Anomalous phases and transformation mechanisms in gas-evaporated titanium fine particles: the corner fcc-indexed structure, the twin origin, the unidentified low-pressure film, and quantitative phase-selection conditions

A 1981 electron-microscopy study of titanium fine particles prepared by the gas-evaporation (metal-smoke) method found hcp particles whose external shape is a truncated rhombic dodecahedron characteristic of the high-temperature bcc phase, implying nucleation in the bcc phase followed by a martensitic bcc-to-hcp transformation, and left four issues explicitly unresolved: (i) the identity and origin of a corner-localized structure giving fcc-indexed diffraction spacings $d_{111}=2.53$ Å and $d_{200}=2.19$ Å ( $a_0=4.38\pm 0.03$ Å) with no identifiable orientation relationship to the hcp matrix; (ii) whether the observed twins (planes indexed $(10\bar{1}1)_{hcp}$ , corresponding to $\{110\}_{bcc}$ ) form in the bcc precursor or during the martensitic transformation; (iii) the identity of a thin film formed in the inner zone at about 1 Torr whose diffraction pattern could not be indexed to any single known titanium or titanium-oxide phase; and (iv) the absence of a quantitative model predicting when particles nucleate as bcc and transform with habit preservation. Later literature -- TiH $_2$ ultrafine particles formed by H $_2$ gas evaporation with twin-accompanied Ti $\leftrightarrow$ TiH $_2$ transformations, identification of cubic phases in evaporated Ti films as TiH $_{1.5}$ and TiO, and modern atom-probe evidence that anomalous fcc 'Ti-X' phases are hydrogen- or oxygen-stabilized -- strongly constrains but does not directly resolve these questions. The problem is to determine the nature of the corner-localized structure and of the low-pressure film, establish the twin-formation mechanism, and supply the quantitative phase-selection account for gas-evaporated titanium particles.

Background

Ultrafine metal particles can be prepared by the gas-evaporation (or 'metal smoke') method: a metal is evaporated in an inert gas at a pressure of order 1--10 Torr, and the vapor nucleates and grows into free particles that drift outward and are collected at different distances ('zones') from the source, with particle size and structure varying by zone. The method was systematized in Japan in the 1960s--1980s through electron-diffraction studies of smoke particles, e.g. by Kimoto and Nishida. Bulk titanium is hexagonal close-packed (hcp, the $\alpha$ phase) at room temperature and transforms to a body-centered cubic (bcc, $\beta$ ) structure above 882 $^\circ$ C. A martensitic transformation is a diffusionless, displacive change of crystal structure in which atoms move cooperatively by fractions of an interatomic spacing, so that a definite lattice orientation relationship is preserved between parent and product; because such transformations preserve external shape, the crystal habit (the polyhedral particle shape bounded by slow-growing facets) can record the lattice of the parent phase rather than the product. Kobayashi, Yatsuya and Mihara (1981) studied Ti particles evaporated in argon at 1--10 Torr (source 1800--2100 $^\circ$ C) by transmission electron microscopy and electron diffraction, in which interplanar spacings $d_{hkl}$ are measured from spot positions. In the intermediate zone at about 10 Torr the particles (mean size about 700 Å, versus about 300 Å elsewhere) were internally hcp, but their habit was a truncated rhombic dodecahedron -- the $\{110\}$ -faceted polyhedron characteristic of bcc metals, with corners truncated so that the truncation ratio (truncated edge length over full edge length) averaged $R=59.5\%$ -- and the lattice relation between the hcp interior and the bcc lattice implied by the habit coincided with the known martensitic bcc-to-hcp orientation relationship. The particles were therefore concluded to nucleate as bcc and to transform martensitically to hcp while retaining the bcc-derived habit. The study left four anomalies unexplained. First, small corner regions of many hcp particles gave weak extra diffraction spots with spacings $d_{111}=2.53$ Å and $d_{200}=2.19$ Å, indexing to an fcc lattice parameter $a_0=4.38\pm 0.03$ Å, with no simple orientation relationship to the hcp matrix; candidate identities include metastable fcc Ti, a titanium hydride of the CaF $_2$ (fluorite) type, in which a face-centered titanium sublattice of $a\approx 4.4$ Å contains interstitial hydrogen, a titanium suboxide such as NaCl-type TiO ( $a\approx 4.18$ Å), or a curvature/projection artifact. Second, some particles were twinned -- two crystal regions related by reflection in a common plane -- with twin planes indexed $(10\bar{1}1)_{hcp}$ , corresponding to $\{110\}$ of the bcc parent, but the stage at which twins form was not established. Third, at the lowest pressure studied (about 1 Torr) a thin film formed in the inner zone of the smoke whose electron-diffraction pattern could not be indexed to any single known titanium or titanium-oxide phase. Fourth, no quantitative model linked the evaporation conditions (pressure, source temperature, cooling rate, growth zone) to the observed prevalence of habit-preserving martensitic transformation. Later work makes these questions sharper rather than moot. The same laboratory showed that TiH $_2$ ultrafine particles form when Ti is evaporated in H $_2$ gas, that their growth involves a martensitic bcc-to-fluorite transformation, and that Ti $\leftrightarrow$ TiH $_2$ interconversions of particles are always accompanied by twin planes (Yanagida, Yatsuya and Mihama, 1987); that cubic phases appearing in evaporated Ti films are CaF $_2$ -type TiH $_{1.5}$ ( $a=0.441$ nm) and NaCl-type TiO ( $a=0.418$ nm) (Yamada, Kasukabe and Yoshida, 1990); and modern atom-probe tomography, a technique that maps composition atom by atom, shows that anomalous fcc 'Ti-X' regions in titanium foils are hydrogen- or oxygen-stabilized (Traylor et al., 2020), while an oxygen-stabilized fcc solid solution has been reported in additively manufactured Ti-6Al-4V (Wang et al., 2022). What the literature has not done is return to gas-evaporated Ti particles themselves and determine the corner structure, the structure and composition of the film, the twin-formation stage, or the quantitative phase-selection conditions.

