# 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 (in ascending order):

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

Isotopes:

 $T_m$ (D20) Pressure Water model / technique Reference $257.5(5)~K$ 1 bar q-TIP4P/F / free energy calculation [14] $263.2~K$ 1 bar TIP4PQ_D2O / free energy calculation [15] $276.83 \pm 0.02 K$ 1 bar experimental value [16]
 $T_m$ (T20) Pressure Water model / technique Reference $259.2(5)~K$ 1 bar q-TIP4P/F / free energy calculation [14] $263.5~K$ 1 bar TIP4PQ_T2O / free energy calculation [15] $277.64 K$ 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: $\Delta T_m (D_2O - H_2 0) = 6.5 K$ (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 [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

## 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. Péter T. Kiss, Péter Bertsyk, and András Baranyai "Testing recent charge-on-spring type polarizable water models. I. Melting temperature and ice properties", Journal of Chemical Physics 137 194102 (2012) Cite error: Invalid <ref> tag; name "KBB_194102" defined multiple times with different content Cite error: Invalid <ref> tag; name "KBB_194102" defined multiple times with different content Cite error: Invalid <ref> tag; name "KBB_194102" defined multiple times with different content Cite error: Invalid <ref> tag; name "KBB_194102" defined multiple times with different content Cite error: Invalid <ref> tag; name "KBB_194102" defined multiple times with different content
4. Eva Muchová, Ivan Gladich, Sylvain Picaud, Paul N. M. Hoang, and Martina Roeselová "The Ice−Vapor Interface and the Melting Point of Ice Ih for the Polarizable POL3 Water Model", Journal of Physical Chemistry A 115 pp. 5973-5982 (2011)
5. 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
6. 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)
7. 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
8. Soohaeng Yoo and Sotiris S. Xantheas "Communication: The effect of dispersion corrections on the melting temperature of liquid water", Journal of Chemical Physics 134 121105 (2011) Cite error: Invalid <ref> tag; name "Yoo" defined multiple times with different content
9. 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)
10. Valeria Molinero and Emily B. Moore "Water Modeled As an Intermediate Element between Carbon and Silicon", Journal of Physical Chemistry B 113 pp. 4008-4016 (2009)
11. 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)
12. Benjamin F. Nicholson, Paulette Clancy and Steven W. Rick "The interface response function and melting point of the prism interface of ice Ih using a fluctuating charge model (TIP4P-FQ)", Journal of Crystal Growth 293 pp. 78-85 (2006)
13. 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
14. 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
15. http://dx.doi.org/10.1039/C2CP42393F Carl McBride , Juan L. Aragones , Eva G. Noya and Carlos Vega "A study of the influence of isotopic substitution on the melting point and temperature of maximum density of water by means of path integral simulations of rigid models", PCCP 14 pp. 15199-15205 (2012)] Cite error: Invalid <ref> tag; name "McBride_1" defined multiple times with different content
16. 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)
17. H. W. Xiang "Vapor Pressure and Critical Point of Tritium Oxide", Journal of Physical and Chemical Reference Data 32 pp. 1707.1711 (2003)
18. 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)