Adaptive hard and tough mechanical response in single-crystal B1 VNx ceramics via control of anion vacancies
Source abstract
Abstract
High hardness and toughness are generally considered mutually exclusive properties for single-crystal ceramics. Combining experiments and ab initio molecular dynamics (AIMD) atomistic simulations at room temperature, we demonstrate that both the hardness and toughness of single-crystal NaCl-structure VNx/MgO(001) thin films are simultaneously enhanced through the incorporation of anion vacancies. Nanoindentation results show that VN0.8, here considered as representative understoichiometric VNx system, is ≈20% harder, as well as more resistant to fracture than stoichiometric VN samples. AIMD modeling of VN and VN0.8 supercells subjected to [001] and [110] elongation reveal that the tensile strengths of the two materials are similar. Nevertheless, while the stoichiometric VN phase cleaves in a brittle manner at tensile yield points, the understoichiometric compound activates transformation-toughening mechanisms that dissipate accumulated stresses. AIMD simulations also show that VN0.8 exhibits an initially greater resistance to both {110}〈11¯0〉 and {111}〈11¯0〉 shear deformation than VN. However, for progressively increasing shear strains, the VN0.8 mechanical behavior gradually evolves from harder to more ductile than VN. The transition is mediated by anion vacancies, which facilitate {110}〈11¯0〉 and {111}〈11¯0〉 lattice slip by reducing activation shear stresses by as much as 35%. Electronic-structure analyses show that the two-regime hard/tough mechanical response of VN0.8 primarily stems from its intrinsic ability to transfer d electrons between 2nd-neighbor and 4th-neighbor (i.e., across vacancy sites) V–V metallic states. Our work offers a route for electronic-structure design of hard materials in which a plastic mechanical response is triggered with loading.
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Research context
OpenAlex topics: Metal and Thin Film Mechanics · Advanced ceramic materials synthesis · Advanced materials and composites
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References (94)
Show source-provided references
1. Controlling cracks in ceramics10.1126/science.286.5442.1097 ↗
2. Ductile and brittle crystals10.1080/14786436708220903 ↗
3. Callister · 2011
4. Supertough wear-resistant coatings with 'chameleon' surface adaptation10.1016/S0040-6090(00)00917-2 ↗
5. Ceramic metal interfacial crack-growth - toughening by controlled microcracks and interfacial geometries10.1016/0001-6160(88)90310-0 ↗
6. Toughness enhancement in hard ceramic thin films by alloy design10.1063/1.4822440 ↗
7. Vacancy-induced toughening in hard single-crystal V0.5Mo0.5Nx/MgO(001) thin films10.1016/j.actamat.2014.06.025 ↗
8. Growth and mechanical properties of 111-oriented V0.5Mo0.5Nx/Al2O3(0001) thin films10.1116/1.5045048 ↗
9. V0.5Mo0.5Nx/MgO(001): Composition, nanostructure, and mechanical properties as a function of film growth temperature10.1016/j.actamat.2016.12.048 ↗
10. Meyers · 1999
11. Dieter · 1976
12. Extra-electron induced covalent strengthening and generalization of intrinsic ductile-to-brittle criterion10.1038/srep00718 ↗
13. The conflicts between strength and toughness10.1038/nmat3115 ↗
14. Crystallographic structure of sputtered cubic δ-VNx films - influence of basic deposition parameters10.1016/0257-8972(93)90232-D ↗
15. Structural and mechanical properties of sputtered cubic and hexagonal NbNx thin films
16. Material selection for hard coatings10.1116/1.573700 ↗
17. Chemical bonding and electronic structure in binary VNy and ternary T1–xVxNy nitrides10.1063/1.366843 ↗
