http://www.worldwidewords.org/articles/aluminium.htm gives you the full answer.
The short answer is that the English chemist who actually got to name it, called it ALUMINIUM. By the time the word reached america, both the -minum and -minium were equally in use. But for some reason, Webster's dictionary only had ALUMINUM as the spelling. And since Webster's was the most popular American dictionary, it was the most often used. And so, most Americans became familiar with only the ALUMINUM spelling.
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