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Water Phase Diagram

V Phase diagrams
V The phase diagram of water
V Density change
V Triple points
link The ice phases

Phase diagrams

Phase diagrams show the preferred physical states of matter at different temperatures and pressure. Within each phase, the material is uniform with respect to its chemical composition and physical state. At typical temperatures and pressures on Earth (marked by an 'E' below) water is a liquid, but it becomes solid (that is, ice) if its temperature is lowered below 273 K and gaseous (that is, water vapor)a if its temperature is raised above 373 K, at the same pressure. Each line (phase line)e on a phase diagram represents a phase boundary and gives the conditions when two phases may stably coexist in any relative proportions (having the same Gibbs free energy). Here, a slight change in temperature or pressure may cause the phases to abruptly change from one physical state to the other. Where three phase lines join, there is a 'triple point', when three phases stably coexist (having identical Gibbs free energies),e but may abruptly and totally change into each other given a slight change in temperature or pressure. Under the singular conditions of temperature and pressure where liquid water, gaseous water and hexagonal ice stably coexist, there is a 'triple point' where both the boiling point of water and melting point of ice are equal. Four phase lines cannot meet at a single point. A 'critical point' occurs at the end of a phase line where the properties of the two phases become indistinguishable from each other, for example when, under singular conditions of temperature and pressure, liquid water is hot enough and gaseous water is under sufficient pressure that their densities are identical. Critical points are usually found at the high temperature end of the liquid-gas phase line.

The phase diagram of water

The phase diagram of water is complex,b having a number of triple points and one, or possibly two, critical points. Many of the crystalline forms may remain metastable in much of the low-temperature phase space at lower pressures. A thermodynamic model of water and ices Ih, III, V and VI [1320] and thermodynamic functions of the phase transitions [1658] have been described. The known ices can be divided, by cluster analysis of their structures [1717], into the low-pressure ices (hexagonal ice, cubic ice and ice-eleven). the high pressure ices (ice-seven, ice-eight and ice-ten) and the others (found in the relatively narrow range of moderate pressures between about 200-2000 MPa). All phases that share phase boundaries with liquid water (ices Ih, III, V and VI and VII) have disordered hydrogen bonding. The phases with ordered hydrogen bonding are found at lower temperatures and are indicated in light blue below. The structural transformation conditions of some of these ices during compression have been described [1795] .

 

