Why Ice Floats

Drop an ice cube into a glass of water and it bobs back up and floats, with a small cap above the surface. It's so familiar that it hardly seems worth a second look, but it's strange. Freeze most liquids and the solid sinks in its own melt: a lump of solid wax drops to the bottom of a pot of melted wax, and most metals behave the same way. Water belongs to a short list of exceptionsThe others include silicon, germanium, gallium, and bismuth. All of them have open, loosely packed crystals; silicon and germanium even share ice's arrangement of four close neighbors around each atom., and that one exception shapes the climate, the seasons in every lake, and life in cold water.

Before we look inside the ice, a question about the floating itself.

Here is a block of ice 30 cm on a side in a tank. Give it a density of , drag it under and let go, or switch the tank to seawater, and watch how much of the block ends up below the surface:

A block lighter than the liquid settles with exactly the fraction of its height under the surface that its density is of the liquid's. Ice at 0.917 g/cm³ in fresh water floats 91.7% under. Water pushes up on anything in it with a force equal to the weight of the water it pushes aside, so a floating block sinks only until the water it has displaced weighs as much as the whole block. In seawater, at 1.025 g/cm³, the same cube floats 89.5% under, which is why icebergs show about a tenth of themselvesReal icebergs carry trapped air bubbles, so glacier ice is often a little lighter than pure ice, and a berg can show a little more than a tenth of itself.. Push the density past the liquid's and no amount of displaced water is heavy enough: the block sinks.

So ice is about 8% lighter than the same volume of liquid water. Put the other way round, water expands by about 9% when it freezes, which is why frozen pipes burst. Ice and liquid water are made of exactly the same molecules, so in ice each molecule must take up more room. To see why, we have to look at one.

A bent molecule

A water molecule is one oxygen atom bonded to two hydrogen atoms. Each hydrogen sits 0.096 nanometers (nm) from the oxygen, a bit under a tenth of a billionth of a meter, and the two bonds meet at an angle of 104.5°. Oxygen pulls on the electrons it shares with each hydrogen much harder than hydrogen does, so those electrons spend more of their time near the oxygen. That leaves the oxygen with a slight negative charge, written δ− ("delta minus"), and each hydrogen with a slight positive charge, δ+.

Drag to turn the molecule, and change the angle between its two bonds from water's 104.5° to a straight 180°. The purple arrow shows how lopsided the molecule's charge is:

At water's real angle the arrow is long: the positive charge sits on the hydrogen side and the negative charge on the far side of the oxygen, so the molecule has two distinct ends. A molecule like this is called polar, and the arrow is its dipole; for water it is 1.85 debye (D), the unit chemists use for it. Straighten the molecule and the arrow vanishes. The two bonds pull in opposite directions and cancel, which is what happens in carbon dioxide, a straight molecule with no ends at all.

The bend comes from the oxygen's other electrons. Besides the two pairs it shares with the hydrogens, the oxygen keeps two pairs to itself, called lone pairs (point at the words to see them). The four pairs push one another as far apart as they can, toward the corners of a tetrahedron, a pyramid with four triangular faces. The lone pairs push a little harder than the bonds do, squeezing the H–O–H angle from the tetrahedron's 109.5° down to 104.5°.

Hydrogen bonds

Opposite charges attract, so the positive hydrogen of one water molecule is drawn to the negative oxygen of another. Drag the right-hand molecule around the left one, turn it with the slider, and watch the energy bar under the molecules:

The pull is strongest, about 27 kilojoules per mole (kJ/mol) in the charge model behind this figure, when one molecule points a hydrogen straight at the other's oxygen. The oxygens are then about 0.28 nm apart and the hydrogen about 0.18 nm from its partner. Turn the molecule so its own hydrogens face the left molecule's hydrogen and the pull becomes a push of more than 70 kJ/mol. This attraction, strong only when things line up, is a hydrogen bond, drawn as a green dashed line. I've kept both molecules flat on the page; in three dimensions the second molecule would also tilt so that one of its lone pairs faced the hydrogen.

