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Wang Y, Li X, Luo J, Woodfield BF, Wang X, Feng T, Yin N, Shi Q, Li G, Li L. An Unexpected Decrease in Vibrational Entropy of Multicomponent Rutile Oxides. J Am Chem Soc 2024; 146:14493-14504. [PMID: 38743872 DOI: 10.1021/jacs.3c14801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/16/2024]
Abstract
High-entropy oxides (HEOs), featuring infinite chemical composition and exceptional physicochemical properties, are attracting much attention. The configurational entropy caused by a component disorder of HEOs is popularly believed to be the main driving force for thermal stability, while the role of vibrational entropy in the thermodynamic landscape has been neglected. In this study, we systematically investigated the vibrational entropy of multicomponent rutile oxides (including Fe0.5Ta0.5O2, Fe0.333Ti0.333Ta0.333O2, Fe0.25Ti0.25Ta0.25Sn0.25O2, and Fe0.21Ti0.21Ta0.21Sn0.21Ge0.16O2) by precise heat capacity measurements. It is found that vibrational entropy gradually decreases with increasing component disorder, beyond what one could expect from an equilibrium thermodynamics perspective. Moreover, all multicomponent rutile oxides exhibit a positive excess vibrational entropy at 298.15 K. Upon examinations of configuration disorder, size mismatch, phase transition, and polyhedral distortions, we demonstrate that the excess vibrational entropy plays a pivotal role in lowering the crystallization temperature of multicomponent rutile oxides. These findings represent the first experimental confirmation of the role of lattice vibrations in the thermodynamic landscape of rutile HEOs. In particular, vibrational entropy could serve as a novel descriptor to guide the predictive design of multicomponent oxide materials.
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Affiliation(s)
- Yaowen Wang
- State Key Laboratory of Inorganic Synthesis and Preparative Chemistry, College of Chemistry, Jilin University, Changchun 130012, P. R. China
| | - Xinbo Li
- State Key Laboratory of Inorganic Synthesis and Preparative Chemistry, College of Chemistry, Jilin University, Changchun 130012, P. R. China
| | - Jipeng Luo
- Thermochemistry Laboratory, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, P. R. China
| | - Brian F Woodfield
- Department of Chemistry and Biochemistry, Brigham Young University, Provo, Utah 84602, United States
| | - Xiyang Wang
- Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Tao Feng
- Department of Materials Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, P. R. China
| | - Nan Yin
- Thermochemistry Laboratory, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, P. R. China
| | - Quan Shi
- Thermochemistry Laboratory, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, P. R. China
| | - Guangshe Li
- State Key Laboratory of Inorganic Synthesis and Preparative Chemistry, College of Chemistry, Jilin University, Changchun 130012, P. R. China
| | - Liping Li
- State Key Laboratory of Inorganic Synthesis and Preparative Chemistry, College of Chemistry, Jilin University, Changchun 130012, P. R. China
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2
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Benisek A, Dachs E, Carpenter MA, Joachim-Mrosko B, Vielreicher NM, Wildner M. Vibrational entropy of disordering in omphacite. PHYSICS AND CHEMISTRY OF MINERALS 2023; 50:36. [PMID: 38037626 PMCID: PMC10682307 DOI: 10.1007/s00269-023-01260-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/23/2023] [Accepted: 10/11/2023] [Indexed: 12/02/2023]
Abstract
The cations of an ordered omphacite from the Tauern window were gradually disordered in piston cylinder experiments at temperatures between 850 and 1150 °C. The samples were examined by X-ray powder diffraction and then investigated using low-temperature calorimetry and IR spectroscopy. The low-temperature heat capacity data were used to obtain the vibrational entropies, and the line broadening of the IR spectra served as a tool to investigate the disordering enthalpy. These data were then used to calculate the configurational entropy as a function of temperature. The vibrational entropy does not change during the cation ordering phase transition from space group C2/c to P2/n at 865 °C but increases with a further temperature increase due to the reduction of short-range order. Supplementary Information The online version contains supplementary material available at 10.1007/s00269-023-01260-7.
