Skip to main content

Advertisement

SpringerLink
Log in

Study of the current density of the electrical resistance sintering technique on microstructural and mechanical properties in a β Ti-Nb-Sn ternary alloy

  • Published:
Applied Physics A Aims and scope Submit manuscript

Abstract

Electrical resistance sintering is a fast method to fabricate metallic samples in the metallurgy field and was used to obtain the Ti-Nb-Sn alloy to be applied as a possible biomaterial. Powders were obtained by mechanical alloying and were then compacted at 193 MPa pressure for 700 ms at several electrical current densities (11, 12 and 13 kA). The structure and microstructure of both powders and samples were evaluated by X-ray diffraction, Field Emission Scanning Electron Microscopy and Electron Backscattered Diffraction. Mechanical properties were evaluated by a microhardness assay and corrosion resistance was performed in Ringer Hartmann’s solution at 37°C. Samples were structured in the α, α” and β phases. The content of the β phase in the samples obtained at 11, 12 and 13 kA was 96.56, 98.12 and 98.02%, respectively. The peripheral zone showed more microporosity than the central zone. The microstructure was also formed by equiaxial bcc-β grains, and the samples obtained at 12 kA presented better microstructure homogeneity. Grain size increased as electric current density rose. The microhardness values fell within the 389–418 HV range and lowered, while electric current density increased. Corrosion tests proved the alloys’ excellent corrosion resistance (0.24–0.45 µA/cm2). The standard deviations of the kinetic parameters of the samples at 11 and 13 kA were much higher in relation to lack of microstructure homogeneity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. N. Eliaz, Corrosion of metallic biomaterials: a review. Mater. 12, 407 (2019). https://doi.org/10.3390/ma12030407

    Article  Google Scholar 

  2. E.J. Evans, Cell damage in vitro following direct contact with fine particles of titanium, titanium alloy and cobalt-chrome-molybdenum alloy. Biomaterials 442, 713–717 (1994). https://doi.org/10.1016/0142-9612(94)90170-8

    Article  Google Scholar 

  3. J.E. Bowerman, B. Conroy, A universal kit in titanium for immediate replacement of the resected mandible. J. Oral. Surg. 6, 223–228 (1969). https://doi.org/10.1016/s0007-117x(68)80041-1

    Article  Google Scholar 

  4. D.G. Barceloux, J. Toxicol. Clin. Toxicol. 37, 265–278 (1999). https://doi.org/10.1081/clt-100102425

    Article  Google Scholar 

  5. J.K. Marquis, Aluminum neurotoxicity: an experimental perspective. Bull. Environ. Contam. Toxicol. 29, 43–49 (1982). https://doi.org/10.1007/BF01606087

    Article  Google Scholar 

  6. M. Long, H.J. Rack, Titanium alloys in total joint replacement-a materials science perspective. Biomaterials 19, 1621–1639 (1998). https://doi.org/10.1016/S0142-9612(97)00146-4

    Article  Google Scholar 

  7. M. Niinomi, Mechanical properties of biomedical titanium alloys. Mater. Sci. Eng. A. 3, 231–236 (1998). https://doi.org/10.1016/j.actbio.2006.11.002

    Article  Google Scholar 

  8. H. Kroger, P. Venesmaa, J. Jurvelin, H. Miettinen, O. Suomalainen, E. Alhava, Bone density at the proximal femur after total hip arthroplasty. Clin. Orthop. Relat. 352, 66–74 (1998)

    Google Scholar 

  9. T. Ozaki, H. Matsumoto, S. Watanabe, S. Hanada, Beta Ti alloys with low young’s modulus. Mater. Trans. 45, 2776–2779 (2004). https://doi.org/10.2320/matertrans.45.2776

    Article  Google Scholar 

  10. I.J. Polmear, Overview: recent developments in light alloys. Mater. Trans. 37, 12–31 (1996). https://doi.org/10.2320/matertrans1989.37.12

