, Uberuaga BP (2015) Defect-interface interactions. Prog Mater Sci 74:125–210. https://doi.org/10.1016/j.pmatsci.2015.02.001

    Article  CAS  Google Scholar 

  40. Wang J, Misra A (2011) An overview of interface-dominated deformation mechanisms in metallic multilayers. Curr Opin Solid State Mater Sci 15(1):20–28. https://doi.org/10.1016/j.cossms.2010.09.002

    Article  CAS  Google Scholar 

  41. Beyerlein IJ, Mara NA, Bhattacharyya D, Alexander DJ, Necker CT (2011) Texture evolution via combined slip and deformation twinning in rolled silver–copper cast eutectic nanocomposite. Int J Plast 27(1):121–146. https://doi.org/10.1016/j.ijplas.2010.05.007

    Article  CAS  Google Scholar 

  42. Cui BZ, Xin Y, Han K (2007) Structure and transport properties of nanolaminate Cu-Nb composite foils by a simple fabrication route. Scripta Mater 56(10):879–882. https://doi.org/10.1016/j.scriptamat.2007.01.038

    Article  CAS  Google Scholar 

  43. Tian YZ, Wu SD, Zhang ZF, Figueiredo RB, Gao N, Langdon TG (2011) Microstructural evolution and mechanical properties of a two-phase Cu–Ag alloy processed by high-pressure torsion to ultrahigh strains. Acta Mater 59(7):2783–2796. https://doi.org/10.1016/j.actamat.2011.01.017

    Article  CAS  Google Scholar 

  44. Saito Y, Utsunomiya H, Tsuji N, Sakai T (1999) Novel ultra-high straining process for bulk materials—development of the accumulative roll-bonding (ARB) process. Acta Mater 47(2):579–583. https://doi.org/10.1016/S1359-6454(98)00365-6

    Article  CAS  Google Scholar 

  45. Valiev RZ, Islamgaliev RK, Alexandrov IV (2000) Bulk nanostructured materials from severe plastic deformation. Prog Mater Sci 45(2):103–189. https://doi.org/10.1016/S0079-6425(99)00007-9

    Article  CAS  Google Scholar 

  46. Estrin Y, Vinogradov A (2013) Extreme grain refinement by severe plastic deformation: a wealth of challenging science. Acta Mater 61(3):782–817. https://doi.org/10.1016/j.actamat.2012.10.038

    Article  CAS  Google Scholar 

  47. Han K, Embury JD, Petrovic JJ, Weatherly GC (1998) Microstructural aspects of Cu-Ag produced by the Taylor wire method. Acta Mater 46(13):4691–4699. https://doi.org/10.1016/S1359-6454(98)00135-9

    Article  CAS  Google Scholar 

  48. Han K, Walsh RP, Ishmaku A, Toplosky V, Brandao L, Embury JD (2004) High strength and high electrical conductivity bulk Cu. Phil Mag 84(34):3705–3716. https://doi.org/10.1080/14786430412331293496

    Article  CAS  Google Scholar 

  49. Sun LX, Tao NR, Lu K (2015) A high strength and high electrical conductivity bulk CuCrZr alloy with nanotwins. Scripta Mater 99:73–76. https://doi.org/10.1016/j.scriptamat.2014.11.032

    Article  CAS  Google Scholar 

  50. Islamgaliev RK, Nesterov KM, Bourgon J, Champion Y, Valiev RZ (2014) Nanostructured Cu–Cr alloy with high strength and electrical conductivity. J Appl Phys. https://doi.org/10.1063/1.4874655

    Article  Google Scholar 

  51. Beyerlein IJ, Mara NA, Wang J, Carpenter JS, Zheng SJ, Han WZ, Zhang RF, Kang K, Nizolek T, Pollock TM (2012) Structure–property–functionality of bimetal interfaces. JOM 64(10):1192–1207. https://doi.org/10.1007/s11837-012-0431-0

    Article  CAS  Google Scholar 

  52. Nizolek T, Mara NA, Beyerlein IJ, Avallone JT, Scott JE, Pollock TM (2014) Processing and deformation behavior of Bulk Cu–Nb nanolaminates. Metallogr Microstruct Anal 3(6):470–476. https://doi.org/10.1007/s13632-014-0172-2

    Article  CAS  Google Scholar 

  53. Lu L, Shen Y, Chen X, Qian L, Lu K (2004) Ultrahigh strength and high electrical conductivity in copper. Science 304(5669):422–426. https://doi.org/10.1126/science.1092905

    Article  CAS  Google Scholar 

  54. Niu R, Han K (2013) Strain hardening and softening in nanotwinned Cu. Scripta Mater 68(12):960–963. https://doi.org/10.1016/j.scriptamat.2013.02.051

