'Investigation of' or 'Investigation into'?

Both are completely legitimate.

Google's NGrams shows that "investigation of" is much more common than "investigation into". While NGrams usually needs to be taken with a grain of salt, this does show us that there is nothing inherently wrong with "investigation of".

Furthermore, comparing "investigation into" against other random prepositions shows that it is much more common than, say, "from".

You might want to consider the proximity of similar words when making you choice. "An investigation of the effects of inhibitors on cells" sounds awkward due to the close proximity of one "of" to another. "An investigation into the effects of inhibitors on cells" in this case may be better. "An investigation into intracellular interactions" also sounds awkward, so in this case "of" would flow better: "An investigation of intracellular interactions."

I've seen non-native speakers use "on" after "investigation;" however, I'd consider that to be incorrect.

"Into" seems to be used more for concepts and non-tangible things

An investigation into the world of magic An investigation into the mind of children an investigation into the lucrative business of art-selling

"Of" seems to be used more with objects

An investigation of chocolate's benefits An investigation of cells organelles

This is NOT a rule I read anywhere, just what I found to be true (most times) when investigating this question

The word "of" can be used (among other uses):
Following a noun (now chiefly nouns of knowledge, communication etc.), to introduce its subject matter; Example: A tale of two cities (Charles Dickens)

Source: http://en.wiktionary.org/wiki/of#Preposition

So at the very least your phrase isn't wrong. But I'm not sure if "into" could be used interchangeably.

Investigation of catalytic phase structure using SEM and TEM methods.

My humble opinion is this for what it's worth:

The given sentence seems alright. The replacement of 'investigation of' by 'investigation into' would, I believe, be correct only when 'catalytic phase structure' is an obvious problem similar to an accident, a crime, etc.

It seems 'investigation of sth' means a study of sth, and in the case you are smelling a rat (i.e. only suspicion), you want the study to tell you if there is anything going wrong.

On the other hand, 'investigation into sth' is used when that sth is definitely a problem, like an accident, a crime, etc.