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Anomalous Oxidative Diffusion in Titanium Pyrotechnic Powders
Author(s) -
Erikson William W.,
Coker Eric N.
Publication year - 2017
Publication title -
propellants, explosives, pyrotechnics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.56
H-Index - 65
eISSN - 1521-4087
pISSN - 0721-3115
DOI - 10.1002/prep.201600092
Subject(s) - fractal dimension , fractal , power law , diffusion , hausdorff dimension , exponent , geometry , mathematics , isothermal process , materials science , thermodynamics , mathematical analysis , physics , linguistics , statistics , philosophy
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 ( 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. The other has a dimension near 2.0, indicating it behaves like traditional material.