X-ray diffraction (XRD) is a powerful tool for characterizing core-shell nanostructures, providing critical insights into their crystallographic phases, lattice parameters, and strain states. The technique relies on the constructive interference of X-rays scattered by atomic planes, producing distinct diffraction patterns that reveal structural details. For core-shell systems, XRD analysis must differentiate between the core and shell phases, assess lattice mismatch effects, and quantify interfacial strains. This requires careful interpretation of peak positions, intensities, and broadening effects.

In epitaxial core-shell nanostructures, the shell grows with a defined crystallographic relationship to the core, often leading to coherent interfaces. The XRD pattern of such systems typically shows a single set of peaks shifted from the bulk positions of either phase due to strain. The direction and magnitude of the shift depend on whether the shell has a larger or smaller lattice parameter than the core. For example, if the shell has a larger lattice constant, the core experiences compressive strain, while the shell undergoes tensile strain. This results in peak shifts toward lower or higher angles, respectively. The average lattice parameter can be estimated using Bragg's law, but separating core and shell contributions requires additional analysis.

Peak broadening in epitaxial systems arises from finite size effects and strain inhomogeneity. Williamson-Hall analysis can deconvolute these contributions by plotting the full width at half maximum (FWHM) against the diffraction angle. A linear fit yields the average crystallite size from the y-intercept and the strain from the slope. For core-shell structures, asymmetric peak broadening may occur due to non-uniform strain distribution across the interface. High-resolution XRD with reciprocal space mapping can further resolve these effects by visualizing diffuse scattering around Bragg peaks, which indicates strain gradients.

Non-epitaxial core-shell nanostructures lack a crystallographic registry between core and shell, leading to incoherent interfaces. Their XRD patterns often display separate peaks for each phase, allowing direct identification. The relative intensities of these peaks provide information about the volume fractions of core and shell. However, peak overlap can complicate analysis, especially when both phases have similar crystal structures. Rietveld refinement is then essential for accurate phase quantification and lattice parameter determination. This method fits the entire diffraction pattern using structural models, accounting for peak shapes, backgrounds, and preferred orientation effects.

Lattice mismatch between core and shell significantly influences the XRD patterns. In epitaxial systems, mismatch induces strain, which can be calculated using the difference between observed and bulk lattice parameters. For cubic crystals, the strain ε along a specific direction is given by ε = (a - a₀) / a₀, where a is the measured lattice parameter and a₀ is the bulk value. The strain state can be anisotropic, particularly in non-spherical nanostructures, requiring analysis of multiple diffraction peaks. In non-epitaxial systems, lattice mismatch may lead to peak broadening due to disorder at the interface, but strain effects are less pronounced.

Interfacial strains in core-shell nanostructures arise from the mechanical equilibrium between core and shell. XRD can detect these strains by comparing the lattice parameters of the nanostructure with those of the isolated phases. For spherical nanoparticles, the strain is isotropic, and the XRD peaks shift uniformly. In anisotropic structures like nanorods or platelets, strain varies with crystallographic direction, causing differential peak shifts. Grazing-incidence XRD is particularly useful for studying such systems, as it enhances sensitivity to near-surface regions where strain gradients are most pronounced.

The thickness of the shell relative to the core also affects the XRD pattern. Thin shells may not produce distinct peaks but instead modify the core's diffraction profile through strain. Thick shells, on the other hand, can generate resolvable peaks, enabling direct measurement of their lattice parameters. The critical thickness for peak resolution depends on the scattering contrast between core and shell, as well as the instrumental resolution. For shells with low crystallinity or amorphous character, their contribution to the XRD pattern may be limited to a diffuse background, complicating analysis.

Thermal effects can further influence XRD characterization of core-shell nanostructures. Differences in thermal expansion coefficients between core and shell introduce additional strains during temperature variations. High-temperature XRD studies can track these changes in real time, revealing the stability limits of the core-shell interface. Phase transitions in either component may also occur, altering the diffraction pattern abruptly. Such transitions are identifiable by the appearance or disappearance of peaks at specific temperatures.

Quantitative analysis of XRD data requires careful consideration of instrumental and sample-related factors. Instrumental broadening must be accounted for when calculating crystallite sizes and strains, typically using a standard reference material. Sample preparation is equally important, as preferred orientation can skew peak intensities, especially in anisotropic nanostructures. Randomizing the sample orientation or using capillary mounts minimizes this effect. For weakly scattering shells, synchrotron XRD provides the necessary intensity and resolution to detect their contribution.

Advanced XRD techniques offer additional insights into core-shell nanostructures. Anomalous XRD exploits the energy dependence of atomic scattering factors near absorption edges to enhance contrast between core and shell elements. This is particularly useful for systems with similar crystal structures but different compositions. Pair distribution function (PDF) analysis of total scattering data probes local atomic arrangements, revealing disorder at the core-shell interface that conventional XRD might miss. These methods complement standard diffraction analysis, providing a more complete picture of the nanostructure.

In summary, XRD is indispensable for characterizing core-shell nanostructures, offering non-destructive, statistically averaged structural information. Distinguishing core and shell phases requires attention to peak positions, intensities, and broadening, with epitaxial and non-epitaxial systems exhibiting distinct signatures. Lattice mismatch and interfacial strains manifest as peak shifts and broadening, quantifiable through careful analysis. While challenges like peak overlap and weak shell scattering exist, combining standard and advanced XRD techniques enables comprehensive characterization of these complex nanomaterials.