journal article·2026-07Open access

Mechanical scaling laws and deformation behavior of nanoporous tantalum microparticles

J.I. Ramallo, N. Vázquez von Bibow, M.A. Monclús, I. McCue, M.C. Fuertes, C.J. Ruestes

Abstract

The mechanical scaling laws of dealloyed nanoporous metals depart from classical Gibson-Ashby predictions for open-cell foams due to a decreased connectivity in their solid network. However, these scaling relations have been established almost exclusively on nanoporous gold produced by electrochemical dealloying, and it is an outstanding question whether the relations apply to nanoporous networks fabricated by other dealloying methods. Here, we investigate the mechanical response of single-crystalline nanoporous tantalum (np-Ta) produced by liquid metal dealloying (LMD) a TiTa alloy in molten CuBi. Nanoindentation of individual microparticles yields an elastic modulus of 10–30 GPa and a hardness of 0.3–1.1 GPa, both scaling with the solid volume fraction in agreement with Gibson-Ashby predictions. This stiffness-density response of np-Ta departs from previous reports on nanoporous gold and is attributed to enhanced ligament connectivity enabled by the thermodynamics of the CuBi metal bath. Molecular dynamics simulations reveal dislocation-dominated plasticity during indentation of np-Ta, consistent with scanning electron microscopy observations of limited densification beneath the indents, ruling out unusual deformation mechanisms as an origin of the observed scaling. These findings identify solvent chemistry in LMD as a tunable lever for ligament connectivity, and thus for the mechanical response of nanoporous metals.
Source: openalex_inverted_index · Quality: baseline

Research context

OpenAlex topics: Nanoporous metals and alloys · Anodic Oxide Films and Nanostructures · nanoparticles nucleation surface interactions

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (100+)

