Abstract
Magnetoelectric composites can be produced by embedding magnetostrictive particles in a piezoelectric matrix derived from a piezoelectric powder precursor. Ferrite magnetostrictive particles, if allowed to percolate, can short the potential difference generated in the piezoelectric phase. Modeling a magnetoelectric composite as an aggregate of bi-disperse hard shells, molecular dynamics was used to explore relationships among relative particle size, particle affinity, and electrical percolation with the goal of maximizing the percolation threshold. It is found that two factors raise the percolation threshold, namely the relative size of magnetostrictive to piezoelectric particles, and the affinity between the magnetostrictive and piezoelectric particles.
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References
Eerenstein W, Mathur ND, Scott JF (2006) Multiferroic and magnetoelectric materials. Nature Publishing Group, Department of Materials Science, University of Cambridge, Cambridge
Grossinger R, Duong GV, Sato-Turtlli R (2008) The physics of magnetoelectric composites. J Magn Magn Mater 320:1972–1977
Ma J, Hu J, Li Z, Nan C-W (2011) Recent progress in multiferric magnetoelectric composites: from bulk to thin films. Adv Mater 23:1062–1087
Bichurin M, Petrov V, Priya S, Bhalla A (2012) Editorial multiferric magnetoelectric composites and their applications. Adv Cond Matter Phys 12:129794
Brito VLO, Cunha SA, Lemos LV, Nunes CB (2012) Magnetic properties of liquid-phase sintered \(\text{CoFe}_{2}\text{O}_{4}\) for application in magneoelastic and magnetoelectric transducers. Sensors 12:10086–10096
Chu Y-H, Martin LW, Holcomb MB, Gajek M, Han S-J, He Q, Balke N, Yang C-H, Lee D, Hu W, Zhan Q, Yang P-L, Fraile-Rodriquez A, Scholl A, Wang SX, Ramesh R (2008) Electric-field control of local ferromagnetism using magnetoelectric multiferric. Department of Materials Science and Engineering, University of California, Berkeley, CA. doi:10.1038/nmat2184
Nan C-W, Song M-IS, Veichland D, Srinivasan G (2008) Multiferric magnetoelectric composites: historical perspective, status, and future directions. J Appl Phys 3:1
Ortega N, Kumar A, Scott JF, Katlyar RS (2015) Multifunctional magnetostatic materials for device applications. J Phys Cond Matter 27:504002
Sharif NSAB (2015) Synthesis and characterization of lead zirconate titanate \((\text{Pb[Zr}_{0.52}\text{Ti}_{0.48}]\text{O}_{3})\) properties via high energy planetary ball milling. Ph.D. dissertation, Manufacturing Engineering, University Malaysia Pahang
Randall CA, Kim N, Kucera J-P, Cao W, Shrout TR (1998) Intrinsic and extrinsic size effects in fine grained morphotropic-phase-boundary lead zirconate titanete ceramics. J Am Ceram 81(3):677–688
Nan C-W, Shen Y, Ma J (2010) Physical properties of composites near percolation. Annu Rev Mater Res 40:131–151
Bunde A, Deiterich W (2000) Percolation in composites. J Electroceram 5(2):81–92
Muchenik TI, Barbero EJ (2014) Micromechanics modeling of magnetoelectric composites. In: Composites and advanced materials, CAMX Conference Proceedings, Orlando FL, Oct 13–16
Muchenik TI, Barbero EJ (2015) Charge, voltage and work-conversion formulas for magnetoelectric laminated composites. Smart Mater Struct. doi:10.1088/0964-1726/24/2/025039
Muchenik TI, Barbero EJ (2016) Magnetoelectric composites. In: Barbero EJ (ed) Multifunctional composites. Create Space Independent Publishing, Charleston
Muchenik TI, Barbero EJ (2016) Prediction of extrinsic charge, voltage, and work-conversion factors for laminated magnetoelectric composites. Smart Matter Struct. doi:10.1088/0964-1726/25/1/015006
Scher H, Zallen R (1970) Critical density in percolation processes. J Chem Phys 53:3759
Bolintineanu DS, Grest GS, Lechman JB, Fierce F, Plimpton SJ, Schunk PR (2014) Particle dynamics modeling methods for colloid suspensions. Comp Part Mech 1:321–356
Staron L, Phillips JC (2015) How large grains increase bulk friction in bi-disperse granular chute flows. Comp Part Mech. doi:10.1007/s40571-015-0068-1
Saitoh K, Magnanimo V, Luding S (2016) The effects of microscopic friction and size distributions on conditional probability distributions in soft particle packings. Comp Part Mech. doi:10.1007/s40571-016-0138-z
Rapaport DC (2014) Molecular dynamics simulation: a tool for exploration and discovery using simple models. J Phys Condens Matter 26:503104–503121
Kusy RP (1977) Influence of particle size ratio on the continuity of aggregates. J Appl Phys 48:5301. doi:10.1063/1.323560
Deepa KS, Nisha SK, Parameswaran P, Sebastian MT, James J (2009) Effect of conductivity on filer on the percolation threshold of composites. Appl Phys Lett 94:142902
Plimpton SJ (1995) Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 117:1–19
Carrera D (2007) Quantum tunneling in chemical reactions. MacMillan, London
Beloborodov IS, Lopatin AV, Vinokur VM (2005) Coulomb effects and hopping transport in granular metals. Rev B 72:125121
