A simplified invariant line analysis for face-centred cubic/body-centred cubic precipitation systems

Comparative Study on the Crystallography of Isothermal and Athermal Precipitations in HCP-BCC System

Due to the diversity of the lattice parameter ratio c/a of hexagonal structure and precipitation mechanism, a systematic overview of this transformation has not been fully established, which draws back the attempt to control crystallographic features of the precipitates and microstructures of applied metals and alloys. Here, a comparative investigation to the crystallography of isothermal and athermal precipitations occurring in the HCP−BCC system was demonstrated in a full range of the lattice parameter ratio by using an invariant deformation element (IDE) model. It was then proposed that a precipitation in the HCP−BCC system could be either of the isothermal type if the observed habit plane Miller index falls into a zone axis of BCC <11w>(w ≠ 0) or HCP 211¯0, or the athermal type when it is found to locate in a zone axis of BCC <11w](w = 0) or HCP [0001]. The crystallographic investigation on the precipitations in the HCP−BCC system in a full range of the lattice parameter may be a practical guide for computing material science when building a crystallographic interface model under an optimised orientation relationship, which is necessary to minimise the transformation system energy.

On the growth morphology and crystallography of the epitaxial Cu7Te4/CdTe interface

The manipulation of interface structures in the epitaxial growth of thin films is very essential, especially for some special heterogeneous structures. Crystallographic calculation method is a powerful tool when analyzing and predicting the structures of the coherent interfaces.

Atomic-scale investigation of a new phase transformation process in TiO2 nanofibers

Crystallography of phase transformation combining transmission electron microscopy (TEM) with in situ heating techniques and X-ray diffraction (XRD) can provide critical information regarding solid-state phase transitions and the transition-induced interfaces in TiO₂ nanomaterials theoretically and experimentally. Two types of reduced titanium oxides (Ti₃O₅, Ti₆O₁₁) are found during ex situ and in situ heating of TiO₂ (B) nanofibers with a specific morphology of the {100} single form (SF) in air and vacuum. The results indicate that the phase transformation process from TiO₂ (B) follows the TiO₂ (B) → Ti₃O₅ → Ti₆O₁₁ → anatase sequence for the nanofibers with the {100} SF. The occurrence of such a phase transition is selective to the morphology of TiO₂ (B) nanofibers. The corresponding orientation relationships (COR) between the four phases are revealed according to the TEM characterization. Four types of coherent interfaces, following the CORs are also found. They are TiO₂ (B)/Ti₃O₅, TiO₂ (B)/Ti₆O₁₁, Ti₆O₁₁/anatase and TiO₂ (B)/anatase respectively. The habit plane for the TiO₂ (B) to Ti₃O₅ transition is calculated as the {100}_TB by using the invariant line model. The detailed atomic transformation mechanism is elucidated based on the crystallographic features of the four phases.

Universal Approach for Predicting Crystallography of Heterogeneous Epitaxial Nanocrystals with Multiple Orientation Relationships

Heteroepitaxial nanocrystals are one of the most fundamentally and technologically important classes of materials systems. The correlation between form, dictated by crystallographic features such as growth habit and direction, and function, in terms of the ultimate physio-chemical properties is well established, thus placing an onus on precise synthesis control of nanocrystal morphology. Yet, nanocrystal heteroepitaxy can be a frustrating, time-consuming iterative process, particularly during the initial stages of development. What is desired is a powerful predictive tool that is able to successfully predict not only the interface or habit plane, but also rationalize the occurrence of epitaxial growth complexities such as multiple orientation relationships (MORs) and high-index faceting planes for a diverse range of materials. Here we provide such a powerful approach that is based on an invariant deformation element (IDE) model, and fundamentally founded on the crystallography of diffusional phase transformations. We demonstrate its impact by detailed computations supported by transmission electron microscopy evidence, for an archetypical complex metal oxide nanocrystal system (that has up to five MORs for three differing growth orientations). The method is then applied to successfully explain growth for different materials ranging from metals to metal carbides to transition metal oxides, even in thin film form. Thus, this relatively simple yet powerful predictive guide significantly reduces the systemic inefficiencies of guesswork and blind growth. Ultimately it can be easily integrated with machine learning techniques toward reliable and efficient advanced nanomaterials fabrication.

Predictable and controllable dual-phase interfaces in TiO₂(B)/anatase nanofibers

The TiO₂(B)/anatase dual-phase nanofiber exhibits enhanced photocatalytic activity when interfaces form during phase transformation of TiO₂. To precisely control the formation of coherent interfaces between TiO₂(B) and anatase, a thorough knowledge of phase transformation particularly from TiO₂(B) to anatase (TA) is required. In our study, a crystallographic model in conjunction with transmission electron microscopy (TEM) was employed to investigate the phase transformation. The coherent interface with a crystallographic orientation relationship of [001]TB//[100]TA, (200)TB//(002)TA, and (020)TB//(020)TA predicted by the crystallography model was also observed by TEM experimentally. In addition, two types of incoherent interfaces that may deteriorate photocatalytic activity were examined and can be eliminated via an accurate tuning of calcination. The fundamental knowledge acquired from this work, therefore, provides a new insight to synthesize more efficient dual-phase TiO₂ photocatalysts.

On the multiple orientation relationship of the Mg/γ-Mg17Al12precipitation system

The six orientation relationships (ORs) found in the Mg/γ-Mg17Al12precipitation system were summarized and systematically interpreted based on the atomic structure of the precipitate γ-Mg12Al17and the invariant deformation element (IDE) model for diffusional phase transformations. It was found that the pseudo-twinning relationship between the six ORs is a reflection of the pseudo-twinning relationship between the close- or near-close-packing planes ({\overline 8}\hskip.75{\overline 7}\hskip.75{\overline 7}), ({\overline 4}11), (033), (411) and (8{\overline 7}\hskip.75{\overline 7}) in the precipitate γ-Mg12Al17. As a result, the Pitsch–Schrader OR is the starting point for the other five ORs. Multiple morphologies, growth directions and habit planes could be rationally interpreted by the IDE model. This implies that a multiple orientation relationship between the variants of precipitates is favourable in order to minimize the gross energy of precipitation systems in which the matrix has a simple structure while the precipitate has a complicated structure, such as Mg/γ-Mg12Al17, Mg/δ-Zn2Zr3and Mg/η-MgZn2couples.

A simplified invariant line analysis for face-centred cubic/body-centred cubic precipitation systems. Erratum

Errors in the paper by Liu, Waclawik & Luo [J. Appl. Cryst.(2010),43, 448–454] are corrected.