How strongly does the bond depend on lining up? Here the right-hand molecule is moved around the left one, keeping its oxygen facing it. Swing it off the line of the left molecule's hydrogen, and slide the distance between the oxygens:

In line, the dip is about 25 kJ/mol deep. Swing 30° off and the best the pair can do is less than 10; by 45° there's almost nothing left, and further round the pair repels at every distance. That's what makes the hydrogen bond special. An ordinary attraction between molecules pulls the same way in every direction, so molecules pack together like marbles. A hydrogen bond only holds when the hydrogen points at the oxygen, so molecules that form them have to take up particular arrangements.

Breaking a hydrogen bond in real water takes roughly 20 kJ/mol, about a twentieth of the 460 kJ/mol it takes to pull a hydrogen off its own oxygen. That's strong enough to give water an unusually high boiling point for such a small moleculeHydrogen sulfide, H₂S, is a heavier molecule of the same shape that makes only weak hydrogen bonds. It boils at −60 °C., and weak enough that in liquid water the bonds break and re-form all the time, each lasting a few trillionths of a second.

Four bonds each

Each water molecule can make four hydrogen bonds. It lends its two hydrogens to two neighbors, and each of its two lone pairs takes a hydrogen from another. Because those four directions point to the corners of a tetrahedron, the four neighbors have to sit at those corners too. When water freezes, every molecule ends up bonded to exactly four others in this way.

Grow a piece of ice outward from one molecule, of neighbors at a time, and drag to look at it from different sides:

The first layer is four neighbors at the corners of a tetrahedron, joined here by dashed lines, each 0.276 nm from the first molecule. Two of its hydrogen bonds run from the first molecule's own hydrogens; the other two come in from its neighbors' hydrogens to its lone pairs. The second layer adds twelve molecules, each again holding its own neighbors at tetrahedral angles. By the third, the bonds close into rings of six molecules, puckered into the shape chemists call a chair, such as the one outlined in orange. Keep going and the rings stack into a regular crystal, the hexagonal form called ice I_h ("ice one h"). Nearly all the ice on Earth, from snowflakes to glaciers, is this kind.

In the crystal each hydrogen lies almost exactly on the line between two oxygens, about 0.1 nm from its own and 0.18 nm from the next; I've drawn it exactly on the line. Every link between two oxygens carries exactly one hydrogen, and every oxygen keeps exactly two. These are the ice rules. Which two of its four links a molecule uses is random and changes from one molecule to the next; this crystal shows one arrangement that follows the rules.

An open crystal

Here is the same crystal as a block of 96 molecules, about 1.4 nm across. Drag to turn it, then press Look down the channels:

Seen along that direction, the molecules line up in a honeycomb, with open hexagonal channels running straight through the crystal. Switch to full-size atoms, which draws each atom out to the distance where it starts to repel other atoms instead of as a small ball, and you can still see through the channels.

The openness comes from the four bonds. In ice, every molecule has four neighbors and no more. Oranges stacked in a pyramid at a market each touch twelve. Four neighbors at tetrahedral angles is a roomy way to pack, and the crystal's geometry fixes exactly how roomy. The pattern repeats in identical boxes called unit cells, each a squashed hexagonal prism holding the equivalent of four molecules. Change its sides, \brass{a} and \purple{c}, and watch the density:

The real cell measures \brass{a} = 0.452 nm along its base and \purple{c} = 0.737 nm tall, a volume of 0.1305 nm³ for four molecules. Weigh that out and you get 0.917 g/cm³, the density of ice we started with. Shrink every side by 5% and the density rises to 1.07, denser than water. A small change in how the molecules sit makes a big change in density, because density goes as the cube of the spacing.

Liquid water at 0 °C packs 0.9998 g into each cubic centimeter with the very same molecules. Melting somehow lets them pack closer.

Melting fills the gaps

When ice melts, its network doesn't vanish so much as loosen. Bonds stretch, bend, and swap partners constantly, and that freedom lets molecules slip into the space the crystal left open. A molecule in liquid water has, on average, a bit more than four neighbors close by, where in ice it had exactly four. More neighbors in the same space means a higher density.

