Data plays a very important role in materials informatics. However, with the convenience of data generation from high throughput experiments and computations, how to extract useful knowledge from the massive data effectively is a challenging and urgent task at the moment. Machine learning, especially, the statistic ones, generally is a black box that lacks of explanations for learning results. Therefore, in this paper, we propose a concept lattices algorithm to mine association rules with designated consequents (CLARDC). Through orderly structure concept lattice, all the concept nodes that containing target features and covering enough samples are searched downwards from the most abstract top concept node. The children concept nodes have more attributes than their parent ones, which is the key point that can differentiate concepts and extract rules. Through CLARDC algorithm, firstly, it can discover the positive or negative relationships between independent attributes and target ones from multi-dimensional data. Secondly, it can adjust threshold to select rules according to the actual situation. Thirdly, it can interpret result rules based on material knowledge. From diamond-like materials data experiment, it shows that CLARDC can extract two attributes ED and CAAM which deeply affect the band gap. Moreover, two attributes have different influence on band gap in different ranges. Also, it finds that different attributes have different influence on the band gap in different ranges. Finally, compared with Prism algorithm, rules obtained by CLARDC can describe the features in multiple perspectives, which are not only more understandable, but also more interactive.