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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).
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==
==Melting point==
The following is a collection of melting points <math>(T_m)</math> for the ice Ih-[[water]] transition (in ascending order):
The following is a collection of melting points <math>(T_m)</math> for the ice Ih-[[water]] transition:
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|<math>146~K</math> || 1 bar || [[TIP3P]]  || <ref name="multiple3"> [http://dx.doi.org/10.1039/b805531a 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)] </ref>
|<math>146~K</math> || 1 bar || [[TIP3P]]  || <ref name="multiple3"> [http://dx.doi.org/10.1039/b805531a 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)] </ref>
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|<math>149~K</math> || 1 bar || [[COS model of water |COS/G3]]  || <ref name="KBB_194102">[http://dx.doi.org/10.1063/1.4767063  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)]</ref>
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|<math>180~K \pm 10~K </math> || 1 bar || [[POL3]]  || <ref>[http://dx.doi.org/10.1021/jp110391q 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)]</ref>
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|<math>186~K</math> || 1 bar || [[SWM4-DP model of water | SWM4-DP]]  || <ref name="KBB_194102"> </ref>
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|<math>190~K</math> || 1 bar || [[SPC]]  || <ref name="multiple3">  </ref>
|<math>190~K</math> || 1 bar || [[SPC]]  || <ref name="multiple3">  </ref>
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|<math>207~K</math> || 1 bar || [[BK water models | BKd1]]  || <ref name="KBB_194102"> </ref>
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|<math>213~K</math> || 1 bar || [[BK water models | BKd2]]  || <ref name="KBB_194102"> </ref>
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|<math>215~K</math> || 1 bar || [[COS model of water |COS/G2]]  || <ref name="KBB_194102"> </ref>
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|<math>215(4)~K</math> || 1 bar || [[SPC/E]] / [[Computation of phase equilibria | free energy calculation]] || <ref name="multiple1"> [http://dx.doi.org/10.1080/00268970600967948  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)]</ref>
|<math>215(4)~K</math> || 1 bar || [[SPC/E]] / [[Computation of phase equilibria | free energy calculation]] || <ref name="multiple1"> [http://dx.doi.org/10.1080/00268970600967948  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)]</ref>
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|<math>225~K</math> || 1 bar || [[TTM3-F model of water |TTM3-F]] ([[Path integral formulation |quantum]]) || <ref>[http://dx.doi.org/10.1021/jz100734w 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)]</ref>
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| <math>227.65 \pm 1.5~K</math> || 1 bar || [[TTM2.1-F]] ([[Path integral formulation |quantum]]) || <ref name="multiple4"> [http://dx.doi.org/10.1021/jp710640e 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)]</ref>
| <math>227.65 \pm 1.5~K</math> || 1 bar || [[TTM2.1-F]] ([[Path integral formulation |quantum]]) || <ref name="multiple4"> [http://dx.doi.org/10.1021/jp710640e 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)]</ref>
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|<math>232(4)~K</math> || 1 bar ||[[TIP4P]] / [[Computation of phase equilibria | free energy calculation]] || <ref name="multiple1"> </ref>
|<math>232(4)~K</math> || 1 bar ||[[TIP4P]] / [[Computation of phase equilibria | free energy calculation]] || <ref name="multiple1"> </ref>
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|<math>233~K</math> || 1 bar || [[BK water models | BKd3]]  || <ref name="KBB_194102"> </ref>
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| <math>242.65 \pm 1.5~K</math> || 1 bar || [[TTM2.1-F]] (classical) || <ref name="multiple4" > </ref>
