i have a rock composed of actinolite altered to biotite and chloite what conditions do that?

Answer 1

You need to provide more information to answer this question.
For example What is the proportion of actinolite in your rock, and what is the proportion of chlorite and biotite?
Are there any other phases presents, like quartz or calcite, pyroxenes, plagioclase. Is there abundant magnetite?
What are the surrounding rocks?
Even though pure actinolite does not have aluminum, most naturally formed actinolites contain aluminum typically 2-4% Al2O3. So, I agree with mountaingym, biotite can alter to chlorite and that's very common. In the alteration of the ocean crust you have typically actinolite and chlorite coexisting in green-schist facies, actinolite is more abundant at increasing temperature.
Nevertheless, actinolite can form also in some hydrothermal veins (the same as chlorite-quartz, and quartz-biotite).
So, you have to observe your sample and construct a mineral paragenesis. What is altering to what.
Biotite forms at temperatures approximately above 350 C,
Chlorite from weathering to temperatures about 350 C,
Actinolite forms at high temperatures above 350 C and as high as 800 C (depending on the composition), but typically lower than 600 C. Then incorporates more aluminum, if available, to transform into hornblende.

Answer 2

I have never heard of actinolite altering to biotite, or to chlorite for that matter, so I checked the chemical formulas of the minerals. Actinolite has calcium, which is not found in either biotite or chlorite. That is not a big deal, you just drive away the calcium. However, both biotite and chlorite have aluminum and actinolite doesn't, so you need a source of aluminum. Also, biotite has potassium, so you need a source for that. In order to have this much ion exchange it sounds like hydrothermal waters are required, which is metamorphic conditions. Since actinolite is commonly found in metamorphic regimes it would seem that after formation the actinolite was re-metamorphosed to these micas. I have trouble in seeing such an environment, since biotite alters to chlorite under weathering conditions. I think the actinolite and biotite formed simultaneously and some of the biotite weathered to chlorite.

Answer 3

Chlorite, I believe, generally results from lower grade (low to medium grade) metamorphism and hydrothermal alteration. Biotite alters to chlorite. So probably you are looking at low grade wet metamorphic alterations.