    Article  Google Scholar 

  11. J.L. Murray, The Nb-Ti (Niobium-Titanium) system. Phase Diagr. 2, 55–61 (1981)

    Article  Google Scholar 

  12. L. Zhu, Q. Zhang, Z. Chen, W. Changdong, C. Ge-Mei, J. Liang, J. Zhanpeng, Z. Ji-Cheng, Measurement of interdiffusion and impurity diffusion coefficients in the bcc phase of the Ti–X (X = Cr, Hf, Mo, Nb, V, Zr) binary systems using diffusion multiples. J. Mater. Sci. 52, 3255–3268 (2017). https://doi.org/10.1007/s10853-016-0614-0

    Article  ADS  Google Scholar 

  13. B. Sharma, S.K. Vajpai, K. Ameyama, Synthesis of ternary Ti-25Nb-11Sn alloy by powder metallurgy route using titanium hydride powder. Mater. Trans. 57, 1440–1446 (2016). https://doi.org/10.2320/matertrans.mh201510

    Article  Google Scholar 

  14. M.S. Yahaya, M. Sulaiman, N.H.N.E. Azham Shah, M.H. Ismail, Microstructures and mechanical properties of Ti-Nb alloy at different composition of Nb produced via powder metallurgy route. Mater. Sci. Forum. 863, 14–18 (2016)

    Article  Google Scholar 

  15. J. Lux, Improved manufacture of electric incandescence lamp laments from tungsten or molybdenum or an alloy thereof. GB Patent. 1906

  16. G.F. Taylor, Apparatus for Making Hard Metal Compositions. U.S. Patent 1,896,854, 7 February 1933

  17. F.V. Lenel, Resistance sintering under pressure. J Alloy Compd. 7, 158–167 (1955). https://doi.org/10.1007/BF03377473

    Article  Google Scholar 

  18. T.L. Istomina, A.A. Baidenko, A.I. Raichenko, M.A. Goldberg, A.V. Svechkov, Influence of premolding pressure in electric-discharge sintering on the physicomechanical properties of a copper-tin-abrasive composite. Sov. Powder Metal. Met. Ceram. 22, 957–960 (1983). https://doi.org/10.1007/BF00805559

    Article  Google Scholar 

  19. G.L. Burenkov, A.I. Raichenko, M. Suraeva, Dynamics of interparticle reactions in spherical metal powders during electric sintering. Sov. Powder Metall. Met. Ceram. 26, 709–712 (1987). https://doi.org/10.1007/BF00797175

    Article  Google Scholar 

  20. S. Grasso, Y. Sakka, G. Maizza, Electric current activated/assisted sintering (ECAS): a review of patents 1906–2008. Sci. Technol. Adv. Mater. 10, 053001 (2009)

    Article  Google Scholar 

  21. R. Orrù, R. Licheri, A.M. Locci, A. Cincotti, G. Cao, Consolidation/synthesis of materials by electric current activated/assisted sintering. Mat. Sci. Eng. R Rep. 63, 127–287 (2009). https://doi.org/10.1016/j.mser.2008.09.003

    Article  Google Scholar 

  22. E.A. Olevsky, D.V. Dudina, Field-Assisted Sintering Science and Applications, first ed., Cham, Switzerland, 2018.

  23. A. Fais, A faster FAST: electro-sinter-forging. Metal Powder Rep. 73, 80–86 (2018). https://doi.org/10.1016/j.mprp.2017.06.001

    Article  Google Scholar 

  24. E. Cannella, C.V. Nielsen, N. Bay, Process investigation and mechanical properties of electro sinter forged (ESF) titanium discs. Int. J. Adv. Manuf. Technol. 104, 1985–1998 (2019). https://doi.org/10.1007/s00170-019-03972-z

    Article  Google Scholar 

  25. U. Anselmi-Tamburini, J.R. Groza, Critical assessment: Electrical field/current application. A revolution in materials processing/sintering. Mater. Sci. Technol. 33, 1855–1862 (2017). https://doi.org/10.1080/02670836.2017.1341692