| <math>242.65 \pm 1.5~K</math> || 1 bar || [[TTM2.1-F]] (classical) || <ref name="multiple4" > </ref>
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|<math>245.5(6)~K</math> || 1 bar || [[TIP4P/Ew]] / [[Computation of phase equilibria | free energy calculation]] || <ref name="multiple1"> </ref>
|<math>245.5(6)~K</math> || 1 bar || [[TIP4P/Ew]] / [[Computation of phase equilibria | free energy calculation]] || <ref name="multiple1"> </ref>
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|<math>248~K</math> || 1 bar || [[TTM3-F]]  || <ref name="Yoo">[http://dx.doi.org/10.1063/1.3573375 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)]</ref>
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| <math>251 \pm 1~K </math>  ||  1 bar || [[Q-TIP4P/F model of water | q-TIP4P/F ]] / [[Computation of phase equilibria#Direct simulation of the two phase system | direct coexistence]]|| <ref>[http://dx.doi.org/10.1063/1.3167790 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)]</ref>
| <math>251 \pm 1~K </math>  ||  1 bar || [[Q-TIP4P/F model of water | q-TIP4P/F ]] / [[Computation of phase equilibria#Direct simulation of the two phase system | direct coexistence]]|| <ref>[http://dx.doi.org/10.1063/1.3167790 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)]</ref>
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|<math>274~K</math> || 1 bar || [[TIP5P]]  || <ref name="multiple3">  </ref>
|<math>274~K</math> || 1 bar || [[TIP5P]]  || <ref name="multiple3">  </ref>
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|<math>274.6~K</math> || 1 bar || [[MW model of water | mW]]  || <ref>[http://dx.doi.org/10.1021/jp805227c 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)]</ref>
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|<math>289~K</math> || 1 bar || [[NvdE]]  || <ref>[http://dx.doi.org/10.1063/1.2360276    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)]</ref>
|<math>289~K</math> || 1 bar || [[NvdE]]  || <ref>[http://dx.doi.org/10.1063/1.2360276    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)]</ref>
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|  <math>303\pm 8~K</math>  || 1 bar ||  [[TIP4P/FQ model of water | TIP4P/FQ]]  ||  <ref>[http://dx.doi.org/10.1016/j.jcrysgro.2006.04.077  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)]</ref>
| <math>411 \pm 4~K</math>  ||10,000 bar ||  [[Becke-Lee-Yang-Parr functional]] ||  <ref name="multiple2"> [http://dx.doi.org/10.1063/1.3153871 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)] </ref>
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|<math>360~K</math> || 1 bar ||  [[Becke-Lee-Yang-Parr functional | BLYP-D]] || <ref name="Yoo"> </ref>
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| <math>411 \pm 4~K</math>  ||10,000 bar ||  [[Becke-Lee-Yang-Parr functional |BLYP]] ||  <ref name="multiple2"> [http://dx.doi.org/10.1063/1.3153871 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)] </ref>
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|  <math>417\pm 3~K</math>  || 2500 bar ||  [[Perdew-Burke-Ernzerhof functional]] ||  <ref name="multiple2" > </ref>
|  <math>417\pm 3~K</math>  || 2500 bar ||  [[Perdew-Burke-Ernzerhof functional]] ||  <ref name="multiple2" > </ref>
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|<math>257.5(5)~K</math> || 1 bar || [[Q-TIP4P/F model of water | q-TIP4P/F ]] / [[Computation of phase equilibria | free energy calculation]]  ||  <ref name="Ramirez1"> [http://dx.doi.org/10.1063/1.3503764  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)]</ref>
|<math>257.5(5)~K</math> || 1 bar || [[Q-TIP4P/F model of water | q-TIP4P/F ]] / [[Computation of phase equilibria | free energy calculation]]  ||  <ref name="Ramirez1"> [http://dx.doi.org/10.1063/1.3503764  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)]</ref>
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|<math>263.2~K</math> || 1 bar || [[TIP4PQ_D2O model of water | TIP4PQ_D2O]] / [[Computation of phase equilibria | free energy calculation]]  ||  <ref name="McBride_1">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)]</ref>
