Negative Stiffness Demonstrated by NiAl Nanofilms
Babicheva Rita 1, Bukreeva Karina 2, Dmitriev Sergey 2*, Mulyukov Radik 2, Zhou Kun 1*
1School of Mechanical and Aerospace Engineering, Nanyang Technological University 50 Nanyang Avenue, Singapore 639798, Singapore
2Institute for Metals Superplasticity Problems, Russian Academy of Sciences
39 Khalturina St., Ufa 450001, Russia
∗E-mail:dmitriev.sergey.v@gmail.com (S.V. Dmitriev), kzhou@ntu.edu.sg (K. Zhou)
Received:
Received: 9 February 2013; revised: 11 April 2013; accepted: 23 April 2013; published online: 23 May 2013
DOI: 10.12921/cmst.2013.19.03.127-135
OAI: oai:lib.psnc.pl:448
Abstract:
This paper studies the uniaxial strain control tension of NiAl nanofilms via molecular dynamics simulations. The nanofilm deforms elastically until fracture at tensile strain is as large as 37%. The stress-strain curve has a range where tensile deformation develops at decreasing tensile stress, thus indicating negative stiffness. Such deformation is thermodynamically
unstable and the nanofilm splits into domains with two different values of elastic strain. Deformation within the unstable range is controlled by motion of the domain walls, resulting in the domains with larger strain grow at the expense of the domains with smaller strain.
Key words:
negative stiffness; NiAl nanofilm; molecular dynamics; intermetallic compound
References:
[1] K. Evans, A. Alderson. Auxetic materials: Functional materials and
structures from lateral thinking! Adv. Mater. 12, 617-628 (2000).
[2] A. Alderson, K.L. Alderson. Auxetic materials. Proceedings of the
Institution of Mechanical Engineers, Part G: J Aerospace Eng. 221(4),
565-575 (2007).
[3] X. F. Wang, T. E. Jones, W. Li, Y. C. Zhou. Extreme Poisson’s
ratios and their electronic origin in B2 CsCl-type AB intermetallic
compounds. Phys. Rev. B 85, 134108-7 (2012).
[4] T. Tian, X.F. Wang, W. Li. Ab initio calculations on elastic properties
in L12 structure Al3X and X3Al-type (X=transition or main group
metal) intermetallic compounds. Solid State Commun. 156, 69-75
(2013).
[5] J.W. Narojczyk, K.W. Wojciechowski. Elastic properties of degener-
ate f.c.c. crystal of polydisperse soft dimers at zero temperature. J.
Non-Cryst. Solids 356, 2026-2032 (2010).
[6] A.A. Vasiliev, S.V. Dmitriev, Y. Ishibashi, T. Shigenari. Elastic
properties of a two-dimensional model of crystals containing parti-
cles with rotational degrees of freedom. Phys. Rev. B 65, 094101-7
(2002).
[7] A.U. Ortiz, A. Boutin, A.H. Fuchs, F.-X. Coudert. Anisotropic elastic
properties of flexible metal-organic frameworks: How soft are soft
porous crystals? Phys. Rev. Lett. 109, 195502-5 (2012).
[8] A.D. Fortes, E. Suard, K.S. Knight. Negative linear compressibility
and massive anisotropic thermal expansion in methanol monohy-
drate. Science 331, 742-746 (2011).
[9] J.N. Grima, D. Attard, R. Gatt. Unusual thermoelastic properties of
methanol monohydrate. Science 331, 687-688 (2011).
[10] J.N. Grima, D. Attard, R. Caruana-Gauci, R. Gatt. Negative lin-
ear compressibility of hexagonal honeycombs and related systems.
Scripta Mater. 65, 565-568 (2011).
[11] D.L. Barnes, W. Miller, K.E. Evans, A. Marmier. Modelling negative
linear compressibility in tetragonal beam structures. Mech. Mater.
46, 123-128 (2012).