18. Elastic constants, Poisson ratios, and the elastic anisotropy of VN(001), (011), and (111) epitaxial layers grown by reactive magnetron sputter deposition10.1063/1.4881817 ↗
19. Growth, nanostructure, and optical properties of epitaxial VNx/MgO(001) (0.80≤x≤1.00) layers deposited by reactive magnetron sputtering10.1039/C6TC02289H ↗
20. Phonon and electron contributions to the thermal conductivity of VNx epitaxial layers
21. An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments10.1557/JMR.1992.1564 ↗
22. Indentation hardness measurements at macro-, micro-, and nanoscale: a critical overview10.1007/s11249-016-0805-5 ↗
23. Gogotsi · 2003
24. Unified approach for molecular dynamics and density-functional theory10.1103/PhysRevLett.55.2471 ↗
25. Surface energies of several ceramics with NaCl structure10.1016/j.susc.2005.10.035 ↗
26. Electronic mechanism of hardness enhancement in transition-metal carbonitrides10.1038/20148 ↗
27. Mechanical instability and ideal shear strength of transition metal carbides and nitrides10.1103/PhysRevLett.87.075503 ↗
28. Vacancy hardening and softening in transition metal carbides and nitrides10.1103/PhysRevLett.86.3348 ↗
29. Slip system determination in cubic carbides by hardness anisotropy10.1098/rspa.1972.0017 ↗
30. Toth · 1971
31. Characterization of misfit dislocations in epitaxial (001)-oriented TiN, NbN, VN, and (Ti,Nb)N film heterostructures by transmission electron-microscopy10.1016/0022-0248(94)90757-9 ↗
32. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set10.1103/PhysRevB.54.11169 ↗
33. Projector augmented-wave method10.1103/PhysRevB.50.17953 ↗
34. Generalized gradient approximation made simple10.1103/PhysRevLett.77.3865 ↗
35. Polymorphic transitions in single-crystals - a new molecular dynamics method10.1063/1.328693 ↗
36. Inherent toughness and fracture mechanisms of refractory transition-metal nitrides via density-functional molecular dynamics10.1016/j.actamat.2018.03.038 ↗
37. D.G. Sangiovanni, F. Tasnadi, L.J.S. Johnson, M. Oden, I.A. Abrikosov, Strength, Transformation Toughening and Fracture Dynamics of Rocksalt-Structure Ti1–xAlxN (0≤x≤0.75) Alloys,
38. Ideal shear strengths of fcc aluminum and copper10.1103/PhysRevLett.82.2713 ↗
39. Dynamic and structural stability of cubic vanadium nitride10.1103/PhysRevB.91.054101 ↗
40. VMD: Visual molecular dynamics10.1016/0263-7855(96)00018-5 ↗
41. Size effects and stochastic behavior of nanoindentation pop in10.1103/PhysRevLett.106.165502 ↗
42. Application of nucleation theory to the rate dependence of incipient plasticity during nanoindentation10.1557/JMR.2004.0276 ↗
43. An alternative method for small pop-in assessment10.1016/S0013-7944(97)00105-7 ↗
44. A model for micropack initiation and propagation beneath hertzian contacts in polycrystalline ceramics10.1016/0956-7151(94)90378-6 ↗
45. Giant pop-ins in nanoindented silicon and germanium caused by lateral cracking10.1557/JMR.2008.0070 ↗
46. Indentation induced dislocation nucleation: The initial yield point10.1016/1359-6454(96)00010-9 ↗
47. Crystal plasticity finite-element analysis versus experimental results of pyramidal indentation into (001) fcc single crystal10.1016/j.actamat.2010.11.042 ↗
48. UT is the energy density absorbed during deformation: area that underlies a stress/strain curve in Fig. 4.
49. It has been shown that the dislocation-core structures exhibit complex polymorph variants and depend on local stoichiometries in ceramic oxides [50-52]. Atomic-level knowledge of these structures is currently lacking for refractory nitrides. Nonetheless, the application of uniform shear deformation to dislocation-free VN and VN0.8 lattices allows us probing the effects induced by anion vacancies on the compound elastic shear stiffness, ideal shear strengths γS, and intrinsic ability to activate lattice slip.
