X-ray free electron lasers are used in measuring diffraction patterns from nanocrystals in the 'diffract-before-destroy' mode by outrunning radiation damage. The finite-sized nanocrystals provide an opportunity to recover intensity between Bragg spots by removing the modulating function that depends on crystal shape, i.e. the transform of the crystal shape. This shape-transform dividing-out scheme for solving the phase problem has been tested using simulated examples with cubic crystals. It provides a phasing method which does not require atomic resolution data, chemical modification to the sample, or modelling based on the protein databases. It is common to find multiple structural units (e.g. molecules, in symmetry-related positions) within a single unit cell, therefore incomplete unit cells (e.g. one additional molecule) can be observed at surface layers of crystals. In this work, the effects of such incomplete unit cells on the 'dividing-out' phasing algorithm are investigated using 2D crystals within the projection approximation. It is found that the incomplete unit cells do not hinder the recovery of the scattering pattern from a single unit cell (after dividing out the shape transforms from data merged from many nanocrystals of different sizes), assuming that certain unit-cell types are preferred. The results also suggest that the dynamic range of the data is a critical issue to be resolved in order to apply the shape transform method practically.

Thermionic energy conversion, a process that allows direct transformation of thermal to electrical energy, presents a means of efficient electrical power generation as the hot and cold side of the corresponding heat engine are separated by a vacuum gap. Conversion efficiencies approaching those of the Carnot cycle are possible if material parameters of the active elements at the converter, i.e., electron emitter or cathode and collector or anode, are optimized for operation in the desired temperature range.

These parameters can be defined through the law of Richardson–Dushman that quantifies the ability of a material to release an electron current at a certain temperature as a function of the emission barrier or work function and the emission or Richardson constant. Engineering materials to defined parameter values presents the key challenge in constructing practical thermionic converters. The elevated temperature regime of operation presents a constraint that eliminates most semiconductors and identifies diamond, a wide band-gap semiconductor, as a suitable thermionic material through its unique material properties. For its surface, a configuration can be established, the negative electron affinity, that shifts the vacuum level below the conduction band minimum eliminating the surface barrier for electron emission.

In addition, its ability to accept impurities as donor states allows materials engineering to control the work function and the emission constant. Single-crystal diamond electrodes with nitrogen levels at 1.7 eV and phosphorus levels at 0.6 eV were prepared by plasma-enhanced chemical vapor deposition where the work function was controlled from 2.88 to 0.67 eV, one of the lowest thermionic work functions reported. This work function range was achieved through control of the doping concentration where a relation to the amount of band bending emerged. Upward band bending that contributed to the work function was attributed to surface states where lower doped homoepitaxial films exhibited a surface state density of ∼3 × 10[superscript 11] cm[superscript −2]. With these optimized doped diamond electrodes, highly efficient thermionic converters are feasible with a Schottky barrier at the diamond collector contact mitigated through operation at elevated temperatures.