Hi M, thank you for your inquiry.
Crystal lovers often feel conflicted about whether or not they should purposefully break a crystal for a variety of reasons. In general, breaking a crystal isn't "wrong" and could be a fork in the road on it's journey. Perhaps you could meditate with it to feel more at peace with the process and receive inner guidance as to why you were drawn to break a piece of it off for your locket in the first place.
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I must share the standard disclaimer that I am not a doctor and cannot give out medical advice. Crystals for healing should be used as a complement to other therapies and not as a replacement for regular medical care. The information offered here is based on a combination of my own personal experiences and that of others on using crystals for healing. My hope is that you will let your own intuition guide your path in working with crystals as well.