Anomalous Oxidative Diffusion in Titanium Pyrotechnic Powders
It has long been observed that oxidation processes in metals tend to follow a parabolic rate law associated with the growth of a surface oxide layer. Here we observe that for certain titanium powders, the expected parabolic law (∝t _{1/2}) is recovered, yet for others, the exponent differs significantly. One explanation for this nonparabolic, anomalous diffusion arises from fractal geometry. Theoretical considerations indicate that the time response of diffusionlimited processes in an object closely follow a powerlaw in time (t ^{n}) with n=(E–D)/2, where E is the object's Euclidean dimension and D is its boundary's Hausdorff dimension. Noninteger, (fractal) values of D will result in n≠1/2. Finite element simulations of several canonical fractal objects were performed to verify the application of this theory; the results matched the theory well. Two different types of titanium powder were tested in isothermal thermogravimetric tests under dilute oxygen. Timedependent mass uptake data were fit with powerlaw forms and the associated exponents were used to determine an equivalent fractal dimension. One Ti powder type has an implied surface dimension of ca. 2.3 to 2.5, suggesting fractal geometry may be operative. Finally, the other has a dimension near 2.0, indicating it behaves like traditional material.
 Authors:

^{[1]};
^{[2]}
 Engineering Sciences Center, Sandia National Laboratories, PO Box 5800 MS 0836 Albuquerque NM 871850836 USA
 Materials Science & Engineering Center, Sandia National Laboratories, PO Box 5800 MS 1349 Albuquerque NM 871851349 USA
 Publication Date:
 Report Number(s):
 SAND20163649J
Journal ID: ISSN 07213115; 638481
 Grant/Contract Number:
 AC0494AL85000
 Type:
 Accepted Manuscript
 Journal Name:
 Propellants, Explosives, Pyrotechnics
 Additional Journal Information:
 Journal Volume: 42; Journal Issue: 3; Journal ID: ISSN 07213115
 Publisher:
 Wiley
 Research Org:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org:
 USDOE National Nuclear Security Administration (NNSA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 36 MATERIALS SCIENCE; anomalous diffusion; titanium; fractal dimension; surface area; metal powder; pyrotechnic
 OSTI Identifier:
 1341406
Erikson, William W., and Coker, Eric N.. Anomalous Oxidative Diffusion in Titanium Pyrotechnic Powders. United States: N. p.,
Web. doi:10.1002/prep.201600092.
Erikson, William W., & Coker, Eric N.. Anomalous Oxidative Diffusion in Titanium Pyrotechnic Powders. United States. doi:10.1002/prep.201600092.
Erikson, William W., and Coker, Eric N.. 2016.
"Anomalous Oxidative Diffusion in Titanium Pyrotechnic Powders". United States.
doi:10.1002/prep.201600092. https://www.osti.gov/servlets/purl/1341406.
@article{osti_1341406,
title = {Anomalous Oxidative Diffusion in Titanium Pyrotechnic Powders},
author = {Erikson, William W. and Coker, Eric N.},
abstractNote = {It has long been observed that oxidation processes in metals tend to follow a parabolic rate law associated with the growth of a surface oxide layer. Here we observe that for certain titanium powders, the expected parabolic law (∝t1/2) is recovered, yet for others, the exponent differs significantly. One explanation for this nonparabolic, anomalous diffusion arises from fractal geometry. Theoretical considerations indicate that the time response of diffusionlimited processes in an object closely follow a powerlaw in time (tn) with n=(E–D)/2, where E is the object's Euclidean dimension and D is its boundary's Hausdorff dimension. Noninteger, (fractal) values of D will result in n≠1/2. Finite element simulations of several canonical fractal objects were performed to verify the application of this theory; the results matched the theory well. Two different types of titanium powder were tested in isothermal thermogravimetric tests under dilute oxygen. Timedependent mass uptake data were fit with powerlaw forms and the associated exponents were used to determine an equivalent fractal dimension. One Ti powder type has an implied surface dimension of ca. 2.3 to 2.5, suggesting fractal geometry may be operative. Finally, the other has a dimension near 2.0, indicating it behaves like traditional material.},
doi = {10.1002/prep.201600092},
journal = {Propellants, Explosives, Pyrotechnics},
number = 3,
volume = 42,
place = {United States},
year = {2016},
month = {11}
}