Limits on quantitative information from high-resolution electron microscopy of YBa₂Cu₃O₇ superconductors

Abstract

High-resolution transmission electron microscopy (HREM) has been used to try to characterize high-temperature superconducting ceramics on a microscopic scale. Recent studies^1,2have concentrated on observing the ordering of oxygen vacancies in YBa₂Cu₃O₇, and have led to the conclusion that the presence of order, but not the degree of order, can be seen in [010] projection images under certain conditions. A related question is whether HREM images are sensitive to the oxygen concentration, that is, to the value of x in YBa₂Cu₃O_7–x. If this were the case, HREM would be a powerful way to detect local fluctuations in oxygen concentration, which may be a factor limiting the critical current. Here we present a series of image simulations in which we examine the sensitivity of HREM to both the degree of order and the oxygen stoichiometry, taking into account the uncertain nature of many of the variables in these calculations. We find a strong dependence of the simulated images on defocus, and on the Debye–Waller factor. As both of these are to some degree unknown, we conclude that although HREM can detect order, it cannot be used with confidence to quantify either the degree of ordering in the material or the oxygen stoichiometry.