E L E C T R O N I C S T R U C T U R E , M A G N E T I S M A N D D Y N A M I C S

S C I E N T I F I C H I G H L I G H T S

1 0 6 H I G H L I G H T S 2 0 2 2 I

calculation of the temperature-dependence of a number of relevant thermodynamic properties including entropy, enthalpy, free energy and heat capacity.

The extracted phonon dispersions were used to evaluate the full elastic tensor, comprising nine distinct stiffness coefficients that relate strains and stresses in the elastic regime. The elastic tensor knowledge made it possible to define the propagation of sound waves in all directions (Figure 98c), revealing large anisotropy, as testified by the different longitudinal sound velocity along the AC and the ZZ directions. Moreover, the elastic moduli and the anisotropy indices were extracted from the elastic tensor to describe the macroscopic mechanical response of black

phosphorus and estimate the response of phosphorene and phosphorene-based materials.

In conclusion, the IXS experiments performed at ID28 made it possible to measure the phonon dispersion curves of black phosphorus along the high-symmetry crystallographic directions, resulting in the retrieval of the full elastic tensor and sound velocities in 3D. The experimental characterisation provides a crucial benchmark for atomistic model calculations, which can then be applied to the prediction of black phosphorus thermodynamic and mechanical properties, providing a solid base for understanding phosphorene-based nanomaterials and designing novel optoelectronic devices exploiting its anisotropy.

PRINCIPAL PUBLICATION AND AUTHORS

Lattice dynamics and elastic properties of black phosphorus, E.A.A. Pogna (a,b), A. Bosak (c), A. Chumakova (c), V. Milman (d), B. Winkler (e), L. Viti (a), M.S. Vitiello (a), Phys. Rev. B 105, 184306 (2022); https:/doi.org/10.1103/PhysRevB.105.184306 (a) NEST, CNR-Istituto Nanoscienze and Scuola Normale Superiore, Pisa (Italy) (b) Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche, Milan (Italy) (c) ESRF (d) Dassault Systémes BIOVIA, Cambridge (UK) (e) Institute of Geosciences, Goethe University Frankfurt, Frankfurt am Main (Germany)

REFERENCES

[1] F. Xia et al., Nat. Commun. 5, 4458 (2014). [2] L. Viti et al., Adv. Mater. 27, 5567 (2015). [3] A.S. Rodin et al., Phys. Rev. Lett. 112, 176801 (2014).

Structure and mechanical properties of biogenic calcite from a sea urchin spine

X-ray scattering was used to compare inorganically formed natural calcite with biogenic calcite from a sea urchin spine. The unique mechanical properties observed in the urchin s spine were revealed to not depend on the material s calcite crystal structure but instead were associated exclusively with its mesoscopic architecture.

Biomineralogy rapidly expands knowledge about the mineral phases produced by living species, with potential

application areas including mechanical support, protection and defence. Calcites of biological origin and single crystals of carbonates interspersed with proteinaceous domains are known for anisotropically distorted lattice parameters and increased atomic displacement parameters (ADP). Diffuse scattering (DS) and inelastic X-ray scattering (IXS) were employed at beamline ID28 to compare inorganically formed natural calcite with biogenic calcite from the Mediterranean sea urchin spine, a species that has existed for 450 million years. The results were compared to the ab-initio model calculations of lattice dynamics. In addition, for the mesocrystal, the data were augmented by evaluating the faceting of the constituent nanocrystals.

Fig. 98: a) Rhombohedral crystal structure of black phosphorus with the armchair (AC) and zigzag (ZZ) directions of prominent electrical and thermal transport, respectively. b) Phonon dispersion curves measured by IXS (small dots), Raman (large dots at G) and from ab-initio calculations (solid lines). c) Angular plot of the retrieved sound velocities derived from IXS (dots) and calculated (lines).