    Article  Google Scholar 

  26. M.C. Rossi, D.L. Bayerlein, J.S. Brandao, J.P.H. Pfeifer, G.S. Rosa, W.M. Silva, L.G. Martinez, M.J. Saeki, A.L.G. Alves, Physical and biological characterizations of TiNbSn/(Mg) system produced by powder metallurgy for use as prostheses material. J Mech. Behav. Biomed. Mater. 115, 104260 (2021). https://doi.org/10.1016/j.jmbbm.2020.104260

    Article  Google Scholar 

  27. M.C. Rossi, D.L. Bayerlein, E.S. Gouvea, V.M.R. Haro, V.A. Escuder, V.B. Amigo, Evaluation of the influence of low Mg content on the mechanical and microstructural properties of beta titanium alloy. J. Mater. Res. Technol. 10, 916–925 (2021). https://doi.org/10.1016/j.jmrt.2020.12.103

    Article  Google Scholar 

  28. G.M.A. Mahran, A.-N.M. Omran, Fabrication of a β Ti–30Nb–4Sn biomedical alloy using mechanical alloying. Sci. Adv. Mater. 10, 1509–1518 (2018). https://doi.org/10.1166/sam.2018.3352

    Article  Google Scholar 

  29. D.R. Adiningsih, E.P. Utomo, The microstructure and mechanical hardness of cast Ti-30Nb-5Sn after solution treatment. IOP Conf Ser Mater Sci Eng. 541, 012049 (2019). https://doi.org/10.1088/1757-899X/541/1/012049

    Article  Google Scholar 

  30. B. Sharma, S.K. Vajpai, K. Ameyama, Synthesis of ternary Ti-25Nb-11Sn alloy by powder metallurgy route using titanium hydride powder. Mater Trans. 57, 1440–1446 (2016). https://doi.org/10.2320/matertrans.MH201510

    Article  Google Scholar 

  31. P. Li, X. Ma, D. Wang, H. Zhang, Microstructural and mechanical properties of β-Type Ti–Nb–Sn biomedical alloys with low elastic modulus. Metals. 9, 712 (2019). https://doi.org/10.3390/met9060712

    Article  Google Scholar 

  32. S. Cai, L. Wang, J.E. Schaffer, J. Gao, Y. Ren, Influence of Sn on martensitic beta Ti alloys. Mater. Sci. Eng. A. 743, 764–772 (2019). https://doi.org/10.1016/j.msea.2018.11.095

    Article  Google Scholar 

  33. H. Matsumoto, S. Watanabe, S. Hanada, Microstructures and mechanical properties of metastable β TiNbSn alloys cold rolled and heat treated. J Alloys Compd. 439, 146–155 (2007). https://doi.org/10.1016/j.jallcom.2006.08.267

    Article  Google Scholar 

  34. M.F. Ijaz, H.Y. Kim, H. Hosoda, S. Miyazaki, Efect of Sn addition on stress hysteresis and superelastic properties of a Ti–15Nb–3Mo alloy. Scripta Mater. 72–73, 29–32 (2014)

    Article  Google Scholar 

  35. M.A. Lagos, I. Agote, T. Schubert, T. Weissgaerber, J.M. Gallardo, J.M. Montes, L. Prakash, C. Andreouli, V. Oikonomou, D. Lopez, J.A. Calero, Development of electric resistance sintering process for the fabrication of hard metals: Processing microstructure and mechanical properties Abbreviations. Int J Refract Metals Hard Mater. 66, 88–94 (2017). https://doi.org/10.1016/j.ijrmhm.2017.03.005

    Article  Google Scholar 

  36. G.K. Williamson, W.H. Hall, X-ray line broadening from filed aluminium and wolfram. Acta Metall. 1, 22–31 (1953). https://doi.org/10.1016/0001-6160(53)90006-6

    Article  Google Scholar 

  37. A.M. Soufiani, F. Karimzadeh, M. Enayati, Formation mechanism and characterization of nanostructured Ti6Al4V alloy prepared by mechanical alloying. Mater. Des. 37, 152–160 (2012). https://doi.org/10.1016/j.matdes.2011.12.044