Simulating real water in three dimensions is too slow for a page like this, but there's a well-known flat version that shows the same thing. Each molecule is a disc with three arms 120° apart, the flat-world version of water's four tetrahedral directions, and two molecules form a hydrogen bond when an arm of each points at the otherIts shape earned it the nickname "the Mercedes-Benz model".. Its ice is a honeycomb. The figure runs 72 of these molecules at a steady pressure, so their box is free to grow and shrink. Raise the temperature past about 0.2, in the model's own units, and compare the box with the dashed outline of the ice it started as:

Once the honeycomb breaks up, the box shrinks to around 80% of the ice's area: the same molecules in much less space. With only 72 molecules the size flickers from moment to moment, so the plot shows a running average. Bonds are now bent or broken, and molecules sit where the hexagonal holes used to be. Heat it further and the box starts to grow again, the ordinary expansion of a liquid as it warms. Cool it back down and it doesn't refreeze, for a reason we'll meet in the next section; the button rebuilds the crystal instead.

The flat model exaggerates. Its liquid is about 25% denser than its ice, against 9% for real water, and it breaks many more bonds when it melts. The reason is the same, though: the open, four-armed network of the solid wastes space that a looser liquid can use.

The price of melting

If melting only loosens the network, it should still cost something: every bond that bends or breaks needs energy. Here is 1 kg of ice from a freezer at −20 °C on a 2 kW stove. Turn the stove on, or drag the heat added, and watch the thermometer:

The temperature climbs, then stops dead at 0 °C. For as long as there's ice in the pot, every bit of heat goes into melting it, and the thermometer doesn't move. Melting the kilogram takes 334 kJ, the same energy that would warm the liquid by 80 °C. Then the water warms steadily to 100 °C and stops again, for much longer: boiling it away takes 2,257 kJ, nearly seven times the cost of melting. Heat that goes into a change of state without changing the temperature is called latent heat.

The two plateaus measure the hydrogen bonds. Per molecule, melting costs 6.0 kJ/mol and boiling 40.7 kJ/mol. Turning ice straight into vapor at 0 °C costs about 51 kJ/mol, a fair estimate of everything that holds a molecule in the crystal, mostly its share of two hydrogen bonds. So melting pays for only about an eighth of the bonding: most bonds survive into the liquid, bent and constantly swapping partners, exactly as the flat model showed. Boiling has to break the rest.

Latent heat also explains why the flat model wouldn't refreeze. Freezing has to start somewhere: a few molecules have to fall into the crystal's pattern at once, and a tiny crystal is fragile, because the molecules on its surface have broken bonds. Until a seed big enough to survive appears, water can stay liquid below 0 °C. It is then called supercooled. Here is a bottle of very clean water in a freezer. Let it cool, then tap it:

The bottle sails past 0 °C as a liquid. Tap it while it's at −8 °C and ice needles shoot through it in a second, and the temperature jumps straight back up to 0 °C. The jump is latent heat at work: freezing releases the heat that melting absorbed, and only about 10% of the water needs to freeze to bring all of it back to 0 °C. After that the rest freezes slowly at 0 °C, as fast as the freezer can carry the heat away. Real bottles often start freezing on their own before anyone taps them, set off by a speck of dust or a scratch; this one waits for you. In tiny, very clean droplets, such as the ones in high clouds, water stays liquid down to almost −40 °C.

Densest at 4 °C

The competition between open and packed doesn't end once the ice is gone. Cold liquid water still holds fleeting patches of open, ice-like bonding, and they're more common the colder the water is. Warming breaks them up, which makes the water denser, while warming also shakes the molecules apart, which makes it less dense. Move the temperature through 0 °C, then zoom in on the liquid:

At 0 °C the density drops from 0.9998 g/cm³ for water to 0.917 for ice. That step is the 9% we started with. Zoomed in, the liquid's curve has a peak: water is densest at 3.98 °C, at 0.99997 g/cm³. Below that the open patches win and the water expands as it cools; above it, ordinary expansion wins. The whole rise from 0 °C to 4 °C is only 0.013%, invisible without the zoom, but it decides which water sinks.

