dataesr/scientific-paragraphs-categorization huggingface dataset:
In this domain, a relationship is established between several parameters including porosity, permeability, fiber diameter, and the tortuosity of the fibrous medium. The pressure drop through different fiber arrangements and metal foams is measured in the creeping flow regime. The outcomes obtained are then manipulated to calculate the permeability of the samples. Compact relationships can be obtained by establishing comparisons with the contemporary experimental results and the data derived by others. (Equations (A23) and (A24)). In the following section, several models predicting the longitudinal "K L " and transversal microscopic "K T " permeability are presented. The permeability is a function of the fiber radius "r" and fiber volume fraction "V f ". Never the less, some models correlate the permeability with other parameters like the maximum fiber packing factor "V fmax ", geometrical constants, and packing structure (square, hexagonal, or other structures) "V a ".
The model requires inputs such as parameters of the fabric architecture and geometry and information concerning the compaction of the preform. Pictures taken for the fabric serve to acquire parameters such as the dimension of the mesopores and Figure  11  shows the modeling methodology. The model requires inputs such as parameters of the fabric architecture and geometry and information concerning the compaction of the preform. Pictures taken for the fabric serve to acquire parameters such as the dimension of the mesopores and architecture of the fiber bundles. The textile data sheet is needed too. In addition, the average volumes of mesopores and fiber bundles are required and are calculated for different fiber volume fractions taking into account a selected unit cell in the warp and weft directions.
When using Level-set methods for image processing  [89] , good agreement was found for predicting the permeability of unidirectional fiber beds, otherwise this result was a function of sample size, and further simulations on more realistic sample size are suggested. Finite difference methods seek approximate solutions of partial differential equations by solving a system linking the values of unknown functions at certain points sufficiently close to each other. Verleye et al. [90]  employed a three-dimensional finite difference solver. The solver works on a regular grid like the lattice Boltzmann method (LBM); however, it works with more acceleration techniques for the resulting partial differential system of equations. The fabrics were drawn in WiseTex, in a second step FlowTex software in order to predict the permeability.
Figures  14  and 15  show the modeling technique, where the homogenization of the Stokes equations is applied within the periodic domain of a textile and yields Darcy's law on the macro-level. The validation of this method on three kinds of fabrics is done with respect to experimental data from the literature; a maximum scattering of 50% is observed. This error was assigned to the sensitivity of the mesopores' size measurement. techniques for the resulting partial differential system of equations. The fabrics were drawn in WiseTex, in a second step FlowTex software in order to predict the permeability. Figures  14  and 15  show the modeling technique, where the homogenization of the Stokes equations is applied within the periodic domain of a textile and yields Darcy's law on the macro-level.
The validation of this method on three kinds of fabrics is done with respect to experimental data from the literature; a maximum scattering of 50% is observed. This error was assigned to the sensitivity of the mesopores' size measurement. Verley et al. [91]  solved the Navier-Stokes and Brinkman equations with the finite difference discretization method. The developed model was implemented into WiseTex software. The simulations showed good agreement when compared to experimental results from the bibliography for monofilament textile. Trochu and Gauvin  [92]  developed a finite difference method that predicts the in-plane permeability values; this model was compared with experimental measurements for fiber mats with irregular shapes. Its application showed many limitations such as computer limitations where a new mesh must be generated at each time step.
Advance in Numerical Methodology In this study, a steady-state simulation considering a theoretical unit cell is launched. The micropores are assumed to be blocked so a single-phase problem is solved. This reduces computational times significantly as well as meshing problems. The meshing and simulating time are short compared to a simulation in a dual scale transient mode (without blocking the micropores). The bundles' shape and dimensions as well as mesopores' sizes are respected in each simulation. Verley et al. [91]  solved the Navier-Stokes and Brinkman equations with the finite difference discretization method. The developed model was implemented into WiseTex software. The simulations showed good agreement when compared to experimental results from the bibliography for monofilament textile.
Hence, the porous structure of the fiber bed is well described and secondary pathways are taken into consideration in the simulation. Figure  18  shows the modeling methodology. As a first step, the bundle width "a" in Figure  19  as well as all the non-compacted fabrics' geometrical data are collected from the fabrics' data sheets. The second step is to predict these data for different fiber volume fractions. A theoretical unit cell is selected. This unit cell is drawn using TexGen software, as shown in Figure  20. The permeability correction factor is inserted into the drawings as shown in Figure  21. In the sixth step, the numerical simulations predicting permeability before and after the insertion of the fiber are launched. Finally, the results are compared to measured experimental results.