[12] E.V. Vakarin, A.V. Talyzin. On the mechanism of negative compress-
ibility in layered compounds. Chem. Phys. 369, 19-21 (2010).
[13] R. S. Lakes, K. W. Wojciechowski. Negative compressibility, negative
Poisson’s ratio, and stability. Phys. Status Solidi 245(3), 545-551
(2008).
[14] J.N. Grima, B. Ellul, D. Attard, R. Gatt, M. Attard. Composites
with needle-like inclusions exhibiting negative thermal expansion:
A preliminary investigation. Compos. Sci. Technol. 70, 2248-2252
(2010).
[15] V. Gava, A.L. Martinotto, C.A. Perottoni. First-principles mode
Gruneisen parameters and negative thermal expansion in α-ZrW2 O8.
Phys. Rev. Lett. 109, 195503-5 (2012).
[16] P.L. de Andres, F. Guinea, M.I. Katsnelson. Bending modes, anhar-
monic effects, and thermal expansion coefficient in single-layer and
multilayer grapheme. Phys. Rev. B 86, 144103-5 (2012).
[17] V.E. Fairbank, A.L. Thompson, R.I. Cooper, A.L. Goodwin. Charge-
ice dynamics in the negative thermal expansion material Cd(CN)2 .
Phys. Rev. B 86, 104113-5 (2012).
[18] A. Rebello, J. J. Neumeier, Z. Gao, Y. Qi, Y. Ma. Giant negative
thermal expansion in La-doped CaFe2 As2 . Phys. Rev. B 86, 104303-
6 (2012).
[19] I.A. Stepanov. Thermodynamics of substances with negative thermal
expansion and negative compressibility. J. Non-Cryst. Solids 356,
1168-1172 (2010).
[20] V.G. Veselago. The electrodynamics of substances with simultane-
ously negative values of ε and μ. Soviet Physics Uspekhi. 10(4),
509-514 (1968).
[21] V. Veselago, L. Braginsky, V. Shklover, C. Hafner. Negative refractive
index materials. J. Comput. Theor. Nanos. 3(2), 189-218 (2006).
[22] I.E. Dzyaloshinskii, E.M. Lifshitz, L.P. Pitaevskii. Reviews of topical
problems: General theory of Van Der Waals’ forces. Soviet Physics
Uspekhi 4(2), 153-176 (1961).
[23] R.S. Lakes, W.J. Drugan. Dramatically stiffer elastic composite ma-
terials due to a negative stiffness phase? J. Mech. Phys. Solids. 50,
979-1009 (2002).
[24] D. Shilkrut, E. Riks. Stability of nonlinear shells: on the example of
spherical shells. Elsevier Science, the Netherlands (2002), 458 p.
[25] X. Wang, H. Hamasaki, M. Yamamura, R. Yamauchi, T. Maeda,
Y. Shirai, F. Yoshida. Yield-point phenomena of Ti-20V-4Al-1Sn at
1073 K and its constitutive modelling. Mater. Trans. (JIM) 50(6),
1576-1578 (2009).
[26] T. Jaglinski, D. Kochmann, D. Stone, R. S. Lakes. Composite mate-
rials with viscoelastic stiffness greater than diamond. Science 315,
620 (2007).
[27] R. S. Lakes, T. Lee, A. Bersie, Y. C. Wang. Extreme damping in
composite materials with negative-stiffness inclusions. Letters to
Nature. Nature 410, 565-567 (2001).
[28] Y. C. Wang, J. G. Swadener, R. S. Lakes. Anomalies in stiffness and
damping of a 2D discrete viscoelastic system due to negative stiffness
components. Thin Solid Films 515, 3171-3178 (2007).
[29] W.J. Drugan. Elastic composite materials having a negative stiffness
phase can be stable. Phys. Rev. Lett. 98, 055502 (2007).
[30] D.M. Kochmann, W.J. Drugan. Analytical stability conditions for
elastic composite materials with a non-positive-definite phase. Proc.
