Revealing Three-Dimensional Structure of an Individual Colloidal Crystal Grain by Coherent X-Ray Diffractive Imaging

Abstract

We present results of a coherent x-ray diffractive imaging experiment performed on a single colloidal crystal grain. The full three-dimensional (3D) reciprocal space map measured by an azimuthal rotational scan contained several orders of Bragg reflections together with the coherent interference signal between them. Applying the iterative phase retrieval approach, the 3D structure of the crystal grain was reconstructed and positions of individual colloidal particles were resolved. As a result, an exact stacking sequence of hexagonal close-packed layers including planar and linear defects were identified. DOI: 10.1103/PhysRevLett.117.138002 Colloidal crystals nowadays are actively exploited as an important model system to study nucleation phenomena in freezing, melting, and solid-solid phase transitions [1][2][3][4][5], jamming and glass formation [6,7]. In addition, colloidal crystals are attractive for multiple applications since they can be used as large-scale templates to fabricate novel materials with unique optical properties such as the full photonic band gap, "slow" photons and negative refraction, as well as materials for application in catalysis, biomaterials, and sensorics [8][9][10][11]. Colloidal crystals grown by self-organization provide a low cost large-scale alternative to lithographic techniques, which are very effective for producing high-quality materials with a desired structure, but are limited in building up a truly three-dimensional (3D) structure and bring high production costs [12]. Recently, significant progress has been achieved in engineering materials with tunable periodic structure on the mesoscale by functionalizing colloids with DNA [13], applying external fields [14,15] or varying the particle shape [16,17].Understanding the real structure of colloidal crystals and its disorder is an important aspect from both fundamental and practical points of view. Even at equilibrium, colloidal crystals can have a finite density of defects, which can be anomalously large for certain colloidal lattices [18]. The opposite can also happen as defects can play a decisive role in the choice of the crystal structure [19,20]. For applications such as photonic crystals most of growth-induced defects can deteriorate their optical properties. On the other hand, controlled incorporation of certain defects can be desirable to enhance the functionality such as creating wave guides [21,22], trapping photons [12,23], and developing optical chips [24]. In these studies, monitoring an internal 3D structure of colloidal crystals including defects in real time remains a challenge [25].Among widely used techniques of the colloidal crystal structure investigation are optical microscopy [26,27] and confocal laser scanning microscopy [28]. However, the range of applications of these methods is strongly reduced by the limited resolution (at best about 250 nm) and the need of a careful refractive index matching, which is not always possible. Furthermore, some of the materials are opaque for visible light which comp...

Ptychographic X‐Ray Imaging of Colloidal Crystals

“…It allows determination of the strain field distribution formed by defects in a nonperfect crystalline material. CXDI was successfully applied for high resolution imaging of defects in colloidal crystal films and colloidal crystal grains . At the same time, conventional CXDI relies on a sample smaller than the incident beam size and a high degree of spatial coherence of X‐rays.…”

Quantifying disorder in colloidal films spin-coated onto patterned substrates

“…Reciprocal-space methods, e.g., using small-angle and ultrasmall-angle scattering [32,33], are the standard for characterizing crystalline structures; however, spatial resolution is important both for identifying subtle differences in disordered structures, as well as for following the kinetics of crystallization. Real-space methods such as those discussed here can also be used in tandem with new developments in coherent x-ray diffractive imaging [34]. In this work, we show that information about orientational order in spin-coated colloidal deposits, obtained by using orientationalorder based Minkowski structure metric [31,35,36], can be complemented by an examination of structural heterogeneity via persistent homology using the first Betti number [37].…”

Dynamical effects in Bragg coherent x-ray diffraction imaging of finite crystals

“…[36]), or by performing Bragg CXDI measurements at several Bragg peaks simultaneously (see, for example, Refs. [16,17,37]). Variations of the values of the shape function inside the crystal describe rather modulations of atomic planes associated with the chosen reflection and not electron density modulations.…”

“…[16]). In Bragg CXDI technique a finite crystalline sample is illuminated by an intense coherent x-ray beam and an interference pattern in the vicinity of a single or several Bragg reflections is recorded [17]. An inversion of such data from reciprocal to real space by means of three-dimensional (3D) Fourier transformation provides a high-resolution image of a continuous scattering density distribution in the crystal.…”