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Why You Can't Have a Snowball Fight on Mars  

Mercury, January/February 1998 Table of Contents

Scott A. Sandford
NASA Ames Research Center

Earth is a very special planet indeed. It is the only place in the solar system where you can pummel your little brother (or, more likely, get pummeled by him) with snowballs.

I made the Walker "kneel down" a few times - that is, lowered the bubble - to warm up the hydraulic fluids. It's hard to remember that the legs of the Cat are working at temperatures a hundred degrees below freezing, when you're sitting in a toasty cabin, but it can be dangerous to forget. While I was doing this I looked out at the life dome rising in the distance. I could pick out people sledding down a hill and further away a crowd in a snowball fight. A scramble like that is more fun on Ganymede than on Earth; somebody a hundred yards away can pick you off with an accurate shot, because low gravity extends the range of your throwing arm.

When I first read the 1984 book Jupiter Project by Gregory Benford, one of my favorite science-fiction authors, I liked the image of the future it presented - people taking their humanity with them to space along with their technology. Alas, this feeling only lasted a moment, for I quickly realized that a snowball fight is not possible on Ganymede. Nor, it turns out, is any kind of snowball fight possible on any planet or moon in our solar system, with the sole exception of snowball fights using ordinary H2O snow on Earth. The spoilsports are the physics of snowball manufacture and certain peculiarities of the H2O molecule.

Cooking Ice

The trouble stems from how water and other materials behave when squeezed, heated, or cooled. Figure 1, a "phase diagram," summarizes this behavior for H2O and carbon dioxide (CO2). On a phase diagram, the horizontal axis represents temperature, with higher temperatures to the right. The vertical axis represents pressure, with higher pressures at the top. The different areas of the plot represent conditions under which the material is gaseous, liquid, or solid. The thick solid lines represent the transitions between these phases.

For example, suppose you put an ice cube in a frying pan and turn on the burner. First the ice cube melts and then the resulting puddle boils away. On the phase diagrams in Figure 1, this is represented by starting at point 'A' and moving horizontally to the right (higher temperature, same pressure) to 'B' and then 'C'.

The behavior differs somewhat if the ice cube starts at a low enough pressure. In this case, raising the temperature does not cause it to melt, but instead evaporate directly, or "sublimate." For water ice to sublimate, the pressure must be lower than 0.6 percent of standard atmospheric pressure; for CO2, lower than 5.1 atmospheres. Therefore, dry ice (CO2 ice) doesn't melt when it warms up at atmospheric pressure, but instead gives off gas directly. On the phase diagrams in Figure 1, ice sublimates if it starts at point 'D' and warms up at constant pressure to 'E' and 'F'.

Incidentally, the process of sublimation is what makes your ice cubes shrink with time in your frost-free freezer. Although the pressure is much higher than 0.006 atmospheres, the dehumidifier in a frost-free freezer removes water vapor from the air - preventing the ice and vapor from reaching the equilibrium implied in the phase diagram.

How about changes in pressure? Suppose we start with gas and squeeze it while holding the temperature constant (that is, move vertically upward on the plot). If the temperature is low enough, the gas will turn into a solid ('E' to 'A'); at higher temperatures, to a liquid ('F' to 'B').

You have probably heard the warning against removing the cap from your car radiator when the engine overheats. This is because your radiator contains liquid water that is both very hot and under pressure. Removing the cap allows the pressure in the radiator to drop precipitously (from, say, 'B' down to 'F'). As a result, the contents of your radiator try to change instantly to steam - your radiator boils over and you are in danger of being badly scalded. People who work with high-pressure air lines have to deal with these pressure effects, too. If humid air seeps into high pressure lines, the H2O vapor in the air can condense into liquid within the lines. This is one reason high-pressure lines often have problems with corrosion.

The Phase Diagrams of H2O and CO2

Figure 1. The low-pressure phase diagrams of water (H2O, left) and carbon dioxide (CO2, right). The different areas of these diagrams represent conditions under which these substances are gaseous, liquid, or solid. At points 'A' and 'D', they are solid; at 'C', 'E', and 'F, gaseous; at 'B', liquid. The thick solid lines represent transitions between phases. Along these lines, two phases can exist together. At the triple point, where the lines intersect, the solid, liquid, and gas can all co-exist. For H2O, the triple point falls at a temperature of 0.0099 degrees Celsius and a pressure of about 0.006 times the pressure of Earth's atmosphere at sea level. For CO2, it falls at -56.6 degrees and 5.1 atmospheres. The heavy dashed lines represent sequences of heating (horizontal) or squeezing (vertical):

1. Start with the ices at 'A'. Keeping the pressure constant, warm them until they reach their solid-liquid transitions. At this point the ices melt. Further heating initially results in warmer liquids ('B'). If you warm the liquids enough, they reach their liquid-gas transitions and evaporate. Further heating results in warmer gases ('C').