    Article  CAS  Google Scholar 

  55. Niu R, Han K, Su Y-F, Besara T, Siegrist TM, Zuo X (2016) Influence of grain boundary characteristics on thermal stability in nanotwinned copper. Sci Rep 6:31410–31410. https://doi.org/10.1038/srep31410

    Article  CAS  Google Scholar 

  56. Mishin OV, Godfrey A (2008) Microstructure of ECAE-processed copper after long-term room-temperature storage. Metall Mater Trans A 39(12):2923–2930. https://doi.org/10.1007/s11661-008-9658-3

    Article  CAS  Google Scholar 

  57. Eftink BP, Li A, Szlufarska I, Mara NA, Robertson IM (2017) Deformation response of AgCu interfaces investigated by in situ and ex situ TEM straining and MD simulations. Acta Mater 138:212–223. https://doi.org/10.1016/j.actamat.2017.07.051

    Article  CAS  Google Scholar 

  58. Eftink BP, Mara NA, Kingstedt OT, Safarik D, Wang S, Lambros J, Robertson IM (2018) Deformation response of cube-on-cube and non-coherent twin interfaces in AgCu eutectic under dynamic plastic compression. Mater Sci Eng, A 712:313–324. https://doi.org/10.1016/j.msea.2017.11.108

    Article  CAS  Google Scholar 

  59. Eftink BP, Mara NA, Kingstedt OT, Safarik DJ, Lambros J, Robertson IM (2014) Anomalous deformation twinning in coarse-grained Cu in Ag60Cu40 composites under high strain-rate compressive loading. Mater Sci Eng, A 618:254–261. https://doi.org/10.1016/j.msea.2014.08.082

    Article  CAS  Google Scholar 

  60. Han K, Goddard R, Niu R, Li T, Nguyen DN, Michel JR, Lu J, Pantsyrny V (2016) Bending behavior of high-strength conductor. IEEE Trans Appl Supercond 26(4):1–4. https://doi.org/10.1109/TASC.2016.2517412

    Article  Google Scholar 

  61. Goddard RE, Han KH, Nguyen DN (2016) Relative strain in Cu-Nb composite wound wire. Microsc Microanal S3:1992–1993. https://doi.org/10.1017/S1431927616010801

    Article  Google Scholar 

  62. Williams PL, Mishin Y, Hamilton JC (2006) An embedded-atom potential for the Cu–Ag system. Modell Simul Mater Sci Eng 14(5):817–833. https://doi.org/10.1088/0965-0393/14/5/002

    Article  CAS  Google Scholar 

  63. Stukowski A (2009) Visualization and analysis of atomistic simulation data with OVITO–the open visualization tool. Modell Simul Mater Sci Eng 18(1):015012–6. https://doi.org/10.1088/0965-0393/18/1/015012

    Article  Google Scholar 

  64. Han K, Lawson AC, Wood JT, Embury JD, Von Dreele RB, Richardson JW (2004) Internal stresses in cold-deformed Cu–Ag and Cu–Nb wires. Philos Magaz 84(24):2579–2593. https://doi.org/10.1080/14786430410001689981

    Article  CAS  Google Scholar 

  65. Datsko J, Yang CT (1960) Correlation of bendability of materials with their tensile properties. J Eng Indus 82(4):309–313. https://doi.org/10.1115/1.3664236

    Article  Google Scholar 

  66. Labossiere PE (2007). https://courses.washington.edu/me354a/chap3.pdf. Accessed 03 May 2019

  67. Han K, Hirth JP, Embury JD (2001) Modeling the formation of twins and stacking faults in the ag–cu system. Acta Mater 49(9):1537–1540. https://doi.org/10.1016/S1359-6454(01)00057-X

    Article  CAS  Google Scholar 

  68. Hong SI, Hill MA (1998) Microstructural stability and mechanical response of Cu–Ag microcomposite wires. Acta Mater 46(12):4111–4122. https://doi.org/10.1016/S1359-6454(98)00106-2

    Article  CAS  Google Scholar 

  69. Dubois JB, Thilly L, Lecouturier F, Olier P, Renault PO (2012) Cu/Nb nanocomposite wires processed by severe plastic deformation for applications in high pulsed magnets: effects of the multi-scale microstructure on the mechanical properties. IEEE Trans Appl Supercond 22(3):6900104–6900104. https://doi.org/10.1109/TASC.2011.2174574

    Article  CAS  Google Scholar 

  70. Wilde G, Divinski S (2019) Grain boundaries and diffusion phenomena in severely deformed materials. Mater Trans 60(7):1302–1315. https://doi.org/10.2320/matertrans.MF201934

    Article  CAS  Google Scholar 

  71. Divinski SV, Reglitz G, Rösner H, Estrin Y, Wilde G (2011) Ultra-fast diffusion channels in pure Ni severely deformed by equal-channel angular pressing. Acta Mater 59(5):1974–1985. https://doi.org/10.1016/j.actamat.2010.11.063

