Lattice dynamics of Ni<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Al</mml:mi></mml:mrow><mml:mprescripts /><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mrow /><mml:mrow /><mml:mrow /></mml:mmultiscripts></mml:mrow></mml:math>

Stassis, C.; Kayser, François; Loong, C.‐K.; Arch, D.K.

doi:10.1103/physrevb.24.3048

Cited by 66 publications

(28 citation statements)

References 17 publications

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“…4 shows the resultant phonons for Pt 3 Al with respect to the cP4-Cu 3 Au (L1 2 ), tI16-Ir 3 Si (DO c 0 ) and tP16-Pt 3 Ga lattices respectively. The upper left-hand panel displays the dispersion curves for L1 2 Ni 3 Al where we find that the DFT predictions are in good agreement with experiment [29]. Interestingly all three phases of Pt 3 Al are mechanically stable in the continuum limit as q / O at G. This is consistent with the predicted values of the elastic moduli C ij that are given in Table 2, where we find again reasonable agreement with experiment for the bulk and shear moduli of cubic Ni 3 Al [29].…”

Section: Mechanical Stabilitysupporting

confidence: 73%

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Theoretical investigation of the Pt3Al ground state

et al. 2010

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Section: Mechanical Stabilitysupporting

confidence: 73%

“…Experimental values for Ni 3 Al are represented by circles [29]. Note that a in upper two figures is cubic lattice parameter whereas a in lower two figures is tetragonal lattice parameter as in Fig.…”

Section: Discussionmentioning

confidence: 98%

Theoretical investigation of the Pt3Al ground state

et al. 2010

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“…The optical modes at 39 meV in the ordered alloy are clearly suppressed by disordering, and the disordered spectra show new intensity around 32 meV. The phonon DOS of the ordered Ni 3 Al was possible to deduce from the experimental spectra by a neutron weight correction based on a comparison with a Born-von Kármán calculation from prior work on single crystals of L1 2 Ni 3 Al [170]. As expected by footnote 36 for ordered Fe 3 Al, there is indeed about 25% of the intensity in the optical mode peak around 39 meV in the neutron-weight corrected spectrum in Fig.…”

Section: Fe 3 Almentioning

confidence: 99%

Vibrational thermodynamics of materials

Fultz¹

2010

Progress in Materials Science

558

428

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Abstract. The literature on vibrational thermodynamics of materials is reviewed. The emphasis is on metals and alloys, especially on the progress over the last decade in understanding differences in the vibrational entropy of different alloy phases and phase transformations. Some results on carbides, nitrides, oxides, hydrides and lithium-storage materials are also covered.Principles of harmonic phonons in alloys are organized into thermodynamic models for unmixing and ordering transformations on an Ising lattice, and extended for non-harmonic potentials. Owing to the high accuracy required for the phonon frequencies, quantitative predictions of vibrational entropy with analytical models prove elusive. Accurate tools for such calculations or measurements were challenging for many years, but are more accessible today. Ab-initio methods for calculating phonons in solids are summarized. The experimental techniques of calorimetry, inelastic neutron scattering, and inelastic x-ray scattering are explained with enough detail to show the issues of using these methods for investigations of vibrational thermodynamics. The explanations extend to methods of data analysis that affect the accuracy of thermodynamic information.It is sometimes possible to identify the structural and chemical origins of the differences in vibrational entropy of materials, and the number of these assessments is growing. There has been considerable progress in our understanding of the vibrational entropy of mixing in solid solutions, compound formation from pure elements, chemical unmixing of alloys, order-disorder transformations, and martensitic transformations. Systematic trends are available for some of these phase transformations, although more examples are needed, and many results are less reliable at high temperatures. Nanostructures in materials can alter sufficiently the vibrational dynamics to affect thermodynamic stability. Internal stresses in polycrystals of anisotropic materials also contribute to the heat capacity. Lanthanides and actinides show a complex interplay of vibrational, electronic, and magnetic entropy, even at low temperatures.A "quasiharmonic model" is often used to extend the systematics of harmonic phonons to high temperatures by accounting for the effects of thermal expansion against a bulk modulus. Non-harmonic effects beyond the quasiharmonic approximation originate from the interactions of thermally-excited phonons with other phonons, or with the interactions of phonons with electronic excitations. In the classical high temperature limit, the adiabatic electron-phonon coupling can have a surprisingly large effect in metals when temperature causes significant changes in the electron density near the Fermi level. There are useful similarities in how temperature, pressure, and composition alter the conduction electron screening and the interatomic force constants. Phononphonon "anharmonic" interactions arise from those non-harmonic parts of the interatomic potential that cannot be accounted for by the quasiharmonic ...

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“…Calculated and experimental phonon DOS of the L1 2 structures. The experimental phonon DOS is calculated from the force constant provided in [4], which are themselves fitted from previous phonon dispersion measurement [38]. …”

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confidence: 99%

First-Principles Computation of the Vibrational Entropy of Ordered and DisorderedNi3Al

1998

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There is increasing evidence that vibrational entropy may significantly contribute to the entropy difference between the ordered and the disordered states of a compound. Through first-principles calculations, we investigate the magnitude of this vibrational entropy difference in Ni 3 Al, a compound where this effect is believed to be especially large. We find the vibrational entropy difference to be essentially zero and temperature independent. [S0031-9007(98)06236-X] PACS numbers: 64.70. Kb, 65.50. + m First-principles theory of order-disorder phase equilibria is a well-established field [1,2]. Typically, only configurational entropy is accounted for, and the effect of lattice vibrations on the free energy difference between the ordered and the disordered states is neglected, although no formal justification of this assumption has ever been presented. On the contrary, recent experimental data [3][4][5][6] seem to indicate that, in many systems, the vibrational entropy difference between the ordered and the disordered states is comparable to the configurational entropy difference. An especially striking example is the Ni 3 Al compound, for which the vibrational entropy difference was estimated from experimental observations to be 0.2k B [4], whereas the configurational entropy difference is at most 0.57k B . If this estimate is correct, it may explain why most first-principles calculations including only configurational entropy consistently overestimate phase transition temperatures. Based on the experimental data of Fultz and co-workers [4], Garbulsky [7] predicted that vibrational effects would shift down the calculated order-disorder transition temperature of Ni 3 Al by 18% from what it would be with a configurational-only entropy model.In order to unambiguously confirm that lattice vibrations indeed play an important role, this experimental evidence needs to be backed by a suitable theoretical investigation. Unfortunately, highly accurate first-principles calculations of the vibrational entropy are very computationally intensive tasks. In this context, several investigators turned to simplified models to estimate the vibrational entropy. In some studies [8,9], the complexity of the first-principles approach was tackled by using a simplified model for the vibrational entropy based on the Debye-Gruneisen approximation. All of these results seem to indicate that vibrational effects can be non-negligible.Calculations of the vibrational entropy difference between disordered and ordered Ni 3 Al (hereafter denoted DS o!d vib ) has so far been performed using only the semiempirical embedded atom method (EAM) [10][11][12]. Although the specific result seems to depend somewhat on the EAM potential used, all authors found values between 0.1k B and 0.3k B , which corresponds to the range of values found experimentally.Although the value of DS o!d vib calculated through EAM agrees with experimental results, there is no consensus on the origin of this difference. The EAM results indicate that disordering causes a nearl...

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Lattice dynamics of NiAl3

Cited by 66 publications

References 17 publications

Theoretical investigation of the Pt3Al ground state

Theoretical investigation of the Pt3Al ground state

Vibrational thermodynamics of materials

First-Principles Computation of the Vibrational Entropy of Ordered and DisorderedNi3Al

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