Partial phonon densities of states of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">Fe</mml:mi><mml:mprescripts /><mml:none /><mml:mn>57</mml:mn></mml:mmultiscripts></mml:math>in Fe-Cr: Analysis by a local-order cluster expansion

Lucas, M. S.; Papandrew, Alexander B.; Fultz, B.; Hu, Michael Y.

doi:10.1103/physrevb.75.054307

Cited by 10 publications

(6 citation statements)

References 26 publications

(30 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There has been recent success, however, in using this inversion method to understand the phonon DOS of ordered thin-film structures of Fe-Cr alloys using phonon data from random solid solutions. 11 For Fe-Co, we found that the cluster analysis method was successful in predicting changes in the pho-non DOS upon ordering in Fe 0.50 Co 0.50 at 300 K. The changes in vibrational entropy with alloying and ordering proved to be small, approximately an order of magnitude smaller than the configurational entropy of ordering. Nevertheless, upon increasing the concentration of Co atoms and Co-Co pairs there was a measurable softening of the low transverse acoustic phonon branch in Fe-Co alloys near the equiatomic composition.…”

Section: Introductionmentioning

confidence: 88%

“…10 Details of the application of this technique to the phonon DOS can be found elsewhere. 11,25,26 Spin variables are used for the two species of atoms, where an Fe atom is assigned the factor = +1, and a Co atom = −1. A cluster is made by connecting a number of points n on the lattice.…”

Section: B Cluster Expansionmentioning

confidence: 99%

“…This choice is simplified by using a least-squares inversion, which is possible because a correlation function matrix for random solid solutions is a Vandermonde matrix. 11 Before inverting, the DOS functions were rescaled to the maximum phonon energy of the Fe 0.50 Co 0.50 DOS to ensure proper normalization of the IDOS functions. The least-squares inversion was performed for the alloys x Co = ͕0.70, 0.60, 0.40, 0.30, 0.20, 0.10, 0͖.…”

Section: B Cluster Expansionmentioning

confidence: 99%

See 2 more Smart Citations

Effects of chemical composition and B2 order on phonons in bcc Fe–Co alloys

Lucas

Muñoz

Mauger

et al. 2010

Journal of Applied Physics

Self Cite

View full text Add to dashboard Cite

The phonon density of states ͑DOS͒ gives insight into interatomic forces and provides the vibrational entropy, making it a key thermodynamic function for understanding alloy phase transformations. Nuclear resonant inelastic x-ray scattering and inelastic neutron scattering were used to measure the chemical dependence of the DOS of bcc Fe-Co alloys. For the equiatomic alloy, the A2 → B2 ͑chemically disordered→ chemically ordered͒ phase transformation caused measurable changes in the phonon spectrum. The measured change in vibrational entropy upon ordering was −0.02Ϯ 0.02 k B /atom, suggesting that vibrational entropy results in a reduction in the orderdisorder transition temperature by 60Ϯ 60 K. The Connolly-Williams cluster inversion method was used to obtain interaction DOS ͑IDOS͒ curves that show how point and pair variables altered the phonon DOS of disordered bcc Fe-Co alloys. These IDOS curves accurately captured the change in the phonon DOS and vibrational entropy of the B2 ordering transition.

show abstract

Section: Introductionmentioning

confidence: 88%

Section: B Cluster Expansionmentioning

confidence: 99%

Section: B Cluster Expansionmentioning

confidence: 99%

See 1 more Smart Citation

Effects of chemical composition and B2 order on phonons in bcc Fe–Co alloys

Lucas

Muñoz

Mauger

et al. 2010

Journal of Applied Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…For a disordered solid solution, Lucas, et al [188,215,216] found strategies to solve for the phonon partial DOS functions from neutron-weighted DOS curves of 40 There are two subtleties: 1) It is assumed that the Debye-Waller factors for the two species of atoms do not differ significantly. This assumption should be adequate at low temperatures.…”

Section: Relates the Interaction Dos (Idos) Functions To The Interactmentioning

confidence: 99%

Vibrational thermodynamics of materials

Fultz¹

2010

Progress in Materials Science

559

428

View full text Add to dashboard Cite

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 ...

show abstract

“…14 For example, with data over a range of chemical compositions, it was shown how local atomic arrangements alter the vibrational entropy of Fe-V, 15,16 Fe-Cr, 17,18 and Fe-Co 19 alloys.…”

Section: Introductionmentioning

confidence: 99%

Electronic structure and vibrational entropies of fcc Au-Fe alloys

et al. 2013

Self Cite

View full text Add to dashboard Cite

Phonon density of states (DOS) curves were measured on alloys of face-centered-cubic (fcc) Au-Fe using nuclear resonant inelastic x-ray scattering (NRIXS) and inelastic neutron scattering (INS). The NRIXS and INS results were combined to obtain the total phonon DOS and the partial phonon DOS curves of Au and Fe atoms, from which vibrational entropies were calculated. The main effect on the vibrational entropy of alloying comes from a stiffening of the Au partial phonon DOS with Fe concentration. Force constants were calculated from first principles for several compositions and show a local stiffening of Au-Au bonds close to Fe atoms. The calculated phonon DOS curves reproduce the experimental trend. The stiffening is attributed to two main effects comparable in magnitude: 1) an increase in electron density in the free-electron-like states, and 2) stronger sd-hybridization.

show abstract

Partial phonon densities of states ofFe57in Fe-Cr: Analysis by a local-order cluster expansion

Cited by 10 publications

References 26 publications

Effects of chemical composition and B2 order on phonons in bcc Fe–Co alloys

Effects of chemical composition and B2 order on phonons in bcc Fe–Co alloys

Vibrational thermodynamics of materials

Electronic structure and vibrational entropies of fcc Au-Fe alloys

Contact Info

Product

Resources

About