    Article  CAS  Google Scholar 

  72. Wang ZB, Divinski SV, Luo ZP, Buranova Y, Wilde G, Lu K (2017) Revealing interfacial diffusion kinetics in ultra-fine-laminated Ni with low-angle grain boundaries. Mater Res Lett 5(8):577–583. https://doi.org/10.1080/21663831.2017.1368036

    Article  CAS  Google Scholar 

  73. Bailey JE, Hirsch PB (1962) The recrystallization process in some polycrystalline metals. Proc R Soc Lond A 267(1328):11–30. https://doi.org/10.1098/rspa.1962.0080

    Article  CAS  Google Scholar 

  74. Pravoverov NL, Tribunskaya IA (1969) Initial recrystallization temperature of sintered silver-transition metal composites. Soviet Powder Metall Metal Ceram 8(12):1006–1011. https://doi.org/10.1007/BF00802031

    Article  Google Scholar 

  75. Humphreys FJ, Hatherly M (2004) The Deformed State. In: Humphreys FJ, Hatherly M (eds) Recrystallization and related annealing phenomena, vol 2. Elsevier, Oxford, p 11-II

    Chapter  Google Scholar 

  76. Hoffman RE, Turnbull D (1951) Lattice and grain boundary self-diffusion in silver. J Appl Phys 22(5):634–639. https://doi.org/10.1063/1.1700085

    Article  CAS  Google Scholar 

  77. Sommer J, Herzig C (1992) Direct determination of grain-boundary and dislocation self-diffusion coefficients in silver from experiments in type-C kinetics. J Appl Phys 72(7):2758–2766. https://doi.org/10.1063/1.352328

    Article  CAS  Google Scholar 

  78. Hong SI, Hill MA, Sakai Y, Wood JT, Embury JD (1995) On the stability of cold drawn, two-phase wires. Acta Metall Mater 43(9):3313–3323. https://doi.org/10.1016/0956-7151(95)00050-6

    Article  CAS  Google Scholar 

  79. Hong SI, Hill MA (1999) Mechanical stability and electrical conductivity of Cu–Ag filamentary microcomposites. Mater Sci Eng, A 264(1):151–158. https://doi.org/10.1016/S0921-5093(98)01097-1

    Article  Google Scholar 

  80. Mote VD, Purushotham Y, Dole BN (2012) Williamson-Hall analysis in estimation of lattice strain in nanometer-sized ZnO particles. J Theor Appl Phys 6(1):6. https://doi.org/10.1186/2251-7235-6-6

    Article  Google Scholar 

  81. Attfield M, Barnes P, Cockcroft JK, Driessen H Determination of Size and Strain. https://pd.chem.ucl.ac.uk/pdnn/peaks/sizedet.htm. Accessed 09 March 2019

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Acknowledgments

This work was undertaken in the National High Magnetic Field Laboratory, which was supported by the National Science Foundation (DMR-1644779) and the State of Florida. Special thanks to Jun Lu for conducting the heat-treatment, William Starch for conducting the wire swaging, and Mary Tyler for editing.

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Appendix

Appendix

Peak broadening due to crystallite size, βL, was calculated using Debye–Scherrer’s formula:

$$\beta_{L} = K \times \lambda /\left( {{\text{size}} \times \cos \theta } \right)$$
(1)

where θ is the Bragg angle, K is the Scherrer constant (0.9 for integral breath of spherical crystals with cubic symmetry), λ is the wavelength of Cu kα radiation.

The strain induced broadening, βs, due to crystal imperfection and distortion was calculated using the formula:

$$\beta_{s} = 4 \times {\text{strain}} \times \sin /\cos$$
(2)

Williamson-Hall (W-H) analysis is a simplified integral breadth method where both size-induced and strain-induced broadening were deconvoluted by considering the peak width as a function of 2θ [80, 81]:

$$\beta_{tot} = \beta_{L} + \beta_{S} = K \times \lambda /\left( {{\text{size}} \times \cos } \right) + 4 \times {\text{strain}} \times \sin \theta /\cos$$
(3)

where βtot is total peak broadening. By rearranging the above equation, we got

$$\beta_{tot} \times \cos \theta = K \times \lambda /{\text{size}} + 4 \times {\text{strain}} \times \sin \theta$$
(4)

Comparing Eq. 4 to the standard equation for a straight line (\(y = c + mx\), c = intercept; m = slope), we obtained the size component from the intercept (/size) and the strain component from the slope (4 × strain) by plotting βtot cosθ versus sinθ.

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Niu, R., Han, K., Xiang, Z. et al. Ultra-high local plasticity in high-strength nanocomposites. J Mater Sci 55, 15183–15198 (2020). https://doi.org/10.1007/s10853-020-05097-1

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