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"Generally, the human race avoids doing anything radical until forced into it."
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A general had a problem: mud. Marines have slogged their way through it for generations. Is it possible to get rid of mud? Without having to carry anything heavy? Marines already have enough to carry.
Dr. Felix Hoenikker, an original thinker, found the "outside-the-box" answer; a single crystal of Ice-Nine would crystallize every bit of water it touched.
And where would the freezing stop? Unfortunately, the melting point of Ice-Nine was 114.4 degrees; once the entire planet locked up, it would probably never melt.
Here's what the world looked like after Ice-Nine was released into the environment, crystallizing all water on Earth, locking it into the Ice-Nine configuration.
In fact, there really is a form of ice called Ice-IX. Ice-IX was discovered in 1968. It exists only under high pressure and does not have the properties of Vonnegut's ice-nine (thankfully!). Kurt Vonnegut's brother held a PhD in physical chemistry from MIT; he published papers on silver iodide and ice formation (cloud seeding). So that's one possible source for the idea.
It has also been suggested that, when Vonnegut was working at General Electric (in public relations), he was inspired by a company story relating to H.G. Wells. When Wells visited G.E. in the 'thirties, Nobelist chemist Irving Langmuir was tasked with keeping Wells entertained during his visit. Langmuir came up with an idea about a form of water that was solid at room temperature. Wells never published a story about it, but Vonnegut thought it was worth using.
Crystallized water, or ice, has a greater variety of crystalline structures than perhaps any other material. Ordinary ice (like you might skate on) has a hexagonal structure; water at different temperatures and pressures forms solids that are rhombohedral, tetragonal, cubic, or orthorhombic in structure. Some forms of "frozen" water are disordered (non-crystalline).
Just so you know, the regular ice in your refridgerator is hexagonal ice, Ice-Ih. That's what makes nice hexagonal snowflakes. Aren't you glad you asked?
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