Show source-provided references
1. Materials by design: Using architecture in material design to reach new property spaces10.1557/mrs.2015.263 ↗
2. Three-dimensional architected materials and structures: Design, fabrication, and mechanical behavior10.1557/mrs.2019.232 ↗
3. Double-network-inspired mechanical metamaterials
4. Enabling three-dimensional architected materials across length scales and timescales
5. Scaling behavior of stiffness and strength of hierarchical network nanomaterials10.1126/science.abd9391 ↗
6. Additive manufacturing of 3D nano-architected metals10.1038/s41467-018-03071-9 ↗
7. Recent trends on studies of nanostructured metals10.1557/s43577-021-00069-5 ↗
8. Surface-chemistry-driven actuation in nanoporous gold10.1038/nmat2335 ↗
9. Metallic muscles and beyond: nanofoams at work10.1007/s10853-015-9317-1 ↗
10. Extreme mechanical resilience of self-assembled nanolabyrinthine materials10.1073/pnas.1916817117 ↗
11. Computationally efficient design of directionally compliant metamaterials10.1038/s41467-018-08049-1 ↗
12. On the consequences of intrinsic and extrinsic size effects on the mechanical response of nanoporous au10.1016/j.matdes.2023.112175 ↗
13. Densification of nanoporous metals during nanoindentation: The role of structural and mechanical properties10.1557/s43578-022-00870-1 ↗
14. Nanoporous gold based optical sensor for sub-ppt detection of mercury ions10.1021/nn4013737 ↗
15. Nanoporous gold: from structure evolution to functional properties in catalysis and electrochemistry10.1021/acs.chemrev.2c00751 ↗
16. Are nanoporous materials radiation resistant?10.1021/nl201383u ↗
17. Nanoporous metals under extremes
18. Dealloying and dealloyed materials10.1146/annurev-matsci-070115-031739 ↗
19. Pattern formation during electrochemical and liquid metal dealloying10.1557/mrs.2017.301 ↗
20. Nano-to submicro-porous β-ti alloy prepared from dealloying in a metallic melt10.1016/j.scriptamat.2011.06.019 ↗
21. Dealloying by metallic melt10.1016/j.matlet.2011.01.054 ↗
22. Dealloying-based interpenetrating-phase nanocomposites matching the elastic behavior of human bone10.1038/s41598-017-00048-4 ↗
23. Open porous α+ β titanium alloy by liquid metal dealloying for biomedical applications10.3390/met10111450 ↗
24. Three-dimensional open-cell macroporous iron, chromium and ferritic stainless steel10.1016/j.scriptamat.2013.01.011 ↗
25. A universal scaling relationship between the strength and Young’s modulus of dealloyed porous Fe0.80Cr0.2010.1016/j.actamat.2019.12.046 ↗
26. Ligament morphology and elastic modulus of porous structure formed by liquid metal dealloying10.1016/j.jmrt.2024.07.091 ↗
27. Topology-generating interfacial pattern formation during liquid metal dealloying10.1038/ncomms9887 ↗
28. Kinetics and morphological evolution of liquid metal dealloying10.1016/j.actamat.2016.05.032 ↗
29. Liquid metal dealloying of titanium-tantalum (Ti-Ta) alloy to fabricate ultrafine Ta ligament structures: A comparative study in molten copper (Cu) and Cu-based alloys10.1016/j.corsci.2020.108600 ↗
30. Topological control of liquid-metal-dealloyed structures10.1038/s41467-022-30483-5 ↗
31. Sub-micron porous niobium solid electrolytic capacitor prepared by dealloying in a metallic melt10.1016/j.matlet.2013.11.036 ↗
32. Self-assembled porous metal-intermetallic nanocomposites via liquid metal dealloying10.1016/j.actamat.2018.10.057 ↗
33. Compressive behavior and connecting topology of monolithic nanoporous niobium10.1080/21663831.2024.2421867 ↗
34. Three-dimensional morphological and chemical evolution of nanoporous stainless steel by liquid metal dealloying10.1021/acsami.7b04659 ↗
35. Nanoporous high-entropy alloy by liquid metal dealloying10.3390/met10101396 ↗
36. Accelerated structural ordering during liquid metal dealloying and its effect on thermal coarsening of nanoporous refractory alloys10.1016/j.scriptamat.2024.116120 ↗
37. Development of 3D interconnected nanoporous TiZrHfNbTaNi high-entropy alloy via liquid metal dealloying and subsequent synthesis of (TiZrHfNbTaNi)Ohigh-entropy oxide10.1016/j.jmrt.2025.02.152 ↗
38. Nanoporous high-entropy alloys fabricated by liquid metal dealloying and surface anodizing for enhanced electrochemical performance in capacitors
39. Formation of 3D interconnected multiphase heterostructures from CoCrFeMnNi high-entropy alloy via liquid metal dealloying using Cu–Ag melts10.1016/j.jmrt.2026.01.127 ↗
40. Indentation response of nanoporous gold from atomistic simulations10.1557/jmr.2018.72 ↗
41. Ultrathin, substrate-integrated, and self-healing nanocapacitors with low-leakage currents and high-operating frequencies10.1109/TCPMT.2016.2602213 ↗
42. Additively manufactured porous tantalum implants10.1016/j.actbio.2014.12.003 ↗
43. Materials design for hypersonics10.1038/s41467-024-46753-3 ↗
44. Alloying effects on the microstructure and properties of laser additively manufactured tungsten materials10.1016/j.msea.2024.147110 ↗
45. Review of recent progress in plasma-facing material joints and composites in the FRONTIER US-Japan collaboration10.1080/15361055.2023.2176687 ↗
46. A powder metallurgy approach to liquid metal dealloying with applications in additive manufacturing10.1016/j.actamat.2022.118213 ↗
47. AQUAMI: An open source python package and GUI for the automatic quantitative analysis of morphologically complex multiphase materials10.1016/j.commatsci.2017.08.012 ↗
48. Gaining new insights into nanoporous gold by mining and analysis of published images10.1038/s41598-018-25122-3 ↗
49. Optimal indent spacing for instrumented nanoindentation of nanoporous gold10.1557/s43579-023-00505-4 ↗
