The higher the level on the item within its grade range will increase the likelihood of earning that materia. For instance, if you want tier 1 fieldcraft demimateria, buy goatskin rings from an armor npc since they're level 20 and 400 gil each and desynth those. Same goes for any tier 1 up to level 29 since 30-4? will give you tier 2.

And of course ask reddit...

http://www.reddit.com/r/ffxiv/commen...t_demimateria/
http://www.reddit.com/r/ffxiv/commen...n_demimateria/
http://www.reddit.com/r/ffxiv/commen...w_to_get_them/
http://www.reddit.com/r/ffxiv/commen...hesis_dairies/