Water phase diagram Very high pressure forms, from theory, [1818] Ice-fifteen Triple point, ice-two, ice-six, ice-fifteen; ~130 K, ~0.8 GPa Triple point, ice-six, ice-eight, ice-fifteen; ~130 K, ~1.5 GPa Ice-thirteen Ice-seven, form at lower pressure, see ref 1428; density (P=0) 1.50 g/cm^3; melting point P=2210+534.2*((T/355)^5.22-1) MPa Triple point, liquid, ice-seven, ice-ten; 1000 K, 47 GPa Critical isochor, density = 322 Kg m-3 Surface of Venus Ice Ih; density (P=0) 0.9167 g/cm^3 melting line of ice VII, Ln(P/2216)=1.73683x(1-355/T)-0.0544606x(1-(T/355)^5)+0.806106x(10^-7)x(1-(T/355)^22); P in MPa, T in Kelvin; opens new site in a pop-up window melting line of ice VI, P=625+707x(((T/273.31)^4.46)-1); P in MPa, T in Kelvin; opens new site in a pop-up window 2nd critical point, ~182 K, ~195 MPa, ~1.1 g cm-3  [580] Surface of Earth (E), Mars (M) and Venus (V); violet line shows mean atmospheric conditions critical point, 647.096 K, 22.064 MPa, 322 Kg m-3 ice Ih-vapor line;  from Murphy and T. Koop [906] Ln(P, Pa)= -5723.265/T +9.550426 -0.00728332T+3.53068LnT; T in Kelvin and >110 K; opens new site in a pop-up window, see also [2064] liquid-vapor line; Ln(P, Pa)=-2836.5744/T^2 -6028.076559/T+19.54263612-0.02737830188T+1.6261698x10^(-5)xT^2+7.0229056x10^(-10)xT^3-1.8680009x10^(-13)xT^4+2.7150305LnT; T in Kelvin; opens new site in a pop-up window Vapor pressure Surface of Mars Ice Ic; density (P=0) 0.92 g/cm^3 Ice-ten Ice-nine; density (P=0) 1.16 g/cm^3 Ice-eight; density (P=0) 1.49 g/cm^3 Ice-two; density (P=0) 1.17 g/cm^3 Phase boundaries [ref 273]; I-II P=176.0+0.918(T-198.15) MPa; II-III P=213+[(T/238)^19.676-1] MPa; II-V P=412.0-7.01(T-239.15) MPa Ice-five; density (P=0) 1.23 g/cm^3; melting point P=346+410*((T/256.15)^8.1-1) MPa; ice V/VI P=625.9+0.06086*(T-273.15)-0.0008571*(T-273.15)^2 MPa Ice-six; density (P=0) 1.31 g/cm^3; melting point P=625+707*((T/273.31)^4.46-1) MPa Ice-seven, form at higher pressure, see ref 1428; density (P=0) 1.50 g/cm^3; melting point P=2210+534.2*((T/355)^5.22-1) MPa Ice Ih; melting point, P=-395.2*((T/273.16)^9.0 -1) MPa Ice XI, ice XI/ice Ih P=(T-72)*67 MPa proposed new solid phase, see ref [1521] supercritical water; pressure > 22.064 MPa and temperature > 647.096 K Triple point, liquid 18.019 cm^3 mol^-1, gas 3.355 m^3 mol^-1, ice Ih 19.66 cm^3 mol^-1; 0.01 °C, 612 Pa Triple point, liquid,15.15 cm^3 mol^-1, ice-five 14.5 cm^3 mol^-1, ice-six 13.8 cm^3 mol^-1; 0.16 °C, 632.4 MPa Triple point, ice-six, ice-seven, ice-eight; ~5 °C, 2.1 GPa Triple point, ice-two, ice-five, ice-six; ~-55 °C, ~620 MPa Ice-three; density (P=0) 1.14 g/cm^3; melting point  P=207+62*((T/251.15)^60-1)MPa; Triple points, (liquid 16.52 cm^3 mol^-1, iceIh 19.4  cm^3 mol^-1, ice-three 15.7 cm^3 mol^-1; -21.985 °C, 209.9 MPa) (liquid 15.90 cm^3 mol^-1, ice-three 15.7 cm^3 mol^-1, ice-five 14.5 cm^3 mol^-1; -16.986 °C, 350.1 MPa) (iceIh, ice-two, ice-three; -34.7 °C, 212.9 MPa) (ice-two, ice-three, ice-five; -24.3 °C, 344.3 MPa); ice 1/III P=186.1-1.335*(T-273.15)-0.1028*(T-273.15)^2 MPa; ice III/V P=344.3-0.275*(T-273.15)-0.01099*(T-273.15)^2 MPa Triple point, liquid 13.36 cm^3 mol^-1, ice-six 13.8 cm^3 mol^-1, ice-seven 11.5 cm^3 mol^-1; 81.85 °C, 2.216 GPa Triple point, ice-seven, ice-eight, ice-ten; 100 K, 62 GPa

 

Phase Diagram, close-up on IceIII Ice-six; density (P=0) 1.31 g/cm^3; melting point P=625+707*((T/273.31)^4.46-1) MPa Ice I>h; density (P=0) 0.9167 g/cm^3 Ice-two; density (P=0) 1.17 g/cm^3 Phase boundaries [ref 273]; I-II P=176.0+0.918(T-198.15) MPa; II-III P=213+99.517*[(T/238.45)^19.676-1] MPa; II-V P=412.0-7.01(T-239.15) MPa Ice-five; density (P=0) 1.23 g/cm^3; melting point P=346+410*((T/256.15)^8.1-1) MPa; ice V/VI P=625.9+0.06086*(T-273.15)-0.0008571*(T-273.15)^2 MPa liquid water, density contours Triple point, liquid,15.15 cm^3 mol^-1, ice-five 14.5 cm^3 mol^-1, ice-six 13.8 cm^3 mol^-1; 0.16 °C, 625.9 MPa Triple point, ice-two, ice-five, ice-six; ~-55 °C, ~620 MPa Ice-three; density (P=0) 1.14 g/cm^3; melting point  P=207+62*((T/251.15)^60-1)MPa; ice 1/III P=198.2-0.42*(T-273.15) MPa; ice III/V P=344.3-0.275*(T-273.15)-0.01099*(T-273.15)^2 MPa Triple point, (liquid 16.52 cm^3 mol^-1, iceIh 19.4  cm^3 mol^-1, ice-three 15.7 cm^3 mol^-1; -22.0 °C, 207.5 MPa) Triple point, (liquid 15.90 cm^3 mol^-1, ice-three 15.7 cm^3 mol^-1, ice-five 14.5 cm^3 mol^-1; -17.0 °C, 346.3 MPa) Triple point, iceIh, ice-two, ice-three; -34.7 °C, 212.9 MPa Triple point, ice-two, ice-three, ice-five; -24.3 °C, 344.3 MPa

The mean surface conditions on Earth, (also atmospheric conditions, Mars and Venus on mousing over Earth) are indicated. The complex central part of the phase diagram is expanded opposite. The critical point and the orange line in the ice-one phase space refer to the low-density (LDA) and high-density (HDA) forms of amorphous water (ice) [16]. Although generally accepted and supported by diverse experimental evidence [754a, 861], the existence of this second, if metastable, critical point is impossible to prove absolutely at the present time and is disputed by some [200, 618, 628, 754b, 1115]. The transition between LDA and HDA is due to the increased entropy and attractive van der Waals contacts in HDA compensating for the reduced strength of its hydrogen bonding.