The second step is to predict these data for different fiber volume fractions. A theoretical unit cell is selected. This unit cell is drawn using TexGen software, as shown in Figure  20. The permeability correction factor is inserted into the drawings as shown in Figure  21. In the sixth step, the numerical simulations predicting permeability before and after the insertion of the fiber are launched. Finally, the results are compared to measured experimental results. In order to take the two pressures drop effects into consideration, a single mutation to the theoretical unit cell is assumed, where a single fiber is inserted inside each mesopore along the flow path and in the same direction. This fiber is small enough that its addition does not affect the total fiber volume fraction. This addition corrected the predicted permeability value.
For plain weave or interlock textiles, since the warp and weft bundles are interlaced together, the mesopore volume is relatively small. Hence, the porous structure of the fiber bed is well described and secondary pathways are taken into consideration in the simulation. Figure  18  shows the modeling methodology. As a first step, the bundle width "a" in Figure  19  as well as all the non-compacted fabrics' geometrical data are collected from the fabrics' data sheets. The second step is to predict these data for different fiber volume fractions. A theoretical unit cell is selected. This unit cell is drawn using TexGen software, as shown in Figure  20. The permeability correction factor is inserted into the drawings as shown in Figure  21. In the sixth step, the numerical simulations predicting permeability before and after the insertion of the fiber are launched.
X-Ray Diffraction (XRD) The crystalline structure of the residues after MLCC test were determined using XRD analyses. XRD spectra were recorded in the 5° -60° range using a Bruker AXS D8 diffractometer (Massachusetts, United States), equipped with a Cu Kα (λ = 0. 154 nm) radiation in configuration θ/2θ. All spectra obtained were analysed using DIFFRAC. EVA software (Bruker, Massachusetts, United States).
The ion-incorporated films were treated with UV/ozone in a Novascan PSDP UV/Ozone cleaner (Boone, IA, USA) to pre-oxidize the precursor and remove the major part of the polymer templates. A two-step high-temperature treatment was subsequently performed in air. The samples were heated up with 10 °C/min rate to 600 °C, kept at temperature for 30 min, then heated to 950 °C with the same rate and kept there for 1 h, before being cooled naturally in air. The fabrication procedure is schematically illustrated in Figure  1. Atomic force microscopy (AFM) measurements were carried out on a Veeco Dimension V scanning probe microscope (Plainview, NY, USA). Veeco RTESPW tips (resonant frequency 267-294 kHz, spring constant 20-80 N/m) were used in the tapping mode. Software WxSM (Version 4. 0 Beta 9. 1, Madrid, Spain) was used to analyze the obtained AFM images  [31].
One-dimensional intensity cuts along the horizontal qy and the vertical qz directions were extracted from the 2D diffraction pattern using the FITGISAXS program in Igor Pro  [32]. The fit of the 1D intensity cuts was achieved using the same program and assuming a hemispherical shape to describe the nanodots supported on the SiO2 substrate  [32, 33]. The fitted variables were the scale factor, dot diameter, dot height, dot separation, the full width half maximum (FWHM) of the Gaussian distribution for the dot diameter, and the positional disorder factor which determines the peak width in the horizontal cuts and is related to the domain size. The dot diameter and the dot height were extracted by fitting the qy and qz cuts, respectively. In order to achieve the best fitting results, the 1D cuts were first fitted using a monodisperse model and later by introducing a dot size polydispersity.
After 1D fitting was achieved, fitting of the 2D patterns was performed. The polydispersity in the dot diameter was taken Atomic force microscopy (AFM) measurements were carried out on a Veeco Dimension V scanning probe microscope (Plainview, NY, USA). Veeco RTESPW tips (resonant frequency 267-294 kHz, spring constant 20-80 N/m) were used in the tapping mode. Software WxSM (Version 4. 0 Beta 9. 1, Madrid, Spain) was used to analyze the obtained AFM images  [31]. SEM images were obtained with a Philips XL30 ESEM, using 5 kV (20 kV) acceleration voltage for BCP films (CFO nanostructures). To reduce the charging effect, the SEM samples were typically coated with a 4 nm Pt/Pd (80:20) layer via Ar + sputtering. Grazing incidence small-angle X-ray scattering (GISAXS) was performed at the MINA beamline at the University of Groningen.
