Journal of Materials Science

, Volume 55, Issue 1, pp 177–190 | Cite as

Uniaxial negative thermal expansion in the mullite- and borax-type PbAlBO4 polymorphs

  • Mathias Gogolin
  • M. Mangir MurshedEmail author
  • Martin Ende
  • Ronald Miletich
  • Thorsten M. Gesing
Composites & nanocomposites


This study presents an investigation on the axial negative thermal expansion of α-PbAlBO4 and β-PbAlBO4. Polycrystalline and single-crystal samples were prepared by solid-state synthesis method, characterized by temperature- and pressure-dependent X-ray and neutron diffraction experiments. The axial negative linear compressibility (NLC) is known for the α-polymorph, although structurally different the β-polymorph also shows similar NLC phenomenon. The lattice thermal expansion was described using the first-order Grüneisen equation of state, where the vibrational energy was calculated using the Debye–Einstein-Anharmonicity model. The density functional theory (DFT)-based phonon density of states and Raman spectra helped to choose the characteristic frequency to model the metric parameters. Lattice thermal expansion was additionally simulated in the quasi-harmonic approximation using the plane-wave DFT approach at the PBEsol level. The apparent departure of the quasi-harmonic approximation model has been discussed in terms of associated thermodynamic functions. The interplay between the topology-induced negative cross-compliance and anisotropic Grüneisen parameter has been identified as the driving force for the axial negative linear compressibility and axial negative thermal expansion.



MG would like to thank the central research development found (CRDF) of the University of Bremen. We gratefully acknowledge the Deutsche Forschungsgemeinschaft (DFG, German science foundation) within the project GE1981/9-1 (# 403459553) and within the large instrument program (INST 144/435-1 FUGG) for his financial support. We gratefully acknowledge the North German Supercomputing Alliance (HLRN) for computational resources. Part of the research conducted at ORNL’s Spallation Neutron Source was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy.

Supplementary material

10853_2019_4013_MOESM1_ESM.docx (1.6 mb)
Supplementary material 1 (DOCX 1654 kb)


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Authors and Affiliations

  1. 1.University of Bremen, Institute of Inorganic Chemistry and CrystallographyBremenGermany
  2. 2.University of Bremen, MAPEX Center for Materials and ProcessesBremenGermany
  3. 3.Department of Mineralogy and CrystallographyUniversity of ViennaViennaAustria

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