Hill RT, Mock JJ, Wolter SD, Jokest NM, Smith DR, Chilkoti A (2012) Plasmon ruler with angstrom length resolution. ACS Nano 6(10):9237–9246
Kadkhodazadeh S, Wagner JB, Kneipp H, Kneipp Katrin (2013) Coexistance of classical and quantum plasmonics in large plasmonic structures with subnanometer gaps. Appl Phys Lett 103:083103
Scholl JA, Garcia-Etxarri A, Koh AL, Dionne JA (2013) Observations of quantum tunneling between two plasmonic nanoparticles. Nano Lett 13:564–569
Zhang J, Shklovskii BI (2004) Density of states and conductivity of a granular metal or array of quantum dots. Phys Rev B 70:153317
Li J, Kim J-K (2007) Percolation threshold of conducting polymer composites containing 3D randomly distributed graphite nanoplatlets. Compos Sci Technol 67:2114–2120
Zhu X (2013) Tutorial on Hertz contact stress. OPTI 512. https://wp.optics.arizona.edu/optomech/wp-content/uploads/sites/53/2016/10/OPTI-521-Tutorial-on-Hertz-contact-stress-Xiaoyin-Zhu.pdf
Popov V (2010) Contact mechanics and friction. Springer, Berlin. doi:10.1007/978-3-642-10803-7_5
Foffi G, Goetz W, Sciortino F, Tartaglia P, Voigtmann T (2003) Mixing effects for the structural relaxation in binary hard-sphere liquids. Phys Rev Lett 91(8):085701
Ottino JM, Khakhar DV (2000) Mixing and segregation of granular materials. Annu Rev Fluid Mech 32:55–91
Parisi G, Zamponi F (2010) Mean-field theory of hard sphere glasses and jamming. Rev Mod Phys 82:789
Brouwers HJH (2006) Particle-size distribution and packing fraction of geometric random packing. Phys Rev E 74:1–14
Kansal AR, Torquato S, Stillinger FH (2002) Computer generation of dense polydisperse sphere packing. J Chem Phys 117(18):8212–8218
Scott GD, Kilgour DM (1969) The density of random close packing of spheres. Br J Appl Phys 2(2):863–866
GRunlan JC, Gerberich WW, Francis LF (2001) Lowering the percolation threshold of conductive composites using particulate polymer microstructure. J Appl Polym Sci 80:69–705
Hasanabadi HM, Wilhelm M, Rodrigue D (2014) A rheological criterion to determine the percolation threshold in polymer nano-composites. Rheol Acta 5:869–882
Stauffer D, Aharmony A (1994) Introduction to percolation theory, 2nd edn. Taylor and Francis, London
Eisberg R, Resnick R (1985) Quantum mechanics of atoms molecules solids nuclei and particles, 2nd edn. Wiley, London
Kruse RL (1989) Programming with data structures. Prentice Hall, Prentice
Nappini S, Magnano Elena (2015) Surface charge and coating of \(\text{CeFe}_{2}\text{O}_{4}\) nanoparticles evidence of preserved magnetic and electronic properties. J Phys Chem C 119:25529–25541
Vaart K, Gajjar P, Epely-Chauvin G, Andreini N, Gray JMNT, Ancey C (2015) An underlying asymmetry within particle-size segregation. Phys Rev Lett 114:238001
Royall CP, Williams SR, Ohtsuka T, Tanaka J (2008) Direct observation of a local structural mechanism for dynamic arrest. Nat Mater. doi:10.1038/nmat2219
Schilling T, Dorosz S, Radu M, Mathue M, Jungblut S, Binder K (2013) Mixtures of qnsiotropic and spherical colloids: phase behavior, confinement, percolation phenomena and kinetics. Eur Phys J Spec Top 222:3039–3052
Suarez M-A, Kem N, Kob W (2009) Out-of-equilibrium dynamics of a fractal model gel. J Chem Phys 130:194904
Amirjanov A, Sobolev K (2008) Optimization of a computer simulation model for packing of concrete aggregates. Part Sci Technol 26(4):380–395
Puertas AM, Fuchs M, Cates ME (2004) Dynamical heterogeneities close to a colloidal gel. J Chem Phys 121(6):2813–2822
Zaccarelli E, Buldyrev SV, La Nave E, Morene AJ, Saika-Voivod I, Sciortino F, Tartaglia P (2005) Model for reversible colloidal gelation. Phys Rev Lett 94:218301
Rohr GS (2001) Structure and bonding in crystalline materials. Cambridge University Press, Cambridge
Rojek J, Nosewicz S, Jursak K, Chmielewski M, Bochenek K, Pietrzak K (2015) Discrete element simulation of powder compaction in cold uniaxial pressing with low pressure. Comp Part Mech 3:513–524
Nakagawa M, Moss JL, Altobelli SA (1999) MRI measurements and granular dynamics simulation of segregation of granular mixture. In: Proceedings of fourth microgravity fluid physics and transport phenomena (NASA/CP-199902085526/SUPPL1)
Acknowledgements
The authors wish to acknowledge use of the West Virginia Super Computing System (Spruce Knob), funded by the National Science Foundation EPSCoR Research Infrastructure Improvement Cooperative Agreement No. 1003907, without access to which the study would not have been possible.
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Barbero, E.J., Bedard, A.J. Electrical percolation threshold of magnetostrictive inclusions in a piezoelectric matrix composite as a function of relative particle size. Comp. Part. Mech. 5, 227–238 (2018). https://doi.org/10.1007/s40571-017-0165-4
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DOI: https://doi.org/10.1007/s40571-017-0165-4