Lakes freeze from the top

Put it all together in a lake. Before you run it, a prediction:

Here is that lake at the end of autumn, at 10 °C from top to bottom, under air at . Time runs at six days per second. Watch the temperature profile on the right as the days go by:

First the surface cools, and as it gets denser it sinks and is replaced by warmer water from below. Within about ten days the whole lake has turned over to 4 °C. After that, cooling the surface makes it lighter, so the coldest water stays on top, quickly reaches 0 °C, and freezes. The ice floats, and it covers the lake like a lid: from then on every bit of heat the lake loses has to conduct up through the ice, and the thicker the ice gets, the more slowly it grows. After two months it's about 60 cm thick, and the water at the bottom is still close to 4 °C. That's where fish spend the winter.

Now turn on If ice sank, which swaps in a liquid that is densest when coldest, as most liquids are, and an ice that sinks. The whole lake cools to 0 °C. Then each new layer of ice drops to the bottom and leaves fresh water exposed to the cold air, so nothing slows the freezing down, and the lake fills with ice from the bottom up until it's frozen solid, in about five months at −10 °C.

I've left out the wind, which stirs the surface and lets real lakes cool somewhat below 4 °C before they freeze over, and the heat stored in the lake bed. Neither changes the order of events.

Why the sea is different

Salt changes both numbers that the lake depended on. Dissolved salt gets in the way of the crystal forming, so seawater freezes below 0 °C. And it weakens the open, ice-like patches in the cold liquid, so the temperature of greatest density drops too, and faster. Slide the salinity, the grams of salt in each kilogram of water, from a lake to the open ocean:

In fresh water the densest temperature, 3.98 °C, sits well above the freezing point, and a lake behaves as we saw. Add salt and the two lines close in. At 24.7 g/kg they cross, at about −1.3 °C, and beyond that seawater simply gets denser all the way down to its freezing point. The open ocean has about 35 g/kg. There's no 4 °C layer to stop the overturning, so cooling surface water keeps sinking and is replaced from below until a whole deep layer is at about −1.9 °C, and only then does ice form. That's one reason the polar seas freeze later and more slowly than lakes at the same latitudeThe freezing point here is from the standard seawater formulas; the line of greatest density is a straight-line approximation through its two well-known points, 3.98 °C for fresh water and the crossing at 24.7 g/kg..

When seawater does freeze, the crystal has no room for salt, which can't fit into the hexagonal lattice. So new sea ice holds much less salt than the water it froze from, and the rest is pushed out into pockets of very salty liquid, called brine, trapped between the ice crystals. The colder the ice, the less brine survives and the saltier it is. While there's enough brine, the pockets join into channels that let it drain downward through the ice; this happens above about 5% brine by volume, which for typical sea ice means warmer than about −5 °C, a rule of thumb known as the "rule of fives". The drained brine is dense and cold, and it sinks, which helps drive the slow deep currents of the world's oceans.

A map of water

Everything so far happened at the pressure of the air around us. Squeeze water hard enough, or pump the air away, and it behaves differently: it can boil at room temperature, or stay solid at 100 °C. A map of which form water takes at each temperature and pressure is called a phase diagram. Pressure on this one runs over nine powers of ten, from a ten-thousandth of the air's pressure up to the pressures deep inside planets. Drag the point, or jump to a kitchen on Mount Everest:

The point where all three meet, the triple point, is at 0.01 °C and only 612 pascals, about 0.6% of the air's pressure. Below that pressure there's no liquid at all: on Mars, where the air's pressure is close to 612 pascals, liquid water can barely exist, and ice warmed by the Sun mostly turns straight into vapor. On Everest the air is a third as thick as at sea level, and water boils at about 71 °C, which is why cooking there is slow. At the other end, the line between liquid and vapor stops at the critical point, 374 °C and about 218 times the air's pressure; past it the liquid and the gas can no longer be told apart.

