Calcified Fragments,

Are collectibles found on the Dreadnought. Eris Morn has you find just 5 initially, although there are 50 total. IGN has a great guide to finding all of them (although it is still a work in progress). If all 50 are collected, players will receive the Touch of Malice, a year 2 exotic weapon. Information about the Touch of Malice is nowhere on the internet, and we assume that few, if any, Guardians have gotten it.

Wormspore,

Is the new armor and weapon material collected around the Dreadnought. This one is pretty obvious, as it follows the same collection method as Spinmetal and the like. Videogamesblogger.com has a good guide on farming techniques for Wormspore if you find yourself in dire need.

Hadium Flakes,

Are used for creating swords. They are also found on the Dreadnought, although in chests. Guardians will receive a side quest from Eris to acquire 25 flakes for the forging of a sword. For help, tentonhammer.com has a good guide on chest farming in the Mausoleum. Future uses for Hadium Flakes are not completely known, although the motivation to collect them for a badass sword seem righteous enough.