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C: Surfaces, Interfaces, Porous Materials, and Catalysis
Metastable States in Pressurized Bulk and Mesoporous Germanium Abderraouf Boucherif, Silvana Radescu, Richard Ares, Andres Mujica, Patrice Melinon, and Denis Machon J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b02658 • Publication Date (Web): 01 May 2018 Downloaded from http://pubs.acs.org on May 4, 2018
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The Journal of Physical Chemistry
Metastable States in Pressurized Bulk and Mesoporous Germanium Abderraouf Boucherif1, Silvana Radescu2, Richard Arès1, Andres Mujica2, Patrice Mélinon3, Denis Machon1,3,* 1 – Laboratoire Nanotechnologies et Nanosystèmes (LN2), CNRS UMI-3463, Université de Sherbrooke, Institut Interdisciplinaire d’Innovation Technologique (3IT), Sherbrooke, Québec, Canada 2 – Departamento de Física and Instituto Universitario de Materiales y Nanotecnología, MALTA Consolider Team, Universidad de La Laguna, La Laguna 38200, Tenerife, Spain 3 – Institut Lumière Matière, Université de Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5306, 69622 Villeurbanne, France
Abstract Combination of porosity and hydrostaticity during compression is used with a view to explore the energy landscape of germanium. In this work, pressure-induced phase transformations in mesoporous crystalline Ge has been investigated by in situ Raman spectroscopy. A pressureinduced amorphization to a low-density amorphous state was observed prior to a reversible poly-amorphic transformation between low- and high-density amorphous states. These pressure-induced transformations show some similarities with the behavior previously reported in nanoparticles. Thermodynamics models developed in the case of nanoparticles are successfully used indicating that, in both cases, the large surface to volume ratio leads to an increase of the system energy, and that mesoporous materials may be considered as the negative image of a collection of nanoparticles. However, an inhomogeneous stress distribution is expected in porous materials because of it being a network with hyperbolic geometry. A control experiment is presented using a reference bulk germanium sample. The diamond to β-tin transformation is observed starting at around 8.0 GPa. On decompression, the metastable ST12 (Ge-III) phase is observed. Ab initio simulations are used to assign and interpret Raman spectra of this phase.
*Corresponding author:
[email protected] 1 ACS Paragon Plus Environment
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Introduction Mesoporous materials may be an alternative to the nanoparticle-based materials because of manufacturing (obtaining ceramics from powders of nanoparticles keeping the interesting related properties) and health implications (nanotoxicology). The large surface-to-volume ratio in both cases enhanced properties related to surface effects such as catalysis, Li insertion, reactivity, batteries and supercapacitors1, 2. However, interfaces and point defects at the surface induce additional contributions in the total energy of the system, leading to a new energy landscapes that modifies phase stabilities and favors the emergence of new phases with potentially interesting properties. Creating mesoporous materials by porosification from the bulk is a way to create interfaces and defects, and mesoporous materials may be considered as the negative image of a collection of nanoparticles. A question that arises is: is the surface energy component of a mesoporous materials equivalent to that of a collection of nanoparticles and will lead to similar metastable states? If the surface area may be considered as equivalent, the curvature of the interface at the nanoscale is different and may lead to others effects (Figure 1). Following the same interest of using high pressure, thermodynamics of mesoporous materials may be explored using pressure-induced transformations. Understanding of phase stability in materials with high surface to volume ratio is a key to control the properties associated to the different structures.
Figure 1 – Geometry of two systems with similar surface-to-volume ratio: a collection of nanoparticles and a mesoporous solid. In the case of nanoparticles, the stress may be continuously and smoothly distributed over the spherical shape. On the contrary, discontinuities in the mesoporous network with a hyperbolic geometry will lead to inhomogeneities in the stress distribution (here, stress in B will be higher than in A). 2 ACS Paragon Plus Environment
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In the case of porous silicon, combination of mesoporosity and pressure allows obtaining metastable states such as low-density (LDA) and high-density (HDA) amorphous states3. Thus, pressure-induced amorphization (PIA) was observed to occur for a porous nanocrystalline variety of p-doped Si compressed to P>10 GPa at room temperature3. Interestingly, the Raman spectrum did not correspond to that of a typical a-Si material based on tetrahedrally bonded units but instead reproduced the vibrational density of states function of a highly coordinated metallic crystalline form such as Si-II (β-Sn structure). It was concluded that PIA had resulted in a direct transformation into the HDA polyamorph, which then back-transformed into the LDA form of a-Si during decompression. More recently, another study on mesoporous Si showed a different sequence of transformation4: X-ray diffraction results indicate that π-Si, compressed in a metastable region, transforms to the primitive hexagonal crystalline phase at ~20 GPa, and formation of the HDA form of a-Si was confirmed during decompression of the high-pressure phase, and the HDA–LDA transformation occurred at around 4.5 GPa. Recompression of the LDA state led to the transformation to the primitive hexagonal structure around 18 GPa. These observations are an interesting indication that the nanostructuration due to the porosity leads to the observation of metastable states and that, depending on the sample, the transformation pathway may vary. Silicon shows strong similarities with germanium but has been more extensively studied because of its technological interest. Similar to bulk silicon, germanium under pressure undergoes a phase transition from the diamond-type structure (Ge-I) to a metallic phase (β-tin structure also named Ge-II) around 10-11 GPa. This transformation is upshifted to pressure above 17 GPa for nanoparticles5. In addition, high-pressure investigations of 5-nm Ge nanoparticles, mainly using EXAFS, have concluded that nanoparticles progressively become amorphous under pressure from the surface to the core. A subsequent LDA-to-HDA polyamorphic transformation may be observed at 17.5 GPa6. Such polyamorphism is also observed in bulk amorphous Ge7 at 11-12 GPa and 7–5.5 GPa, respectively, during increasing/decreasing pressure. On amorphous thin films, similar transformations are found but are dependent on the sample morphologies8. It is worth noting that, despite all these works, no experimental Raman spectrum of the High-Density Amorphous (HDA) state has been presented up to now except by simulations7.
