Why is there no word for the clean,fresh smell immediately after it has rained on a Summer's day?

There is one! Petrichor.

The term was coined in 1964 by two Australian researchers, Bear and Thomas, for an article in the journal Nature. In the article, the authors describe how the smell derives from an oil exuded by certain plants during dry periods, whereupon it is absorbed by clay-based soils and rocks. During rain, the oil is released into the air along with another compound, geosmin, producing the distinctive scent.

Because we just say it smells like rain

thanks for the 3rd answer.... i always wondered whether it had a name but never thought of looking lol

I don't know, but there should be one...