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Title: 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 non-parabolic, anomalous diffusion arises from fractal geometry. Theoretical considerations indicate that the time response of diffusion-limited processes in an object closely follow a power-law 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. Non-integer, (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. Time-dependent mass uptake data were fit with power-law 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]
  1. Engineering Sciences Center, Sandia National Laboratories, PO Box 5800 MS 0836 Albuquerque NM 87185-0836 USA
  2. Materials Science & Engineering Center, Sandia National Laboratories, PO Box 5800 MS 1349 Albuquerque NM 87185-1349 USA
Publication Date:
Report Number(s):
SAND-2016-3649J
Journal ID: ISSN 0721-3115; 638481
Grant/Contract Number:
AC04-94AL85000
Type:
Accepted Manuscript
Journal Name:
Propellants, Explosives, Pyrotechnics
Additional Journal Information:
Journal Volume: 42; Journal Issue: 3; Journal ID: ISSN 0721-3115
Publisher:
Wiley
Research Org:
Sandia National Lab. (SNL-NM), 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 non-parabolic, anomalous diffusion arises from fractal geometry. Theoretical considerations indicate that the time response of diffusion-limited processes in an object closely follow a power-law in time (tn) with n=(E–D)/2, where E is the object's Euclidean dimension and D is its boundary's Hausdorff dimension. Non-integer, (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. Time-dependent mass uptake data were fit with power-law 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}
}