2. Start with the ices at 'D'. Raising their temperature does not cause them to run into their solid-liquid transitions, but rather into their solid-gas transitions. The ices evaporate directly into the gas phase in a process called sublimation. Further heating warms the resulting gases ('E' and 'F').

3. Start with gases at 'E'. Holding their temperature constant, squeeze them until they reach their solid-gas transitions. At this point the gases condense directly into solids ('A'). For CO2 and most other materials, more pressure will not produce any additional changes ('G' on right diagram). For H2O, however, additional pressure pushes the solid to the solid-liquid transition, where it melts ('G' on left diagram).

4. Start with gases at 'F'. Squeezing them pushes them to their solid-liquid transitions, where they condense directly into liquids ('B'). For CO2 and most other materials, further squeezing pushes the material to the solid-liquid transition, where it solidifies ('H'). For H2O, squeezing the liquid doesn't do anything (until reaching extremely high pressures off the top of the diagram). Diagram by Scott A. Sandford.

Grace Under Pressure

Snowball Compaction

Figure 2. Making a snowball. First, squeeze the snow hard enough that it moves vertically up the phase diagram to the solid-liquid transition ('A' to 'B'). Then release the pressure ('B' to 'A'). While at the solid-liquid transition ('B') some of the edges of the ice crystals melt. When you release the pressure, they refreeze, cementing the snow together. If you squeeze too hard, the snow goes all the way up to 'C' and the snowball melts completely away. This is one reason your gloves get so wet when you make snowballs on a warm day.

On a very cold day, the snow may start at location 'A´' and proceed up to 'B´' and 'C´'. At 'C´', you are squeezing as hard as you can, but the pressure is insufficient to reach the solid-liquid transition. Because no melting occurs, when you release the pressure you are left with a loose handful of snow rather than a snowball. Diagram by Scott A. Sandford.

So far, the phase transitions discussed have been identical for H2O and CO2. The two diagrams in Figure 1 indeed look very similar. But there is a crucial difference: namely, the slope of the nearly vertical line between the solid and liquid phases. For CO2, this line slopes upward and to the right - the normal behavior of almost all materials. However, for H2O, the line slopes upward and to the left. This seemingly minor change reflects major differences in the behavior of H2O under pressure.

What happens if we take gaseous CO2, squash it at a temperature at which it will liquefy (above -56.6 degrees Celsius), and squeeze harder and harder? It will turn into a liquid and eventually into a solid. In Figure 1, this is represented by the line 'F' to 'B' to 'H'. If we crank up the pressure still further, nothing new happens; we move up the diagram, but CO2 remains solid. Below -56.6 degrees Celsius, squeezing turns CO2 gas directly into a solid without the liquid go-between ('E' to 'A' to 'G'). Thus, if you squeeze CO2 and most other substances hard enough, they eventually solidify.

Water behaves very differently. If you start with water vapor hotter than 0.0099 degrees Celsius and squeeze, the gas condenses into liquid, just as CO2 did. After this point, however, additional squeezing does not turn the liquid water into solid ice. It stays liquid. (Under extreme conditions, this is not exactly true; I'll revisit this issue later.) In Figure 1, this process is represented by the line 'F' to 'B' to 'H'. Water also behaves differently at lower temperatures, below 0.0099 degrees Celsius. Applying pressure causes the gas to condense directly into a solid, as with CO2. But if you apply more pressure, the H2O ice melts. In Figure 1, this is represented by the line 'E' to 'A' to 'G'. This behavior is very different from that of CO2, which stays solid no matter how hard you squeeze. If you squeeze H2O hard enough, it eventually liquefies.

This peculiarity is associated with the fact that solid H2O is less dense than liquid water. Water ice floats in water - a very unusual behavior. Dry ice, for example, sinks in liquid CO2. Most solids are essentially as dense as those substances can possibly be, and further squeezing cannot make them significantly more compact. Yet when you squeeze H2O ice, it can ease the squeeze by turning into a liquid, making itself smaller and denser.

