X-ray cross correlation analysis uncovers hidden local symmetries in disordered matter

Abstract

We explore the different local symmetries in colloidal glasses beyond the standard pair correlation analysis. Using our newly developed X-ray cross correlation analysis (XCCA) concept together with brilliant coherent X-ray sources, we have been able to access and classify the otherwise hidden local order within disorder. The emerging local symmetries are coupled to distinct momentum transfer (Q) values, which do not coincide with the maxima of the amorphous structure factor. Four-, 6-, 10-and, most prevalently, 5-fold symmetries are observed. The observation of dynamical evolution of these symmetries forms a connection to dynamical heterogeneities in glasses, which is far beyond conventional diffraction analysis. The XCCA concept opens up a fascinating view into the world of disorder and will definitely allow, with the advent of free electron X-ray lasers, an accurate and systematic experimental characterization of the structure of the liquid and glass states.coherent X-ray diffraction ͉ higher-order correlations ͉ structure D isordered matter, such as glasses and liquids, does not exhibit translational symmetry and in turn is able to accommodate different local symmetries in the same system, among them the icosahedral local order, which belongs to the forbidden motifs in periodic structures. This mysterious and so far experimentally inaccessible localized order within disorder has been fascinating scientists for many decades (1-5), because it is held responsible for the undercooling of liquids and the existence of the glass state. Similarly, nonperiodic materials have always attracted the attention of materials scientists, because they do carry-through these structural degrees of freedom-a unique potential to display novel smart functions (6-8).The microscopic understanding of the structure and properties of crystals has advanced rapidly during the last decades. The translational invariance of the crystalline state allowed the introduction of the Brillouin Zone concept, thus enabling an elegant and powerful theoretical description of the thermal, electronic and magnetic properties. At the same time, crystal diffraction has continuously been developed to such a fine art that even complex biological structures can be solved today with atomic resolution (when forced to form a crystal). In severe contrast to this, the local microscopic structure of disordered matter has remained a challenge and a mystery (1-3). Our lack of knowledge on the local order within disorder constrains the development of a better understanding of the properties of liquids and glasses (9). In turn, the open question of how the structure of the liquid and amorphous states can be accessed experimentally has become one of the holy grails in condensed matter science (10).The fundamental limits of conventional (X-ray, neutron, electron) diffraction from disordered materials are accountable for this situation, because such techniques only allow to extract the pair distribution function g(r) ϭ n 0 Ϫ2 ͗(0)(r)͘ of the single particle density (r) ϭ ͚...

X-ray cross-correlation analysis and local symmetries of disordered systems: General theory

“…The authors of Ref. 1 have introduced the four-point angular cross-correlation function ͑CCF͒ C q ͑⌬͒ defined as C q ͑⌬͒ = ͗I͑q, ͒I͑q, + ⌬͒͘ − ͗I͑q, ͒͘ 2 ͗I͑q, ͒͘ 2 , ͑1͒…”

Beyond simple exponential correlation functions and equilibrium dynamics in x-ray photon correlation spectroscopy

“…The collective nature of the structural dynamics near the hard-sphere glass transition was further captured in a recent coherent x-ray scattering study that investigated cross correlations in the time-dependent scattered intensity along different wave vector transfer directions. Temporal correlations between intensity patterns with different azimuthal symmetries indicated the prevalence of certain transitions between different preferred forms of local order and particularly the long persistence of icosahedral-symmetry (five-fold-symmetry) packings [22].…”

Quantifying Angular Correlations between the Atomic Lattice and the Superlattice of Nanocrystals Assembled with Directional Linking

“…25,35,45 However, a persisting problem of these protocols is that they are prone to introduce defects in the superlattice structure with some degree of granularity and significantly smaller grain sizes, which poses difficulties in determining the angular correlation with a meaningful statistical distribution. 11,17,24,41,46,47 Using a conductive MC on the basis of PbS NCs, 35 we show how X-ray cross correlation analysis (XCCA) [48][49][50][51] (Fig. 1c) with the corresponding real-space image (Fig.…”

“…Note that the real shape and binding mode of the ligand sphere may be more complex than that displayed in In order to determine the angular correlations and unit cell parameters within each domain quantitatively, we applied an XCCA approach (see Methods for XCCA details). [48][49][50][51][59][60][61][62] This method is based on the evaluation of a two-point angular cross-correlation function (CCF) that can be calculated for each diffraction profile as 48,49 (…”