R. Soc. A (2012) 468, 2230–2254.
[31] C.-M. Lee, V. N. Goverdovskiy. A multi-stage high-speed railroad
vibration isolation system with “negative” stiffness. J. Sound Vib.
331, 914-921 (2012).
[32] A. Carrella, M.J. Brennan, T.P. Waters, K. Shin. On the design of a
high-static–low-dynamic stiffness isolator using linear mechanical
springs and magnets. J. Sound Vib. 315(3), 712-720 (2008).
[33] A.V. Dyskin, E. Pasternak. Elastic composite with negative stiffness
inclusions in antiplane strain. Int. J. Eng. Sci. 58, 45-56 (2012).
[34] J. Yang, Y.P. Xiong, J. T. Xing. Dynamics and power flow behaviour
of a nonlinear vibration isolation system with a negative stiffness
mechanism. J. Sound Vib. 332(1), 167-183 (2013).
[35] D. M. Kochmann, W. J. Drugan. Infinitely stiff composite via a
rotation-stabilized negative-stiffness phase. Appl. Phys. Lett. 99,
011909 (2011).
[36] T. Zhu, J. Li. Ultra-strength materials. Progr. Mater. Sci. 55(7), 710-
757 (2010).
[37] J.R. Greer, J.T.M. De Hosson. Review: Plasticity in small-sized
metallic systems: Intrinsic versus extrinsic size effect. Prog. Mater.
Sci. 56(6), 654-724 (2011).
[38] S. Li, X. Ding, J. Deng, T. Lookman, J. Li, X. Ren, J. Sun, A. Saxena.
Superelasticity in bcc nanowires by a reversible twinning mechanism.
Phys. Rev. B 82, 205435-12 (2010).
[39] N. Abdolrahim, I.N. Mastorakos, H.M. Zbib. Deformation mech-
anisms and pseudoelastic behaviors in trilayer composite metal
nanowires. Phys. Rev. B 81, 054117-5 (2010).
[40] C. Ni, H. Ding, C. Li, L.T. Kong, X.J. Jin. Pseudo-elasticity and ultra-
high recoverable strain in cobalt nanowire: A molecular dynamics
study. Scripta Mater. 68, 191-194 (2013).
[41] V.K. Sutrakar, D.R. Mahapatra. Superplasticity in intermetallic NiAl
nanowires via atomistic simulations. Mater. Lett. 64, 879-881 (2010).
[42] V.K. Sutrakar, D.R. Mahapatra. Asymmetry in structural and thermo-
mechanical behavior of intermetallic NiAl nanowire under tensile/compressive
loading: A molecular dynamics study. Intermetallics 18, 1565-1571
(2010).
[43] V.K. Sutrakar, D.R. Mahapatra. Stress-induced phase transformation
and pseudo-elastic/pseudo-plastic recovery in intermetallic Ni–Al
nanowires. Nanotechnology 20 , 295705-9 (2009).
[44] V.K. Sutrakar, D.R. Mahapatra. Single and multi-step phase transfor-
mation in CuZr nanowire under compressive/tensile loading. Inter-
metallics 18, 679–687 (2010).
[45] V.K. Sutrakar, D.R. Mahapatra. Stress-induced martensitic phase
transformation in Cu–Zr nanowires. Mater. Lett. 63, 1289–1292
(2009).
[46] A.V. Savin, I.P. Kikot, M.A. Mazo, A.V. Onufriev. Two-phase stretch-
ing of molecular chains. PNAS, doi:10.1073/pnas.1218677110 (2013).
[47] C. Miehe, M. Lambrecht, E. Gurses. Analysis of material instabilities
in inelastic solids by incremental energy minimization and relaxation
methods: evolving deformation microstructures in finite plasticity. J.
Mech. Phys. Solids 52, 2725-2769 (2004).
