firmament vs vault of heaven

firmament

noun
  • In the geocentric Ptolemaic system, the eighth celestial sphere which carried the fixed stars; (countable, by extension) any celestial sphere. 

  • The abode of God and the angels; heaven. 

  • The vault of the heavens, where the clouds, sun, moon, and stars can be seen; the heavens, the sky. 

  • The field or sphere of an activity or interest. 

vault of heaven

How often have the words firmament and vault of heaven occurred in a corpus of books? (source: Google Ngram Viewer )