GRAIN GROWTH IN UNSTRAINED GLACIAL ICE

Abstract
We use theories for grain growth driven by surface tension and curvature of grain boundaries to explain published data on grain growth in cold (≤-10°C) glacial ice that is not deforming rapidly. Among other results, we propose that small grain sizes in Wisconsinan ice are caused by large concentrations of soluble impurities. Major observations that we seek to explain are Gow, (1), (2) ; Gow and Williamson, (3) ; Duval and Lorius, (4) ; and Alley et al., (5) (i) in most post-Wisconsinan ice and firn, the average cross-sectional area of grains increases linearly with time. The rate of increase is nearly the same in firn and ice, although it may be slightly less in ice ; (ii) Grain sizes are smaller in ice rich in volcanic tephra than in adjacent, clean ice ; (iii) Bubbles, which form on grain boundaries at the firn-ice transition, separate from grain boundaries in a discrete depth interval below the transition ; and (iv) Grain size decreases downward across the firn-ice transition. When grain growth is driven by grain-boundary curvature and surface tension, grain-growth theory (reviewed by Higgins, (6)) predicts that the average cross-sectional area of grains in pure, fully consolidated materials will increase linearly with time. Bubbles, inert second-phase particles (microparticles), and dissolved impurities can slow grain growth and cause deviation from this linear area-time relation. For typical glacial ice, including Wisconsinan ice, we calculate that microparticles are too sparse to affect grain growth significantly, a conclusion reached previously by Duval and Lorius (4). For tephra-rich layers such as those in the Byrd core, however, we calculate that microparticles slow grain growth significantly, in accord with observations (Gow and Williamson, (3)) ; impurity drag and strain probably are important in the Byrd tephra layers also. Model calculations show that compression of bubbles deeper than the firn-ice transition reduces their mobility below that of grain boundaries so that bubble-boundary separation should occur ; such separation is observed (Gow and Williamson, (3). Observed bubble-boundary separation requires about 10 % of the driving force for grain growth and should reduce growth rates by about 10 %. Such a change would be largely masked by observational error, but may be observed. The downward decrease in grain size across the Holocene-Wisconsinan boundary correlates with a downward increase in soluble impurities, especially NaCl (Petit et al., (7)). The correlation has the form expected if the grain-size decrease is caused by the impurity increase. Furthermore, the interaction energy between grain boundaries and Nacl required to cause the grain-size decrease is of the same order as our best estimate of this interaction energy. We thus propose that the small grain sizes in Wisconsinan ice are caused by high concentrations of NaCl and possibly other soluble impurities.