 

The high-pressure phase line between ice-ten (X) and ice-eleven (XI) [81] is still subject to experimental verification. The melting point line between supercritical water and high pressure ice has been established [691, 2096]. Ice VII possesses higher and lower pressure forms [1428]. A phase diagram of water at higher temperatures, up to 9000 K, has been proposed [1671].

 

Both the critical points are shown as red circles in the phase diagram, above. Beyond the critical point in the liquid-vapor space (towards the top right, above), water is supercritical existing as small but liquid-like hydrogen-bonded clusters dispersed within a gas-like phase [456, 894, 1962], where physical properties, such as gas-like or liquid-like behavior, vary in response to changing density and the normal distinction between gas and liquid has disappeared [1766] . The critical isochor (density 322 kg m-3) is shown as the thin dashed line extension; this may be thought of as dividing more-liquid-like and more-gas-like properties [540].d The properties of supercritical waterc are very different from ambient water. For example, supercritical water is a poor solvent for electrolytes, which tend to form ion pairs. However, it is such an excellent solvent for non-polar molecules, due to its low dielectric constant and poor hydrogen bonding, that many are completely miscible. Viscosity and dielectric both decrease substantially whereas auto-ionization increases substantially. The physical properties of water close to the critical point (near-critical) are particularly strongly affected [677], Extreme density fluctuations around the critical point causes opalescent turbidity. Many properties of cold liquid water change above about 200 MPa (for example, viscosity, self-diffusion, compressibility, Raman spectra and molecular separation), which may be explained by the presence of a high density liquid phase containing interpenetrating hydrogen bonds.  The chemical properties of water are also greatly changed at high temperatures and pressures due to the changes in ionization, solubility, diffusivity and reactivity due to decreasing hydrogen-bonding [1116]. [Back to Top to top of page]

Density changes

As pressure increases, the ice phases become denser. They achieve this by initially bending bonds, forming tighter ring or helical networks, and finally including greater amounts of network inter-penetration. This is particularly evident when comparing ice-five with the metastable ices (ice-four and ice-twelve) that may exist in its phase space.

3-D Pressure-Temperature-volume graph

 

3-D Pressure-Temperature-Density graph, liquid-gas data derived from ref 540

 

2-D Pressure-Temperature-Density graph, liquid-gas data derived from ref 540

 

The liquid-vapor density data for the graphs above, opposite and below were obtained from the IAPWS-95 equations [540].

 

Other phase diagrams for water are presented elsewhere [681]. The density of supercooled (emulsified) water under pressure has recently been determined [1685 ].

 

 

 

 

 

The two graphs below show the variation in the density of liquid, gaseous and supercritical water with temperature and pressure. The density of liquid water increases with increasing pressure and decreases with increasing temperature.

Variation in the density of liquid, gaseous and supercritical water with temperature and pressure

Density of liquid and solid water along the phase line

 

Seen opposite is the density of liquid and solid (that is the ices) water along the liquid-solid phase line. Note that temperature varies along this phase line (as shown dashed). Hexagonal ice is less dense than liquid water whereas the other ices found in equilibrium with water are all denser with phase changes occurring on the approach of the liquid and solid densities.

 

 

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Triple points

Triple points occur where three phase lines join and the three phases may coexist at equilibrium.

 

Thermodynamic data for the triple points of water
Triple points MPa °C ΔH, kJ mol-1

