Yes, finer is a Scrabble word!

Adjective

1. (comparative of `fine') greater in quality or excellence

2. Being satisfactory or in satisfactory condition

3. Minutely precise especially in differences in meaning

4. Thin in thickness or diameter

5. Characterized by elegance or refinement or accomplishment

6. Of textures that are smooth to the touch or substances consisting of relatively small particles

7. Free from impurities; having a high or specified degree of purity