"Mathematically, the thermal expansion will be almost exactly half what you calculate"- actually, no....
my calculation, as I said, was not rigorous by ANY stretch of the imagination- but if you look at the far more rigorous calculations I linked to in answer to podrock you will see the number I got was quite close to the ones derived by taking a far more complete approach- trust me nick, I wouldnt have put it up without checking first... my 1 line calculation was, as I said, only to show that you can get in the ballpark with back of the envelope calculation...