[48] E.Gurses, C. Miehe. On evolving deformation microstructures in
non-convex partially damaged solids. J. Mech. Phys. Solids 59, 1268-
1290 (2011).
[49] G.P. Purja Pun,Y. Mishin. Development of an interatomic potential
for the Ni-Al system. Phil. Mag. 89, 3245-3267 (2009).
[50] S. Nose. A unified formulation of the constant temperature molecular
dynamics methods. J. Chem. Phys. 81, 511-519 (1984).
This paper studies the uniaxial strain control tension of NiAl nanofilms via molecular dynamics simulations. The nanofilm deforms elastically until fracture at tensile strain is as large as 37%. The stress-strain curve has a range where tensile deformation develops at decreasing tensile stress, thus indicating negative stiffness. Such deformation is thermodynamically
unstable and the nanofilm splits into domains with two different values of elastic strain. Deformation within the unstable range is controlled by motion of the domain walls, resulting in the domains with larger strain grow at the expense of the domains with smaller strain.
Key words:
negative stiffness; NiAl nanofilm; molecular dynamics; intermetallic compound
References:
[1] K. Evans, A. Alderson. Auxetic materials: Functional materials and
structures from lateral thinking! Adv. Mater. 12, 617-628 (2000).
[2] A. Alderson, K.L. Alderson. Auxetic materials. Proceedings of the
Institution of Mechanical Engineers, Part G: J Aerospace Eng. 221(4),
565-575 (2007).
[3] X. F. Wang, T. E. Jones, W. Li, Y. C. Zhou. Extreme Poisson’s
ratios and their electronic origin in B2 CsCl-type AB intermetallic
compounds. Phys. Rev. B 85, 134108-7 (2012).
[4] T. Tian, X.F. Wang, W. Li. Ab initio calculations on elastic properties
in L12 structure Al3X and X3Al-type (X=transition or main group
metal) intermetallic compounds. Solid State Commun. 156, 69-75
(2013).
[5] J.W. Narojczyk, K.W. Wojciechowski. Elastic properties of degener-
ate f.c.c. crystal of polydisperse soft dimers at zero temperature. J.
Non-Cryst. Solids 356, 2026-2032 (2010).
[6] A.A. Vasiliev, S.V. Dmitriev, Y. Ishibashi, T. Shigenari. Elastic
properties of a two-dimensional model of crystals containing parti-
cles with rotational degrees of freedom. Phys. Rev. B 65, 094101-7
(2002).
[7] A.U. Ortiz, A. Boutin, A.H. Fuchs, F.-X. Coudert. Anisotropic elastic
properties of flexible metal-organic frameworks: How soft are soft
porous crystals? Phys. Rev. Lett. 109, 195502-5 (2012).
[8] A.D. Fortes, E. Suard, K.S. Knight. Negative linear compressibility
and massive anisotropic thermal expansion in methanol monohy-
drate. Science 331, 742-746 (2011).
[9] J.N. Grima, D. Attard, R. Gatt. Unusual thermoelastic properties of
methanol monohydrate. Science 331, 687-688 (2011).
[10] J.N. Grima, D. Attard, R. Caruana-Gauci, R. Gatt. Negative lin-
ear compressibility of hexagonal honeycombs and related systems.
Scripta Mater. 65, 565-568 (2011).
[11] D.L. Barnes, W. Miller, K.E. Evans, A. Marmier. Modelling negative
linear compressibility in tetragonal beam structures. Mech. Mater.
46, 123-128 (2012).
[12] E.V. Vakarin, A.V. Talyzin. On the mechanism of negative compress-
ibility in layered compounds. Chem. Phys. 369, 19-21 (2010).
[13] R. S. Lakes, K. W. Wojciechowski. Negative compressibility, negative
Poisson’s ratio, and stability. Phys. Status Solidi 245(3), 545-551
(2008).