    Article  Google Scholar 

  38. L.M. Zou, C. Yang, Y. Long, Z.Y. Xiao, Y.Y. Li, Fabrication of biomedical Ti-35Nb-7Zr-5Ta alloys by mechanical alloying and spark plasma sintering. Powder Metall. 55, 65–70 (2012). https://doi.org/10.1179/1743290111Y.0000000021

    Article  Google Scholar 

  39. J. Málek, F. Hnilica, J. Veselý, B. Smola, Heat treatment and mechanical properties of powder metallurgy processed Ti-35.5 Nb-57Ta beta-titanium alloy. Mater. Charact. 84, 225–231 (2013). https://doi.org/10.1016/j.matchar.2013.08.006

    Article  Google Scholar 

  40. L. Lutterotti, S. Matthies, H.R. Wenk, MAUD: a friendly java program for material analysis using diffraction. IUCr Newsl. CPD. 21, 14–15 (1999)

    Google Scholar 

  41. C.M. Lee, C.P. Ju, J.H.C. Lin, Structure property relationship of cast Ti-Nb alloys. J. Oral Rehabil. 29, 314–322 (2002). https://doi.org/10.1046/j.1365-2842.2002.00825.x

    Article  Google Scholar 

  42. C. Slama, M. Abdellaoui, Microstructure characterization of nanocrystalline (Ti0.9W0.1) C prepared by mechanical alloying. Int. J. Refract. Met. Hard Mater. 54, 270–278 (2016). https://doi.org/10.1016/j.ijrmhm.2015.07.018

    Article  Google Scholar 

  43. H.J. Fecht, Nanostructure formation by mechanical attrition. Nanostruct. Mater. 6, 33–42 (1995)

    Article  Google Scholar 

  44. L. Zhang, X. Guo, Microstructural evolution, thermal stability and microhardness of the Nb–Ti–Si-Based alloy during mechanical alloying. J. Met. 8, 403 (2018). https://doi.org/10.3390/met8060403

    Article  Google Scholar 

  45. A.F. Mohamed, A dislocation model for the minimum grain size obtainable by milling. Acta Mater. 51, 4107–4119 (2003). https://doi.org/10.1016/s1359-6454(03)00230-1

    Article  ADS  Google Scholar 

  46. K.V. Sanjay, A. Kei, A novel powder metallurgy processing approach to prepare fine-grained Ti rich TiAl-based alloys from pre-alloyed powders. J. Intermet. 42, 146–155 (2013). https://doi.org/10.1016/j.intermet.2013.06.006

    Article  Google Scholar 

  47. A.L. Patterson, The scherrer formula for X-Ray particle size determination. Phys. Rev. 56, 978–982 (1939). https://doi.org/10.1103/physrev.56.978

    Article  MATH  ADS  Google Scholar 

  48. P. Singh, A. Abhash, B.N. Yadav, M. Shafeeq, I.B. Singh, D.P. Mondal, Effect of milling time on powder characteristics and mechanical performance of Ti4wt%Al alloy. Powder Technol. 342, 275–287 (2018). https://doi.org/10.1016/j.powtec.2018.09.075

    Article  Google Scholar 

  49. A. Khorsand Zak, W.H. Abd Majid, M.E. Abrishami, R. Yousefi, Solid State Sci. 13, 251 (2011)

    Article  ADS  Google Scholar 

  50. L.K. Singh, A. Bhadauria, S. Jana, T. Laha, Effect of sintering temperature and heating rate on crystallite size, densification behaviour and mechanical properties of Al-MWCNT nanocomposite consolidated via spark plasma sintering. Acta Metall Sin-Engl. 31, 1019–1030 (2018). https://doi.org/10.1007/s40195-018-0795-4

    Article  Google Scholar 

  51. B.N. Kim, K. Hiraga, K. Morita, H. Yoshida, Y.J. Park, Y. Sakka, Dynamic grain growth during low-temperature spark plasma sintering of alumina. Scr. Mater. 80, 29–32 (2014). https://doi.org/10.1016/j.scriptamat.2014.02.015