50. Polymorphism of dislocation core structures at the atomic scale10.1038/ncomms4239 ↗
51. Determination of the structure and properties of an edge dislocation in rutile TiO210.1016/j.actamat.2018.10.015 ↗
52. Nonstoichiometric 012 dislocation in strontium titanate10.1016/j.actamat.2017.06.017 ↗
53. Plastic-deformation of ceramic materials10.1016/0025-5416(76)90054-9 ↗
54. Hardness and elastic properties of covalent/ionic solid solutions from first-principles theory10.1063/1.2904857 ↗
55. Microscopic theory of hardness and design of novel superhard crystals10.1016/j.ijrmhm.2012.02.021 ↗
56. Trends in the elastic response of binary early transition metal nitrides10.1103/PhysRevB.85.064101 ↗
57. The correspondence between stresses S¯ recorded during AIMD mechanical testing and the cubic elastic constants C¯ is described by A¯¯·C¯=S¯, where: A¯¯= {(0, 1, 0), (0, 1, 0), (1, 0, 0), (1/2, 1/2, –1), (0, 1, 0), (1/2, 1/2, 1), (1/2, –1/2, 0), (–√2/6, √2/6, √2/3), (1/3, –1/3, 1/3)}; C¯= (C11, C12, C44); S¯=(σxx〈001〉, σyy〈001〉, σzz〈001〉, σxx〈110〉, σyy〈110〉, σzz〈110〉, σxz{110}〈1-10〉, σxy{111}〈1-10〉, σxz{111}〈1-10〉). AIMD effective (or average) elastic constants C∼ij are obtained by norm minimization, i.e., C∼ij= minC||A¯¯·C¯–S¯||. The actual elastic stiffnesses are, instead, explicitly calculated from the initial (≤2% deformation) slopes of stress vs. strain curves: σzz during [001] elongation → C11, σxz during {110}〈11¯0〉 shearing → G110, and σxz during {111}〈11¯0〉 shearing → G111u.
58. The subscript “u” in G111u indicates that this is an unrelaxed shear moduli, i.e., calculated by imposing {110}〈11¯0〉 shear deformation without relaxing stress components other than σxz. In simulations that allow relaxation, the correspondent shear moduli would be G111r = 3⋅C44⋅(C11–C12)/(C11–C12+4⋅C44).
59. The relationships that link the C11, C12, C44, G110, G111u elastic constants and moduli to the stress components σij (recorded during AIMD mechanical testing that applies a generic deformation (δij) to a supercell with generic orientation) are determined by appropriate rotations (R) of σ and δ matrixes. The stress (σ') and strain (δ') tensors in a coordinate system with 〈001〉 crystallographic axes parallel to x, y, and z Cartesian directions are calculated via: σ' = R⋅σ⋅R–1 and δ' = R⋅δ⋅R–1. Note that two different rotations need to be applied in the case of deformation applied to supercells with [111] vertical orientation.
60. We note that the choice of the vacancy arrangements in VN0.8 supercells may affect the results of elastic constants, as described in Ref. [61].