Problem Statement

Complete the structural and mechanistic account of titanium fine particles prepared by inert-gas evaporation that Kobayashi, Yatsuya and Mihara (1981) left unresolved. The particles are produced by evaporating Ti in argon at pressures of order 1--10 Torr with source temperatures 1800--2100 $^\circ$ C; collected particles are internally hcp yet bounded by a bcc-derived truncated rhombic dodecahedron habit, attributed to nucleation in the high-temperature bcc phase followed by a martensitic bcc-to-hcp transformation. Four linked questions must be answered. (1) Corner structure: determine the nature and origin of the small regions at the corners of the hcp particles that yield extra diffraction spots with spacings $d_{111}=2.53$ Å and $d_{200}=2.19$ Å, i.e. an fcc-indexed lattice parameter $a_0=4.38\pm 0.03$ Å -- in particular whether these regions are a distinct phase, namely a titanium hydride (CaF $_2$ -type TiH $_{2-x}$ ), a titanium suboxide or oxynitride, or genuinely metastable fcc Ti, or instead a projection or curvature artifact -- and, where they are a distinct phase, determine its crystal structure, chemical composition, and crystallographic orientation relationship, if any, to the surrounding hcp matrix, for which none was found in the original data. (2) Twin origin: establish at which stage the observed twins with planes indexed $(10\bar{1}1)_{hcp}$ , corresponding to $\{110\}$ of the bcc parent, form -- in the bcc precursor before transformation, during the martensitic bcc-to-hcp transformation, or during subsequent strain relaxation. (3) Low-pressure film: identify the structure and composition of the thin film that condenses in the inner zone of the evaporation smoke at about 1 Torr (absent at collection distances beyond about 8 cm), whose electron-diffraction pattern could not be indexed to any single known titanium or titanium-oxide phase, and determine whether the film consists of a single phase or a mixture of phases. (4) Quantitative phase selection: provide a quantitative, predictive account -- calibrated experiment or validated model -- of how background-gas pressure, source temperature, cooling rate, and growth-zone position determine whether Ti particles nucleate in the bcc phase and transform martensitically with habit preservation (as observed at about 10 Torr in the intermediate zone) versus condensing in other forms, including the nucleation kinetics. These four deliverables serve one common objective: a complete, predictive identification-and-mechanism account of phase selection and anomalous-phase formation in gas-evaporated titanium particles. Parts (1)--(3) are the constituent identifications of the anomalous microstructure of these particles, and part (4) is the quantitative generalization of the phase-selection account.

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