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The formation of ice within a pore is dependent on the size of the pore. Nucleation of ice crystals becomes more difficult as pore size decreases. The freezing point depression of pore water is related to the pore radius by the well-known Gibbs-Thomson equation 
|1n(T/T0) = − 2ΔGV/ΔHr||(3)|
where T = water temperature in pore (K), To = freezing point, ΔG = G(matrix/ice) − G(matrix/water), G = interfacial energy, V = molar volume of water, ΔH = latent heat of fusion, and r = pore radius . As the pore radius decreases, the freezing point of water in the pore decreases. This effect has been observed in many porous materials for many different fluids , and is also observed for water in cement paste. Calorimetric results of hardened cement paste [19,20,21,22,23] from 10 ºC to −60 ºC show three well-defined peaks at approximately −8 ºC, −23 ºC, and −40 ºC. Ice formation does not occur above −8 ºC due to the freezing point depression of the pore water, caused by both pore size effects, as given by eq.(3), and the high ionic strength of the pore solution. The peak at −8 ºC is due to freezing bulk water in the macropores. The peak at −23 ºC corresponds to the freezing of the smaller capillary pores, while the rather broad peak at −40 ºC represents the low temperature transition of supersaturated solution in gel pores. Very little additional freezing occurs below this last peak. Calorimetric studies have been performed down to a temperature of −175 ºC, and there is no indication of bulk ice formation below this point [19,20]. There is, however, some evidence for a freezing of an adsorbed water film at approximately −90 ºC [21,22].