Herein, we report—for the first time—on the additive‐free bulk synthesis of Ti3SnC2. A detailed experimental study of the structure of the latter together with a secondary phase, Ti2SnC, is presented through the use of X‐ray diffraction (XRD), and high‐resolution transmission microscopy (HRTEM). A previous sample of Ti3SnC2, made using Fe as an additive and Ti2SnC as a secondary phase, was studied by high‐temperature neutron diffraction (HTND) and XRD. The room‐temperature crystallographic parameters of the two MAX phases in the two samples are quite similar. Based on Rietveld analysis of the HTND data, the average linear thermal expansion coefficients of Ti3SnC2 in the a and c directions were found to be 8.5 (2)·10−6 K−1 and 8.9 (1)·10−6 K−1, respectively. The respective values for the Ti2SnC phase are 10.1 (3)·10−6 K−1 and 10.8 (6)·10−6 K−1. Unlike other MAX phases, the atomic displacement parameters of the Sn atoms in Ti3SnC2 are comparable to those of the Ti and C atoms. When the predictions of the atomic displacement parameters obtained from density functional theory are compared to the experimental results, good quantitative agreement is found for the Sn atoms. In the case of the Ti and C atoms, the agreement is more qualitative. We also used first principles to calculate the elastic properties of both Ti2SnC and Ti3SnC2 and their Raman active modes. The latter are compared to experiment and the agreement was found to be good.

Herein, we report on the crystal structures of Nb2AlC and TiNbAlC—actual composition (Ti0.45,Nb0.55)2AlC—compounds determined from Rietveld analysis of neutron diffraction patterns in the 300–1173 K temperature range. The average linear thermal expansion coefficients of a Nb2AlC sample in the a and c directions are, respectively, 7.9(5) × 10−6 and 7.7(5) × 10−6 K−1 on one neutron diffractometer and 7.3(3) × 10−6 and 7.0(2) × 10−6 K−1 on a second diffractometer. The respective values for the (Ti0.45,Nb0.55)2AlC composition—only tested on one diffractometer—are 8.5(3) × 10−6 and 7.5(5) × 10−6 K−1. These values are relatively low compared to other MAX phases. Like other MAX phases, however, the atomic displacement parameters (APDs) show that the Al atoms vibrate with higher amplitudes than the Ti and C atoms, and more along the basal planes than normal to them. When the predictions of the APDs obtained from density functional theory are compared to the experimental results, good quantitative agreement is found for the Al atoms. In case of the Nb and C atoms, the agreement was more qualitative.

Herein, we report on the temperature‐dependent crystal structures of Ti 3 AlC 2 and Ti 3 Al 0.8 Sn 0.2 C 2 in the 373–1273 K temperature range, as determined by Rietveld analysis of high‐temperature neutron diffraction time‐of‐flight data. The compositions are 86(1) wt% Ti 3 AlC 2 and 14(1) wt% TiC 0.92(2) for the sample with no Sn , and 95(1) wt% Ti 3( Al 0.8 Sn 0.2) C 2 and 5(1) wt% Ti 2 AlC for the solid solution with Sn . The average linear volumetric thermal expansion is 8.0(2) × 10−6 K −1 for Ti 3 AlC 2 and 8.2(5) × 10−6 K−1 for Ti 3( Al 0.8 Sn 0.2) C 2. The average linear thermal expansion in the a and c directions, respectively, are 7.6(2) × 10−6 K−1 and 8.9(2) × 10−6 K−1 for Ti 3 AlC 2. For Ti 3( Al 0.8 Sn 0.2) C 2, the respective values are 8.0(5) × 10−6 K−1 and 8.6(6) × 10−6 K−1. In the case of the solid solution, the quadratic thermal expansion coefficients are also given. Detailed bond lengths analysis shows that the thermal expansions along the a and c directions are controlled by the thermal expansions of the Ti – C , and Ti – Al bond lengths, respectively. The atomic displacement parameters (ADPs) show that the Al and Sn atoms vibrate with a higher amplitude than the Ti and C atoms. Consistent with first‐principles calculations, the ADPs of the Al/Sn site(s) in Ti 3( Al 0.8 Sn 0.2) C2 are lower than the ADPs of Al in Ti 3 AlC 2.

