as in Brillouin Zone?
Roughly, somewhere between BRILL-oo-ahn and BWEE-woo-uhn.
The last syllable is the tricky one for English speakers, since it involves a nasalized vowel. It’s like you were saying “en”, like the letter, but stopping yourself before you actually pronounce the consonant sound. I would pronounce is BREE-oo-en, with the understanding that the last syllable is pronounced as above.
Bree-loo-in, in as in (th)an(ks). Accent may be on first syllable
This is the dilemma of the scientist – when you invite your speaker with the very foreign name, do you pronounce it correctly (assuming you know how to and can), so that you show respect for his name, but confuse the hell out of everyone else who’s not familiar with the correct pronunciation of his name, or do you pronounce it in the standard mispronunciation, so everyon e knows who he or she is, but insult your guest?
I’ve always heard it pronounced BRI(LL)-you-o(n), with the "LL’ sort of swallowed and that final "n nasalized.