Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Synthesis, characterization and quantitative analysis of porous metal microstructures: Application to microporous copper produced by solid state foaming

1 Department of Applied Engineering, Safety and Technology, Millersville University, Millersville, PA, USA
2 US Army Research Laboratory, Aberdeen Proving Ground, MD, USA

Special Issues: Advanced microstructural characterization of materials

Porous metals can be created through a wide variety of processing techniques, and the pore morphology resulting from these processes is equally diverse. The structural and functional properties of metal foams are directly dependent on the size, shape, interconnectedness and volume fraction of pores, so accurately quantifying the pore characteristics is of great importance. Methods for analyzing porous materials are presented here and applied to a copper-based metallic foam generated through solid state foaming via oxide reduction and expansion. This process results in large voids (10s of microns) between sintered particles and small pores (10 microns to less than 50 nm) within particles. Optical and electron microscopy were used to image the porosity over this wide range, and the pore characteristics were quantified using image segmentation and statistical analysis. Two-dimensional pore analysis was performed using the Chan-Vese method, and two-point correlation and lineal path functions were used to assess three-dimensional reconstructions from FIB tomography. Two-dimensional analysis reveals distinct size and morphological differences in porosity between particles and within them. Three-dimensional analysis adds further information on the high level interconnectedness of the porosity and irregular shape it takes, forming tortuous pathways rather than spherical cells. Mechanical polishing and optical microscopy allow large areas to be created and analyzed quickly, but methods such as focused ion beam (FIB) sectioning can provide additional insight about microstructural features. In particular, after FIB milling is used to create a flat surface, that surface can be analyzed for structural and compositional information.
  Article Metrics

Keywords microporous; metallic foam; FIB tomography; pore morphology; Chan-Vese method; two point correlation function; lineal path function

Citation: Mark A. Atwater, Kris A. Darling, Mark A. Tschopp. Synthesis, characterization and quantitative analysis of porous metal microstructures: Application to microporous copper produced by solid state foaming. AIMS Materials Science, 2016, 3(2): 573-590. doi: 10.3934/matersci.2016.2.573