Herein we report on the thermal expansions and temperature-dependent crystal structures of select ternary carbide Mn+1AXn (MAX) phases in the Ti–Al–C phase diagram in the 100−1000 °C temperature range. A bulk sample containing 38(±1) wt. % Ti5Al2C3 (“523”), 32(±1) wt. % Ti2AlC (“211”), 18(±1) wt. % Ti3AlC2 (“312”), and 12(±1) wt. % (Ti0.5Al0.5)Al is studied by Rietveld analysis of high-temperature neutron diffraction data. We also report on the same for a single-phase sample of Ti3AlC2 for comparison. The thermal expansions of all the MAX phases studied are higher in the c direction than in the a direction. The bulk expansion coefficients—9.3(±0.1)×10−6 K−1 for Ti5Al2C3, 9.2(±0.1) ×10−6 K−1 for Ti2AlC, and 9.0(±0.1)×10−6 K−1 for Ti3AlC2—are comparable within one standard deviation of each other. In Ti5Al2C3, the dimensions of the Ti–C octahedra for the 211-like and 312-like regions are comparable to the Ti–C octahedra in Ti2AlC and Ti3AlC2, respectively. The isotropic mean-squared atomic displacement parameters are highest for the Al atoms in all three phases, and the values predicted from first-principles phonon calculations agree well with those measured.

To study the structural behavior of brucite at high temperature, we conducted in situ neutron diffraction experiments of a deuterated brucite powder sample, Mg(OD)2, in the temperature range 313–583 K. The sample was stable up to 553 K, above which it started to decompose into periclase (MgO) and D2O vapor. Rietveld analyses of the obtained data were performed using both single-site and three-site split-atom hydrogen models. Our results show that with increasing temperature, unit-cell parameter c increases at a rate ~7.7 times more rapidly than a. This large anisotropy of thermal expansion is primarily due to rapid increase in the interlayer thickness along the c-axis on heating. The amplitudes of thermal vibration for Mg, O, and D increase linearly with increasing temperature; however, the rate of the increase for the lighter D is much larger. In addition, D vibrates anisotropically with a higher magnitude within the (001) plane, as confirmed by our first-principles phonon calculations. On heating, the interatomic distances between a given D and its associated O and D from the adjacent [MgO6] layer increase, whereas the O–D bond length decreases. This behavior suggests weakened D···O and D···D interlayer interactions but strengthened O–D bonding with increasing temperature.

Density functional calculations are used to investigate the electronic structure of two-dimensional 5d tantalum carbides with honeycomb-like lattice structures. We focus on changes in the low-energy bands near the Fermi level with dimensionality. We find that the Ta 5d states dominate, and the extended nature of the wave functions makes them weakly correlated. The carbide sheets are prone to long-range magnetic order and we evaluate their stability to enhanced electron-electron interactions through a Hubbard U correction. Lastly, we find that the splitting of the bands near the Fermi level caused by spin-orbit interaction decreases with increasing dimensionality. In the lowest-dimensionality (n - 1) case, the band splitting pushes a conduction band above the Fermi level and leads to a semi-metallic state. Copyright (C) EPLA, 2013

Journal of the American Ceramic SocietyVolume 95, Issue 10 p. 3352-3354 Comment Comment on “Ti5Al2C3: A New Ternary Carbide Belonging to MAX Phases in the Ti–Al–C System” Nina J. Lane, Corresponding Author Nina J. Lane Department of Materials Science and Engineering, Drexel University, Philadelphia, Pennsylvania, 19104Author to whom correspondence should be addressed. e-mail: lane@drexel.eduSearch for more papers by this authorMichael Naguib, Michael Naguib Department of Materials Science and Engineering, Drexel University, Philadelphia, Pennsylvania, 19104Search for more papers by this authorJun Lu, Jun Lu Department of Physics, Chemistry, and Biology (IFM), Linköping University, Linköping, SE-581 83 SwedenSearch for more papers by this authorPer Eklund, Per Eklund Department of Physics, Chemistry, and Biology (IFM), Linköping University, Linköping, SE-581 83 SwedenSearch for more papers by this authorLars Hultman, Lars Hultman Department of Physics, Chemistry, and Biology (IFM), Linköping University, Linköping, SE-581 83 SwedenSearch for more papers by this authorMichel W. Barsoum, Michel W. Barsoum Department of Materials Science and Engineering, Drexel University, Philadelphia, Pennsylvania, 19104Search for more papers by this author Nina J. Lane, Corresponding Author Nina J. Lane Department of Materials Science and Engineering, Drexel University, Philadelphia, Pennsylvania, 19104Author to whom correspondence should be addressed. e-mail: lane@drexel.eduSearch for more papers by this authorMichael Naguib, Michael Naguib Department of Materials Science and Engineering, Drexel University, Philadelphia, Pennsylvania, 19104Search for more papers by this authorJun Lu, Jun Lu Department of Physics, Chemistry, and Biology (IFM), Linköping University, Linköping, SE-581 83 SwedenSearch for more papers by this authorPer Eklund, Per Eklund Department of Physics, Chemistry, and Biology (IFM), Linköping University, Linköping, SE-581 83 SwedenSearch for more papers by this authorLars Hultman, Lars Hultman Department of Physics, Chemistry, and Biology (IFM), Linköping University, Linköping, SE-581 83 SwedenSearch for more papers by this authorMichel W. Barsoum, Michel W. Barsoum Department of Materials Science and Engineering, Drexel University, Philadelphia, Pennsylvania, 19104Search for more papers by this author First published: 20 June 2012 https://doi.org/10.1111/j.1551-2916.2012.05299.xCitations: 11Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume95, Issue10October 2012Pages 3352-3354 RelatedInformation