    Article  Google Scholar 

  52. J. Besson, M. Abouaf, Grain growth enhancement in alumina during hot isostatic pressing. Acta Metall. Mater. 39, 2225–2234 (1991). https://doi.org/10.1016/0956-7151(91)90004-K

    Article  Google Scholar 

  53. E.A. Olevsky, S. Kandukuri, L. Froyen, Consolidation enhancement in spark-plasma sintering: impact of high heating rates. J. Appl. Phys. 102, 114913 (2007). https://doi.org/10.1063/1.2822189

    Article  ADS  Google Scholar 

  54. B. Sharma, K. Nagano, M. Kawabata, K. Ameyama, Microstructure and mechanical properties of hetero-designed Ti-25Nb-25Zr alloy fabricated by powder metallurgy route. Lett. Mater. 9, 511–516 (2019). https://doi.org/10.3390/met10121615

    Article  Google Scholar 

  55. K. Ameyama, N. Horikawa, M. Kawabata, Unique mechanical properties of harmonic structure designed materials. Tetsu-to-Hagane. 105, 124–126 (2019)

    Article  Google Scholar 

  56. H.R. Wenk, P. Van Houtte, Texture and anisotropy. Rep. Prog. Phys. 67, s1367 (2004)

    Article  ADS  Google Scholar 

  57. J.W. Christian, Proc. ICSMA 2: 2nd Int. Conf. on Strength of Metals and Alloys Vol. 1, ASM (1970) p. 29.

  58. M. Kawata. X-Ray analysis of residual stress and texture in ground carbon steels; Master theses; Toyohashi Univ. Tech., March 45–47, (1982).

  59. A. Biesiekierski, J. Wang, M. Abdel-Hady Gepreel, C. Wen, A new look at biomedical Ti-based shape memory alloys. Acta Biomater. 8, 1661–1669 (2012). https://doi.org/10.1016/j.actbio.2012.01.018

    Article  Google Scholar 

  60. Y. Li, C. Yang, H. Zhao, S. Qu, X. Li, Y. Li, New developments of ti-based alloys for biomedical applications. Materials. 7, 1709–1800 (2014). https://doi.org/10.3390/ma7031709

    Article  ADS  Google Scholar 

  61. M. Niinomi, Recent metallic materials for biomedical applications. Metall. Mater. Trans. A. 33, 477–486 (2002). https://doi.org/10.1007/s11661-002-0109-2

    Article  Google Scholar 

  62. H.C. Hsu, S.C. Wu, Y.S. Hong, W.F. Ho, Mechanical properties and deformation behavior of as-cast Ti-Sn alloys. J. Alloys Compd. 479, 390–394 (2009). https://doi.org/10.1016/j.jallcom.2008.12.064

    Article  Google Scholar 

  63. J.L. Murray. In :J. L.Murray (Ed.),Alloy Phase Diagrams, ASM International, Materials Park, Ohio, 1987, p. 294.

  64. W.D. Callister, Materials Science and Engineering: An Introduction, Seventhed (Wiley, New York, 2007)

    Google Scholar 

  65. T. Sato, S. Hukai, Y.C. Huang, The Ms points of binary titanium alloys. J. Aust. Inst. Met. 5, 149–153 (1960)

    Google Scholar 

  66. E. Gouvea, M. Lagos, A. Vicente, D. Lopez, I. Agote, J.A. Calero, V. Amigó, Ti-27Nb-8Mo Beta Alloy Developed by Electric Resistance Sintering. Euro PM 2019 – Spark Plasma Sintering.

  67. A. Amigó-Mata, E. Gouvea, M.A. Lagos, D. López, I. Jesús-Romero, I. Agote, A. Vicente-Escuder, J.A. Calero, Effect of ERS Process Parameters on the Microstructure and Mechanical Properties of Ti6Al4V, Euro PM2019 – Spark Plasma Sintering.

  68. E.P. Utomo, I. Kartika, A. Anawati, Effect of Sn on mechanical hardness of as-cast Ti-Nb-Sn alloys. (2018) https://doi.org/10.1063/1.5038328.

