A crystal’s shape is determined by its intrinsic chemistry, a property that determines its final shape from the simplest of details. Sometimes, however, the lack of symmetry in a crystal renders the surface energy of its faces unrecognizable, confusing any theoretical estimates of its shape.
Theorists at Rice University say they have found a way to circumvent this puzzle by arbitrarily assigning hidden energies to their surfaces or, in the case of two-dimensional materials, their edges. Yes, it seems like cheating, but just as a magician finds a chosen card in the deck and narrows down the possibilities, a little algebraic skill can help solve the problem of predicting the shape of a crystal.
The method described Nature Computational Scienceshows that using what they call auxiliary edge energies can again align predictions with the Wolff design, a geometric description that has been used for more than a century to determine how crystals reach their final equilibrium shape.
Written by materials physicist Boris Jacobson, lead author and graduate student Luqing Wang, and colleagues at the George R. Brown Rice School of Engineering, the open-access paper presents algorithms using arbitrary numbers for right-hand factors in equations and still provides the correct unique-form solution.
“The shape question is compelling, but researchers have tried for years to calculate the surface energy for asymmetric crystals and have failed,” said Jacobson. “It turns out we went down a rabbit hole, but we knew that if nature can find a solution in gazillions of atomic motions, there must be some way for us to figure it out.”
He said the recent surge in interest in 2D materials has prompted new research. “We had a ‘eureka’ moment: After we changed our geometric thinking to algebraic thinking, we added closing equations with arbitrary parameters,” Jacobson said. “They look useless, but we ran everything through the computer and we noticed a clear shape was coming out,” he said.
“It was difficult to convince our investigators that the limiting energy really cannot be determined, but that a solution can still be found,” Wang said. Source
Source: Port Altele
