In inspiration:
First the external intercostals plus the diaphragm contract to bring about Inspiration:
Then, contraction of external intercostal muscles > elevation of ribs & sternum > increased front- to-back dimension of thoracic cavity > lowers air pressure in lungs > air moves into lungs
After that: contraction of diaphragm > diaphragm moves downward > increases vertical dimension of thoracic cavity > lowers air pressure in lungs > air moves into lungs.
In expiration:
First thing that would happen would be the relaxation of external intercostal muscles & diaphragm > return of diaphragm, ribs, & sternum to resting position > restores thoracic cavity to preinspiratory volume > increases pressure in lungs > air is exhaled.