{
  "abstract": "We investigated the low-temperature thermal expansion of the $α$ phase and the $ω$ phase, a high-pressure polymorph of titanium, by X-ray diffraction measurements from approximately 5 to 300 K, together with first-principles calculations. Single-phase bulk polycrystalline $ω$-Ti was synthesized at 7.7 GPa and 500 $^\\circ$C and recovered to ambient pressure. Although the two phases exhibit very similar volumetric thermal expansion, their axial responses are markedly different. In $α$-Ti, the $c$-axis thermal expansion coefficient becomes negative below approximately 50 K and reaches a minimum of $-0.71 \\times 10^{-6}$ K$^{-1}$ at 20 K. Both experiment and theory indicate substantially smaller $c$-axis negative thermal expansion than previously reported from single-crystal length measurements. In contrast, $ω$-Ti expands nearly isotropically along the $a$ and $c$ axes, and its $c/a$ ratio remains nearly temperature independent and close to the ideal bcc-derived value. The $c$/$a$ ratio of $α$-Ti decreases with increasing temperature. Debye-Grüneisen analysis yielded Debye temperatures of $427 \\pm 5$ K and $409 \\pm 12$ K and effective Grüneisen parameters of $1.33 \\pm 0.04$ and $1.23 \\pm 0.04$ for $α$-Ti and $ω$-Ti, respectively. The first-principles calculations reproduce the volumetric thermal expansion of both phases and capture the overall trends of their axial responses.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33302",
  "author_total": 3,
  "authors": [
    {
      "name": "Norimasa Nishiyama"
    },
    {
      "name": "Atsushi Togo"
    },
    {
      "name": "Yoshitaka Matsushita"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0v01f1vg6pm2n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33302",
  "fulltext_url": null,
  "id": "0v01f1vg6pm2n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33302",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mtrl-sci"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.33302",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0v01f1vg6pm2n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.33302",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33302"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Low-temperature thermal expansion of the $α$ and $ω$ phases of titanium",
  "title_text": "Low-temperature thermal expansion of the α and ω phases of titanium",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/0v01f1vg6pm2n",
  "venue": "arXiv",
  "versions": []
}