10,11,28 In general, phonon calculations use a linear approximation method except as annotated where a finite displacement method is used. These calculation procedures are similar to those previously reported for MgB 2 and metal-substituted derivatives of MgB 2 ( e.g., (Mg 1− xM x)B 2) where (M = Al, Ti, Sc, Cd, Ba). The typical setup for calculations uses a Δ k value ranging between 0.01 to 0.02 Å −1 (or less i.e., a grid mesh ranging from 45 × 45 × 30 to 19 × 19 × 14), 26 with a plane wave basis set cut-off of 990 eV, an ultra-fine (or better) customized setup to ensure total energy convergence of less than 5 × 10 −6 eV per atom, a maximum force of less than 0.01 eV Å −1, a maximum stress of less than 0.02 GPa and maximum displacements of less than 5 × 10 −4 Å. In general, the local density approximation (LDA) and generalized gradient approximation (GGA), with norm-conserving pseudopotentials, are used in separate DFT calculations to provide a measure of computational fidelity. 19,20,26 For higher dimension superlattices ( e.g., 4 c), where a large computational resource is required for all reciprocal directions, calculations are limited to key, high symmetry reciprocal space directions such as ΓA, ΓK and ΓM. Superlattices in the c axis direction are constructed by multiplying the unit cell along the appropriate direction and imposing reduced symmetries to suit the superlattice construction, in line with procedures described in our earlier publications. Crystal structure visualizations, schematics and bond lengths were generated using Crystal-Maker X version 10.5.3 software based on the MgB 2.cif file. 21 All structures are optimized for geometry, including cell parameters, starting from the MgB 2 crystal information file (.cif) for P6/ mmm group symmetry (No. Calculation procedures Electronic Band Structure (EBS) and PD calculations are undertaken using Density Functional Theory (DFT) as implemented in the Cambridge Serial Total Energy Package (CASTEP) of Materials Studio (MS) 20. To deconvolute spectra from sample-PE composites, absorption results for each composite are divided by measurements at the same temperature for PE only under the same conditions. The OPUS 8.0 software is used for data acquisition and analysis. Spectra are collected at specific temperatures in the range 6 K to 296 K five separate spectra are collected at each temperature and averaged to improve quality of signal to noise ratios. The spectrometer is fitted with a 6 μm multilayer Mylar beam splitter and a Si Bolometer from Infrared Laboratories Ltd equipped with a 13 μm cut-on long-pass cold filter to record the transmittance spectrum between 20–650 cm −1. The THz/Far IR beamline is equipped with a Bruker IFS 125/HR Fourier transform (FT) spectrometer, and for this work, the spectrometer is coupled to a 6 K closed loop pulse-tube (CLPT) cryostat from Cryo-Industries of America. Images of the He-cryostat and the insertable sample holder for transmission measurements, which are later converted to absorption values, are shown in ESI † (Fig. Pellets with high ratios of MgB 2 did not provide clear transmittance signals consequently, subsequent work focused on pellets with 4% and 5% MgB 2 content. Ratios of MgB 2 : PE between 70 : 30, 50 : 50, 35 : 65, 15 : 85, 5 : 95, 4 : 96 and 3 : 97 were initially scanned at room temperature to determine optimum ratios for transmission of a signal. Because the expected level of absorption from samples under experimental conditions was unknown, a wide range of MgB 2 : PE mixtures were prepared for preliminary analysis. 25įine-grained MgB 2 is a black powder and so absorbs strongly in the IR region. 23 Powders of each sample were thoroughly mixed with polyethylene (PE) powder using a mortar and pestle inside a nitrogen filled glove box, and pressed into small 3 mm diameter, hollow stainless disks, included in a die set from PIKE. Lattice parameters ( a = 3.07534(5) Å and c = 3.52318(9) Å) and cell volume (28.857(1) Å 3) values obtained using Rietveld refinement as well as T c are consistent with previous studies of carbon doped MgB 2. The lattice parameters, transition temperature ( T c) and cell volume for carbon doped Mg 11B 2 decreased after carbon doping compared to those for pure Mg 11B 2. The superconducting transitions for these MgB 2 samples are shown in Fig. Experimental Pure MgB 2 powders, one synthesized in-house and another outsourced from Sigma Aldrich, as well as a sample of 10% carbon doped Mg 11B 2 powder (made in-house with 10% C400 and boron 11B isotope) were used for THz/Far IR analysis. We utilise DFT computation to identify potential superlattice constructs for MgB 2 that explain these low frequency observations. THz/Far Infrared synchrotron absorption experiments on pure and doped MgB 2 samples show that the absorption spectral weight at low wavenumber ( i.e., 100 K).
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