# Difference between revisions of "Ice Ih"

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, $b=a\sqrt3$, 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 $(T_m)$ for the ice Ih-water transition:

 $T_m$ Pressure Water model / technique Reference $146~K$ 1 bar TIP3P [2] $190~K$ 1 bar SPC [2] $215(4)~K$ 1 bar SPC/E / free energy calculation [3] $225~K$ 1 bar TTM3-F (quantum) [4] $227.65 \pm 1.5~K$ 1 bar TTM2.1-F (quantum) [5] $232(4)~K$ 1 bar TIP4P / free energy calculation [3] $242.65 \pm 1.5~K$ 1 bar TTM2.1-F (classical) [5] $245.5(6)~K$ 1 bar TIP4P/Ew / free energy calculation [3] $251 \pm 1~K$ 1 bar q-TIP4P/F / direct coexistence [6] $252(6)~K$ 1 bar TIP4P/2005 / free energy calculation [3] $272(6)~K$ 1 bar TIP4P/Ice / free energy calculation [3] $273.15 K$ 1 bar experimental value $274~K$ 1 bar TIP5P [2] $289~K$ 1 bar NvdE [7] $411 \pm 4~K$ 10,000 bar Becke-Lee-Yang-Parr functional [8] $417\pm 3~K$ 2500 bar Perdew-Burke-Ernzerhof functional [8]

Isotopes:

 $T_m$ (D20) Pressure Water model / technique Reference $257.5(5)~K$ 1 bar q-TIP4P/F / free energy calculation [9] $276.83 \pm 0.02 K$ 1 bar experimental value [10]
 $T_m$ (T20) Pressure Water model / technique Reference $259.2(5)~K$ 1 bar q-TIP4P/F / free energy calculation [9] $277.64 K$ 0.6629 kPa experimental value [11]

It is worth pointing out that the calculations presented in the work of Ramírez and Herrero [9] 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: $\Delta T_m (D_2O - H_2 0) = 6.5 K$ (experimental value: 3.68 K) and $\Delta T_m (T_2O - H_2 0) = 8.2 K$ (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 [12] 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

## References

1. K. Röttger, A. Endriss, J. Ihringer, S. Doyle and W. F. Kuhs "Lattice constants and thermal expansion of H2O and D2O ice Ih between 10 and 265 K", Acta Crystallographica Section B 50 pp. 644-648 (1994)
2. C. Vega, J. L. F. Abascal, M. M. Conde and J. L. Aragones "What ice can teach us about water interactions: a critical comparison of the performance of different water models", Faraday Discussions 141 pp. 251-276 (2009) Cite error: Invalid <ref> tag; name "multiple3" defined multiple times with different content Cite error: Invalid <ref> tag; name "multiple3" defined multiple times with different content
3. Carlos Vega, Maria Martin-Conde and Andrzej Patrykiejew "Absence of superheating for ice Ih with a free surface: a new method of determining the melting point of different water models", Molecular Physics 104 pp. 3583-3592 (2006) Cite error: Invalid <ref> tag; name "multiple1" defined multiple times with different content Cite error: Invalid <ref> tag; name "multiple1" defined multiple times with different content Cite error: Invalid <ref> tag; name "multiple1" defined multiple times with different content Cite error: Invalid <ref> tag; name "multiple1" defined multiple times with different content
4. Francesco Paesani, Soohaeng Yoo, Huib J. Bakker and Sotiris S. Xantheas "Nuclear Quantum Effects in the Reorientation of Water",Journal of Physical Chemistry Letters 1 pp. 2316-2321 (2010)
5. Francesco Paesani and Gregory A. Voth "Quantum Effects Strongly Influence the Surface Premelting of Ice", Journal of Physical Chemistry C 112 pp. 324-327 (2008) Cite error: Invalid <ref> tag; name "multiple4" defined multiple times with different content
6. Scott Habershon, Thomas E. Markland, and David E. Manolopoulos "Competing quantum effects in the dynamics of a flexible water model", Journal of Chemical Physics 131 024501 (2009)
7. José L. F. Abascal, Ramón García Fernández, Carlos Vega and Marcelo A. Carignano, "The melting temperature of the six site potential model of water", Journal of Chemical Physics, 125 166101 (2006)
8. Soohaeng Yoo, Xiao Cheng Zeng, and Sotiris S. Xantheas "On the phase diagram of water with density functional theory potentials: The melting temperature of ice Ih with the Perdew–Burke–Ernzerhof and Becke–Lee–Yang–Parr functionals", Journal of Chemical Physics 130 221102 (2009) Cite error: Invalid <ref> tag; name "multiple2" defined multiple times with different content
9. R. Ramírez and C. P. Herrero "Quantum path integral simulation of isotope effects in the melting temperature of ice Ih", Journal of Chemical Physics 133, 144511 (2010) Cite error: Invalid <ref> tag; name "Ramirez1" defined multiple times with different content Cite error: Invalid <ref> tag; name "Ramirez1" defined multiple times with different content
10. N.N. Smirnova, T.A. Bykova, K. Van Durme and B. Van Mele "Thermodynamic properties of deuterium oxide in the temperature range from 6 to 350 K", The Journal of Chemical Thermodynamics 38 pp. 879-883 (2006)
11. H. W. Xiang "Vapor Pressure and Critical Point of Tritium Oxide", Journal of Physical and Chemical Reference Data 32 pp. 1707.1711 (2003)
12. Shunle Dong and Jichen Li "The test of water potentials by simulating the vibrational dynamics of ice", Physica B 276-278 pp. 469-470 (2000)