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Affiliation(s)
- Artur Benisek
- Chemistry and Physics of Materials, University of Salzburg, Jakob-Haringer-Str. 2a, 5020 Salzburg, Austria
| | - Edgar Dachs
- Chemistry and Physics of Materials, University of Salzburg, Jakob-Haringer-Str. 2a, 5020 Salzburg, Austria
| | - Michael A. Carpenter
- Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge, CB2 3EQ UK
| | - Bastian Joachim-Mrosko
- Institute of Mineralogy and Petrography, University of Innsbruck, Innrain 52, 6020 Innsbruck, Austria
| | - Noreen M. Vielreicher
- Chemistry and Physics of Materials, University of Salzburg, Jakob-Haringer-Str. 2a, 5020 Salzburg, Austria
| | - Manfred Wildner
- Institute of Mineralogy and Crystallography, University of Vienna, Josef-Holaubek-Platz 2, 1090 Vienna, Austria
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Hossain MD, Borman T, Oses C, Esters M, Toher C, Feng L, Kumar A, Fahrenholtz WG, Curtarolo S, Brenner D, LeBeau JM, Maria JP. Entropy Landscaping of High-Entropy Carbides. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2021; 33:e2102904. [PMID: 34476849 DOI: 10.1002/adma.202102904] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2021] [Revised: 07/02/2021] [Indexed: 06/13/2023]
Abstract
The entropy landscape of high-entropy carbides can be used to understand and predict their structure, properties, and stability. Using first principles calculations, the individual and temperature-dependent contributions of vibrational, electronic, and configurational entropies are analyzed, and compare them qualitatively to the enthalpies of mixing. As an experimental complement, high-entropy carbide thin films are synthesized with high power impulse magnetron sputtering to assess structure and properties. All compositions can be stabilized in the single-phase state despite finite positive, and in some cases substantial, enthalpies of mixing. Density functional theory calculations reveal that configurational entropy dominates the free energy landscape and compensates for the enthalpic penalty, whereas the vibrational and electronic entropies offer negligible contributions. The calculations predict that in many compositions, the single-phase state becomes stable at extremely high temperatures (>3000 K). Consequently, rapid quenching rates are needed to preserve solubility at room temperature and facilitate physical characterization. Physical vapor deposition provides this experimental validation opportunity. The computation/experimental data set generated in this work identifies "valence electron concentration" as an effective descriptor to predict structural and thermodynamic properties of multicomponent carbides and educate new formulation selections.
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Affiliation(s)
- Mohammad Delower Hossain
- Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA, 16802, USA
| | - Trent Borman
- Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA, 16802, USA
| | - Corey Oses
- Center for Autonomous Materials Design and Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC, 27708, USA
| | - Marco Esters
- Center for Autonomous Materials Design and Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC, 27708, USA
| | - Cormac Toher
- Center for Autonomous Materials Design and Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC, 27708, USA
| | - Lun Feng
- Department of Materials Science and Engineering, Missouri University of Science and Technology, Rolla, MO, 65409, USA
| | - Abinash Kumar
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - William G Fahrenholtz
- Department of Materials Science and Engineering, Missouri University of Science and Technology, Rolla, MO, 65409, USA
| | - Stefano Curtarolo
- Center for Autonomous Materials Design and Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC, 27708, USA
| | - Donald Brenner
- Department of Materials Science and Engineering, North Carolina State University, Raleigh, NC, 27695, USA
| | - James M LeBeau
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Jon-Paul Maria
- Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA, 16802, USA
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Shulumba N, Hellman O, Raza Z, Alling B, Barrirero J, Mücklich F, Abrikosov IA, Odén M. Lattice Vibrations Change the Solid Solubility of an Alloy at High Temperatures. PHYSICAL REVIEW LETTERS 2016; 117:205502. [PMID: 27886477 DOI: 10.1103/physrevlett.117.205502] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2015] [Indexed: 06/06/2023]
Abstract
We develop a method to accurately and efficiently determine the vibrational free energy as a function of temperature and volume for substitutional alloys from first principles. Taking Ti_{1-x}Al_{x}N alloy as a model system, we calculate the isostructural phase diagram by finding the global minimum of the free energy corresponding to the true equilibrium state of the system. We demonstrate that the vibrational contribution including anharmonicity and temperature dependence of the mixing enthalpy have a decisive impact on the calculated phase diagram of a Ti_{1-x}Al_{x}N alloy, lowering the maximum temperature for the miscibility gap from 6560 to 2860 K. Our local chemical composition measurements on thermally aged Ti_{0.5}Al_{0.5}N alloys agree with the calculated phase diagram.
