Causal emergent principles and relations for mechanical properties of covalent and ionic crystals

A knowledge and data-synergized intelligent computation architecture for materials was proposed within the data science paradigm. As a vital operation, two digital ensemble descriptors implying chemical composition and structural trend for crystals were created using the features contained in the Periodic Table of elements without a priori assumption, which affords causal emergence and regulation principles for the mechanical response of covalent and ionic solids. In addition to a linear correlation among structural state/mechanical response parameters, causal analytic relations in an exponential form between structural and thermodynamic state/mechanical response parameters and a digital ensemble descriptor were unveiled through least squares regression, in which the coefficients are classified in accordance with symmetry principles on the atom and lattice. Thereafter, the underlying physicochemical mechanisms of chemical pressure and chemical bonding are found responsible for the mechanical responses of bulk modulus and hardness of solids. At last, a physical prediction model was established for crystalline solids and demonstrated the feasibility of the predictive design of novel superhard materials. It is believed that by constructing suitable digital ensemble descriptors, this intelligent computation architecture and consequent physical prediction models on the basis of causal analytic relations are able to generalize by depicting crystalline solids with covalent and ionic bonds in other crystallographic structures.