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Quasielastic spectra S(q,ω) of pure liquid germanium and Ge98X2 alloys with X = Au, In, Ce. For clarity the spectra are shifted by 0.3 each. The lines are fits with equation (2). Inset: line width as a function of q². The lines are fits with equation (3).
Source publication
Self- and inter-diffusion coefficients in liquid Ge and dilute Ge-based GeSi, Ge-Au, Ge-In, Ge-Ce and Ge-Gd alloys-containing 2 at% additions, respectively, are measured using a comprehensive approach of measuring techniques: Quasielastic neutron scattering, in-situ long-capillary experiments combined with X-ray radiography, and a long-capillary ex...
Citations
... Incoherent quasielastic neutron scattering (QENS) [5][6][7] provides a powerful experimental tool to investigate diffusion in liquids [5] including liquid metals and metallic alloys [8][9][10][11][12][13][14]. In this paper, the results of time-of-flight (TOF) QENS experiments and molecular dynamics (MD) simulations of the self-diffusion of atoms in pure liquid Ga and a Ga 1−x Ni x alloy at the small Ni concentration of x = 0.02 are presented. ...
... with a spectral half-width Γ(Q). The collected experimental spectra S exp (Q i , ω) are convoluted with the energy resolution function of the spectrometer R(Q, ω) [10,13,14]. Moreover, a background function b(Q, ω) = b 0 (Q) − b 1 (Q)ω (in one of the simplest approximations) is added. ...
The atomic mobility in liquid pure gallium and a gallium-nickel alloy with 2 at% of nickel is studied experimentally by incoherent quasielastic neutron scattering. The integral diffusion coefficients for all-atom diffusion are derived from the experimental data at different temperatures. DFT-based ab-initio molecular dynamics (MD) is used to find numerically the diffusion coefficient of liquid gallium at different temperatures, and numerical theory results well agree with the experimental findings at temperatures below 500 K.
Machine learning force fields derived from ab-initio molecular dynamics (AIMD) overestimate within a small 6% error the diffusion coefficient of pure gallium within the genuine AIMD. However, they better agree with experiment for pure gallium and enable the numerical finding of the diffusion coefficient of nickel in the considered melted alloy along with the diffusion coefficient of gallium and integral diffusion coefficient, that agrees with the corresponding experimental values within the error bars. The temperature dependence of the gallium diffusion coefficient D Ga (T) follows the Arrhenius law experimentally for all studied temperatures and below 500 K also in the numerical simulations. However, D Ga (T) can be well described alternatively by an Einstein-Stokes dependence with the metallic liquid viscosity following the Arrhenius law, especially for the MD simulation results at all studied temperatures. Moreover, a novel variant of the excess entropy scaling theory rationalized our findings for gallium diffusion. Obtained values of the Arrhenius activation energies are profoundly different in the competing theoretical descriptions, which is explained by different temperature-dependent prefactors in the corresponding theories. The diffusion coefficient of gallium is significantly reduced (at the same temperature) in a melted alloy with natural nickel, even at a tiny 2 at% concentration of nickel, as compared with its pure gallium value. This highly surprising behavior contradicts the existing excess entropy scaling theories and opens a venue for further research.
... We have provided an overview of experiments carried out in the framework of the ESA XRMON project in microgravity 63 . Comparison with low Si-content interdiffusion experiment (Ge-GeSi2at% hourglass) from MAPHEUS-3 (microgravity) with the diffusion coefficient effectively corresponding to the Si self-diffusion. ...
X-ray radioscopy enables the in-situ monitoring of metal alloy processes and then gives access to crucial information on the dynamics of the underlying phenomena. In the last decade, the utilisation of this powerful imaging technique has been adapted to microgravity platforms such as sounding rockets and parabolic flights. The combination of microgravity experimentation with X-ray radioscopy has resulted in a leap in the understanding of fundamental science and has opened new paths in the fields of materials science. The present review focuses on the short history of this research, which includes facility developments, microgravity experiments and results obtained by partners of the XRMON (In-situ X-Ray MONitoring of advanced metallurgical processes under microgravity and terrestrial conditions) research project in the framework of the MAP (Microgravity Application Promotion) programme of the European Space Agency. Three illustrative research topics that were advanced significantly through the use of X-ray radioscopy will be detailed: solidification of metal alloys, metallic foam formation and diffusion in melts.
... Diffusion coefficients in liquid metals are usually of the order of∼5×10 −5 cm 2 s −1 [56], and Ge self-diffusion in liquid Ge at its melting temperature is∼1.3×10 −4 cm 2 s −1 [57]. Consequently, the maximum temperature of the RESET was chosen to be artificially extremely high in order to simulate the atomic transport kinetic in the melted region. ...
