Editing Ice Ih

[[Image:Ice_Ih.png|thumb|right]]
'''Ice Ih''', also known as hexagonal ice, is a proton disordered [[Ice phases |ice phase]] having the space group P6<sub>3</sub>/mmc. Ice Ih has the following lattice parameters at 250 K:  ''a''=4.51842 &Aring;, <math>b=a\sqrt3</math>, and ''c''=7.35556 &Aring; with four molecules per  unit cell 
(in Table 3 of <ref>[http://dx.doi.org/10.1107/S0108768194004933 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)]</ref>). 
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 <math>(T_m)</math> for the ice Ih-[[water]] transition (in ascending order):
:{| border="1"
|- 
| <math>T_m</math> || Pressure || [[Water models|Water model]] / technique  || Reference
|-  
|<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>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>
|-  
|<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>
|-  
|<math>186~K</math> || 1 bar || [[SWM4-DP model of water | SWM4-DP]]  || <ref name="KBB_194102"> </ref>
|-  
|<math>190~K</math> || 1 bar || [[SPC]]  || <ref name="multiple3">  </ref>
|-  
|<math>207~K</math> || 1 bar || [[BK water models | BKd1]]  || <ref name="KBB_194102"> </ref>
|-  
|<math>213~K</math> || 1 bar || [[BK water models | BKd2]]  || <ref name="KBB_194102"> </ref>
|-  
|<math>215~K</math> || 1 bar || [[COS model of water |COS/G2]]  || <ref name="KBB_194102"> </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>
|-
|<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>
|- 
| <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>232(4)~K</math> || 1 bar ||[[TIP4P]] / [[Computation of phase equilibria | free energy calculation]] || <ref name="multiple1"> </ref>
|-  
|<math>233~K</math> || 1 bar || [[BK water models | BKd3]]  || <ref name="KBB_194102"> </ref>
|- 
| <math>242.65 \pm 1.5~K</math> || 1 bar || [[TTM2.1-F]] (classical) || <ref name="multiple4" > </ref>
|-
|<math>245.5(6)~K</math> || 1 bar || [[TIP4P/Ew]] / [[Computation of phase equilibria | free energy calculation]] || <ref name="multiple1"> </ref>
|-
|<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>
|-
| <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>252(6)~K</math>  ||  1 bar || [[TIP4P/2005]] / [[Computation of phase equilibria | free energy calculation]] || <ref name="multiple1"> </ref>
|-
|<math>272(6)~K</math> || 1 bar ||[[TIP4P/Ice]] / [[Computation of phase equilibria | free energy calculation]] || <ref name="multiple1"> </ref>
|- 
| <math>273.15 K</math> || 1 bar || <FONT COLOR="#9400D3">experimental value</FONT> ||
|-  
|<math>274~K</math> || 1 bar || [[TIP5P]]  || <ref name="multiple3">  </ref>
|-  
|<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>
|-  
|<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>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>360~K</math> || 1 bar ||  [[Becke-Lee-Yang-Parr functional | BLYP-D]] || <ref name="Yoo"> </ref>
|-
| <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>
|-
|  <math>417\pm 3~K</math>  || 2500 bar ||  [[Perdew-Burke-Ernzerhof functional]] ||  <ref name="multiple2" > </ref>
|}
'''Isotopes:'''
:{| border="1"
|- 
| <math>T_m</math> (D<sub>2</sub>0) || Pressure || [[Water models|Water model]] / technique  || Reference
|-  
|<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>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>
|- 
| <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>
|}

:{| border="1"
|- 
| <math>T_m</math> (T<sub>2</sub>0) || Pressure || [[Water models|Water model]] / technique  || Reference
|-  
|<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>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>
|- 
| <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>
|}
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). 
<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)]

==Radial distribution function==
The following is a plot of the oxygen-oxygen [[radial distribution function]] for the [[TIP4PQ/2005]] model at 77K
:[[Image:rdf_Ih_OO_77K_TIP4PQ2005.png]]
'''Related reading'''
*[http://dx.doi.org/10.1039/b418934e Carlos Vega, Carl McBride, Eduardo Sanz and Jose L. F. Abascal "Radial distribution functions and densities for the SPC/E, TIP4P and TIP5P models for liquid water and ices Ih, Ic, II, III, IV, V, VI, VII, VIII, IX, XI and XII", Physical Chemistry Chemical Physics '''7''' pp. 1450 - 1456 (2005)]

==Phonon density of states==
In
<ref>[http://dx.doi.org/10.1016/S0921-4526(99)01699-3  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)  ]</ref>
the phonon density of states for the [[POL1]], [[TIPS2]], [[TIP4P]], [[TIP3P]], [[SPC]], [[R|Rowlinson]], [[MCY]], and [[BF]] [[water models | models for water]] are compared to experiment.
==Entropy==
:''Main article: [[Entropy of ice phases]]''
==Experimental data==
*[http://dx.doi.org/10.1063/1.2183324  Rainer Feistel and Wolfgang Wagner "A New Equation of State for H2O Ice Ih", Journal of Physical and Chemical Reference Data '''35''' pp. 1021- (2006)]
==References==
<references/>
'''Related reading'''
*[http://dx.doi.org/10.1021/ja01315a102 Linus Pauling "The Structure and Entropy of Ice and of Other Crystals with Some Randomness of Atomic Arrangement", Journal of the American Chemical Society '''57''' pp. 2674 - 2680 (1935)]
*[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/10.1063/1.3507916 Ikutaro Hamada "A van der Waals density functional study of ice Ih", Journal of Chemical Physics '''133''' 214503 (2010)]

==External links==
*[http://www.lsbu.ac.uk/water/ice1h.html Hexagonal Ice (Ice Ih)] page on [http://www.lsbu.ac.uk/water/ Martin Chaplin's Water Structure and Science] web site.
{{numeric}}
[[category: water]]