For decades, borides have been primarily studied as crystallographic oddities. With such a wide variety of structures (a quick survey of the Inorganic Crystal Structure Database counts 1253 entries for binary boron compounds!), it is surprising that the applications of borides have been quite limited despite a great deal of fundamental research. If anything, the rich crystal chemistry found in borides could well provide the right tool for almost any application. The interplay between metals and the boron results in even more varied material's properties, many of which can be tuned via chemistry. Thus, the aim of this review is to reintroduce to the scientific community the developments in boride crystal chemistry over the past 60 years. We tie structures to material properties, and furthermore, elaborate on convenient synthetic routes toward preparing borides.

Rediscovering the Crystal Chemistry of Borides.

In the search for a highly active bulk material for the hydrogen evolution reaction (HER) under acidic conditions, we developed a simple solvothermal approach to synthesize Pd2B nanosheets supported on carbon, which achieves a low overpotential for the HER, 15.3 mV at 10 mA cm−2, a small Tafel slope of 22.5 mV dec−1 and a high exchange current density (j0) of 2.84 mA cm−2. The atomic structure evolution from Pd to Pd2B catalyst during synthesis is analyzed in detail via experimental and theoretical calculations, which shows that the slow insertion of B is assisted by the layer-by-layer fcc-to-hcp phase transition. Theoretical calculations further revealed that both the subsurface B and the lattice expansion after the hcp lattice formation play a key role to boost the HER activity. Since the Pd2B crystal is the global minimum in the Pd–B alloy, the success in the synthesis and demonstration of high HER activity paves the way towards further exploration of the catalytic performance for this stable metal boride material.

Metal boride better than Pt: HCP Pd2B as a superactive hydrogen evolution reaction catalyst

Anisotropic, i.e. hkl-dependent microstrain broadening of Bragg peaks as observed in powder-diffrac- tion measurements often obstructs finding a good descrip- tion of the peak profiles during Rietveld refinement. This review describes strategies to model this type of structural line broadening. Emphasis is put, further, on the possible physical background of the refined width parameters in terms of compositional, thermal and elastic microstrain. Methods are described to extract thus quantitative micro- structural information. Moreover, it is shown how the ani- sotropy of the microstrain broadening can reveal the aniso- tropy of intrinsic properties of the solid, which may otherwise be difficult to determine, e.g. compositional lat- tice-parameter changes or elastic compliance.

Understanding anisotropic microstrain broadening in Rietveld refinement

On AgRhO2, and the new quaternary delafossites AgLi1/3Ms2/3O2, syntheses and analyses of real structures

The way in which nonstoichiometry and order and disorder interrelate in solid phase compounds is discussed. Nonstoichiometry due to the presence of structural vacancies is widely found in such solid phase compounds as transition metal carbides, nitrides, and oxides, and in related ternary interstitial compounds. It is shown that it is nonstoichiometry that determines the disordered or ordered distribution of atoms and vacancies. A review is given of the current status of research into structural order?disorder phase transitions in nonstoichiometric compounds with basal cubic and hexagonal crystal lattices. Symmetry analysis results for disorder-order and order?order phase transformations are considered in detail. Key superstructure types that form in nonstoichiometric compounds with vacancies in one or two sublattices are also described.

Nonstoichiometry and superstructures

The crystal structure of the Pd 6 B phase has been elucidated employing selected-area electron diffraction and X-ray and neutron powder diffraction methods. It is based on a cubic close packed arrangement of Pd with B occupying of the interstitial octahedral sites in an ordered way, such that a monoclinic (C2/c) superstructure results. The crystal structure contains isolated [BPd 6 ] octahedral entities providing large distances between nearest neighbour boron atoms. Depending on the way of preparation, the same Pd 6 B phase can occur for the same composition in two different 'manifestations' having considerably different lattice parameters, which has a microstructural origin. Various phase equilibria between the ordered Pd 6 B phase and the disordered interstitial solid solution of boron in cubic close packed palladium have been investigated to clarify the corresponding regions in the phase diagram Pd-B.