The instrument is based on a Cu rotating anode (X-ray wavelength of λ = 0. 15413 nm, photon energy of 8 keV) and has a beam dimension of about 0. 5 mm. The used sample-to-detector distance is about 3 m and incident angles ranging from 0. 15 • to 0. 25 • were used. Two-dimensional patterns were acquired using a Vantec2000 Bruker detector (Leiderdorp, The Netherlands) and 2D GISAXS patterns are presented as a function of the horizontal q y and vertical q z scattering vector, with q y = 2π λ sin 2θ f cos α f and q z = 2π λ [sin(α i ) + sin α f ], where 2θ f and α f are the horizontal and vertical scattering angles, respectively. One-dimensional intensity cuts along the horizontal q y and the vertical q z directions were extracted from the 2D diffraction pattern using the FITGISAXS program in Igor Pro  [32].
GNXAS software was used to model the atomic environment around the absorbing atom. In this approach, the local atomic arrangement around the absorbing atom is decomposed into model atomic configurations containing 2, 3,. , n atoms. The theoretical EXAFS signal χ(k) is given by the sum of the two-body γ 2 , γ 3 ,. , γ n , and η 2 , η 3 ,. , η n three-body contributions, respectively, which take into account all the possible single and multiple scattering (MS) paths between the n atoms. The fitting of χ(k) to the experimental EXAFS signal allows refining the relevant structural parameters of the different coordination shells. The suitability of the model is also evaluated by comparison of the experimental EXAFS signal Fourier transform (FT) with the FT of the calculated k 2 χ(k) function. The fit parameters that were allowed to vary during the fitting procedure were the coordination numbers (CN), the distances R(Å), the Debye-Waller factors (σ) and the angles of the η n contributions.
6 eV). The measurement was done at a pressure below 5 × 10 -9 mbar. The spot size was 1000 µm. The energy resolution was set to 1. 26 eV and the electron take-off angle with respect to the surface normal was 37 •. The spectra were analyzed using the least-squares curve-fitting program Winspec, developed at the LISE laboratory, University of Namur, Belgium. A Shirley background was used. Binding energies are reported with a precision of ±0. 1 eV and referenced to the C1s peak at 284. 6 eV  [34, 35]. Magnetic properties of the samples were investigated with a Quantum Design MPMS XL SQUID magnetometer, using the reciprocating sample option (RSO). The M-T curves were obtained at 100 Oe during heating the sample from 5 to 350 K at a rate of 5 K/min. Prior to the measurements, samples went through either the FC (field-cooling) process, in which samples were cooled from 350 to 5 K (10 K/min) in a 100 Oe field, or the ZFC (zero-field-cooling) process during which samples were cooled from 350 to 5 K (10 K/min) in zero field.
After annealing at 950 • C the atomic arrangement is further perfected. The oscillations and FT magnitudes become almost identical to the CFO commercial nanopowder, suggesting an inverse spinel crystalline structure of the nanodots. The EXAFS spectra from the commercial CFO nanopowder and the final nanodots (annealed at 950 • C) were energy-calibrated, averaged and further analyzed using the GNXAS software. The simulation curves are plotted in Figure  6  as solid red lines, which fit the experimental results very well for both the standard and the nanodots. The two-body and three-body simulation results at the Co K-edge are listed in Tables  3  and 4 , respectively, those at the Fe K-edge are listed in Tables  S2  and S3  (in Supplementary Materials). The atomic distances are in good agreement with the literature values for the inverse spinel structure  [40] [41] [42] [43] [44].
Characterizations Analysis The chemical composition is obtained by an elemental analysis conducted with X-ray fluorescence spectroscopy and carried out using S2 RANGER instrument from Bruker. X-ray investigation is performed using Bruker D2 phaser diffractometer with a continuous scanning mode and Cu Kα radiation (λ =0. 1541 nm). The lines are measured in the 2θ range (5-100) ° by an increment of 0. 02° for each 0. 1 s. The software used for evaluation the X-ray diffraction diagrams is DIFFRAC. EVA with ICDD PDF2. Sampling from the same vial is performed to achieve reliable X-ray diffraction diagrams as function of PCA rate. Sampling is repeated two times for the unmilled coproducts (fly ash and slag) and four times for the coproducts milled for 15 min with two different PCA rates. IR spectroscopy is performed by a Thermo Scientific Nicolet IS10 instrument equipped with Smart iTR (with Diamond Plate) accessory.
