Simulation of reactive nanolaminates using reduced models: I. Basic formulation

Abstract Development and testing are described of a reduced model for the simulation of transient reactions in Ni/Al nanolaminates. The model relies on a simplified description of local atomic mixing rates, expressed in terms of an evolution equation for a dimensionless time scale that reflects the age of the mixed layer. The latter is obtained from a theoretical analysis of the quasi-1D evolution equation of a conserved scalar, which also yields canonical curves for the mean composition and its relevant moments as function of the local bilayer age. The reduced model is tested against results of the detailed model of Besnoin et al. [E. Besnoin, S. Cerutti, O.M. Knio, T.P. Weihs, J. Appl. Phys. 92 (2002) 5474–5481] for different scenarios, including self-propagating reactions, and ignition thresholds. Results show that the reduced model predictions are in good agreement with those obtained using the detailed model. By achieving order-of-magnitude increase in computation efficiency, the present model reduction formalism offers a path towards modeling transient reaction fronts in multiple space dimensions.

[1]  J. Gachon,et al.  On the mechanism of heterogeneous reaction and phase formation in Ti/Al multilayer nanofilms , 2005 .

[2]  Mitra L Taheri,et al.  Imaging of Transient Structures Using Nanosecond in Situ TEM , 2008, Science.

[3]  Vedat S. Arpaci,et al.  Conduction Heat Transfer , 2002 .

[4]  L. Battezzati,et al.  Solid state reactions in Al/Ni alternate foils induced by cold rolling and annealing , 1999 .

[5]  A. Merzhanov,et al.  Gasless Combustion of Ti–Al Bimetallic Multilayer Nanofoils , 2004 .

[6]  Mark A. Rodriguez,et al.  Self-propagating, high-temperature combustion synthesis of rhombohedral AlPt thin films , 2006 .

[7]  Jerrold A. Floro,et al.  Propagation of explosive crystallization in thin Rh–Si multilayer films , 1986 .

[8]  P. Mossino.  Some aspects in self-propagating high-temperature synthesis , 2004 .

[9]  J. C. Jaeger,et al.  Conduction of Heat in Solids , 1952 .

[10]  A. J. Gavens,et al.  Al/Ni formation reactions: characterization of the metastable Al9Ni2 phase and analysis of its formation , 2003 .

[11]  J. Weissmüller,et al.  Structural evolution and phase formation in cold-rolled aluminum–nickel multilayers , 2001 .

[12]  K. Barmak,et al.  Reactive phase formation in sputter-deposited Ni/Al multilayer thin films , 1997 .

[13]  Carl V. Thompson,et al.  Self‐propagating explosive reactions in Al/Ni multilayer thin films , 1990 .

[14]  Omar M. Knio,et al.  Numerical study of the effect of heat losses on self-propagating reactions in multilayer foils , 2001 .

[15]  C. Thompson,et al.  Explosive silicidation in nickel/amorphous‐silicon multilayer thin films , 1990 .

[16]  X. Qiu,et al.  Experimental evidence of two-stage formation of Al3Ni in reactive Ni/Al multilayer foils , 2007 .

[17]  David P. Adams,et al.  Direct observation of spinlike reaction fronts in planar energetic multilayer foils , 2009 .

[18]  Zuhair A. Munir,et al.  The combustion synthesis of multilayer NiAl systems , 1994 .

[19]  L. Kecskes,et al.  Exothermic reactions in cold-rolled Ni/Al reactive multilayer foils , 2008 .

[20]  Omar M. Knio,et al.  Joining of stainless-steel specimens with nanostructured Al/Ni foils , 2004 .

[21]  Z. A. Munir,et al.  Combustion synthesis of mechanically activated powders in the Ta–Si system , 2004 .

[22]  Omar M. Knio,et al.  Effect of varying bilayer spacing distribution on reaction heat and velocity in reactive Al/Ni multilayers , 2009 .

[23]  Timothy P. Weihs,et al.  Effect of intermixing on self-propagating exothermic reactions in Al/Ni nanolaminate foils , 2000 .

[24]  Omar M. Knio,et al.  Effect of reactant and product melting on self-propagating reactions in multilayer foils , 2002 .

[25]  G. Spinolo,et al.  Combustion synthesis of ZrAl intermetallic compounds , 1997 .

[26]  Timothy P. Weihs,et al.  Self-propagating formation reactions in Nb:Si multilayers , 1999 .

[27]  Omar M. Knio,et al.  Numerical predictions of oscillatory combustion in reactive multilayers , 1999 .

[28]  J. Perepezko,et al.  Deformation-induced synthesis and structural transformations of metallic multilayers , 2004 .

[29]  J. B. Holt,et al.  Combustion and plasma synthesis of high-temperature materials , 1990 .