Answer: The black material is probably sooty mold growing on honeydew secretions caused by insects feeding on the plants. Treating the insects should also stop the sooty mold.
Aphids are soft bodied insects that suck the plants juices. Typically you will find aphids feeding on the tender new growth at the tips of the branches. Whitefly is a small white colored flying insect (looks a bit like a little white fruit fly) that rises up when the plant is disturbed. Both of these can be treated with insecticidal soap or horticultural oil sprays.
However, before you spray, I would strongly suggest you consult with your local county extension to make sure one of these is truly the culprit. (On crepe myrtle for example this could be a fungal infection such as mildew rather than an insect problem.) Based on knowing specifically what the problem is, they will have the most up to date recommendations on what to use and how/when is best to apply it for maximum results. Good luck with your crepe myrtles!
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