Squeeze ice hard enough and the open crystal can't survive. Above about 200 million pascals (MPa), two thousand times the air's pressure, the molecules rearrange into denser crystals, numbered by the order they were discovered: ice III, V, VI, VII and more, each still holding four hydrogen bonds per molecule but packed more tightly, and each sinking in water. At a few billion pascals, pressures found deep inside the largest icy moons and some planets, ice VII stays solid at 100 °C and above.

Now look closely where ice I_h meets the liquid. Every other boundary on the map leans to the right as pressure rises: squeeze something and it takes a higher temperature to melt or boil it. The line between ordinary ice and water leans the other way. Squeezing ice lowers its melting point, because pressure favors whichever form takes less room, and for ordinary ice that's the liquid. Put a block of ice at under a piston and raise the pressure:

At the air's pressure ice melts at 0 °C. Each extra 13.5 MPa, about 135 times the air's pressure, lowers its melting point by one degree. So ice at −5.5 °C, about the temperature of a skating rink, only melts above roughly 65 MPa: 650 kg pressing on a single square centimeter. Above about 200 MPa, at −22 °C, ordinary ice gives way to ice III and the line turns back to the right.

Why ice is slippery

For a century, textbooks explained skating with exactly this: the blade's pressure melts a film of water under it, and the skater glides on the film. It's a tidy story, and the numbers don't support it. Here is a skater on a rink. Change their weight, how much of the blade touches the ice, and how cold the ice is:

A 70 kg skater standing flat on a blade presses on the ice with about 1 MPa, which lowers its melting point by less than a tenth of a degree. Rock onto a short stretch of the blade and it's about 5 MPa. Even balanced on one sharp edge, with only a quarter of a square centimeter touching, the pressure is about 27 MPa and the melting point drops to about −2 °C. That's not enough on a rink at −5.5 °C, and nowhere near enough on a pond at −20 °C, where skating is just as easy. Pressure melting can only be the main story within a degree or two of 0 °C.

So what does make ice slippery? The current understanding has two parts, and how they share the work is still being studied. First, friction: a moving blade heats the ice where it slides, and at skating speeds that heat can melt a very thin film of water, so the faster you go, the more it helps. Second, the surface of ice is unusual even when nothing is moving. The molecules in the top layer have bonds on only one side, and they hold on more loosely than the molecules inside. Below 0 °C, this outermost layer is more mobile than the crystal below it, and experiments and simulations suggest these loosely held molecules can roll and slide under a load. Both effects come from the same hydrogen bonds: strong enough to build a crystal, easy enough to disturb at its edges.

How snowflakes grow

A snowflake is a single crystal of ice, grown straight from water vapor as it falls through a cloud. Its six-fold symmetry comes straight from the honeycomb we looked down earlier: the crystal's flat top and bottom, called the basal faces, are hexagons, and its six sides are the prism faces. Which faces grow faster depends, surprisingly sensitively, on the temperature. Slide the temperature of the cloud:

Near −2 °C crystals grow as thin hexagonal plates. Around −6 °C they grow as long columns and needles instead. Below −10 °C they flip back to plates, and by −22 °C they're columns again. The Japanese physicist Ukichiro Nakaya mapped this in the 1930s by growing snow crystals on a rabbit hair in a cold chamber, and the switching still isn't fully explained; it seems to come from how easily new layers of molecules can start on each kind of face, which changes with temperature in different ways for the two faces.

Humidity decides the rest. In dry air a crystal grows slowly into a simple prism. In air loaded with vapor, growth is fast, and anything sticking out reaches further into the vapor and grows faster still, so corners sprout arms and arms sprout branches. Move the point across the morphology diagram:

The classic six-armed star, the stellar dendrite, grows only in a narrow window: moist air between about −12 and −17 °C. Long thin needles need moist air near −5 °C. Much snow falls as small plates, columns, and irregular bits; the famous stars need just the right conditions.