[14] J.N. Grima, B. Ellul, D. Attard, R. Gatt, M. Attard. Composites
with needle-like inclusions exhibiting negative thermal expansion:
A preliminary investigation. Compos. Sci. Technol. 70, 2248-2252
(2010).
[15] V. Gava, A.L. Martinotto, C.A. Perottoni. First-principles mode
Gruneisen parameters and negative thermal expansion in α-ZrW2 O8.
Phys. Rev. Lett. 109, 195503-5 (2012).
[16] P.L. de Andres, F. Guinea, M.I. Katsnelson. Bending modes, anhar-
monic effects, and thermal expansion coefficient in single-layer and
multilayer grapheme. Phys. Rev. B 86, 144103-5 (2012).
[17] V.E. Fairbank, A.L. Thompson, R.I. Cooper, A.L. Goodwin. Charge-
ice dynamics in the negative thermal expansion material Cd(CN)2 .
Phys. Rev. B 86, 104113-5 (2012).
[18] A. Rebello, J. J. Neumeier, Z. Gao, Y. Qi, Y. Ma. Giant negative
thermal expansion in La-doped CaFe2 As2 . Phys. Rev. B 86, 104303-
6 (2012).
[19] I.A. Stepanov. Thermodynamics of substances with negative thermal
expansion and negative compressibility. J. Non-Cryst. Solids 356,
1168-1172 (2010).
[20] V.G. Veselago. The electrodynamics of substances with simultane-
ously negative values of ε and μ. Soviet Physics Uspekhi. 10(4),
509-514 (1968).
[21] V. Veselago, L. Braginsky, V. Shklover, C. Hafner. Negative refractive
index materials. J. Comput. Theor. Nanos. 3(2), 189-218 (2006).
[22] I.E. Dzyaloshinskii, E.M. Lifshitz, L.P. Pitaevskii. Reviews of topical
problems: General theory of Van Der Waals’ forces. Soviet Physics
Uspekhi 4(2), 153-176 (1961).
[23] R.S. Lakes, W.J. Drugan. Dramatically stiffer elastic composite ma-
terials due to a negative stiffness phase? J. Mech. Phys. Solids. 50,
979-1009 (2002).
[24] D. Shilkrut, E. Riks. Stability of nonlinear shells: on the example of
spherical shells. Elsevier Science, the Netherlands (2002), 458 p.
[25] X. Wang, H. Hamasaki, M. Yamamura, R. Yamauchi, T. Maeda,
Y. Shirai, F. Yoshida. Yield-point phenomena of Ti-20V-4Al-1Sn at
1073 K and its constitutive modelling. Mater. Trans. (JIM) 50(6),
1576-1578 (2009).
[26] T. Jaglinski, D. Kochmann, D. Stone, R. S. Lakes. Composite mate-
rials with viscoelastic stiffness greater than diamond. Science 315,
620 (2007).
[27] R. S. Lakes, T. Lee, A. Bersie, Y. C. Wang. Extreme damping in
composite materials with negative-stiffness inclusions. Letters to
Nature. Nature 410, 565-567 (2001).
[28] Y. C. Wang, J. G. Swadener, R. S. Lakes. Anomalies in stiffness and
damping of a 2D discrete viscoelastic system due to negative stiffness
components. Thin Solid Films 515, 3171-3178 (2007).
[29] W.J. Drugan. Elastic composite materials having a negative stiffness
phase can be stable. Phys. Rev. Lett. 98, 055502 (2007).
[30] D.M. Kochmann, W.J. Drugan. Analytical stability conditions for
elastic composite materials with a non-positive-definite phase. Proc.
R. Soc. A (2012) 468, 2230–2254.
[31] C.-M. Lee, V. N. Goverdovskiy. A multi-stage high-speed railroad
vibration isolation system with “negative” stiffness. J. Sound Vib.
331, 914-921 (2012).
[32] A. Carrella, M.J. Brennan, T.P. Waters, K. Shin. On the design of a
high-static–low-dynamic stiffness isolator using linear mechanical
springs and magnets. J. Sound Vib. 315(3), 712-720 (2008).