61. Effects of atomic ordering on the elastic properties of TiN- and VN-based ternary alloys10.1016/j.tsf.2014.09.048 ↗
62. Mass transport properties of quasiharmonic vs. anharmonic transition-metal nitrides10.1016/j.tsf.2019.05.016 ↗
63. Structural phase-transition at 205 K in stoichiometric vanadium nitride10.1103/PhysRevB.38.12908 ↗
64. Interface-induced electronic structure toughening of nitride superlattices10.1016/j.surfcoat.2017.06.065 ↗
65. Statistical models of fracture10.1080/00018730300741518 ↗
66. Role of the crystal lattice structure in predicting fracture toughness10.1103/PhysRevLett.123.205503 ↗
67. Ductile versus brittle behaviour of crystals10.1080/14786437408213555 ↗
68. Schmid's factors (m) resolve the applied shear stress onto different crystallographic directions.
69. Nanomechanics of Refractory Transition-Metal Carbides: A Path to Discovering Plasticity in Hard Ceramics10.1111/jace.13686 ↗
70. Effects of alloying on the ductility of MoSi2 single crystals from first-principles calculations10.1088/0965-0393/6/4/013 ↗
71. The activation-energy for dislocation nucleation at a crack10.1016/0022-5096(94)90013-2 ↗
72. Experimental and computational studies on toughness enhancement in Ti-Al-Ta-N quaternaries10.1116/1.4997431 ↗
73. Chemical bonding in stoichiometric and substoichiometric vanadium nitride10.1006/jssc.1994.1135 ↗
74. Effects of phase stability, lattice ordering, and electron density on plastic deformation in cubic TiWN pseudobinary transition-metal nitride alloys10.1016/j.actamat.2015.10.039 ↗
75. Restricting dislocation movement in transition metal carbides by phase stability tuning10.1126/science.1060512 ↗
76. Vacancy ordering in VN1–x10.1107/S0021889878012893 ↗
77. Vacancy effects in the x-ray photoelectron spectra of TiNx10.1103/PhysRevB.28.3214 ↗
78. Electronic structure of non-stoichiometric zirconium nitrides ZrNx10.1016/0038-1098(84)90373-9 ↗
79. Vacancy-induced changes in the electronic structure of transition metal carbides and nitrides: calculation of x-ray photoemission intensities10.1007/BF01303812 ↗
80. Sputter-cleaned epitaxial VxMo1-xNy/MgO(001) thin films analyzed by x-ray photoelectron spectroscopy: 1. Single-crystal V0. 48Mo0. 52N0. 6410.1116/11.20130301 ↗
81. Sputter-cleaned epitaxial VxMo1-xNy/MgO(001) thin films analyzed by x-ray photoelectron spectroscopy: 2. Single-crystal V0.47Mo0. 53N0. 9210.1116/11.20130601 ↗
82. Vacancy hardening in single-crystal TiNx(001) layers10.1063/1.1568521 ↗
83. Nitrogen concentration dependent mechanical properties of TiNx single-phase films (0.75≤x≤0.99)10.1016/j.ceramint.2016.03.123 ↗
84. Negative effect of vacancies on cubic symmetry, hardness and conductivity in hafnium nitride films10.1016/j.scriptamat.2015.07.002 ↗
85. Elastic-constants of single-crystal transition-metal nitride films measured by line-focus acoustic microscopy10.1063/1.351651 ↗
86. Acoustic microscopy measurement of elastic constants and mass density, Ultrasonics, Ferroelectrics and Frequency Control
87. Valence electron concentration as an indicator for mechanical properties in rocksalt structure nitrides, carbides and carbonitrides10.1016/j.actamat.2018.04.033 ↗
88. Phonon anomalies in VN and their electronic origin10.1103/PhysRevLett.43.868 ↗
89. C11 and C12 values are also calculated from the slopes of VN0.86 phonon branches shown in figure 1 of [88]. The frequency vs. q data have been extracted from the figure using the open-source software Plot Digitizer [90]. Linear regression of phonon-frequency vs. q-vector-lengths data (→ acoustic velocities vhkl), together with a VN0.86 lattice parameter (a = q–1 = 4.105Å) and mass density (ρ=6035 kg⋅m–3) taken from table 1 in Ref. [20], allows us to extract [Cij = vhkl2⋅ρ] the C11, C12, and C44 elastic constants via the relationships listed in table 1 of [91].
90. Extracting data from figures with software was faster, with higher interrater reliability than manual extraction10.1016/j.jclinepi.2016.01.002 ↗
91. Thermoelasticity of stressed materials and comparison of various elastic constants10.1103/PhysRev.162.776 ↗
92. Supertoughening in B1 transition metal nitride alloys by increased valence electron concentration10.1016/j.actamat.2010.12.013 ↗
93. Using the density of understoichiometric VNx samples (5970 and 5980 kg⋅m–3) published in [86], we estimate N compositions x ≈ 0.7 - 0.8.
94. We have performed additional DFT calculations at 0 K (400 eV cutoff energy) for{110}〈11¯0〉 and {110}〈11¯0〉 deformation of the supercells used in AIMD. We obtained G110 = 310 GPa and G111u = 270 GPa.