Numerical modeling of self-propagating reactions in Ru/Al nanoscale
multilayer foils
K. Woll1), I.E. Gunduz2), C. Pauly3), C.C. Doumanidis4), S. F. Son2), C. Rebholz5), F.
Mücklich3)
1
Institute for Applied Materials, Karlsruhe Institute of Technology (KIT), 76344 Eggenstein-Leopoldshafen,
Germany
2
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA
3
Department for Materials Science and Engineering, Saarland University, 66123 Saarbrücken, Germany
4
Department of Mechanical Engineering, Khalifa University of Sci, Tech. and Research, Abu Dhabi, UAE
5
Department of Mechanical and Manufacturing Engineering, University of Cyprus, 1678 Nicosia, Cyprus
Supplementary Material
S1) Microstructure of Ru/Al multilayer
Figure S1: Transmission electron image of an as prepared Ru/Al multilayer with a bilayer
thickness of 176 nm. The Ru and Al sublayer are shown in dark and light contrast,
respectively. The bilayer thickness  and the pre-mixing width  as used in the main text are
indicated. The inset focuses on the interfaces and proves the absence of intermetallic phase
formation.
S2) Thermal-physical properties of the elements and the Ru-Al phases
TABLE SI: Densities and enthalpies of the individual phases
Density
Enthalpy
Species
(kg/m3)
(J/mol)
Aluminum
*
2700
solid 2: -8282.5824 + 25.0307T + 4.410-3T2 - 8.980910-6T3
1
liquid 2: -795.991 + 31.7482T
1
Ruthenium
12450
RuAl
8286 3
solid 2: -8475.49 + 27,4688T – 1.110-3T2 – 1.34310-6T3
liquid 2: -17161.807 + 51.8816T
solid 4,*: -69939.78 + 26.2551T + 1.6510-3T2 – 2.231910-9T3
According to the CALPHAD calculations by Prins et al., the first summand takes a value of -61939.78 J/mol 4.
However, based on their data, the calculated value for the enthalpy of formation of RuAl is only -53000 J/mol.
We added 8000 J/mol to achieve the experimentally found heat of formation of -62000 J/mol.
TABLE SII: Enthalpy of melting and thermal conductivity of the individual phases
Enthalpy of melting
Species
Thermal conductivity (W/mK)
(J/mol)
Aluminum
10711 2
-0.0398·T + 251.12 5
Ruthenium
38589 2
-0.019·T + 119.71 5
RuAl
63000
75 6
References
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Physical Chemistry (Springer, 2012), Vol. 19B5.
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microstructure and processing (review). Intermetallics 13, 5-21 (2005).
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(2003).
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Phys. Chem. Ref. Data 1, 279-421 (1972).
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