# Ice Ih

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Ice Ih, also known as hexagonal ice, is a proton disordered ice phase having the space group P63/mmc. Ice Ih has the following lattice parameters at 250 K: a=4.51842 Å, ${\displaystyle b=a{\sqrt {3}}}$, and c=7.35556 Å with four molecules per unit cell (in Table 3 of [1]). The proton ordered form of ice Ih is known as ice XI, which (in principle) forms when ice Ih is cooled to below 72K (it is usually doped with KOH to aid the transition).

## Melting point

The following is a collection of melting points ${\displaystyle (T_{m})}$ for the ice Ih-water transition (in ascending order):

 ${\displaystyle T_{m}}$ Pressure Water model / technique Reference ${\displaystyle 146~K}$ 1 bar TIP3P [2] ${\displaystyle 149~K}$ 1 bar COS/G3 [3] ${\displaystyle 180~K\pm 10~K}$ 1 bar POL3 [4] ${\displaystyle 186~K}$ 1 bar SWM4-DP [3] ${\displaystyle 190~K}$ 1 bar SPC [2] ${\displaystyle 207~K}$ 1 bar BKd1 [3] ${\displaystyle 213~K}$ 1 bar BKd2 [3] ${\displaystyle 215~K}$ 1 bar COS/G2 [3] ${\displaystyle 215(4)~K}$ 1 bar SPC/E / free energy calculation [5] ${\displaystyle 225~K}$ 1 bar TTM3-F (quantum) [6] ${\displaystyle 227.65\pm 1.5~K}$ 1 bar TTM2.1-F (quantum) [7] ${\displaystyle 232(4)~K}$ 1 bar TIP4P / free energy calculation [5] ${\displaystyle 233~K}$ 1 bar BKd3 [3] ${\displaystyle 242.65\pm 1.5~K}$ 1 bar TTM2.1-F (classical) [7] ${\displaystyle 245.5(6)~K}$ 1 bar TIP4P/Ew / free energy calculation [5] ${\displaystyle 248~K}$ 1 bar TTM3-F [8] ${\displaystyle 251\pm 1~K}$ 1 bar q-TIP4P/F / direct coexistence [9] ${\displaystyle 252(6)~K}$ 1 bar TIP4P/2005 / free energy calculation [5] ${\displaystyle 272(6)~K}$ 1 bar TIP4P/Ice / free energy calculation [5] ${\displaystyle 273.15K}$ 1 bar experimental value ${\displaystyle 274~K}$ 1 bar TIP5P [2] ${\displaystyle 274.6~K}$ 1 bar mW [10] ${\displaystyle 289~K}$ 1 bar NvdE [11] ${\displaystyle 303\pm 8~K}$ 1 bar TIP4P/FQ [12] ${\displaystyle 360~K}$ 1 bar BLYP-D [8] ${\displaystyle 411\pm 4~K}$ 10,000 bar BLYP [13] ${\displaystyle 417\pm 3~K}$ 2500 bar Perdew-Burke-Ernzerhof functional [13]

Isotopes:

 ${\displaystyle T_{m}}$ (D20) Pressure Water model / technique Reference ${\displaystyle 257.5(5)~K}$ 1 bar q-TIP4P/F / free energy calculation [14] ${\displaystyle 263.2~K}$ 1 bar TIP4PQ_D2O / free energy calculation [15] ${\displaystyle 276.83\pm 0.02K}$ 1 bar experimental value [16]
 ${\displaystyle T_{m}}$ (T20) Pressure Water model / technique Reference ${\displaystyle 259.2(5)~K}$ 1 bar q-TIP4P/F / free energy calculation [14] ${\displaystyle 263.5~K}$ 1 bar TIP4PQ_T2O / free energy calculation [15] ${\displaystyle 277.64K}$ 0.6629 kPa experimental value [17]

It is worth pointing out that the calculations presented in the work of Ramírez and Herrero [14] used the melting point of the q-TIP4P/F model as its "reference state". It is perhaps more fruitful to examine the relative changes upon isotopic substitution: ${\displaystyle \Delta T_{m}(D_{2}O-H_{2}0)=6.5K}$ (experimental value: 3.68 K) and ${\displaystyle \Delta T_{m}(T_{2}O-H_{2}0)=8.2K}$ (experimental value: 4.49 K).

The following is a plot of the oxygen-oxygen radial distribution function for the TIP4PQ/2005 model at 77K

## Phonon density of states

In [18] the phonon density of states for the POL1, TIPS2, TIP4P, TIP3P, SPC, Rowlinson, MCY, and BF models for water are compared to experiment.

## Entropy

Main article: Entropy of ice phases