  • 1. Banhart J (2001) Manufacture, characterisation and application of cellular metals and metal foams. Prog Mater Sci 46: 559–632.    
  • 2. Banhart J (2013) Light-Metal Foams - History of Innovation and Technological Challenges. Adv Eng Mater15: 82–111.
  • 3. Ashby MF, Evans AG, Fleck NA, et al. (2000) Metal Foams: A Design Guide. Boston: Butterworth-Heineman.
  • 4. Lefebvre L-P, Banhart J, Dunand DC (2008) Porous Metals and Metallic Foams: Current Status and Recent Developments. Adv Eng Mater 10: 775–787.    
  • 5. Ashby MF, Tianjian LU (2003) Metal foams: A survey. Science In China (Series B) 46: 521–532.    
  • 6. Banhart J (2007) Metal Foams - from Fundamental Research to Applications. In: Raj B, Ranganathan S, Rao KBS, Matthew MD, Shankar P, eds. Frontiers in the Design of Materials: Universities Press (India).
  • 7. Banhart J (2006) Metal Foams: Production and Stability. Adv Eng Mater 8:781–794.
  • 8. Ashby MF (1983) Mechnical properties of cellular solids. Metallurgical Transactions A 14A: 1755–1769.
  • 9. Davies GJ, Zhen S (1983) Metallic foams: their production, properties and applications. J Mater Sci 18: 1899–1911.
  • 10. Garcia-Avila M, Rabiei A (2015) Effect of Sphere Properties on Microstructure and Mechanical Performance of Cast Composite Metal Foams. Metals 5: 822–835.
  • 11. Shin H-C, Dong J, Liu M (2003) Nanoporous Structures Prepared by an Electrochemical Deposition Process. Adv Mater 15:1610–1614.
  • 12. Shin H-C, Liu M (2004) Copper Foam Structures with Highly Porous Nanostructured Walls. Chem Mater 16: 5460–5464.    
  • 13. Nam D, Kim R, Han D, et al. (2011) Effects of (NH4)2SO4 and BTA on the nanostructure of copper foam prepared by electrodeposition. Electrochim Acta 56: 9397–9405.    
  • 14. Kim JH, Kim RH, Kwon HS (2008) Preparation of copper foam with 3-dimensionally interconnected spherical pore network by electrodeposition. Electrochemistry Communications 10: 1148–1151.    
  • 15. Kennedy A (2012) Porous Metals and Metal Foams Made from Powders. In: Kondoh K, ed. Powder Metallurgy Rijeka,Croatia InTech.
  • 16. Torres Y, Pavón JJ, Rodríguez JA (2012) Processing and characterization of porous titanium for implants by using NaCl as space holder. J Mater Process Tech 212: 1061–1069.    
  • 17. Wenjuan N, Chenguang B, GuiBao Q, et al. (2009) Processing and properties of porous titanium using space holder technique. Mater Sci Eng A 506: 148–151.    
  • 18. Xie S, Evans JRG (2004) High porosity copper foam. J Mater Sci 39: 5877–5880.
  • 19. Torres Y, Lascano S, Bris J, et al. (2014) Development of porous titanium for biomedical applications: A comparison between loose sintering and space-holder techniques. Mat Sci Eng C 37: 148–155.
  • 20. Laptev A, Bram M, Buchkremer HP, et al. (2004) Study of production route for titanium parts combining very high porosity and complex shape. Powder Metallurgy 47: 85–92.    
  • 21. Paserin V, Marcuson S, Shu J, et al. (2004) CVD technique for Inco nickel foam production. Adv Eng Mater 6: 454–459.    
  • 22. Hodge AM, Biener J, Hsiung LL, et al. (2005) Monolithic nanocrystalline Au fabricated by the compaction of nanoscale foam. J Mater Res 20: 554–557.
  • 23. Tai MC, Gentle A, Silva KSBd, et al. (2015) Thermal Stability of Nanoporous Raney Gold Catalyst. Metals 5: 1197–1211.
  • 24. Lin B, Kong L, Hodgson PD, et al. (2014) Impact of the De-Alloying Kinetics and Alloy Microstructure on the Final Morphology of De-Alloyed Meso-Porous Metal Films. Nanomaterials 4: 856–878.
  • 25. Davis NG, Teisen J, Schuh C, et al. (2001) Solid-state foaming of titanium by superplastic expansion of argon-filled pores. J Mater Res 16: 1508–1519.
  • 26. Dunand DC. (2004) Processing of Titanium Foams. Adv Eng Mater 6: 369–376.
  • 27. Elzey DM, Wadley HNG (2001) The Limits Of Solid State Foaming. Acta Mater 49: 849–859.
  • 28. Kearns MW (1987) inventor Formation of Porous Bodies patent 4,659,546.
  • 29. Oppenheimer S, Dunand DC (2010) Solid-state foaming of Ti–6Al–4V by creep or superplastic expansion of argon-filled pores. Acta Mater 58: 4387–4397.
  • 30. Li H, Oppenheimer SM, Stupp SI, et al. (2004) Effects of Pore Morphology and Bone Ingrowth on Mechanical Properties of Microporous Titanium as an Orthopaedic Implant Material. Mater T JIM 45: 1124–1131.    
  • 31. Atwater MA, Darling KA, Tschopp MA (2016) Solid-State Foaming by Oxide Reduction and Expansion: Tailoring the Foamed Metal Microstructure in the Cu–CuO System with Oxide Content and Annealing Conditions. Adv Eng Mater 18: 83–95.
  • 32. Atwater MA, Darling KA, Tschopp MA (2014) Towards Reaching the Theoretical Limit of Porosity in Solid State Metal Foams: Intraparticle Expansion as a Primary and Additive Means to Create Porosity. Adv Eng Mater 16: 190–195.    
  • 33. Caselles V, Kimmel R, Sapiro G (1997) Geodesic active contours. Int J Comput Vision 22: 61–79.    
  • 34. Whitaker RT (1998) A level-set approach to 3d reconstruction from range data. Int J Comput Vision 29: 203–231.    
  • 35. Chan TF, Vese LA (2001) Active contours without edges. IEEE T Image Process 10: 266–277.
  • 36. Samuels LE (2003) Metallographic Polishing by Mechanical Methods. 4th ed. Materials Park, OH: ASM International.
  • 37. Mingard KP, Jones HG, Gee MG (2013) Metrological challenges for reconstruction of 3-D microstructures by focused ion beam tomography methods. J Microsc 253: 93–108.
  • 38. Volkert CA, Minor AM (2007) Focused Ion Beam Microscopy and Micromachining. MRS Bull 32: 389–395.    
  • 39. Suryanarayana C, Ivanob E, Boldyrev VV. (2001) The science and technology of mechanical alloying. Mater Sci Eng A 304–306:151–158.
  • 40. Suryanarayana C (2001) Mechanical alloying and milling. Prog Mater Sci 46:1–184.
  • 41. Suryanarayana C, Koch CC (2000) Nanocrystalline materials – Current research and future directions. Hyperfine Interact 130:5–44.