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Affiliation(s)
- Nina Shulumba
- Department of Physics, Chemistry, and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden
- Functional Materials, Saarland University, Campus D3 3, D-66123 Saarbrücken, Germany
| | - Olle Hellman
- Department of Physics, Chemistry, and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden
- Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA
| | - Zamaan Raza
- Department of Physics, Chemistry, and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden
| | - Björn Alling
- Department of Physics, Chemistry, and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden
- Max-Planck-Institut für Eisenforschung GmbH, D-40237 Düsseldorf, Germany
| | - Jenifer Barrirero
- Department of Physics, Chemistry, and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden
- Functional Materials, Saarland University, Campus D3 3, D-66123 Saarbrücken, Germany
| | - Frank Mücklich
- Functional Materials, Saarland University, Campus D3 3, D-66123 Saarbrücken, Germany
| | - Igor A Abrikosov
- Department of Physics, Chemistry, and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden
- Materials Modeling and Development Laboratory, NUST "MISIS," 119049 Moscow, Russia
| | - Magnus Odén
- Department of Physics, Chemistry, and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden
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Benisek A, Dachs E, Salihović M, Paunovic A, Maier ME. The vibrational and configurational entropy of α-brass. THE JOURNAL OF CHEMICAL THERMODYNAMICS 2014; 71:126-132. [PMID: 24926103 PMCID: PMC4047615 DOI: 10.1016/j.jct.2013.11.012] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/09/2013] [Revised: 11/09/2013] [Accepted: 11/12/2013] [Indexed: 06/03/2023]
Abstract
The heat capacities of two samples of a fcc Cu-Zn alloy with the composition CuZn15 and CuZn34 were measured from T = 5 K to 573 K using relaxation and differential scanning calorimetry. Below ∼90 K, they are characterised by negative excess heat capacities deviating from ideal mixing by up to -0.20 and -0.44 J · mol-1 · K-1 for CuZn15 and CuZn34, respectively. The excess heat capacities produce excess vibrational entropies, which are less negative compared to the excess entropy available from the literature. Since the literature entropy data contain both, the configurational and the vibrational part of the entropy, the difference is attributed to the excess configurational entropy. The thermodynamics of different short-range ordered samples was also investigated. The extent of the short-range order had no influence on the heat capacity below T = 300 K. Above T = 300 K, where the ordering changed during the measurement, the heat capacity depended strongly on the thermal history of the samples. From these data, the heat and entropy of ordering was calculated. The results on the vibrational entropy of this study were also used to test a relationship for estimating the excess vibrational entropy of mixing.
