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{\bf Grain Boundary Properties and Grain Growth:  A1 Foils, A1 Films}

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Katayun Barmak, Wayne E. Archibald, Anthony D. Rollett\\
Department of Materials Science \& Engineering\\
Carnegie Mellon University\\
Pittsburgh, PA  15213\\

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and\\

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Shlomo Ta'asan, David Kinderlehrer\\
Department of Mathematical Sciences\\
Carnegie Mellon University\\
Pittsburgh, PA  15213
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Relative grain boundary energy as a function of misorientation angle
has been measured in cube-oriented, i.e., <100> fiber-textured, 120
$\mu$m-thick A1 foil using orientation imaging microscopy and a
statistical multiscale method.  The energies of low-angle boundaries
increase with misorientation angle, in good agreement with the
Read-Shockley model.  The relative energies of high-angle boundaries
exhibit little variation with misorientation.  Examination of the
grain structure of <111> fiber-textured, 100 nm-thick A1 films
annealed at 400 $\deg${C} for 0.5-10 h shows 5 and 6 sided grains to be
the most frequent, and the fraction of four-sided grains to be
significant.  the mean number of sides is slightly lower than the
expected value of 6 for two-dimensional structures.  Of lognormal,
gamma and Rayleigh distributions, gamma gives the best fit to the
grain size data in the films; however, the difference between gamma
and lognormal is small.  Grain growth is not self-similar and
stagnates after one hour of annealing.  The evoluion of the grain size
distribution with time indicates that the growth stagnation in the
films is neither consistent with boundary pinning by grooving nor with
conventional treatments of solute drag.  Surface, elastic-strain and
plastic-strain energy driving forces do not play a significant role
int he grain growth and the subsequent stagnation since the films are
strongly textured even in the as-depoisted state.  The steady-state
distributions of reduced grain area for two-dimensional, Monte Carlo
and partial differential equation based simulations show excellent
agreement with each other, even when anisotropic boundary energies are
used.  However, comparison with experimental distributions reveals
a significantly higher population of small grains in the experiments.

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