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High-temperature neutron diffraction and first-principles study of temperature-dependent crystal structures and atomic vibrations in Ti3AlC2, Ti2AlC, and Ti5Al2C3
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10.1063/1.4803700
/content/aip/journal/jap/113/18/10.1063/1.4803700
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/18/10.1063/1.4803700

Figures

Image of FIG. 1.
FIG. 1.

Unit cells of (a) TiAlC, (b) TiAlC, and (c) TiAlC showing lattice parameters and and the unique Ti, Al, and C lattice sites as constrained by symmetry, along with the refinable atomic position parameters.

Image of FIG. 2.
FIG. 2.

Pole figure for 000 and recalculated from the orientation distribution of HIPPO data for (a) TiAlC, (b) TiAlC, and (c) TiAlC at , and (d) TiAlC, (e) TiAlC, and (f) TiAlC at . Sample cylinder axis is in the center of pole figures.

Image of FIG. 3.
FIG. 3.

Rietveld analysis of neutron diffraction data measured on HIPPO at for the multiphase sample from (a) detector bank and (b) detector bank. Raw data points are shown as red + symbols and the calculated profile is shown as a solid green line. Underneath, markers show calculated peak positions of each phase. From top to bottom: ( (green), 523 (blue), 312 (red), and 211 (black). Difference curve ( ) is shown in bottom of each panel as a solid purple line.

Image of FIG. 4.
FIG. 4.

Compositions (wt. %) of each phase in the Ti–Al–C sample as a function of temperature upon heating and cooling. Dashed lines indicate limits for ±1% range.

Image of FIG. 5.
FIG. 5.

Temperature dependences of the thermal strains of the lattice parameters and interatomic distances in (a) TiAlC, (b) TiAlC, and (c) TiAlC for the multiphase sample. In (b), the results for predominantly single-phase TiAlC are also shown. (d) Volume expansion of TiAlC (blue circles), TiAlC (red solid squares), TiAlC (black diamonds), and (green triangles) in the multiphase sample, and pure TiAlC (open red squares). Room temperature values were extrapolated to use for and . Errors for volume expansions in (d) are typically smaller than symbol size.

Image of FIG. 6.
FIG. 6.

Temperature dependence of (a) and (b) lattice parameters, and (c) Ti–C and (d) Ti–Al interatomic distances in TiAlC (blue), TiAlC (red), and TiAlC (black). Refer to Fig. 1 for notations of Ti and C atoms. Errors are typically smaller than symbol size.

Image of FIG. 7.
FIG. 7.

Temperature dependence of isotropic thermal motion during heating and cooling for Ti (red), Al (blue), and C (black) atoms in (a) TiAlC, (b)TiAlC, and (c) TiAlC. Symbols are values determined from HTND. The lines refer to values calculated from first-principles phonon calculations. Errors are typically smaller than symbol size.

Image of FIG. 8.
FIG. 8.

Temperature dependence of isotropic thermal motion of Al in TiAlC (blue circles), TiAlC (black diamonds), and TiAlC (red solid squares) in the multiphase (mult.) sample, and in pure in TiAlC (red open squares) determined from HTND. of Al in predominantly single-phase TiAlN (green half-filled squares) and TiAlN (purple triangles) are also shown, determined from HTND in Refs. , respectively. The lines refer to values calculated from first-principles phonon calculations, where the calculated values for TiAlN and TiAlN are from Ref. . Errors are typically smaller than symbol size.

Tables

Generic image for table
Table I.

Space groups and atomic positions of atoms in TiAlC, TiAlC, and TiAlC.

Generic image for table
Table II.

Profile agreement factors for Rietveld refinements of neutron diffraction data collected during heating and cooling for the multiphase Ti–Al–C sample.

Generic image for table
Table III.

Thermal expansions from HTND for Ti–Al–C phases in the sample studied in this work, along with those from other studies determined through HTXRD and dilatometry. Numbers in parentheses are estimated standard deviations in the last significant digit of the refined parameters.

Generic image for table
Table IV.

Temperature-dependent and lattice parameters from Rietveld refinement of neutron diffraction data collected during heating and cooling. Numbers in parentheses are estimated standard deviations in the last significant figure of the refined parameters. Room temperature values are extrapolated to from linear interpolation.

Generic image for table
Table V.

Interatomic distances in TiAlC, TiAlC, and TiAlC in the multiphase sample from Rietveld refinement of neutron diffraction data collected during heating and cooling, along with their expansions. All values are extrapolated to from linear interpolation. Numbers in parentheses are estimated standard deviations in the last significant digit of the refined parameters.

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/content/aip/journal/jap/113/18/10.1063/1.4803700
2013-05-10
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: High-temperature neutron diffraction and first-principles study of temperature-dependent crystal structures and atomic vibrations in Ti3AlC2, Ti2AlC, and Ti5Al2C3
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/18/10.1063/1.4803700
10.1063/1.4803700
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