## Saturday, December 01, 2007

### Phase Diagram of Water

Matter comes in different forms, we learn at school: solid, liquid, and as gas. December days in Canada give us plenty of occasions to experience these different forms of matter - phases, as they are called in physics and chemistry - in the case of water: ice and snow, the both annoying and beautiful appearances of solid water, the liquid form in rain and fog, and if the Sun succeeds to disperse the fog, tiny water droplets have evaporated, and the water has been transformed into invisible gas.

Ice melts at a temperature of 0°C (or 273.15 Kelvin), and water boils at 100°C (or 373.15 Kelvin). However, to be precise, these melting and boiling temperatures are not fixed - they depend on the ambient pressure. On top of a mountain, say the Puy de Dôme, air pressure is lower than in the lowlands, and as consequence, water boils at temperatures below 100°C.

To get a better overview how the occurrence of the different phases of water - solid ice, liquid water, gaseous vapour - depends on temperature and pressure, it's a good idea to plot in a diagram the transition lines between the different phases as a function of these two parameters. Such a diagram is called a phase diagram. And a simplified version of the phase diagram of water looks like this:

The x-axis of the diagram shows the temperature T in units of Kelvin (K). Keep in mind that 0°C = 273.15 K and 100°C = 373.15 K - both temperatures are marked by the grey vertical lines. The y-axis shows the pressure p in units of Megapascal (MPa), where 0.1 MPa = 1000 hPa = 1000 mbar and the standard atmospheric pressure is 1013 mbar. Since pressure covers a huge range of values from the very small to the very large, a convenient way to represent this is the usage of a logarithmic scale. Thus, the phase diagram manages to represent pressure from 1/100.000 of ambient pressure to 1 million times ambient pressure. Ambient pressure is marked by the horizontal grey line.

The blue line in the diagram is the melting line - it separates ice from liquid water - and the light-blue line the boiling line, which divides liquid and gaseous water. The green line is the so-called sublimation line, across which ice transforms directly to the gaseous states, without the intermediate step of liquid water. All three lines meet at one point (marked by the black dot) which is called the triple point - at this value of temperature and pressure, all three forms of water can coexist. At sufficiently high pressure, water solidifies even at temperatures well above room temperature: these transitions to different sorts of ice (distinct by the respective crystal structures) are shown as the red and orange line. Trying to understand these different phases of ice is a topic still under investigation, both by experiment and by theory.

One feature of the diagram might seem strange at first sight: The boiling line separating liquid and gaseous water ends at one point. This is a very generic feature of all liquid matter: At high enough pressure, the distinction between liquid and gas gets lost - essentially, the difference in density between gas and liquid becomes zero, and the latent heat of condensation/evaporation vanishes. The end point of the boiling line, marked by the grey dot, is called the critical point. If temperature and pressure can be chosen such that the fluid is very close to the critical point, it will develop bubbles of gas containing small droplets of liquid containing small bubbles of gas... and as a result of bubbles and droplets of many different sizes, covering the range of wavelengths of visible light, the system becomes opaque. This quite spectacular effect is called critical opalescence.

But of course, we can also recover our mundane everyday experience with water in the diagram: If we increase temperature at constant ambient pressure, following the horizontal grey line, we cross the blue melting line at 0°C, and the light-blue boiling line at 100°C - that's the melting of ice and the boiling of water as we know it. And we see that if ambient pressure is reduced, for example during stormy weather or on top of a mountain, the crossing of the horizontal line and the boiling line shifts to lower temperature: Water will boil at temperatures below 100°C. At a height of 2000 m above sea level, for example, water boils at about 94°C - things to keep in mind if boiling an egg on a mountain.

If you look closely, you can note that the blue melting line is slightly inclined, meaning that with increasing pressure, the melting temperature drops slightly. This effect is often invoked as an explanation for the low friction of skates on ice: The pressure applied by the weight of the skater reduces the melting temperature of ice, causing a thin film of liquid water, on which the blade of the skate glides nearly without friction, or so goes the story. This, however, is not the whole truth: the small, pressure-induced reduction of the melting temperature is not sufficient to produce this effect. While it's correct that the reduction of friction is caused by a slippery film of water on the surface of the ice, this film is created by complicated mechanisms whose details are still under debate.

So, an elementary plot such as the phase diagram of water can still hide some surprises and riddles for us.

Phase diagram data via www.chemicalogic.com. Source for the sublimation and melting lines: W. Wagner, A. Saul, A. Pruß: International Equations for the Pressure along the Melting and along the Sublimation Curve for Ordinary Water Substance, J. Phys. Chem. Ref. Data 23, No 3 (1994) 515 (PDF file from NIST). Source for the saturation line: IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam (IAPWS-IF97).

