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The sample, sealed in the fused quartz tube, was loaded into a thin-walled Al2O3 container for the QENS measurements, which were carried out at the time-of-flight spectrometer TOFTOF at the Heinz Maier-Leibnitz neutron source (FRM II) in Munich (47, 48). Two incident neutron wavelengths λi = 4.4 and 7 Å were used to obtain a broad q and energy transfer range along with a high resolution of about 90 μeV (full width at half maximum).

Spectra were collected as a function of temperature in a high-vacuum, high-temperature Nb furnace. Raw time-of-flight data were normalized to a vanadium standard and interpolated to constant q to obtain the dynamic structure factor S(q,ω) using the FRIDA-1 software (see http://sourceforge.net/projects/frida/ for source code). All spectra were found to be well described by a model composed of the quasi-elastic scattering from the alloy melt and a flat background to approximate the processes too fast to be accurately measured by the spectrometer. The S(q,ω) obtained in the measurements, where λi = 7 Å, was additionally modeled to include the elastic scattering from the container. In general, the model S(q,ω) readsEmbedded Imagewhere R(q,ω) is the instrumental resolution function, N is a normalization factor, A0 is the magnitude of the elastic scattering, and b(q,ω) is a constant but q-dependent background. The symbol ⨂ denotes a numerical convolution. The quasi-elastic scattering was found to be best described with a single Lorentzian of the form (see fig. S1)Embedded Imagewhere Γ is the half width at half maximum. Below q2 ~ 0.6 Å−2, the incoherent scattering from Ge and Te dominates and the coherent contributions from thermal diffusion (Rayleigh line) and acoustic modes are effectively contained in the flat background of the observed quasi-elastic spectra (49). A mean Ge/Te self-diffusion coefficient was determined viaEmbedded Image

An analysis was also carried out in the time domain first by obtaining the ISF S(q,t) (or density correlation function) via cosine Fourier transform of the measured S(q,ω) and normalizing to the instrumental resolution function R(q,t). In general, the data were then fitted with a simple exponential decay asEmbedded Imagewhere f(q) is the amplitude, τ is the structural relaxation time, and the constant c is an offset that takes care of any remaining elastic scattering. It should be noted that this is in line with the model used for S(q,ω), as the Fourier transform of a Lorentzian is a simple exponential. To ensure consistency of the analyses in both energy transfer and time domain, we restricted the fitting range in the energy transfer domain to [−1,1] meV and in the time domain to the data points after 0.65 ps. At higher energy transfers and shorter times, the spectra are dominated by phononic vibrations and fast relaxation processes. The self-diffusion coefficient was obtained from the time domain analysis viaEmbedded Image

The values of DGe/Te reported in the manuscript represent an average of the values obtained in both analyses.

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