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In this work, we intend to study the high-pressure transformations of mesoporous Ge to compare with the literature results reporting the behavior in nanoparticles, bulk and amorphous Ge. In addition, to infer the effect of hydrostaticity provided by the pressuretransmitting medium, a control experiment is also presented on the initial p-doped Ge wafer, before porosification. Ab initio simulations are used to characterize the Raman spectra of a metastable phase (Ge-III) appearing in this experiment. The observed pressure-induced transformations are described using theoretical models of increasing complexity. First, a model based on the Gibbs approach taking into account interface energy gives an overview of the transformation in mesoporous and bulk germanium. Then, a Ginzburg-Landau approach introduces the kinetics of the transformation to discuss the competition between amorphization and polymorphic transformations.
Experimental and simulation techniques The Raman experiment was carried out using a Horiba Labram HR Evolution Raman spectrometer operated with a 532 nm wavelength compatible with our high pressure setup (Diamond Anvil Cell - DAC), which can detect an inelastic signal down to about 6 cm−1. Laser power was set at 5 mW at the entrance of the DAC to avoid heating. The beam was focused on the sample using a 50x objective, with beam diameter ~2 µm at the sample. The scattered light was collected in backscattering geometry using the same objective. High pressure was generated using a membrane DAC with low-fluorescence diamonds. Mesoporous Ge samples were placed into a 125 µm chamber drilled in an indented stainless steel gasket. Paraffin oil was used as the pressure-transmitting medium (PTM). We chose a viscous liquid to minimize the invasion of the nanopores. The pressure was probed by the shift of the R1 fluorescence line of a small ruby chip. All the calculations were performed within the ab initio framework of the density functional theory (DFT), using the pseudopotential and plane waves method of calculation, as implemented in the VASP code9, 10, 11. The parameters of the calculation are similar to those used in Ref.12 for Ge. The 3d semicore electrons as well as the 4s and 4p valence electrons of Ge were dealt with explicitly in the calculations, for which a projector augmented-wave (PAW) scheme was used13, 14, with a kinetic-energy cutoff in the plane wave expansions of 375 eV. The so-called PBEsol generalized gradient approximation (GGA) to the exchangecorrelation (XC) functional was employed15, although calculations with the GGA functional by Perdew et al. (PBE)16, as well as the local spin-density approximation (LSDA) (17 as 4 ACS Paragon Plus Environment
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parametrized in
18
) to the XC functional were also performed for testing purposes. For the
integration over the Brillouin zone of the ST12 (Ge-III) phase we used 8x8x8 MonkhorstPack grids. The relaxation of the structural degrees of freedom of ST12, both internal parameters and cell parameters, was driven by the calculated values of the corresponding forces and components of the stress tensor, with the converged configurations having residual forces less than 5 meV/A and maximum anisotropy in the diagonal components of the stress tensor less than 0.1 GPa. All these calculations correspond to hydrostatic pressures spanning the region of interest and zero temperature, with the small effect of the zero point energy neglected. For the phonon calculations we used an implementation of the density functional perturbation theory (DFPT), with subsequent assignment of modes upon the symmetry analysis of the eigenvectors. Mesoporous germanium (see figure 2) samples were prepared by electrochemical etching of p-type (resistivity 12.10-6 ohm.cm) Ge substrate in hydrofluoric acid solution (HF(49%): Ethanol (5:1, v-v)) under bipolar current during 120 min. A current density J+ = 1.5 mA/cm² during 1 sec was for etching and a current and J-= -1.5 mA/cm² during 1 sec for passivation. As a result, a ~ 800 nm mesoporous layer is obtained with an average pore diameter ranging from 5 to 8 nm. More details about the process could be found in ref.19,
20
. After this
21
treatment, the sample remains crystalline .
Figure 2 - Typical TEM picture of mesoporous germanium showing a sponge-like morphology.
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The Journal of Physical Chemistry
Raman spectra of mesoporous Ge and initial Ge wafer are shown on figure 3a. It is worth noting that despite the doping by Ga atoms, the initial Ge spectrum does not show any modification compare to an undoped bulk Ge sample (i.e., no Fano profile, no disordering effect). This is in agreement with previous measurements on p-doped Ge22. The main peak at 300 cm-1 is the T2g mode, the unique first-order Raman-active mode expected for the diamond structure. After porosification, the Raman spectrum has changed drastically with i) a change of the profile of the main peak and ii) appearance of a broad band at ~80 cm-1. The simulated phonon density of state (pDOS) of the diamond structure is in very good agreement with the recorded spectrum of the mesoporous Ge (Fig. 3b). This is an indication that the q = 0 Raman selection rules are broken due to the appearance of defects (surface and point defects) during the porosification. In addition, the profile change of the high-frequency peak may be consistent with a phonon confinement model19 related to the reduced propagation path between nanopores.
After Porosification
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Figure 3 – (a) Raman spectra of Ge wafer before porosification and mesoporous Ge (b) Comparison of the Raman spectrum of mesoporous Ge along with the calculated phonon density of state of the diamond structure (Ge I). Results
Mesoporous germanium under pressure Raman spectra of mesoporous Ge during compression and decompression are shown on figure 4. During the first range of compression (P