You can find much more about the phase diagram of water - and about the properties of water in general - at Water Structure and Science by Martin Chaplin.

The physics behind the slickness of ice has been discussed by Robert Rosenberg in Why Is Ice Slippery?, Physics Today, December 2005, pages 50-55 (doi 10.1063/1.2169444, subscription required).

This post is part of our 2007 advent calendar A Plottl A Day.

stevelinton said...

Does anyone know
what is going on at high pressure? Two effects are notable:

1. The melting point drops significantly between about 100 and 1000 atmospheres and then rises sharply

2. The colour of the line changes several times. What does this signify?

stefan said...

Hi Steve,

the second question is the easy one: The different colours represent transitions to different kinds of ice, with different crystal structure. They are called hexagonal ice-one (Ih), ice-three (III), ice-five (V), ice-six (VI) and ice-seven (VII)...

You can find much more detail at Martin Chaplin's page on the phase diagram of water - there are also more detailed graphs for the different phases of ice, and details about their thermodynamic and crystal properties. To me, it seems intuitively clear that if you compress liquid water ever more, at one point you may force the molecules into a crystal structure, even if the thermal motion remains high.

However, I do not know if the endpoint of this line in the plot marks just the end of our current knowledge and available data, or if it is another kind of critical point.

Moreover, I have no explanation for the kink and the minimal temperature for liquid water at about 250 K and 200 MPa you are asking about.

Maybe someone else has an intuitive explanation? Is this something generic, or is it another anomaly of water, similar to the minimal density at 4°C?

Best, Stefan

Arun said...

After water, probably the next most important one for humans is the phase diagram of iron + carbon.

e.g.,
http://www.msm.cam.ac.uk/phase-trans/images/FeC.gif

This is to encourage you to expound on that hopefully in terms of what is happening at an atomic level. :)

Arun said...

http://www.uwgb.edu/dutchs/PETROLGY/Ice%20Structure.HTM

QUASAR9 said...

Hi Stefan, an interesting and informative post

"The pressure applied by the weight of the skater reduces the melting temperature of ice, causing a thin film of liquid water, on which the blade of the skate glides nearly without friction, - or so goes the story.
This, however, is not the whole truth: the small, pressure-induced reduction of the melting temperature is not sufficient to produce this effect. While it's correct that the reduction of friction is caused by a slippery film of water on the surface of the ice, this film is created by complicated mechanisms whose details are still "under debate".

QUASAR9 said...

And from the properties of water,
to water repellent properties

Klaus said...

Sorry Bee and Stefan for popping in with off topic:

Nonetheless I think this is an important contribution recently added.

Best

Klaus

Klaus said...

Hi again,

Diesmal auf dem Punkt:

http://www.br-online.de/cgi-bin/ravi?v=alpha/centauri/v/&g2=1&f=021027.rm

Best Klaus

stefan said...

Dear Arun,

thank you for the link to the page on Ice Structure. I hadn't seen it before - they have there really nice illustrations of the crystallography of ice!

As for the phase diagram of Iron Carbide, true, steel is some important stuff ;-). What I am not sure about - even though the diagram looks pretty complicated, it may be easier to calculate than that of water? If you look at the x-axis, which is here not pressure, but the carbon content of the iron, it is quite small, so the iron remains metallic with impurities of carbon (solid solution, as they call it), and all kind of calculating techniques for pure metals, band structure etc, may still work.

But true, in general, as soon as you look at the phase diagrams of mixtures or alloys, all kinds of complications can set in, and if your material is magnetic, besides the different crystallographies, you will end up with different magnetic phases as well... the material scientist's paradise ;-)

Best, Stefan

stefan said...

Dear Klaus,

thank you for the link to the Harald Lesch show about water. I wonder, is there a similar show in English? I believe Alpha Centauri is quite unique!

Best, Stefan

stefan said...

Hi Quasar,

ah, superhydrophobic materials ... sounds dangerous ;-).. A few years ago, a big manufacturer of bathroom ceramics in my native Saarland experimented with water-repellent nano-coatings for their stuff, I don't know hwat has happened to that.

Best, Stefan

One atom of sour stuff and two atoms of water-stuff. Deutsch ist doch eine schÃ¶ne Sprache.

changcho said...

Thanks, very interesting - the phase diagram of water (a 'simple' liquid) still contains a few surprises and curious behavior. This issue of 'critical opalescence', showing the same aspect at all different scales sounds like a fractal phenomena to me.

Manchester_87 said...

hi

I was wondering if someone can explain to me how is water phase diagram specifically the solid-liquid interphase related to the density of water? how can u relate the negative slope to the idea of water having low density at low temperature?

Thanks