Simulation of atomic redistribution in Ge-Sb-Te (GST)-based memory cells during SET/RESET cycling is needed in order to understand GST memory cell failure and to design improved non-volatile memories. However, this type of atomic scale simulations is extremely challenging. In this work, we propose to use a simplified GST system in order to catch the basics of atomic redistribution in Ge-rich GST (GrGST) films using atomistic kinetic Monte Carlo simulations. Comparison between experiments and simulations shows good agreements regarding the influence of Ge excess on GrGST crystallization, as well as concerning the GST growth kinetic in GrGST films, suggesting the crystallized GST ternary compound to be off-stoichiometric. According to the simulation of atomic redistribution in GrGST films during SET/RESET cycling, the film microstructure stabilized during cycling is significantly dependent of the GST ternary phase stoichiometry. The use of amorphous layers exhibiting the GST ternary phase stoichiometry placed at the bottom or at the top of the GrGST layer is shown to be a way of controlling the microstructure evolution of the film during cycling. The significant evolution of the local composition in the amorphous solution during cycling suggests a non-negligible variation of the crystallization temperature with operation time.
... Most interdiffusion experiments are based either on the long capillary method (LC) [20][21][22] or the shear cell method (SC) [23][24][25], which in various modifications represents the current state of the art. The measurement methods provide interdiffusion coefficients with an approximate accuracy of 20-30% for LC and 5-15% for SC [26,27], which makes it clear that interfering factors cannot be completely excluded. ...
Interdiffusion coefficients are key parameters for the solidification process of liquid alloys. However, the determination of interdiffusion coefficients in liquid metals at high temperatures is a challenging and extensive task, due to a variety of potential systematic errors. In recent years we have developed an X-ray in situ shear cell method for the measurement of interdiffusion coefficients in binary metallic melts. This technique enables the monitoring of the experiment in order to exclude fatal errors. Utilizing X-ray contrast, the method also provides a time-resolved concentration distribution. Such an in situ data set contains significantly more information than ex situ evaluated experiments. Available analyzing strategies do not fully exploit this potential yet. We present three new analyzing approaches that are able to retrieve a concentration-dependent interdiffusion coefficient from only one in situ data set. In that way, larger concentration differences become accessible for an experiment, which considerably decreases efforts. Using simulations, the approaches are checked for robustness. Furthermore, the approaches are run on real in situ data from a binary (0 to 9 at% Au-content) Al–Au alloy at 1000 °C which results in a concentration-dependent interdiffusion coefficient within the measured concentration range.
... 4 Interdiffusion remains important for industrial applications and has been studied in the context of neutral liquids 5,6 and liquid metals. [7][8][9] In stellar environments, interdiffusion controls the distribution of elements throughout a star, impacting its evolution. [10][11][12] Additionally, diffusive mixing of thermonuclear fuel in inertial confinement fusion experiments 13 can spoil the burn conditions through radiative losses. ...
The characteristics of atomic-scale mixing are determined by diffusive processes driven by gradients. One such process is interdiffusion, a process driven by density gradients. We consider the various options for formulating interdiffusion in terms of Green-Kubo autocorrelation functions and the thermodynamic factor. Through models for the direct correlation function, we generalize expressions for the thermody-namic factor to include different electron and ion temperatures, electron degeneracy, finite-temperature exchange, and strong coupling. Additionally, a Gaussian autocorrelation function (GAF) is employed for a binary ionic mixture, yielding a simple analytic transport model for interdiffusion. The GAF model is shown to be accurate for moderately and strongly coupled plasmas.
... This was originally proposed by Andrade [53]. Figure 3 shows the self-diffusion coefficients of a number of pure metals and water at their respective melting (4), as a function of molar volume V m , melting temperature T m and the molar mass M m . Only diffusion measured by QENS are used, for Ge [54], Al [55,56], alkali metals [57], Cu [24], Ni [58], Fe [25], and water [59]. The resulting constant of equation (4) is found to be 1.06 ± 0.11 × 10 −9 m kg 1/2 s −1 K −1/2 mol −1/6 , which describes both the self-diffusion coefficients of the Hg and alkali metals at their melting point. ...
We report the temperature dependent atomic dynamics in mercury investigated with quasi-elastic neutron scattering between 240 and 350 K. The self-diffusivity follows an Arrhenius behavior over the entire investigated temperature range, with an activation energy of 41.8 ± 1.4 meV. The standard deviation is in the order of 5%, significantly more precise than previously reported measurements in the literature. Similar to alkali metal melts, the self-diffusion coefficient close to the melting point can be predicted with an effective atom radius of 1.37 Å. This shows a dominant contribution from the repulsive part of the interatomic potential to the mass transport. We observed deviations from the Stokes/Sutherland-Einstein relation and indications of an increasing collective nature of the dynamics with decreasing temperature. Thus, a transport mechanism of uncorrelated binary collisions cannot fully describe the temperature dependence of the self-diffusion.