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| <math>276.83 \pm 0.02 K</math> || 1 bar || <FONT COLOR="#9400D3">experimental value</FONT> || <ref>[http://dx.doi.org/10.1016/j.jct.2005.09.005  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)]</ref>
| <math>276.83 \pm 0.02 K</math> || 1 bar || <FONT COLOR="#9400D3">experimental value</FONT> || <ref>[http://dx.doi.org/10.1016/j.jct.2005.09.005  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)]</ref>
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|<math>259.2(5)~K</math> || 1 bar || [[Q-TIP4P/F model of water | q-TIP4P/F ]] / [[Computation of phase equilibria | free energy calculation]]  ||  <ref name="Ramirez1"> </ref>
|<math>259.2(5)~K</math> || 1 bar || [[Q-TIP4P/F model of water | q-TIP4P/F ]] / [[Computation of phase equilibria | free energy calculation]]  ||  <ref name="Ramirez1"> </ref>
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|<math>263.5~K</math> || 1 bar || [[TIP4PQ_T2O model of water | TIP4PQ_T2O]] / [[Computation of phase equilibria | free energy calculation]]  ||  <ref name="McBride_1"> </ref>
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| <math>277.64  K</math> || 0.6629 kPa || <FONT COLOR="#9400D3">experimental value</FONT> || <ref>[http://dx.doi.org/10.1063/1.1565352 H. W. Xiang "Vapor Pressure and Critical Point of Tritium Oxide", Journal of Physical and Chemical Reference Data '''32''' pp. 1707.1711 (2003)]</ref>
| <math>277.64  K</math> || 0.6629 kPa || <FONT COLOR="#9400D3">experimental value</FONT> || <ref>[http://dx.doi.org/10.1063/1.1565352 H. W. Xiang "Vapor Pressure and Critical Point of Tritium Oxide", Journal of Physical and Chemical Reference Data '''32''' pp. 1707.1711 (2003)]</ref>
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It is worth pointing out that the calculations presented in the work of Ramírez and  Herrero <ref name="Ramirez1"> </ref> used the melting point of the [[Q-TIP4P/F model of water | q-TIP4P/F model]] as its "reference state". It is perhaps more fruitful to examine the relative changes upon isotopic substitution: <math>\Delta T_m (D_2O - H_2 0) = 6.5 K</math> (experimental value: 3.68 K) and <math>\Delta T_m (T_2O - H_2 0) = 8.2 K</math> (experimental value: 4.49 K).
'''Related reading'''
<br/>'''Related reading'''


*[http://dx.doi.org/10.1039/b703873a Jose L. F. Abascal and C. Vega "The melting point of hexagonal ice (Ih) is strongly dependent on the quadrupole of the water models", PCCP '''9''' pp. 2775 - 2778 (2007)]
*[http://dx.doi.org/10.1039/b703873a Jose L. F. Abascal and C. Vega "The melting point of hexagonal ice (Ih) is strongly dependent on the quadrupole of the water models", PCCP '''9''' pp. 2775 - 2778 (2007)]
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*[http://dx.doi.org/10.1021/jp0743121 E. G. Noya, C. Menduiña, J. L. Aragones, and C. Vega "Equation of State, Thermal Expansion Coefficient, and Isothermal Compressibility for Ices Ih, II, III, V, and VI, as Obtained from Computer Simulation", Journal of Physical Chemistry C '''111''' pp. 15877 - 15888 (2007)]
*[http://dx.doi.org/10.1021/jp0743121 E. G. Noya, C. Menduiña, J. L. Aragones, and C. Vega "Equation of State, Thermal Expansion Coefficient, and Isothermal Compressibility for Ices Ih, II, III, V, and VI, as Obtained from Computer Simulation", Journal of Physical Chemistry C '''111''' pp. 15877 - 15888 (2007)]
*[http://dx.doi.org/10.1016/S1293-2558(03)00092-X Sten Andersson and B.W. Ninham "Why ice floats on water", Solid State Sciences '''5''' pp. 683-693 (2003)]
*[http://dx.doi.org/10.1016/S1293-2558(03)00092-X Sten Andersson and B.W. Ninham "Why ice floats on water", Solid State Sciences '''5''' pp. 683-693 (2003)]
*[http://dx.doi.org/10.1063/1.3507916 Ikutaro Hamada "A van der Waals density functional study of ice Ih", Journal of Chemical Physics '''133''' 214503 (2010)]


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