[33] A.V. Dyskin, E. Pasternak. Elastic composite with negative stiffness
inclusions in antiplane strain. Int. J. Eng. Sci. 58, 45-56 (2012).
[34] J. Yang, Y.P. Xiong, J. T. Xing. Dynamics and power flow behaviour
of a nonlinear vibration isolation system with a negative stiffness
mechanism. J. Sound Vib. 332(1), 167-183 (2013).
[35] D. M. Kochmann, W. J. Drugan. Infinitely stiff composite via a
rotation-stabilized negative-stiffness phase. Appl. Phys. Lett. 99,
011909 (2011).
[36] T. Zhu, J. Li. Ultra-strength materials. Progr. Mater. Sci. 55(7), 710-
757 (2010).
[37] J.R. Greer, J.T.M. De Hosson. Review: Plasticity in small-sized
metallic systems: Intrinsic versus extrinsic size effect. Prog. Mater.
Sci. 56(6), 654-724 (2011).
[38] S. Li, X. Ding, J. Deng, T. Lookman, J. Li, X. Ren, J. Sun, A. Saxena.
Superelasticity in bcc nanowires by a reversible twinning mechanism.
Phys. Rev. B 82, 205435-12 (2010).
[39] N. Abdolrahim, I.N. Mastorakos, H.M. Zbib. Deformation mech-
anisms and pseudoelastic behaviors in trilayer composite metal
nanowires. Phys. Rev. B 81, 054117-5 (2010).
[40] C. Ni, H. Ding, C. Li, L.T. Kong, X.J. Jin. Pseudo-elasticity and ultra-
high recoverable strain in cobalt nanowire: A molecular dynamics
study. Scripta Mater. 68, 191-194 (2013).
[41] V.K. Sutrakar, D.R. Mahapatra. Superplasticity in intermetallic NiAl
nanowires via atomistic simulations. Mater. Lett. 64, 879-881 (2010).
[42] V.K. Sutrakar, D.R. Mahapatra. Asymmetry in structural and thermo-
mechanical behavior of intermetallic NiAl nanowire under tensile/compressive
loading: A molecular dynamics study. Intermetallics 18, 1565-1571
(2010).
[43] V.K. Sutrakar, D.R. Mahapatra. Stress-induced phase transformation
and pseudo-elastic/pseudo-plastic recovery in intermetallic Ni–Al
nanowires. Nanotechnology 20 , 295705-9 (2009).
[44] V.K. Sutrakar, D.R. Mahapatra. Single and multi-step phase transfor-
mation in CuZr nanowire under compressive/tensile loading. Inter-
metallics 18, 679–687 (2010).
[45] V.K. Sutrakar, D.R. Mahapatra. Stress-induced martensitic phase
transformation in Cu–Zr nanowires. Mater. Lett. 63, 1289–1292
(2009).
[46] A.V. Savin, I.P. Kikot, M.A. Mazo, A.V. Onufriev. Two-phase stretch-
ing of molecular chains. PNAS, doi:10.1073/pnas.1218677110 (2013).
[47] C. Miehe, M. Lambrecht, E. Gurses. Analysis of material instabilities
in inelastic solids by incremental energy minimization and relaxation
methods: evolving deformation microstructures in finite plasticity. J.
Mech. Phys. Solids 52, 2725-2769 (2004).
[48] E.Gurses, C. Miehe. On evolving deformation microstructures in
non-convex partially damaged solids. J. Mech. Phys. Solids 59, 1268-
1290 (2011).
[49] G.P. Purja Pun,Y. Mishin. Development of an interatomic potential
for the Ni-Al system. Phil. Mag. 89, 3245-3267 (2009).
[50] S. Nose. A unified formulation of the constant temperature molecular
dynamics methods. J. Chem. Phys. 81, 511-519 (1984).