Why do arms grow at all, instead of the crystal staying a hexagon? Because the vapor has to travel to the crystal, and the corners get to it first. Here is a simple model of that, a grid of hexagonal cells where each cell holds some water vapor. Vapor spreads between neighboring cells; cells touching the crystal collect a little extra; any cell that reaches a threshold freezes and joins the crystal. The blue shading is the vapor, and you can watch the crystal drain it from the air around it. Try a star, a fern, or a plate:

The model knows nothing about real snow beyond two rules: vapor spreads out, and ice collects it. Yet the six-fold grid and those two rules are enough to grow plates, stars with side branches, and fern-like arms, depending only on how much vapor the air holds and how fast the crystal takes it up. Real snowflakes add the face-by-face growth rates of the last two figures, and the changing conditions as a flake falls through a cloud. Every arm of one crystal sees the same conditions at the same moment, which is why the six arms of a real snowflake often match each other so closely, while no two snowflakes, which take different paths through the cloud, quite match.

All from one bend

Two hydrogens and two lone pairs make four directions to bond in. Four bonds at tetrahedral angles make an open crystal, and an open crystal floats on its own melt, melts when squeezed, and sets the six-fold pattern of every snowflake. The same bonds, mostly surviving into the liquid, make melting and boiling expensive and leave water densest at 4 °C, so in winter the ice ends up on top of the lake, insulating the water underneath, while the sea, with its salt, plays by slightly different rules. Few molecules this small do so much, and almost all of it comes from the shape of one molecule and the way it holds on to its neighbors.

References

1. W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein, “Comparison of simple potential functions for simulating liquid water,” Journal of Chemical Physics 79 (1983), 926–935. The three-charge model used in the hydrogen-bond figures.
2. J. D. Bernal and R. H. Fowler, “A theory of water and ionic solution, with particular reference to hydrogen and hydroxyl ions,” Journal of Chemical Physics 1 (1933), 515–548. The ice rules.
3. L. Pauling, “The structure and entropy of ice and of other crystals with some randomness of atomic arrangement,” Journal of the American Chemical Society 57 (1935), 2680–2684.
4. K. A. T. Silverstein, A. D. J. Haymet, and K. A. Dill, “A simple model of water and the hydrophobic effect,” Journal of the American Chemical Society 120 (1998), 3166–3175. The flat three-armed model in the melting figure.
5. G. S. Kell, “Density, thermal expansivity, and compressibility of liquid water from 0° to 150 °C,” Journal of Chemical and Engineering Data 20 (1975), 97–105. The density curve.
6. N. P. Fofonoff and R. C. Millard, Algorithms for Computation of Fundamental Properties of Seawater, UNESCO Technical Papers in Marine Science 44 (1983). The freezing point of seawater.
7. K. M. Golden, S. F. Ackley, and V. I. Lytle, “The percolation phase transition in sea ice,” Science 282 (1998), 2238–2241. The rule of fives for brine drainage.
8. W. Wagner, T. Riethmann, R. Feistel, and A. H. Harvey, “New equations for the sublimation pressure and melting pressure of H₂O ice Ih,” Journal of Physical and Chemical Reference Data 40 (2011), 043103; and W. Wagner and A. Pruss, “International equations for the saturation properties of ordinary water substance,” Journal of Physical and Chemical Reference Data 22 (1993), 783–787. The phase boundaries in the map.
9. R. Rosenberg, “Why is ice slippery?,” Physics Today 58, no. 12 (2005), 50–55.
10. B. Weber and others, “Molecular insight into the slipperiness of ice,” Journal of Physical Chemistry Letters 9 (2018), 2838–2842.
11. U. Nakaya, Snow Crystals: Natural and Artificial (Harvard University Press, 1954).
12. K. G. Libbrecht, “The physics of snow crystals,” Reports on Progress in Physics 68 (2005), 855–895.
13. C. A. Reiter, “A local cellular model for snow crystal growth,” Chaos, Solitons & Fractals 23 (2005), 1111–1119. The growth model in the last figure.

Further reading

• Ice Ih and Phases of ice on Wikipedia, for the crystal structure and the high-pressure forms.
• Properties of water on Wikipedia, for the density maximum and the other ways water departs from ordinary liquids.
• K. G. Libbrecht, Snow Crystals: A Case Study in Spontaneous Structure Formation (Princeton University Press, 2022), for the full story of how snowflakes grow.