Four recent x-ray diffraction measurements of ambient liquid water are reviewed here. Each of these measurements represents a significant development of the x-ray diffraction technique applied to the study of liquid water. Sources of uncertainty from statistical noise, Q-range, Compton scattering, and self-scattering are discussed. The oxygen-hydrogen contribution to the measured x-ray scattering pattern was subtracted using literature data to yield an experimental determination, with error bars, of the oxygen-oxygen pair-distribution function, g_OO(r), which essentially describes the distribution of molecular centers. The extended Q-range and low statistical noise of these measurements has significantly reduced truncation effects and related errors in the g_OO(r) functions obtained. From these measurements and error analysis, the position and height of the nearest neighbor maximum in g_OO(r) were found to be 2.80(1) Å and 2.57(5) respectively. Numerical data for the coherent differential x-ray scattering cross-section I_X(Q), the oxygen-oxygen structure factor S_OO(Q), and the derived g_OO(r) are provided as benchmarks for calibrating force-fields for water.

Calcium silicate hydrate (CSH) is the major volume phase in the matrix of Portland cement concrete. Total x-ray scattering measurements with synchrotron x rays on synthetic CSH(I) shows nanocrystalline ordering with a particle diameter of 3.5(5) nm, similar to a size-broadened 1.1 nm tobermorite crystal structure. The CSH component in hydrated tricalcium silicate is found to be similar to CSH(I). Only a slight bend and additional disorder within the CaO sheets is required to explain its nanocrystalline structure.

Here we present diffraction data that yield the oxygen-oxygen pair distribution function, g_OO(r) over the range 254.2–365.9 K. The running O-O coordination number, which represents the integral of the pair distribution function as a function of radial distance, is found to exhibit an isosbestic point at 3.30(5) Å. The probability of finding an oxygen atom surrounding another oxygen at this distance is therefore shown to be independent of temperature and corresponds to an O-O coordination number of 4.3(2). Moreover, the experimental data also show a continuous transition associated with the second peak position in g_OO(r) concomitant with the compressibility minimum at 319 K.

A defining characteristic of silicate melts is the degree of polymerization (tetrahedral connectivity), which dictates viscosity and affects compressibility. While viscosity of depolymerized silicate melts increases with pressure consistent with the free-volume theory, isothermal viscosity of polymerized melts decreases with pressure up to ~3–5 GPa, above which it turns over to normal (positive) pressure dependence. Here we show that the viscosity turnover in polymerized liquids corresponds to the tetrahedral packing limit, below which the structure is compressed through tightening of the inter-tetrahedral bond angle, resulting in high compressibility, continual breakup of tetrahedral connectivity and viscosity decrease with increasing pressure. Above the turnover pressure, silicon and aluminium coordination increases to allow further packing, with increasing viscosity and density. These structural responses prescribe the distribution of melt viscosity and density with depth and play an important role in magma transport in terrestrial planetary interiors.

A combination of theory, X-ray diffraction (XRD) and extended x-ray absorption fine structure (EXAFS) are used to probe the hydration structure of aqueous Na⁺. The high spatial resolution of the XRD measurements corresponds to Q_max = 24 Å⁻¹ while the first-reported Na K-edge EXAFS measurements have a spatial resolution corresponding to 2k = Q_max = 16 Å⁻¹. Both provide an accurate measure of the shape and position of the first peak in the Na–O pair distribution function, g_NaO(r). The measured Na–O distances of 2.384 ± 0.003 Å (XRD) and 2.37 ± 0.024 Å (EXAFS) are in excellent agreement. These measurements show a much shorter Na–O distance than generally reported in the experimental literature (Na–O_avg ∼ 2.44 Å) although the current measurements are in agreement with recent neutron diffraction measurements. The measured Na–O coordination number from XRD is 5.5 ± 0.3. The measured structure is compared with both classical and first-principles density functional theory (DFT) simulations. Both of the DFT-based methods, revPBE and BLYP, predict a Na–O distance that is too long by about 0.05 Å with respect to the experimental data (EXAFS and XRD). The inclusion of dispersion interactions (–D3 and –D2) significantly worsens the agreement with experiment by further increasing the Na–O distance by 0.07 Å. In contrast, the use of a classical Na–O Lennard-Jones potential with SPC/E water accurately predicts the Na–O distance as 2.39 Å although the Na–O peak is over-structured with respect to experiment.