Upon annealing cold-pressed Ti2AlC, −325 mesh powders, at 1500 °C for 8 h in argon, the resulting partially sintered sample contained 43(±2) wt.% of the layered ternary carbide Ti5Al2C3. Herein, the X-ray powder diffraction pattern of Ti5Al2C3 is reported for the first time and its structure and stoichiometry are confirmed through high-resolution transmission electron microscopy. This phase has a trigonal structure (space group P3m1) with a unit cell consisting of 3 formula units and cell parameters of a = 3.064 Å, c = 48.23 Å. The lattice parameters determined through first principles calculations agree reasonably well with the experimentally determined values. At 147.1 GPa, the calculated bulk modulus falls between the bulk moduli of Ti2AlC and Ti3AlC2. The transformation from Ti2AlC to Ti5Al2C3 is topotactic.

Herein, we compare the thermal vibrations of atoms in select ternary carbides with the formula M(n+1)AX(n) ("MAX phases," M = Ti, Cr; A = Al, Si, Ge; X = C, N) as determined from first-principles phonon calculations to those obtained from high-temperature neutron powder diffraction studies. The transition metal carbides TiC, TaC, and WC are also studied to test our methodology on simpler carbides. Good qualitative and quantitative agreement is found between predicted and experimental values for the binary carbides. For all the MAX phases studied-Ti3SiC2, Ti3GeC2, Ti2AlN, Cr2GeC and Ti4AlN3-density functional theory calculations predict that the A element vibrates with the highest amplitude and does so anisotropically with a higher amplitude within the basal plane, which is in line with earlier results from high-temperature neutron diffraction studies. In some cases, there are quantitative differences in the absolute values between the theoretical and experimental atomic displacement parameters (ADPs), such as reversal of anisotropy or a systematic offset of temperature-dependent ADPs. The mode-dependent Gruneisen parameters are also computed to explore the anharmonicity in the system.

Herein we use first principles calculations to study the energy of the (112 1) twin boundary in Zr, Zn, Mg, Ti, and Be. This boundary is important for understanding the microyielding and damping of hexagonal close packed metals. The (112 1) twin boundary is unique in that it is comprised of – and can form by the glide of – basal dislocations nucleating at every c-lattice parameter. The effect of the number of atoms between boundaries on the boundary energy, and the resulting lattice strains of the relaxed structures, are quantified. It is shown that the energies obtained converge within 32-64 atoms/supercell. The structures with higher second-order elastic constant term, c44, also have higher boundary energies. We further show that the critical resolved shear stresses of the basal dislocations at 0 K, which make up the (112 1), twin are so low as to be below the threshold of the first principles calculations. Corresponding author, lane@drexel.edu

In this work, we report on the temperature‐dependent crystal structures of the isostructural, layered hexagonal phases Ti2AlN and Cr2GeC determined by Rietveld analysis of high temperature neutron powder diffraction data of fully dense, polycrystalline, bulk samples in the 100° to 1100°C temperature range. For both phases, the A‐group atoms, Al and Ge, vibrate with the highest amplitude and do so anisotropically within the basal plane. All bonds expand linearly with temperature, with the highest relative thermal expansion occurring in the Ti–Al and Cr–Ge bonds. The thermal expansion coefficients in the a‐ and c‐direction are, respectively, 10.3(±0.2) × 10−6 and 9.3(±0.2) × 10−6 K−1 for Ti2AlN and 12.8(±0.3) × 10−6 and 14.6(±0.3) × 10−6 K−1 for Cr2GeC. The unit cell volume expansions observed by HTND are 10.0(±0.2) × 10−6 K−1 for Ti2AlN and 13.4(±0.3) × 10−6 K−1 for Cr2GeC.