This (almost) unique property is in part due to the water molecule's ability to form strong hydrogen bonds. In hydrogen bonding, the H atoms in H2O form attachments to adjacent molecules. Such bonding is weaker than the covalent or ionic bonding that holds together molecules, but stronger than the normal intermolecular "van der Waals" forces. Hydrogen bonds are like the sticky portions of Post-It notes - stickier than just pushing two pieces of ordinary paper together, but less sticky than glue. It is hydrogen bonding between H2O molecules that makes the folds in your wet shower curtain stick together. This ability to grab things firmly but not tightly is one of the reasons that H2O is so very important for life. Because of it, liquid water can mediate much of the complex chemistry that occurs in living organisms.

Ice Can Be Welded

Based on this understanding of H2O and its phase diagram, let's consider the physics of snowball manufacture. To make a snowball, you scoop up some snow and compress it between your cupped hands, after which you hopefully have a ball that hangs together. What makes the loose snow stick together?

Many people assume that the heat from their hands melts enough of the snow to make it cohere. However, if heat were responsible, a snowball would be made from the outside in, and you'd have to hold it long enough for sufficient heat to enter. But if you cut a snowball in half, it looks pretty much the same throughout; there's nothing special about its outer layers to indicate they were heated first. Moreover, snowballs can be compacted quickly.

If heat mattered, it would be easier to make a snowball with your bare hands than with gloves on. This is clearly not the case (thank goodness). If you need further proof, try this: Drop two spoons in the snow and let them chill to snow temperature. Then pick the spoons up with gloved hands, so that you don't warm them, and use them to pack a snowball. You can make a perfectly good snowball this way, although the delay may cost you the snowball fight.

Alternatively, some people theorize that snowballs hang together because the intricate ice crystals in the snowflakes get tangled. If so, fluffy snow would make better snowballs than denser snow. In fact, the opposite is often the case.

The real explanation is revealed by the H2O phase diagram (see Figure 2). Suppose you are strong enough that you can squeeze snow hard enough to raise its pressure from 'A' to 'C' or, equivalently, 'A´' to 'C´'. If the snow is warm enough, you can squeeze it sufficiently hard that it reaches the solid-liquid transition line. At this point, some of the ice crystals melt in order to take up less space. If you then release the pressure, the snow drops away from the solid-liquid transition line, and the ice that melted refreezes. In Figure 2, this amounts to moving from 'A' to 'B' and back to 'A'. The refreezing liquid bonds the ice crystals together. Voilà! A snowball.

Now suppose you want to have a snowball fight on a very cold day. As you squeeze the snow it proceeds vertically up the phase diagram, but because of the low temperature, you can't squeeze hard enough to reach the solid-liquid transition. You're squeezing as hard as you can ('A´' to 'B´' to 'C´'), but you can't get any melting. When you release the pressure, you find that you are holding a loose handful of snow, rather than a snowball.

Feeling Minnesota

So, how cold is too cold? It depends on how hard you can squeeze. Some quick-and-dirty measurements with scales in my laboratory indicate that my hand can apply a pressure of about 0.07 atmospheres (1 pound per square inch, or 7 kilopascals) without straining too much. I can get as high as 0.2 atmospheres if I use my arms to squeeze instead of my hands. Thus, squeezing a snowball only adds a minor pressure to the pressure that the air is already exerting on the snow (1 atmosphere). Consequently, you can't expect to make a snowball with your hands if the snow is more than a few degrees below freezing.

At lower temperatures, you would need herculean pressures. At -25 degrees Celsius (-13 degrees Fahrenheit), a summer's day at the South Pole, it would take 2,000 atmospheres (30,000 pounds per square inch) to make a snowball. This would crush a submarine, let alone a handful of snow. Maybe that's why I've never participated in a snowball fight during any of my trips to Antarctica.

Prospects are even worse on deep-freeze worlds such as Ganymede, Pluto, and Mars. After Earth, Mars is the next warmest place in the solar system where there is any substantial amount of water ice. But with typical temperatures between -120 and -40 degrees Celsius (-180 and -40 degrees Fahrenheit), the snows of Mars are way too far to the left of the phase diagram to mold with our hands. Even the warmest temperature recorded by Mars Pathfinder, -9 degrees Celsius, would preclude snowballs.

But wait, you say, what if I were willing to drag around a hydraulic press? Could I make snowballs on Mars then? Sorry. So far, we have only considered the low-pressure part of the phase diagram. At very high pressures, H2O gets weirder still. Figure 3 shows that H2O can actually exist in a number of different solid forms depending on the temperature and pressure. The entire phase diagram shown in Figure 2 corresponds to a tiny horizontal strip near the bottom of Figure 3.