Methods Powder X-ray scattering experiments. The same highly pure magnetite powder (Fe 3-δ O 4 with δ < 0. 0001) as used in previous studies  3, [25] [26] [27]  was packed in a 0. 5-mm diameter quartz capillary and sealed under Ar atmosphere in a glove bag. Preliminary measurements were performed on beam line ID15B at ESRF, Grenoble and full data were collected on ESRF instrument ID11 with wavelength λ = 0. 15720 (1) Å using a FReLoN camera for diffraction pattern acquisition. A nitrogen cryostream was used to collect patterns between 90 and 400 K in 10 K steps. Small anomalies seen in several refined quantities around 250-300 K in Fig. 3   hot air blower was used to collect data between 498 and 923 K in 50 K steps. Empty capillary data were collected at 90, 200, 473, 573, 673, 773, and 873 K.
For each data set, the temperature was stabilised for 10 min and then data were collected for 10 min using the accumulation mode of the detector for 10-s exposure frames. Data were also collected from CeO 2 and Si standards at 300 K to calibrate the instruments and determine instrumental parameters. Instrument calibration and image integration was performed with the pyFAI software  28. The instrument model was recalibrated for every temperature in the cryostat data sets in order to allow for slight detector shifts. A fixed instrument model was used for the hot air blower data. Data sets were converted to scattering intensities S(Q) as a function of scattering vector Q and these were transformed to PDFs G(r), where r is interatomic distance, using the pdfgetx3 suite  29. Parameters values Q min = 1 Å -1 , Q max = 31 Å -1 , and r poly = 0.
9 Å were applied to all data sets to enable structural changes in G(r) to be analysed consistently across the full temperature range. Representative S(Q) and G(r) plots are shown in Fig. 1  and Supplementary Fig. 1. Structural models for PDF analysis. Structural models used to fit magnetite PDFs at all temperatures were based on the supercell of the low-temperature structure with monoclinic space group Cc symmetry, which contains 56 unique atoms with 168 variable coordinates. A cubic model previously refined against 130 K powder X-ray and neutron data  25, 26  was used as the reference undistorted structure. The VESTA software  30  was used to generate a supercell of the cubic structure with metric a = b = √2a c , c = 2a c , α = β = γ = 90°, where a c is the cubic spinel cell parameter, and atomic coordinates p u in Cc space group symmetry are shown in Supplementary Table  1.
This model has f V = 0. The previously reported 90 K monoclinic Cc structure  3   1 ) Å, β = 90°). Atomic positions were shifted slightly in order to preserve the magnitude of the distortions as generated by the ISO-DISTORT program  31. This approximation was found to have little effect on fits of the Cc model to the 90 K PDF (Rw = 11. 5% for monoclinic cell parameters vs. Rw = 11. 6% with metric constraints). Coordinates p d for this fully distorted reference structure (f V = 1) are shown in Supplementary Table  2. To vary the magnitude of the structural distortion, seven structural models were constructed by taking linear combinations of the undistorted and distorted coordinates p = p u + f V (p dp u ) for values of the Verwey shift f V from 0 to 1. 2 in increments of 0. 2. PDF fits. Refinements of structural models including simulation of termination ripples were performed with the PDFgui software  32.
Acknowledgements We acknowledge financial support from  European Research Council (ERC)  and  Science and Technology Facilities Council  ( STFC ) for provision of beam time at  ESRF. This work was also supported by the  French "Investissements d'Avenir" program , project  ISITE-BFC  (contract  ANR-15-IDEX-0003 ). We thank  Professor J. M. Honig  ( Purdue University ) for provision of the high-quality magnetite sample.