Herein, we use first principles calculations to study the energy of the (11 (2) over bar1) twin boundary in Zr, Zn, Mg, Ti, and Be. This boundary is important for understanding the microyielding and damping of hexagonal close-packed metals. The (11 (2) over bar1) twin boundary is unique in that it is composed of-and can form by the glide of-basal dislocations nucleating at every c lattice parameter. The effect of the number of atoms between boundaries on the boundary energy, and the resulting lattice strains of the relaxed structures are quantified. It is shown that the energies obtained converge within 32-64 atoms/supercell. The structures with a higher second-order elastic constant term, c(44), also have higher boundary energies. It is further shown that the critical resolved shear stresses of the basal dislocations at 0 K, which make up the (11 (2) over bar1) twin, are so low as to be below the threshold of the first principles calculations.

A new nanocrystalline phase of titanium aluminum fluoride, with a stoichiometry of Ti2AlF9-exact stoichiometry measured herein is Ti2.1Al0.9F9,-was synthesized by the fluorination of Ti2AlC in anhydrous hydrofluoric acid at 55 degrees C for 2 h. The results from X-ray diffraction, scanning and high-resolution transmission electron microscopy and selected area diffraction, together with crystal structure solution via simulated annealing, confirmed the formation of a nanocrystalline material with a trigonal structure belonging to the R3 space group. The structure can also be viewed as being comprised of corner-sharing octahedra that are arranged in a distorted simple cubic arrangement. Thermogravimetric analysis, in argon, indicates that this phase is stable up to approximate to 850 degrees C. Density functional theory calculations estimate the band gap to be approximate to 5 eV and the bulk modulus to be approximate to 109 GPa.

Herein, we report on the Raman spectra of the following ternary hexagonal carbides and nitrides (MAX phases): Ta4AlC3, Ta2AlC and Ti4AlN3. We also present the Raman‐active modes of α‐ and β‐Ta4AlC3, Nb4AlC3 and Ti4AlN3, – also referred to as the 413 MAX phases – as predicted from first principles calculations using density functional theory. We compare the obtained experimental and calculated results with previous studies on Ta2AlC and Ti4AlN3. The vibrational behavior associated with the Raman‐active modes for the 413 phases has been identified for the first time. In general, the agreement is good between theory and experiment. The experimental and calculated results indicate that the modes at low wavenumbers ‐ dominated by the Al atoms ‐ are a weak function of chemistry and the differences in energy can be traced to variations in the reduced mass. The modes at higher wavenumbers are dominated by the C and N atoms and show a strong dependence on the unit cell chemistry, with the Ta–C bond being stiffer than the Nb–C bond, which is in turn stiffer than Ti–N. Copyright © 2011 John Wiley & Sons, Ltd.

Cold-pressed alpha-Ta4AlC3 powders were annealed up to 1750 degrees C to test first-principles predictions of alpha-beta phase-stability reversal at 1600 degrees C. Up to 1600 degrees C, the alpha-Ta4AlC3 samples were stable with no indications of any alpha-beta transformation, as shown by the strong characteristic X-ray diffraction peaks of alpha-Ta4AlC3 and the zigzag stacking observed by transmission electron microscopy. These results show that, in this experimental situation, high temperature alone is not sufficient to cause the alpha-beta transformation. (C) 2011 Elsevier Ltd. All rights reserved.

Herein, we use first principles calculations to study the energy of the ($11\overline{2}1$) twin boundary in Zr, Zn, Mg, Ti, and Be. This boundary is important for understanding the microyielding and damping of hexagonal close-packed metals. The ($11\overline{2}1$) twin boundary is unique in that it is composed of---and can form by the glide of---basal dislocations nucleating at every $c$ lattice parameter. The effect of the number of atoms between boundaries on the boundary energy, and the resulting lattice strains of the relaxed structures are quantified. It is shown that the energies obtained converge within 32--64 atoms/supercell. The structures with a higher second-order elastic constant term, ${c}_{44}$, also have higher boundary energies. It is further shown that the critical resolved shear stresses of the basal dislocations at 0 K, which make up the ($11\overline{2}1$) twin, are so low as to be below the threshold of the first principles calculations.

Herein, we report on the crystal structures of the isostructural Ti3SiC2 and Ti3GeC2 phases determined by Rietveld analysis of neutron diffraction data in the 100° to 1100 ° C temperature range. The results show that the Si and Ge atoms vibrate anisotropically with the highest amplitudes and within the basal planes. The equivalent isotropic thermal motion behavior does not differ significantly between the two phases; the anisotropic thermal motion, interatomic distances, and bond angles, however, show strikingly different behavior. Furthermore, while the Ti-Si bonds increase linearly with increasing temperature, the Ti-Ge bonds apparently do not. The anisotropic motion of the Ge atoms in the basal plane with the correlated motion between the Ti and the Ge atoms is invoked as a possible explanation. The volume expansions are 9.00.1 10 �6 K �1 and 8.70.1 10 �6 K �1 for Ti3SiC2 and Ti3GeC2, respectively; the expansions along the a and c axes are a

An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.