The high-pressure phase diagram of H2O

Figure 3. The high-pressure phase diagram of H2O. On this pressure scale, the entire area represented by Figure 1 or 2 - including the entire liquid-gas transition line - is an infinitesimal slice along the lower axis. At very high pressures, H2O can exist in exotic solid forms: Ice II, Ice III, Ice IV, and so on. Everyday ice is Ice I.

Note that the solid-liquid transition line does not extend up and to the left forever. Instead it meets Ice III and then turns to the right, as for normal materials. For this reason, if you squeeze liquid H2O really hard, it ultimately turns into one of the exotic solid phases. There is no region of stability for liquid water below -25 degrees Celsius (-13 degrees Fahrenheit). Crushing snow below this temperature does not cause any melting. Diagram by Scott A. Sandford, adapted from General Chemistry by Gordon Barrow, p. 311.

The everyday ice in our sodas is called Ice I. At extremely high pressures, H2O ice can take on exotic crystalline forms: Ice II, Ice III, and so on. (Fortunately there isn't a form of ice called Ice IX which has the apocalyptic properties Kurt Vonnegut described in "Cat's Cradle". The solid-liquid transition line does not extend up and to the left forever. Instead it collides with the area of stability of Ice III and then turns and heads up and to the right, as for most other materials.

By the way, water also acts strangely at very low temperatures, off the left edge of Figure 3. When it is very cold - as in comets and interstellar molecular clouds - non-crystalline ice can form (see Amorphous Ice).

No Winter Olympics on Mars

The high-pressure ice phases and the reversal of solid-liquid transition line have several implications for the subject at hand. I stated earlier that if you started with H2O gas or solid and squeezed, it would eventually turn into a liquid, and stay a liquid. That's not quite right. If you squeeze liquid water really hard (more than 4,000 atmospheres) it will ultimately transform into Ice V, VI, or VII, depending on the temperature.

More important, below -25 degrees Celsius, squashing snow (Ice I) doesn't result in any melting; it just turns Ice I into ices II, III, and so on. No melting, no snowball. If you were desperate for a snowball fight on Mars on any but the very warmest days, you'd need a heated hydraulic press. Of course, you could always throw solid chunks of ice cut out of the ground, but we all know that our mothers wouldn't let us do that.

I'm afraid this will also make it difficult to ice-skate on Mars. When you skate, you are gliding on a thin layer of water that forms between your blade and the ice. The weight of your body on the skate blades puts pressure on the ice, which helps to form the water layer. To be sure, the formation of the water layer is more complicated than a simple pressure effect. (See Samuel Colbeck's article in the October 1995 issue of the American Journal of Physics.)

So, snowball fights in our solar system are out, except on Earth. How about "snowball" fights using something other than frozen H2O, say, methane or carbon monoxide on Pluto or carbon dioxide on Mars? Alas, those other compounds have unfavorable phase diagrams. No amount of compression will get them to melt and pack into snowballs. Benford's scene just isn't possible. I find this more than a little sad. Still, it makes you appreciate all the more how special Earth really is.

Now, if you're like me, you are already wondering whether there aren't any other materials that behave like water - with solid-liquid transition lines that slope up and to the left. There are, but only under pressure and temperature conditions in which humans couldn't survive. For example, plutonium can exist in a form that melts when squeezed. If you had plutonium dust at 640 degrees Celsius (1184 degrees Fahrenheit) you might be able to squeeze it hard enough between your hands to get it to melt. Thus, if you were capable of surviving in a high-pressure blast furnace and had a strong grip, you could make a plutonium snowball out of plutonium snow. Of course, you would have to be extremely careful about it. If you made it too big, above critical mass, the resulting explosion would end the snowball fight for good.

So there you have it, the reason you can't have a snowball fight on Mars. At least on present-day Mars. A little terraforming might change that conclusion, but that's another article.

Skater

Skating on thick ice. On a 1988-89 expedition to Antarctica, geologist Ralph Harvey took a break from meteorite-hunting to try on his skates. Skating on the world's largest ice sheet is even tougher than usual, because the cold temperatures make it difficult for the blades to generate a layer of water on which they can glide. This challenge is compounded by the rough surface of the ice and by the wind. It takes a few minutes to skate a mile downwind and the better part of an hour to return upwind. Photo by Roberta Score (perhaps best known as the discoverer of the martian meteorite Allan Hills 84001).

Electron-microscope pictures and electron diffraction patterns

Taking shape. These electron-microscope pictures (left column) and electron diffraction patterns (right) reveal the structure - or structurelessness - of ices on scales of a millionth of a meter (µm). Amorphous ices, formed when water vapor and other gases are deposited at low temperatures and pressures, exhibit no physical structure, as evidenced by their fairly featureless electron diffraction pattern (top row). But as these ices are warmed, the molecules within them shift into more organized arrangements. The resulting structures manifest themselves as visible crystals, which scatter electrons into well-defined directions (center and bottom). Photos courtesy of David Blake, NASA Ames Research Center.