... An experimental study of diffusion properties in metal melts is a hard task. Progress in this field is connected with the arising of new techniques in the last two decades [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. In particular, modern precise measurements provided a finding that small additions in dilute germanium weakly affect its diffusion coefficients in spite of the very big difference between their atomic mass [20]. ...
... Progress in this field is connected with the arising of new techniques in the last two decades [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. In particular, modern precise measurements provided a finding that small additions in dilute germanium weakly affect its diffusion coefficients in spite of the very big difference between their atomic mass [20]. Nevertheless, despite big progress spreading to binary and multicomponent alloys, the discrepancy in experimental results remains up to the present time, even for pure liquid metals. ...
The recently developed by us semi-analytical representation of the mean spherical approximation in conjunction with the linear trajectory approximation is applied to the quantitative study of self-diffusivities in liquid Cu, Ag and Au at different temperatures. The square-well model is employed for the description of the interatomic pair interactions in metals under study. It is found that our theoretical results are in good agreement with available experimental and computer-simulation data and can be considered as a prediction when such data are absent.
... An upper bound on the Ge-rich core for this case can be made by assuming that the excess Ge gathered in the initial transient is all deposited in the center of the fiber in the final transient, as pure Ge. The initial transient will contribute 2πRδ∆C, where ∆C is the excess Ge at the liquid interface; R is the outer radius of the core, and δ is the width of the transient, given by D/V, with D the diffusion coefficient (1x 10 −4 cm 2 /s [39,40]), and V the velocity of the phase front (0.7 mm/s). The value of ∆C was approximated as [(C 0 /k)-C 0 ], where C 0 is the initial concentration (6%), and k=0.23 is the equilibrium partition coefficient [41]. ...
CO2 laser annealing of SiGe core, glass-clad optical fibers is a powerful technique for the production of single-crystal cores with spatially varying Ge concentrations. Laser power, laser scan speed and cooling air flow alter the Ge distribution during annealing. In this work, near-single crystal fibers exhibiting a central axial feature with peak Ge concentration ∼15 at% higher than the exterior of the semiconductor core have been prepared. Preferential transmission of near infrared radiation through the Ge-rich region, and spectral data confirm its role as a waveguide within the semiconductor core. This proof-of-concept step toward crystalline double-clad structures is an important advancement in semiconductor core optical fibers made using the scalable molten core method.
Germanene is a two‐dimensional germanium (Ge) analogous of graphene, and its unique topological properties are expected to make it a material for next‐generation electronics. However, no germanene electronic devices have yet been reported. One of the reasons for this is that germanene is easily oxidized in air due to its lack of chemical stability. Therefore, growing germanene at solid interfaces where it is not oxidized is one of the key steps for realizing electronic devices based on germanene. In this study, the behavior of Ge at the solid interface at high temperatures is observed by transmission electron microscopy (TEM). To achieve such in situ heating TEM observation, this work fabricates a graphene/Ge/graphene encapsulated structure. In situ heating TEM experiments reveal that Ge like droplets move and coalesce with other Ge droplets, indicating that Ge remains as a liquid phase between graphene layers at temperatures higher than the Ge melting point. It is also observed that Ge droplets incorporate the surrounding amorphous Ge as Ge nuclei, thereby increasing its size (domain growth). These results indicate that Ge crystals can be grown at the interface of van der Waals materials, which will be important for future germanene growth at solid interfaces.
This study aims to establish predictive formulas for the temperature dependence of impurity diffusion coefficient based on a hard-sphere (HS) model and the measurement results. The impurity diffusion coefficients of Sb, Bi, and In in liquid Sn were measured using the shear cell technique and stable density layering at 773 K and 973 K (500 °C and 700 °C, respectively) with suppression of natural convection. The temperature dependence of the impurity diffusion coefficient can be predicted by multiplying the ratio of the solvent to the solute of the following three factors by the self-diffusion coefficient of the solvent as the slope: (i) the square of mean atomic diameter, (ii) the first peak of the pair distribution function calculated by the HS model, and (iii) the square root of the converted atomic weight. If the ratio of the atomic diameter is close to one, the temperature dependence of the impurity diffusion coefficient can also be predicted with an accuracy similar to the abovementioned relationship by multiplying the following two factors by the self-diffusion coefficient of the solvent as the slope: (i) the atomic diameter ratio of the solvent to the solute and (ii) the thermodynamic factor. The predictive formulas based on the HS model showed an accuracy of approximately ±10 pct for the experimental values from 573 K to 973 K (300 °C to 700 °C).