ΔS,

J mol-1 K-1

ΔV cm3 mol-1 Ref. D2O [717]
gas liquid Ih 0.000611657 0.010   536 661 Pa, 3.82 °C [70]
gas->liquid
-44.9 -165 -22050 1833  
gas->Ih
-50.9 -186 -22048
liquid->Ih
-5.98 -22 1.634
gas Ih XI 0 -201.0   717 0 MPa, -197°C
liquid Ih III 209.9 -21.985   537 220 MPa, -18.8°C
liquid->Ih
-4.23 -16.9 2.434 1833  
liquid->III
-3.83 -15.3 -0.839
Ih->III
0.39 1.6 -3.273
Ih II III 212.9 -34.7   537 225 MPa, -31.0°C
Ih->II
-0.75 -3.2 -3.919 1833  
Ih->III
0.17 0.7 -3.532
II->III
0.92 3.8 0.387
II III V 344.3 -24.3       537 347 MPa, -21.5°C
II->III
1.27 5.1 0.261 1833  
II->V
1.20 4.8 -0.721
III->V
-0.07 -0.2 -0.982
II VI XV       1582 ~0.8 GPa, -143°C
liquid III V 350.1 -16.986   537 348 MPa, -14.5°C
liquid->III
-4.61 -18.0 -0.434 1833  
liquid->V
-4.69 -18.3 -1.419
III->V
-0.07 -0.2 -0.985
liquid IV XII ~500-600 ~-6   1300  
II V VI ~620 ~-55   539  
liquid V VI 632.4 0.16   537 629 MPa, 2.4°C
liquid->V
-5.27 -19.3 -0.949 1833  
liquid->VI
-5.29 -19.4 -1.649
V->VI
-0.02 -0.5 -0.700
VI VIII XV       1582 ~1.5 GPa, -143°C
VI VII VIII 2,100 ~5   8 1950 MPa, ~0°C
VI->VII -0.09 -o.3 -1.0 1833  
VI->VIII -1.20 -4.2 -1.0
VII->VIII -1.10 -3.9 0.0
liquid VI VII 2,216 81.85   537 2060 MPa, 78°C
liquid->VI -6.36 -18.0 -0.59 1833  
liquid->VII -6.36 -18.0 -1.64
VI->VII 0.0 0.0 -1.05
VII VIII X 62,000 -173   538  
liquid VII X 43,000 >700   612a  
47,000 ~727   612b
liquid VII Superionic ~40,000 ~1000   1572  
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Footnotes

a Gaseous water is water vapor. In science and engineering, the word 'steam' is also used for water vapor, but usually when above the boiling point of water. As commonly used in the English language, 'steam' also may mean the white cloud of fine liquid water droplets of condensed water vapor that is produced by a boiling kettle, for example. Water is present in the atmosphere in both liquid and gaseous forms. For example, when we breathe out we expire an aerosol of fine (nm - µm+ radius) water droplets plus water vapor. This aerosol has been detected by a water-cluster-detecting breath sensor developed for detecting drunk or drowsy drivers [1801]. [Back]

 

Phase diagram of water, if it behaved like a more typical  material of its molecular weight room temperature and pressure

 

b If water behaved more typically as a low molecular weight material, its phase diagram may have looked rather like this (where 'x' marks ambient conditions on earth). [Back]

c Supercritical water presents a reactive environment [1507]. Neutron diffraction has shown that tetrahedral liquid-like states are observed in supercritical water at above a threshold density, while below this threshold density gas-like water forms small, trigonal, sheet-like configurations [1508]. Under extreme conditions (e.g. 2.38 g cm-3, 3000 K), dense hot water may be extremely reactive [1564]. [Back]

 

d This is outwardly similar to the loci of the CP maximum, and the thermal expansion and compressibility maxima, (the 'Widom' line [1715]). Above the line is a more 'liquid-like' material and below the line is a more 'gas-like' environment. However, the Widom lines for isobaric heat capacity, isochoric heat capacity, isothermal compressibility, isobaric thermal expansion, mass density and the molar internal energy all differ, particularly at higher pressures [1923]. A case has been put for a different line (the `Frenkel line') that separates liquid and gas-like fluids on their dynamic properties above the critical point [1961]. [Back]

 

e On a phase line the Gibbs free energies of the two phases (G1, G2) must be equal and remain equal if conditions change causing movement along the phase line. Thus

Change in Gibbs free energy with temperature at constant pressure plus change in Gibbs free energy with pressure at constant temperature is constant

But, Change in Gibbs free energy with temperature at constant pressure is the entropy where S is the entropy, and Change in Gibbs free energy with pressure  at constant temperature is the volume where V is the volume

Therefore change in pressure with temperature equals the change in entropy with volume which equals the latent heat for the phase change divided by the temperature times the change in volume where L is the latent heat (enthalpy change) for the phase change. This is the Clausius-Clapeyron equation. At a triple point, the Gibbs free energies of the three phases (G1, G2, G3) must be equal and the entropy and enthalpy (latent heat) changes for all three phase changes (1goes to2, 2goes to3, 1goes to3) at that point may be calculated, given the pressure, temperature (change in pressure with temperature) and volume changes. [Back]

 

 

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This page was last updated by Martin Chaplin on 10 April, 2014


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