Synchrotron X-ray microdiffraction ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> XRD) services are conducted for industrial minerals to identify their crystal impurities in terms of crystallinity and potential impurities. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> XRD services generate huge loads of images that have to be screened before further processing and storage. However, there are insufficient effective labeled samples to train a screening model since service consumers are unwilling to share their original experimental images. In this article, we propose a physics law-informed federated learning (FL) based <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> XRD image screening method to improve the screening while protecting data privacy. In our method, we handle the unbalanced data distribution challenge incurred by service consumers with different categories and amounts of samples with novel client sampling algorithms. We also propose hybrid training schemes to handle asynchronous data communications between FL clients and servers. The experiments show that our method can ensure effective screening for industrial users conducting industrial material testing while keeping commercially confidential information.