|MadSci Network: Engineering|
Well, strictly speaking, the answer is no: an alloy is a metallic substance composed of two or more elements, where one type of atom either replaces or squeezes in between the other type. It all comes down to the way the atoms bond in metals and polymers, rather than melting temperature, as you seemed to imply in your message.
Not-so-strictly speaking, if you change "alloy" to "combination of materials in general", the answer is sure - why not?
First, let's look at the "no" answer. In metals, you get metallic bonding - the atomic nuceli arrange themselves into nice (mostly) orderly 3-d grids, with the electrons free to move around in between, kind of the like the mortar that holds bricks together. In polymers, you typically have covalent bonding - electrons are shared between neighboring atoms. In polymers, the atoms form long chains or large networks of atoms joined by sharing individual electrons, kind of like a mass of spaghetti that's stuck together in a clump. So, in answer to your question about forming alloys with metals and plastics, it'd be like saying that you want to chemically bond brick, mortar, and spaghetti. OK, that's a bit of a reach, but hopefully you get the idea!
As for trying to combine metals and polymers into materials together, that is absolutely possible - they're just called composites rather than alloys. That implies that the metal parts and polymer parts remain distinct and separate, but are pretty firmly attached to one another in the mixture. Such a material could certainly be designed to have a set of properties that are better than either the metal or polymer alone. There's an interesting list of some different composite combinations at the wikipedia website, and some information on specific metal-polymer nanocomposites and their applicaitons.
Hopefully this helps clear things up. If you're an engineer at UVA, I'm guessing you'll get a chance to take an introductory Materials Science course at some point - they'll probably cover a lot of this in more detail there!
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