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On the formation and crystal structure of the Pd6B Phase.

The mean square atomic displacement parameter of Pd in the fcc interstitial solid solution PdB y , (u 2 Pd (y)), was determined for atomic ratios of y = 0.050, 0.100, and 0.184 using neutron powder diffraction data obtained at 15 K and 300 K. The values determined are significantly larger than those determined for pure Pd, (u 2 Pd (0)), at the same temperatures. Assuming that the dynamic (thermal) contribution to (u 2 Pd (y)) equals (u 2 Pd (0)), the static mean square atomic displacement parameter (u 2 Pd (y))) st = (u 2 Pd (y)) - (u 2 Pd (0)) was obtained as 0.0020(1) A 2 to 0.0027(1) A 2 . (u 2 Pd (y)) st showed no systematic variation with y or the sample temperature. This contrasts with an expected y(1 - y) concentration dependence for (u 2 Pd (y)) st . Comparison of (u 2 Pd (y)) st with values for the static mean square displacements of the metal atoms in different defect-NaCl type transition metal nitrides and carbides indicates that the current values for Pd in PdB y are exceptionally small.

Static displacements of Pd in the solid solution PdBy (0 < y < 0.2) as determined by neutron diffraction

The Pd–B system in the composition range of the solid solution PdBy has been the subject of a number of investigations as it provides an attractive model system for interstitial compounds. No consensus about the crystal structures and phase boundaries, particularly in the low-temperature regime, has been reached in the earlier works. In the light of very recent results on the crystal structure and composition ranges of the low-temperature phases, on the basis of X-ray, electron, and neutron diffraction analyses, a tentative phase diagram is presented which is compatible with practically all previous results.

The Pd-rich part of the Pd - B phase diagram

A powder diffraction method is presented for reconstructing probability density functions for the composition, p(y), of a PdBy solid solution material with composition (y)- dependent lattice parameter from the simultaneous analysis of all reflections in the powder diffraction patterns. The method is applied to the decomposition of a solid solution in a miscibility gap: two 'boundary phases' appear which gradually approach but don't attain fully the compositions of the expected equilibrium phases whereas a significant amount of material with intermediate compositions remains.

A time-resolved X-ray powder diffraction method to trace the decomposition of PdBy solid solutions.

Abstract The atomic structure of the incommensurate Pd5B1-z phase has been analysed in detail by selected area electron diffraction and neutron-powder diffraction. That structure is based on a close-packed cubic arrangement of Pd atoms with the B atoms occupying the octahedral sites in a long-range ordered fashion. The ordering pattern of B is an incommensurately modulated one with a modulation vector of a length which changes with the B content (~PdB0.18-0.19) to adapt the ordering pattern continuously to the actual composition. The structure can be conceived to be constituted from “isolated” BPd6 units (also occurring in the previously reported Pd6B phase) and edge-sharing B2Pd10 octahedra units, which occur in a ratio reflecting the actual B content. As predicted on the basis of elastic interactions between B atoms, nearest neighbour B-B pairs occur (the B2Pd10 double octahedra units) in the structure of the Pd5B1-z phase, whereas occurrence of second-nearest neighbour B-B pairs is avoided. For the ideal composition Pd5B the crystal structure of the Pd5B1-z phase corresponds to that of monoclinic UCl5 with U playing the role of B and Cl that of Pd.

Tilmann Georg Berger

Papers

On the formation and crystal structure of the Pd6B Phase.

Static displacements of Pd in the solid solution PdBy (0 < y < 0.2) as determined by neutron diffraction

The Pd-rich part of the Pd - B phase diagram

A time-resolved X-ray powder diffraction method to trace the decomposition of PdBy solid solutions.

The incommensurate crystal structure of the Pd5b1-z phase; B ordering driven by elastic interaction between B atoms