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Name: Mark F.
Status: educator
Grade: 9
Location: NY
Country: N/A
Date: May 2006

Question:
Water freezes to a lower density, so it floats on its own liquid. This occurs between 4 and 0'C.

Is there another liquid that expands when cooled? Over what temperature range (are they all as small as the 4C' in water)? Can you add something to water so that it expands more between 4 and >0'C? Can you add something to water so that it expands over a larger temperature range than 4 to 0'C?



Replies:
I think you are confusing two phenomena here:

1. The density of water ice is less than liquid water at all temperatures. So ice floats in water that is at room temperature as well as water at 0 C. Of course the ice is melting and the temperature of the ice and the water are different, but the melting of an ice cube is slow enough to allow one to observe that ice floats on water that is well above the melting point.

2. The density of liquid water at about 4 C is slightly greater than temperatures either greater than or less than that temperature. (Stated another way, the molar volume of ice at 4 C is less than the molar volume of ice above and below that temperature.) The cause of this behavior is the presence of lower volume "ice-like" transient structures in liquid water, even above its melting point. These are lower density than the surrounding "normal" water, but become less abundant as the temperature increases. So what you have below 4 C. is a liquid composed of "normal" water containing "low density" (higher molar volume) transient configurations of water molecules. The "normal" part of the liquid increases in volume as the temperature increases. However, the "low density" ice-like transient structures begin to fall apart as the temperature increases. This causes the water to become more dense as these low density (higher molar volume) transient aggregates disappear. So one factor is increasing with increasing temperature; the other factor is decreasing with increasing temperature. This results in a roughly parabolic dependence of volume (or density) versus temperature.

Regarding how to eliminate this behavior: Most solutes, even at moderate to low concentrations hydrate, that is, they have clusters of water molecules attracted to the solute. In almost all cases I know of this makes the density / temperature behavior of the solution "normal". That is there is no increase, then decrease in density as temperature increases; only the "normal" decrease in density as temperature is increased. I don't know any way to increases the peculiar behavior of pure water.

A related topic of great practical interest are solids that have a negative thermal expansion. These include some metal alloys, some fibers such as Aramid, and a number of ceramics -- ZrW2O8. This ceramic decreases in volume from very low temperature to very high temperature (0.3 to 1050 Kelvin's).

In ideal solids the atoms vibrate in such a way that the restoring force is proportional to the distance the atom moves from its equilibrium position (Hooke's Law). The atoms of a lattice such as ZrW2O8 show significant deviations from Hooke's Law -- namely the restoring force becomes a bit weaker when the atoms are at larger distances from their equilibrium position. This type of vibration is called anharmonic vibration, in contrast to Hooke's Law vibrations, that are called harmonic vibrations. In most solids this deviation is small and the temperature coefficient of thermal expansion is positive. But in these ceramics the anharmonic vibrations are 10 times greater than normal solids. These types of ceramic materials are of technological interest because it is hoped to be able to combine them with other "normal" ceramics to produce materials that have zero thermal expansion over a wide temperature range. Such materials would have wide application in many areas of science and technology.

Vince Calder



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