  69. S.S. Da Rocha, G.L. Adabo, G.E.P. Henriques, M.A. Nóbilo, Vickers hardness of cast commercially pure titanium and Ti-6Al-4V alloy submitted to heat treatments. Braz. Dent. J. 17, 126–129 (2006). https://doi.org/10.1590/s0103-64402006000200008

    Article  Google Scholar 

  70. C.R.M. Afonso, K. Martinez-Orozco, V. Amigo, C.A.D. Rovere, J.E. Spinelli, C.S. Kiminami, Characterization, corrosion resistance and hardness of rapidly solidified Ni-Nb alloys. J. Alloys Compd. 829, 154529 (2020). https://doi.org/10.1016/j.jallcom.2020.154529

    Article  Google Scholar 

  71. N. Mavros, T. Larimian, J. Esqivel, R.K. Gupta, R. Contieri, T. Borkar, Spark plasma sintering of low modulus titanium-niobium-tantalum-zirconium (TNTZ) alloy for biomedical applications. Mater. Design. 183, 108163 (2019). https://doi.org/10.1016/j.matdes.2019.108163

    Article  Google Scholar 

  72. Q. Kong, X. Lai, X. An, W. Feng, C. Lu, J. Wu, C. Wu, L. Wu, Q. Wang, Mater. Today Commun. 23, 101130 (2020). https://doi.org/10.1016/j.mtcomm.2020.101130

    Article  Google Scholar 

  73. F.E.T. Heakal, K.A. Awad, Electrochemical corrosion and passivation behavior of titanium and its Ti-6AL-4V alloy in low and highly concentrated HBr solutions. Int. J. Electrochem. Sci. 7, 6539–6554 (2011)

    Google Scholar 

  74. A.A. Ahmed, M. Mhaede, M. Wollmann, L. Wagner, Effect of micro shot peening on the mechanical properties and corrosion behavior of two microstructure Ti–6Al–4V alloy. Appl. Surf. Sci. 363, 50–58 (2016). https://doi.org/10.1016/j.apsusc.2015.12.019

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors thank the AMES Company for the materials development.

Funding

This work was supported by the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) [grant: 2019/24237–6]; Ministerio de Economía y Competitividad de España for the research project RTI2018-097810-B-I00 and the European Commission through FEDER.

Author information

Authors and Affiliations

  1. Institut de Tecnologia de Materials, Universitat Politècnica de València, Camí de Vera s/n, 46022, Valencia, Spain

    Mariana Correa Rossi, Eber de Santi Gouvêa, Montserrat Vicenta Haro Rodríguez, Angel Vicente Escuder & Vicente Amigó Borrás

  2. Department of Chemistry and Biochemistry, Institute of Biosciences (IBB), São Paulo State University, Botucatu, Brazil

    Margarida Juri Saeki

Authors
  1. Mariana Correa Rossi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eber de Santi Gouvêa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Montserrat Vicenta Haro Rodríguez
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Margarida Juri Saeki
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Angel Vicente Escuder
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Vicente Amigó Borrás
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Conceptualization: [Mariana Correa Rossi], Methodology: [Mariana Correa Rossi], Formal analysis and research: [Mariana Correa Rossi], [Vicente Amigó Borrás]; Writing—original draft preparation: [Mariana Correa Rossi]; Writing—review and editing: [Margarida Saeki],[Vicente Amigó Borrás]; Data acquisition [Eber de Santi Gouvêa], [Montserrat Vicenta Haro Rodríguez], [Angel Vicente Escuder] Funding acquisition: [Mariana Correa Rossi],[Vicente Amigó Borrás]; Supervision: [Vicente Amigó Borrás].

Corresponding author

Correspondence to Mariana Correa Rossi.

Ethics declarations

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that may have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rossi, M.C., de Santi Gouvêa, E., Rodríguez, M.V.H. et al. Study of the current density of the electrical resistance sintering technique on microstructural and mechanical properties in a β Ti-Nb-Sn ternary alloy. Appl. Phys. A 127, 796 (2021). https://doi.org/10.1007/s00339-021-04937-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00339-021-04937-4

Keywords

Search

Navigation