a .mat file is an exported Bryce-specific material file. They can only be created in Bryce, and only used in Bryce. You make a .mat file by creating a material in Bryce, adding it to your material presets (by displaying the Material Library and clicking Add), and you can export them to a file by highlighting one (or more, using ctrl-click) of the materials in the Material Library and clicking Export. That's it. Their only purpose is to exchange material settings with your friends, for use ONLY within Bryce, or to organize your own materials collection, if you have a whole bunch and don't want to fill up your Materials Library with endless variations. You can export all your mats and delete them from the Library, importing them again as necessary.