Like most materials, water ice comes in both crystalline and amorphous forms. In crystalline form, the atoms and molecules are arranged in a well-defined, repeating structure. This regular ordering minimizes the structure's energy and gives rise to favored directions for strength, cleavage, light refraction, and other properties. Examples of crystals include diamonds, quartz, table salt, and sugar.

In contrast, the atoms and molecules in amorphous materials are jumbled together without any long-range order. These materials do not have favored directions. Examples include glass and soot. Amorphous materials are "metastable" - that is, their atoms and molecules would actually prefer to rearrange into crystals if they could. At low temperatures, for example, atom and molecules lack the energy to move into a regular structure.

Ices made from H2O can exist in a large number of crystalline forms depending on the temperature and pressure. The ice in your refrigerator (temperature slightly below freezing, pressure about 1 atmosphere) is referred to as hexagonal ice because the molecules stack in a form that has a six-sided symmetry. At lower temperatures (110 to 220 kelvins, about -160 to -50 degrees Celsius), the ice prefers to stack with a four-sided symmetry and is called cubic ice. But if you form an ice by condensing water vapor at still-lower temperatures, the result is amorphous.

Until the past decade, scientists largely ignored amorphous ice, in part because it is harder to make, in part because nobody expected random jumbles of H2O molecules to be very interesting. But this conventional wisdom has now been overturned. Just as there are many forms of crystalline ice, there are multiple forms of amorphous ice. The different crystalline forms occur when the molecules are stacked in different ways. You might think that amorphous ices, which have no stacking order, are all be the same. Jumbled is jumbled, right?

Apparently not. At low pressures, amorphous ice comes in at least three forms: a high-density form (stable between 10 and 38 kelvins); a lower-density form (38 to 131 kelvins); and a third form (131 to 148 kelvins). In addition, this summer Peter Jenniskens and his colleagues at NASA Ames Research Center found that small chunks of amorphous ice may persist even after an ice crystallizes.

Each amorphous form has its own special kind of disorder. It is analogous to a pile of wooden blocks. Suppose you dump a box of blocks onto the floor in a big pile. The blocks in the pile have no particular ordering, just like high-density, low-temperature amorphous ice. Now scatter the blocks so that no block is on top of another. There is still no long-range order, but the disorder is now very different. This represents the lower-density, higher-temperature amorphous ice.

Many astrophysical sites experience low pressures, low temperatures, or both - ideal conditions for forming amorphous ice. Comets are one example. If comets are dominated by amorphous ice, it could have significant implications for cometary activity, such as the jets that comets squirt into space. When amorphous ice warms up and crystallizes, the molecules rearrange themselves into more-stable, less-energetic orientations. As a result, energy is released. Thus, as a comet approaches the Sun, its ice may transform from amorphous to crystalline, generating energy. This energy further warms the ice and accelerates cometary activity.

Amorphous ice may also be important in the interstellar medium where it coats dust grains in dense molecular clouds, the birthplaces of stars. These amorphous ices, like those in comets, aren't just made up of H2O. They also contain methanol, methane, carbon monoxide, carbon dioxide, and ammonia. In dense molecular clouds, the ices are irradiated by ultraviolet photons and charged particles. As seen in laboratory experiments, such radiation creates complex organic compounds in the ice. These compounds, under certain conditions, are known to transform into amino acids as well as other chemicals of biological interest. Once produced in the interstellar medium, some of these materials will wind up in new planetary systems.

This year, Louis Allamandola and his colleagues, also at Ames, discovered that the organic residues made in this manner have a tantalizing property: When dropped in liquid water, they spontaneously organize into droplets that contain internal structure, are surrounded by membrane-like walls, and are capable of processing light energy. In short, they exhibit some of the properties of proto-cells. Maybe amorphous ice has played a significant role in the origin of life - here and throughout the Galaxy.

SCOTT A. SANDFORD is a researcher at the NASA Ames Research Center in Mountain View, Calif. Among other things, he is working on the Stardust comet sample-return mission, due for launch in 1999 and return to Earth in 2006. Sandford was on the team that found Allan Hills 84001, the martian meteorite that may contain signs of past life on Mars [see Editorial, September/October 1996, p. 2]. His email address is sandford@ssa1.arc.nasa.gov.

 
 

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