Incommensurately modulated crystal structures and phase transitions of Cu_3+xSi

Cinthia Antunes Corrêa^1,2, Morgane Poupon¹, Jaromír Kopeček¹, Robert Král¹, Petra Zemenová¹, Jérôme Lecourt³, Nicolas Barrier³, Olivier Perez³, Petr Brázda¹, Mariana Klementová¹, Lukáš Palatinus¹.

¹Institute of Physics of the CAS, v.v.i., Na Slovance 2, 182 21 Prague 8, Czechia

²Department of Physics of Materials, Charles University in Prague, Ke Karlovu 5, Prague 2, Czechia

³CRISMAT, Normandie Universit, UNICAEN, 6Bd Marechal Juin, Caen, France

cinthiacac@gmail.com

The region with approximate composition Cu3+xSi of the phase diagram of Cu-Si undergoes two phase transitions with increasing temperature: η” at room temperature, η’ and η at high temperature [1]. Even though the phase diagram is well established, recent studies have revealed new aspects from both the phase transitions and the crystal structures [2,3]. In this work we prepared samples by arc-melting with nominal composition Cu₇₇Si₂₃, Cu₇₆Si₂₄ and Cu₇₅Si₂₅. Samples were annealed at 650 °C during 24 h for homogenization. Temperature-dependent powder X-ray diffraction (TD-PXRD), temperature-dependent single crystal X-ray diffraction (TD-SCRXD), and DSC between 30 °C and 700 °C were combined for elucidating the crystal structures of the Cu3+xSi phases. Six phases were observed with increasing temperature: η’’’, η’’, η’, η3, η2 and η1. Five of the observed phases are incommensurately modulated. Sample Cu76Si24 was used during the temperature-dependent SCXRD. The average structure at room temperature has unit cell parameters a = 4.0700(3) Å, c = 14.6848(7) Å, it is similar for the three compositions studied and for η’’’ and η’’. Although the point group of the complete diffraction pattern is , the average structure can be described in the space group . The average structure can be described by three repetitions of hexagonal and honeycomb shaped layers (Fig. 1a). The modulation is revealed by large anisotropic distribution of electron density around the Cu atoms of the layer B. Two modulation vectors are necessary to index the complete diffraction pattern (Fig. 1b): q₁= and q₂=, where  (point group ) for η’’, and ,  (point group )  for η’’’. Both structures could be solved in (3+2)D superspace by Superflip [4], superspace groups  and  for η’’ and η’’’, respectively. The modulation function of both structures have amplitudes comparable to the size of the unit cell, discontinuities and windows. Given the complexity of the modulation and the small number of reflections measured, the function could not be parametrized to be refined using the superspace formalism, and a supercell approximation had to be used. Since  for η’’, a 4x4x3 supercell could  be used, while the smallest possible approximation for η’’’ was a 14x14x3 supercell. The refinement was performed in Jana2006 [5].

Temperature-dependent powder X-ray diffraction of the samples Cu₇₄Si₂₆ and Cu₇₈Si₂₂ was measured every 30 °, from 30 °C to 700 °C with heating rate of 5 °C/min. Two cycles of heating and cooling were measured to verify the reversibility of the transitions. Three additional phases, which were not present in the phase diagram, were observed, the transitions were reversible and reproducible with small hysteresis in the transition temperatures. Le Bail fitting of the powder patters was performed in Jana2006 using the models obtained by SCXRD, pseudo-Voigt profile, manual background combined with fifteen terms of Legendre polynomials. Initially the main reflections were indexed using cyclic refinement, and the modulation vectors were refined separately for each temperature, after the cyclic refinement. Except for the phase η3, powder patterns of the sample Cu₇₈Si₂₂ presented the same transitions as for the sample Cu₇₄Si₂₆ and only this sample will be shown. From the six phases observed in the sample Cu₇₄Si₂₆, five were completely indexed. Our study shows that the phase diagram might be more complex than that reported in the literature.

Figure. 1: (a) Cu₃Si structure viewed along a - Cu - black, Si - grey. Strongly modulated honeycomb layer filled with copper causes two variants of the structure shown in (b) above, modulation vectors for η’’ q1=(α,β,1/3) and q2=(-α-β,β,1/3), where α=β=0.2509(10), and below, for η’’’ α=0.23458(7), β=0.28171(7).

[1] Olesinki, R.W., Abbaschian, G.J., Bull. Alloy Phase Diagrams 7, 170 (1986).

[2] Corrêa C.A. et al., Acta Crystallographica B73, 767-774 (2017).

[3] Corrêa C.A. et al., Intermetallics 91, 129-139 (2017).

[4] Palatinus, L. and Chapuis, G., J. Appl. Cryst. 40, 786–790 (2007).

[5] Petříček V., Dušek M., Palatinus L., Z. Krist. 229 (5) 345–352 (2014).