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Thermal conductivity of amorphous ice

  Thermal conductivity of amorphous ice was measured and analyzed by Kouchi et al. (1992a) (see also Kouchi et al., 1992b), and was found to be extremely low. Its value have been found to be tex2html_wrap_inline1398 at temperatures T=125 to tex2html_wrap_inline1402 K, which may be compared with the thermal conductivity of crystalline ice (Klinger, 1975) approximated by

  equation210

The thermal conductivity of amorphous ice, tex2html_wrap_inline1404 , is at least on the order of tex2html_wrap_inline1406 times the previous estimate by Klinger (1980), which has been used in many papers on the thermal history of comets. Furthermore this tex2html_wrap_inline1404 is as small as tex2html_wrap_inline1410 of the fine particle regolith on the Moon surface, which has one of the smallest thermal conductivities among natural materials.

To see how low the tex2html_wrap_inline1404 is, let us estimate heat conduction time scales in amorphous ice. The time t for heat to reach distance R by conduction is estimated from

displaymath1418

where tex2html_wrap_inline1420 and tex2html_wrap_inline1422 are density and specific heat per unit mass of amorphous ice, respectively. The value of tex2html_wrap_inline1424 is on the order of tex2html_wrap_inline1426 at tex2html_wrap_inline1428 K. For tex2html_wrap_inline1430 km, size of a small cometary nucleus, we have tex2html_wrap_inline1432 yr, comparable with the age of the solar system ( tex2html_wrap_inline1434 yr). Even for a body as small as tex2html_wrap_inline1436 cm, the time required is tex2html_wrap_inline1438 yr! This indicates that amorphous ice is an extremely good thermal insulator.

Corresponding to the small conductivity, the sound speed tex2html_wrap_inline1440 is also very small. Sound speed tex2html_wrap_inline1440 is related to the thermal conductivity as

displaymath1444

where tex2html_wrap_inline1446 is phonon mean free path in amorphous ice. The smallest estimate of tex2html_wrap_inline1446 is a few Å, size of an H tex2html_wrap_inline1146 O molecule. Thus tex2html_wrap_inline1440 should be

displaymath1454



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Mon Sep 16 16:23:29 JST 1996