  • 42. Koch CC (1989) Materials synthesis by mechanical alloying. Annu Rev Mater Sci 19: 121–143
  • 43. Koch CC (1993) The synthesis and structure of nanocrystalline materials produced by mechanical attrition: A review. Nanostruct Mater 2: 109–129.
  • 44. Koch CC, Cho YS (1992) Nanocrystals by high energy ball milling. Nanostruct Mater 1: 207–212.    
  • 45. Lü L, Lai MO (1998) Mechanical alloying. Boston: Kluwer Academic Publishers.
  • 46. Krill CE, Klein R, Janes S, et al. (1995) Thermodynamic stabilization of grain boundaries in nanocrystalline alloys. Mater Sci Forum 181: 443–448.
  • 47. Koch CC, Scattergood RO, Darling KA, et al. (2008) Stabilization of nanocrystalline grain sizes by solute additions. J Mater Sci 43: 7264–7272.
  • 48. Trelewicz JR, Schuh CA (2009) Grain boundary segregation and thermodynamically stable binary nanocrystalline alloys. Phys Rev B 79:1–13.
  • 49. Li J, Wang J, Yang G (2009) On the stagnation of grain growth in nanocrystalline materials. Scripta Mater 60: 945–948.    
  • 50. Rajgarhia RK, Saxena A, Spearot DE, et al. (2010) Microstructural stability of copper with anitmony dopants at grain boundaries: experiments and molecular dynamics simulations. J Mater Sci 45: 6707–6718.    
  • 51. Rajgarhia RK, Spearot DE, Saxena A (2010) Plastic deformation of nanocrystalline copper-antimony alloys. J Mater Res 25: 411–421.    
  • 52. Rajgarhia RK, Spearot DE, Saxena A. (2010) Behavior of dopant-modified interfaces in metallic nanocrystalline materials. JOM 62: 70–74.
  • 53. Atwater MA, Mula S, Scattergood RO, et al. (2013) Thermal Stability of Nanocrystalline Copper Alloyed with Antimony. Metall Mater Trans A 44: 5611–5616.
  • 54. Liu XJ, Wang CP, Ohnuma I, et al. (2000) Thermodynamic assessment of the phase diagrams of the Cu-Sb and Sb-Zn systems. J Phase Equilib 21: 432–442.    
  • 55. MSIT®, Bätzner C, Ferro R, et al. (2007) Cu-Sb-Zn (Copper-Antimony-Zinc). In: Ilyenko GES, ed. Non-Ferrous Metal Ternary Systems Selected Copper Systems: Phase Diagrams, Crystallographic and Thermodynamic Data: Springer-Verlag.
  • 56. Banhart J, Baumeister J (1998) Production Methods for Metallic Foams. MRS Proceedings 521.
  • 57. Murray NGD, Dunand DC. (2003) Microstructure evolution during solid-state foaming of titanium. Compos Sci Technol 63: 2311–2316.
  • 58. Zhang Z, Wang Y, Qi Z, et al. (2009) Generalized Fabrication of Nanoporous Metals (Au, Pd, Pt, Ag, and Cu) through Chemical Dealloying. J Phys Chem C 113: 12629–12636.    
  • 59. Cheng I-C, Hodge A (2013) Strength scale behavior of nanoporous Ag, Pd and Cu foams. Scripta Mater 69: 295–298.    
  • 60. Liu R, Antoniou A (2012) A relation between relative density, alloy composition and sample shrinkage for nanoporous metal foams. Scripta Mater 67: 923–926.    
  • 61. Spowart JE (2006) Automated serial sectioning for 3-D analysis of microstructures. Scripta Mater 55: 5–10.    
  • 62. Bart-Smith H, Bastawros A-F, Mumm DR, et al. (1998) Compressive deformation and yielding mechanisms in cellular Al alloys determined using X-ray tomography and surface strain mapping. Acta Mater 46: 3583–3592.    
  • 63. Maire E (2012) X-Ray Tomography Applied to the Characterization of Highly Porous Materials. Ann Rev Mater Res 42: 163–178.
  • 64. Rack A, Haibel A, Bütow A, et al. Characterization of Metal Foams with Synchrotron Tomography and 3D Image Analysis. 16th World Conference on Nondestructive Testing.
  • 65. Elmoutaouakkil A, Salvo L, Maire E, et al. (2002) 2D and 3D Characterization of Metal Foams Using X-ray Tomography. Adv Eng Mater 4: 803–807.
  • 66. Midgley PA, Weyland M, Yates TJV, et al. (2006) Nanoscale scanning transmission electron tomography. J Microsc 223: 185–190.
  • 67. Rösner H, Parida S, Kramer D, et al. (2007) Reconstructing aNanoporousMetal in Three Dimensions: An Electron Tomography Study of Dealloyed Gold Leaf. Adv Eng Mater 9: 535–541.
  • 68. Tschopp MA, Darling KA, Atwater MA (2014) Surpassing the Theoretical Limit of Porosity in Conventional Solid-State Foaming: Microstructure Characterization of Length Scales in a Copper Metal Foam. Army Research Laboratory, ARL-TR-7139.
  • 69. VanLeeuwen BK, Darling KA, Koch CC, et al. (2011) Novel technique for the synthesis of ultra-fine porosity metal foam via the inclusion of condensed argon through cryogenic mechanical alloying. Mater Sci Eng A 528: 2192–2195.    
  • 70. Vázquez M, Moore D, He X, et al. (2014) Focussed ion beam serial sectioning and imaging of monolithic materials for 3D reconstruction and morphological parameter evaluation. Analyst 139: 99–104.
  • 71. Xu W, Ferry M, Mateescu N, et al. (2007) Techniques for generating 3-D EBSD microstructures by FIB tomography. Mater Charact 58: 961–967.    
  • 72. Kubis AJ, Shiflet GJ, Dunn DN, et al. (2004) Focused Ion-Beam Tomography. Metall Mater Trans A 35:1935–1943.    
  • 73. Yazzie KE, Williams JJ, Phillips NC, et al. (2012) Multiscale microstructural characterization of Sn-rich alloys by three dimensional (3D) X-ray synchrotron tomography and focused ion beam (FIB) tomography. Mater Charact 70: 33–41.
  • 74. Vivet N, Chupin S, Estrade E, et al. (2011) 3D Microstructural characterization of a solid oxide fuel cell anode reconstructedby focused ion beam tomography. J Power Sources 196: 7541–7549.
  • 75. Nagasekhar AV, Cáceres CH, Kong C (2010) 3D characterization of intermetallics in a high pressure die cast Mg alloy using focused ion beam tomography. Mater Charact 61: 1035–1042.
  • 76. West GD, Thomson RC (2009) Combined EBSD/EDS tomography in a dual-beam FIB/FEG–SEM. J Microsc 233: 442–450.
  • 77. Winter DAMd, Schneidenberg CTWM, Lebbink MN, et al. (2009) Tomography of insulating biological and geological materials using focused ion beam (FIB) sectioning and low-kV BSE imaging. J Microsc 233: 372–383    
  • 78. Kizilyaprak C, Daraspe J, Humbel BM (2014) Focused ion beam scanning electron microscopy in biology. J Microsc 254: 109–114.