50. Elastic and plastic Poisson’s ratios of nanoporous gold10.1016/j.scriptamat.2015.08.002 ↗
51. Molecular dynamics modeling of nanoindentation10.1002/9781119084501.ch14 ↗
52. The nanoindentation puzzle: Putting the pieces together using simulations at different scales: R. Janisch, d. Mordehai
53. 3D stochastic bicontinuous microstructures: Generation, topology and elasticity10.1016/j.actamat.2018.01.005 ↗
54. Topological changes and deformation mechanisms of nanoporous ta under compression
55. Effect of tip roundness on the nanoindentation of Fe crystals10.1007/s11249-020-01295-9 ↗
56. Indentation and scratching of iron by a rotating tool–a molecular dynamics study
57. Atomistic simulation of tantalum nanoindentation: Effects of indenter diameter, penetration velocity, and interatomic potentials on defect mechanisms and evolution10.1016/j.msea.2014.07.001 ↗
58. Planar defect nucleation and annihilation mechanisms in nanocontact plasticity of metal surfaces10.1103/PhysRevLett.109.075502 ↗
59. LAMMPS-a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales10.1016/j.cpc.2021.108171 ↗
60. Visualization and analysis of atomistic simulation data with OVITO–the open visualization tool10.1088/0965-0393/18/1/015012 ↗
61. Extracting dislocations and non-dislocation crystal defects from atomistic simulation data10.1088/0965-0393/18/8/085001 ↗
62. Grain boundary effects in high-temperature liquid-metal dealloying: a multi-phase field study10.1038/s41524-023-01076-7 ↗
63. Morphology selection in dealloying: A phase field study of the coupling among kinetic mechanisms
64. Pattern formation during dealloying10.1016/S1359-6462(03)00471-8 ↗
65. Formation of nanoporous Ta structure on Ti-Ta alloy based on a novel surface dealloying process10.1016/j.jallcom.2025.179945 ↗
66. Nanomechanical and nanotribological properties of nanostructured coatings of tantalum and its compounds on steel substrates10.3390/nano11092407 ↗
67. XPS depth-profile of the suboxide distribution at the native oxide/Ta interface10.1016/j.elspec.2008.10.004 ↗
68. Ag effects on the elastic modulus values of nanoporous Au foams10.1557/jmr.2009.0184 ↗
69. On the topological, morphological, and microstructural characterization of nanoporous metals10.1557/mrs.2017.303 ↗
70. Nanoindentation. Mechanical engineering series10.1115/1.1704625 ↗
71. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments10.1557/JMR.1992.1564 ↗
72. Scaling equation for yield strength of nanoporous open-cell foams10.1016/j.actamat.2006.09.038 ↗
73. ALD functionalized nanoporous gold: thermal stability, mechanical properties, and catalytic activity10.1021/nl200993g ↗
74. Fabrication and thermo-mechanical behavior of ultra-fine porous copper10.1007/s10853-014-8622-4 ↗
75. Interface dominated mechanical properties of ultra-fine grained and nanoporous Au at elevated temperatures10.1016/j.actamat.2016.08.071 ↗
76. Nanomechanical behaviour of open-cell nanoporous metals: Homogeneous versus thickness-dependent porosity10.1016/j.mechmat.2016.06.014 ↗
77. Microstructural effect on time-dependent plasticity of nanoporous gold10.1016/j.ijplas.2018.05.011 ↗
78. Indentation size effect for spherical nanoindentation on nanoporous gold10.1016/j.scriptamat.2017.09.002 ↗
79. Beating thermal coarsening in nanoporous materials via high-entropy design
80. Open-cell tungsten nanofoams: Chloride ion induced structure modification and mechanical behavior10.1016/j.rinp.2020.103062 ↗
81. Diamond-structured nanonetwork gold as mechanical metamaterials from bottom-up approach10.1038/s41427-023-00483-y ↗
82. Compressive properties of nanoporous gold through nanoindentation: an analytical approach based on the expanding cavity model10.1007/s12540-020-00740-7 ↗
83. Understanding the interdependence of penetration depth and deformation on nanoindentation of nanoporous silver10.3390/met9121346 ↗
84. Investigation of the influence of nanoscale porosity in the interfacial layers on the mechanical properties of helium plasma-exposed tungsten10.1021/acsaenm.3c00183 ↗
85. The mechanics of three-dimensional cellular materials
86. Ashby · 2000
87. Interpreting anomalous low-strength and low-stiffness of nanoporous gold: Quantification of network connectivity10.1016/j.actamat.2016.07.033 ↗
88. Scaling equation for the elastic modulus of nanoporous gold with “fixed” network connectivity10.1063/1.4984108 ↗
89. Scaling between elasticity and topological genus for random network nanomaterials10.1016/j.eml.2024.102147 ↗
90. Local heterogeneity in the mechanical properties of bicontinuous composites made by liquid metal dealloying10.1063/1.4971776 ↗
91. Atomistic insights into metal hardening10.1038/s41563-020-00815-1 ↗
92. The role of computer simulation in nanoporous metals—A review10.3390/ma8085060 ↗
93. Anomalous compliance and early yielding of nanoporous gold10.1016/j.actamat.2015.04.021 ↗
94. Hardening under compression in Au foams10.1016/j.actamat.2016.02.030 ↗
95. Nanoindentation of nanoporous tungsten: A molecular dynamics approach10.1016/j.commatsci.2022.111336 ↗
96. Deformation behavior of nanoporous gold nanoparticles during compression10.1016/j.actamat.2025.120723 ↗
97. Revealing nanoscale plasticity of metallic nanosponges with correlative and scale-bridging 3D microscopy and modelling10.1038/s43246-025-00914-z ↗
98. Focused ion beam characterization of deformation resulting from nanoindentation of nanoporous gold10.1557/mrc.2017.138 ↗
99. Image segmentation and analysis for densification mapping of nanoporous gold after nanoindentation10.1557/s43580-021-00099-w ↗
100. Mechanical properties of nanoporous gold10.1039/9781849735285-00051 ↗