I agree that both are acceptable, though unlike Nathan I would say #2 is both more pleasant-sounding and more correct.
Perfect aspect describes things that have attained a particular state of being: “The sample had been prepared” describes the state the sample was in at the time, rather than a particular preparing action. So technically “seven days after the sample had been prepared” could mean “seven days after (a date on which the sample was in a prepared state [which was a further two days after the preparation occurred])”.
I really doubt any English speaker would read the sentence in a way so contrary to its obvious intent, though, so I think you’re on safe ground either way.
Both can be correct, but it depends. Unless there are some interesting contexual issues we don’t know about then I would say neither is correct.
Assuming we are just talking about 2 actions in the past, one coming before the other, then past perfect (had been) refers to the the action that happened first with past simple (grew) used for the second action.
So, I suggest:
“Seven days after the sample had been prepared, the crystalline domains grew even further.”
A good way (usually for native speakers) to test this is to turn the phrase around and see how it looks. So, “The crystalline domains grew even further seven days after the sample had been prepared.”
If you use “had grown” that means you’re making some reference to another action that happened AFTER the crystals growing. In your example no other action is refered to, so past simple fits best.
I think part of the issue is that the meaning in either sentence is ambiguous. The problem isn’t necessarily the first tense; the problem is the “… had grown even further.” part. “Seven days after” is a specific time, whereas “… had grown …” suggests a time period. Did the crystals grow on the seventh day only, or did they grow over the whole week? Resolving this would solve the tense issue and avoid the overuse of the weak “had” or “was” and replaced it with something more specific:
The crystalline domains grew for seven days after the sample had been prepared. [I think that “was” doesn’t sound right here.]
Seven days after preparing the sample, its crystalline domains began to grow.
Or maybe you meant something like this:
The sample’s crystalline domains have grown substantially since the sample was prepared seven days ago. [This suggests you don’t know when they actually grew.]
When the time point is not specified, I think “had been” is preferred:
The sample’s crystalline domains had grown substantially since the sample had been prepared.
Not to go off topic – but a better way to write this is to remove the passive voice altogether.
Seven days after I prepared the sample, I noticed the crystalline domains had grown even further.
(Or, second person:)
Seven days after you had prepared the sample, you notice the crystalline domains have grown even further.
Seven days after Jim prepared the sample, he noticed the crystalline domains had grown even further.
The “was prepared” and “had been prepared” are passive voices, and they confuse the sentence somewhat, because there’s no observer to pinpoint the time of the preparation and the time of the later observation.
Neil’s point makes sense, too. I think removing the passive voice removes some of the ambiguity, though, because we know that the person that prepared the sample 7 days ago is also observing the growth.
However, if the passive voice is used because the observer doesn’t matter, or for the sake of a clinical log, than I would add an observer to the second part, to lock time into place:
Seven days after the sample was prepared, it was noted that the crystalline domains had grown even further.
And “had grown even further” isn’t even passive voice, so there’s really no reason to stick “I noticed” or whatever in there. The sentence is about the crystalline domains, not about the observer. Don’t take the emphasis away from where it should be.
Now: Who wants to help design Crystalline Domains: The IF?