This article has been cited by

  • 1. Mark A. Atwater, Thomas L. Luckenbaugh, B. Chad Hornbuckle, Kristopher A. Darling, Advancing commercial feasibility of intraparticle expansion for solid state metal foams by the surface oxidation and room temperature ball milling of copper, Journal of Alloys and Compounds, 2017, 724, 258, 10.1016/j.jallcom.2017.07.029
  • 2. Laura N. Guevara, Christopher B. Nelson, Gaurav Hans, Cammie L. Atwater, Mark A. Atwater, Effects of milling time on the development of porosity in Cu by the reduction of CuO, AIMS Materials Science, 2017, 4, 4, 939, 10.3934/matersci.2017.4.939
  • 3. Mark A. Atwater, Getting more porosity from powder metal foams through intraparticle expansion, Metal Powder Report, 2017, 10.1016/j.mprp.2017.08.069
  • 4. Mark A. Atwater, Laura N. Guevara, Kris A. Darling, Mark A. Tschopp, Solid State Porous Metal Production: A Review of the Capabilities, Characteristics, and Challenges, Advanced Engineering Materials, 2018, 1700766, 10.1002/adem.201700766
  • 5. Swantje Bargmann, Benjamin Klusemann, Jürgen Markmann, Jan Eike Schnabel, Konrad Schneider, Celal Soyarslan, Jana Wilmers, Generation of 3D representative volume elements for heterogeneous materials: a review, Progress in Materials Science, 2018, 10.1016/j.pmatsci.2018.02.003
  • 6. Mark A. Atwater, Thomas L. Luckenbaugh, B. Chad Hornbuckle, Kristopher A. Darling, Solid State Foaming of Nickel, Monel, and Copper by the Reduction and Expansion of NiO and CuO Dispersions, Advanced Engineering Materials, 2018, 10.1002/adem.201800302
  • 7. Mark A. Atwater, Reconsidering functional powder metallurgy with intraparticle porosity, Metal Powder Report, 2019, 10.1016/j.mprp.2019.01.004
  • 8. Mark A. Atwater, Sean J. Fudger, Christopher B. Nelson, B.Chad Hornbuckle, Steven J. Knauss, Samuel A. Brennan, Kristopher A. Darling, Multi-stage pore development in Ag foams by the reduction of Ag2O and CuO mixtures, Materials & Design, 2019, 108273, 10.1016/j.matdes.2019.108273

Reader Comments

your name: *   your email: *  

Copyright Info: 2016, Mark A. Tschopp, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved