E. MacA. Gray

Modelling Dislocation‐Induced Anisotropic Line Broadening in Rietveld Refinements Using a Voigt Function. II. Application to Neutron Powder Diffraction Data

In paper I [Wu et al. (1998). J. Appl. Cryst. 31, 356–362] an approach was developed to the problem of modelling dislocation-induced X-ray or neutron-diffraction-line broadening. This paper applies those findings to the Rietveld refinement of the neutron powder diffraction profiles of deuterium-cycled LaNi5 and β-PdD0.66. These interstitially modified materials exhibit, respectively, strong and weak anisotropic strain broadening. The broadening in LaNi5 is consistent with a dislocation slip system a/3 (\bar 2110) {0\bar 110}, in agreement with transmission electron microscopy studies. In PdD0.66 the model predicts a regular distribution of screw dislocations, which remains to be confirmed by other techniques.

Modelling dislocation-induced anisotropic line broadening in Rietveld refinements using a Voigt function. I. General principles

The theory of dislocation-induced X-ray or neutron diffraction line broadening developed by Krivoglaz et al. and Wilkens has been adapted for Rietveld refinement of the powder diffraction profile by fitting a Voigt function to each peak. Information on both the type of slip system and the density of dislocations in the crystallites may then be found by evaluating the shape parameter and the index-dependent breadth of the Voigt function.

A neutron diffraction investigation of the LaNi5D phase diagram

Phase boundaries in the LaNi5D system determined by in situ neutron diffraction experiments have shown good agreement with those predicted from the LaNi5D pressure—composition phase diagram by intersecting extrapolated pressure plateaux and pure phase isotherms. Lattice parameter measurements show strong dilational strain in the α phase and severe compressive strain in the β phase in the two-phase region. In addition, there are systematic changes in linewidths in the two-phase region. Taken together, these provide strong evidence that the partially hydrided powder is microscopically inhomogeneous, i.e. individual micron-sized particles contain coexisting nanoscale α and β phase domains. The alternative model, consisting of a mixture of particles which are wholly α and particles which are wholly β phase, is not supported by these data. We observed hysteresis in the lattice parameters of the β phase and the linewidths of the α phase in the two-phase region, implying a fundamental asymmetry in the D absorption and desorption mechanisms.

An equation of state for deuterium gas to 1000 bar

An equation expressing the molar volume of deuterium to better than 0.1% up to a pressure of 1000 bar at temperatures from 273 to 423 K has been produced by fitting a modified van der Waals equation to experimental data. The equation fits all available data between 123 and 423 K but is also useful for extrapolation to at least 623 K at an estimated accuracy of 0.2%. This equation is more accurate than existing equations for deuterium below 1000 bar by about an order of magnitude.

Stability of the hydrogen absorption and desorption plateaux in LaNi5H Part 2: Effects of absorbing and desorbing large aliquots of hydrogen

Abstract There are several reports in the literature of experimental parameters, such as aliquot size, pressure drive and even hydrogenator volume, causing shifts in the measured pressures of the absorption and desorption plateaux of metal hydrides. Several models have been proposed to explain them, both as microstructural realities and as experimental artefacts. We review these models and conclude that most published experimental evidence of generic “large-aliquot” effects can be qualitatively explained as artefacts resulting from temperature gradients in the hydride bed. Some new results for LaNi5H are reported, including an effect on plateau length which does not seem to be explainable as an artefact. It is predicted that measurements with constant pressure over the sample will avoid artefactual large-aliquot effects.

Neutron diffraction study of the LaNi5–D system during activation

Abstract The microstructural changes occurring during the initial absorption of deuterium by virgin LaNi 5 at 40°C have been investigated using in-situ neutron powder diffraction. Rietveld profile refinement was used to determine the α and β phase proportions, lattice parameters and microstrains. In absorption, we found that in the two-phase region (i) the lattice parameters of the α and β phases were (within resolution) independent of the phase proportions; (ii) the α-phase diffraction peaks remained essentially unbroadened relative to the virgin metal; (iii) the β-phase peaks were relatively broad with the usual anisotropy of breadth. These findings imply that, as nuclei of β phase form for the first time in a particle that is wholly α phase, the lattice expansion causes pure β crystallites containing a very high density of lattice defects to fracture off the particle, i.e., decrepitate. Hence the nanoscale mixing and strong mechanical interaction between the α and β phases noted in multiply cycled material are not observed during the initial absorption of D atoms, because the lattice parameter misfit cannot be accommodated. In desorption, and subsequently, there is sufficient accommodation of the lattice parameter mismatch between the α and β phases for them to coexist in the same powder particle.

Stability of the hydrogen absorption and desorption plateaux in LaNi5H Part 3: experimental observations of compositional inhomogeneities due to temperature gradients

Abstract It has been predicted by Pons and Dantzer that temperature gradients due to the released enthalpy of H absorption-desorption will generate macroscopic inhomogeneities of the α β phase proportions in metal hydrides. We used in situ X-ray diffraction and in situ neutron diffraction respectively to study the growth of β-LaNi5H at the free surface, and β-LaNi5D in the bulk of powdered samples. It was found that a macroscopic compositional inhomogeneity does occur, and can be so severe that the free surface of the sample remains pure α phase while the bulk of the sample is rich in β phase.

Synchrotron powder diffraction line broadening analysis of dislocations in LaNi5-H

Abstract In situ synchrotron powder diffraction data for the LaNi5–H system were collected and the dislocation structures formed during the hydrogen activation cycle were studied by Rietveld refinement analysis in which anisotropic line broadening was modeled by dislocation scattering. Marginal line broadening was observed in the α phase formed by the very first hydrogen absorption by virgin metal. It is best modeled by dislocation a/3〈 2 110〉 on basal {0001} slip planes, with density 1010–1011/cm2. In the β phase (LaNi5H≈6) and the activated α phase (LaNi5H≈0.4, postdesorption), in contrast, the majority of dislocations is prismatic with a {0 1 10} slip plane and the same Burgers vector, with only a small proportion (∼ 15%) of dislocations having basal slip planes. High dislocation densities of the order of 1012/cm2 are associated with distributed strain fields of intermediate range. These results support the proposition that the dislocation structure is inheritable during the α–β phase transition, with the dislocations from the first-formed α phase on basal planes, and the majority created during nucleation and growth of the β phase on the prismatic planes, all being retained during subsequent phase transitions.

Stability of the hydrogen absorption and desorption plateaux in LaNi5–H: Part 5: H capacity

Abstract A systematic study was made by gravimetry, carefully preserving the system mass zero, of the positions of the α/α+β and α+β/β phase boundaries and the plateau lengths in LaNi 5 –H, while absorption–desorption cycling under various conditions of temperature and pressure. Our findings include: (i) in agreement with previous studies, the initial capacity of the virgin intermetallic is in excess of H / M =1.1; (ii) however, the initial desorption plateau is shorter than the initial absorption plateau by nearly 0.1 in H / M , owing to the trapping of H, possibly in lattice defects; (iii) absorption–desorption cycling at any temperature in impure hydrogen shortens the plateaux (capacity degradation), greatly exacerbated by elevated temperature; (iv) however, the total H capacity remains relatively constant, with an exchange of H between ‘reversible’ sites and trap sites, manifest as the drift in the α/α+β phase boundary noted above. The reality of the H trapping owing to activation has been proved by independent techniques, such as deep-inelastic neutron scattering. It is unlikely that this H is initially trapped in the form of LaH x , although this and other La–Ni hydrides do form during extended cycling at elevated temperatures.

Stability of the hydrogen absorption and desorption plateaux in LaNi5H Part 1: Hysteresis dynamics and location of the equilibrium isotherm

Abstract Several aspects of pressure hysteresis in LaNi 5 H x have been experimentally investigated by the aliquot method. These aspects include the important question of the existence of a unique equilibrium absorption or desorption isotherm, and the supposed “large-aliquot” effect, which will be dealt with in a subsequent paper. In this paper, a systematic survey of hysteresis as a function of the measurement time and step length on the plateaux is reported. We found that there is a minimum achievable hysteresis, even after very long measurement times (such as 10 days for one hysteresis loop); therefore, we conclude that a unique isotherm does not exist. We found evidence to suggest that neither plateau should be regarded as being closer to equilibrium than the other. Instead, the plateaux appear to be near equilibria in two thermodynamically distinct systems.