The macroscopic strain was measured along the load axis using a strain gauge (clip-on extensometer Sandner EXA-15). For each sample composition, tensile tests were carried out prior to the neutron diffraction studies to determine Young's modulus and the yield stress. Diffraction patterns were collected at a minimum of three and up to five stress levels, up to a maximum value of about 70% of the yield stress. At each load step, measurements at a minimum of five and up to ten angles were performed. To validate our method for data collection and analysis, ferritic (b. c. c. ) and austentic (f. c. c) phases in steels and cast iron samples were studied on the SPODI diffractometer at a monochromator angle of 155 using Ge(551) for a wavelength of 1. 5483 A ˚. The instrument offers a good angular resolution to separate the ferrite and austenite peaks and to observe their shifts under load at high precision.
544 A ˚. This setup offers a good angular resolution, sufficient for the analysis of strains. Samples of 8 mm diameter were measured under uniaxial tension at 0, 10, 20 and 30 kN. X-ray diffraction experiments were carried out on Ti-6Al-2Sn-4Zr-6Mo on the High Energy Materials Science beamline (HEMS) at the synchrotron facility DESY in Hamburg, Germany  (Schell et al. , 2014). An energy of 98. 25 keV (corresponding to a wavelength of 0. 12619 A ˚) was used to investigate tensile samples of 6 mm diameter. Since full Debye-Scherrer rings were obtained, no rotation was necessary to cover the different orientations of the load axis, which was kept perpendicular to the incident beam, i. e. = 90. The data were collected in 10 N steps up to 30 kN. For texture analysis, neutron pole-figure measurements were carried out on the STRESS-SPEC instrument at the MLZ  (Brokmeier et al.
EBSD maps were measured on a Hitachi SU5000 field-emission scanning electron microscope equipped with an Oxford Instruments NordlysII EBSD detector and an ULTIM MAX EDX detector. The employed acceleration voltage was 20 kV. EBDS and EDX signals were collected simultaneously with the sample inclined by 70 towards the EBSD detector. Data evaluation was performed with the Oxford Instruments AZTec and CHANNEL5 software. The EDX analysis was carried out in standardless mode.
Data evaluation For the data evaluation, a software package was developed enabling the choice of all mentioned models and, optionally, the texture implementation. For dual-phase alloys, a possible load transfer from one phase to the other can be quantified. The hkl-dependent strains ðhklÞ = ½dðhklÞ À d 0 =d 0 were obtained from the changes in the reflection positions under load in a set of diffraction patterns. An example diffraction pattern for Ti64 measured on D20 is shown in Fig. 3. To fit all free variables, at least three or five different Bragg peaks are needed for the cubic and hexagonal symmetries, respectively. The Bragg reflections were chosen to cover the maximum range of crystal directions to track the dependencies of the compliance tensor components. For the ferritic phase (Im3m) of the different iron and steel alloys, reflections {110}, {200}, {211}, {220} and {310} were evaluated, and for the austenitic phase (Fm3m) reflections {111}, {200}, {220}, {311} and {222}.
Results All obtained data were fitted with all available models except the  Voigt (1928)  model. The calculations based on the approach by Voigt showed large instabilities concerning the fitting routine, led to multiple results or did not converge. Therefore the results for  Voigt (1928)  are only shown once, for the structural steel S235JR. The values for the single-phase alloys agree well with available literature data. The results for the ferritic phase are listed in Table  1. Finkel (2016)    The single-crystal elastic constants and bulk properties for S235JR measured on SPODI. The anisotropy A is calculated after  Zener (1948). For the Voigt model, the fitting routine does not converge to a single solution. 204. 8, 138. 9 and 124. 2 GPa for the texture adaptation shows good agreement in both cases.
Acknowledgements We gratefully acknowledge beam time and experimental support at the  Heinz Maier-Leibnitz Zentrum , the  Institut Laue-Langevin  and the  Deutsches Elektronen Synchrotron. Special thanks are extended to  Mr Armin Kriele  for valuable support during sample preparation for the metallurgical investigations. The authors would like to thank  Dr Roland Hessert  ( MTU Aero Engines AG ) for providing some of the sample material.
ACKNOWLEDGEMENTS This work has been carried out within the framework of the  EUROfusion Consortium  and has received funding from the  Euratom  research and training programme 2014-2018 and  2019-2020  under grant agreement No  633053. The views and opinions expressed herein do not necessarily reflect those of the  European Commission. This work was supported in part by the  U. S. Department of Energy (DoE)  under grant  DE-SC0014210  and by discretional funding of the  Department of Engineering Physics  and the College of Nuclear Engineering at the  University of Wisconsin -Madison, USA.