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Affiliation(s)
- Artur Benisek
- Materialforschung und Physik, Universität Salzburg, Hellbrunnerstr. 34, A-5020 Salzburg, Austria
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Muñoz JA, Lucas MS, Delaire O, Winterrose ML, Mauger L, Li CW, Sheets AO, Stone MB, Abernathy DL, Xiao Y, Chow P, Fultz B. Positive vibrational entropy of chemical ordering in FeV. PHYSICAL REVIEW LETTERS 2011; 107:115501. [PMID: 22026683 DOI: 10.1103/physrevlett.107.115501] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2010] [Indexed: 05/31/2023]
Abstract
Inelastic neutron scattering and nuclear resonant inelastic x-ray scattering were used to measure phonon spectra of FeV as a B2 ordered compound and as a bcc solid solution. The two data sets were combined to give an accurate phonon density of states, and the phonon partial densities of states for V and Fe atoms. Contrary to the behavior of ordering alloys studied to date, the phonons in the B2 ordered phase are softer than in the solid solution. Ordering increases the vibrational entropy by +0.22±0.03 kB/atom, which stabilizes the ordered phase to higher temperatures. First-principles calculations show that the number of electronic states at the Fermi level increases upon ordering, enhancing the screening between ions, and reducing the interatomic force constants. The effect of screening is larger at the V atomic sites than at the Fe atomic sites.
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Affiliation(s)
- J A Muñoz
- California Institute of Technology, W. M. Keck Laboratory 138-78, Pasadena, California 91125, USA
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7
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Manley ME, Fultz B, Nagel LJ. Heat capacity and microstructure of ordered and disordered Pd3V. ACTA ACUST UNITED AC 2009. [DOI: 10.1080/13642810008208589] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- M. E. Manley
- a Division of Engineering and Applied Science , Mail 138-78, California Institute of Technology, Pasadena , CA , 91125 , USA
| | - B. Fultz
- a Division of Engineering and Applied Science , Mail 138-78, California Institute of Technology, Pasadena , CA , 91125 , USA
| | - L. J. Nagel
- b Engineering Technology, West Texas A&M University , Canyon , TX , 79016 , USA
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8
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Bogdanoff PD, Fultz B. Vibrational entropies of alloying and compound formation: Experimental trends. ACTA ACUST UNITED AC 2009. [DOI: 10.1080/13642819908205747] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- P. D. Bogdanoff
- a Keck Laboratory of Engineering Materials , California Institute of Technology , Mail 138-78, Pasadena , California , 91125 , USA
| | - B. Fultz
- a Keck Laboratory of Engineering Materials , California Institute of Technology , Mail 138-78, Pasadena , California , 91125 , USA
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Yildirim H, Kara A, Rahman TS. Structural, vibrational and thermodynamic properties of Ag(n)Cu(34-n) nanoparticles. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:084220. [PMID: 21817372 DOI: 10.1088/0953-8984/21/8/084220] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We report results of a systematic study of structural, vibrational and thermodynamical properties of 34-atom bimetallic nanoparticles from the Ag(n)Cu(34-n) family using model interaction potentials as derived from the embedded atom method and invoking the harmonic approximation of lattice dynamics. Systematic trends in the bond length and dynamical properties can be explained largely from arguments based on local coordination and elemental environment. Thus an increase in the number of silver atoms in a given neighborhood introduces a monotonic increase in bond length, while an increase of the copper content does the reverse. Moreover, for the bond lengths of the lowest-coordinated (six and eight) copper atoms with their nearest neighbors (Cu atoms), we find that the nanoparticles divide into two groups with the average bond length either close to (∼2.58 Å) or smaller than (∼2.48 Å) that in bulk copper, accompanied by characteristic features in their vibrational density of states. For the entire set of nanoparticles, we find vibrational modes above the bulk bands of copper/silver. We trace a blue shift in the high-frequency end of the spectrum that occurs as the number of copper atoms increases in the nanoparticles, leading to shrinkage of the bond lengths from those in the bulk. The vibrational densities of states at the low-frequency end of the spectrum scale linearly with frequency as for single-element nanoparticles, with a more pronounced effect for these nanoalloys. The Debye temperature is found to be about one-third of that of the bulk for pure copper and silver nanoparticles, with a non-linear increase as copper atoms increase in the nanoalloy.
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Affiliation(s)
- Handan Yildirim
- Department of Physics, University of Central Florida, Orlando, FL 32816, USA
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10
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Bogdanoff PD, Fultz B. The role of phonons in the thermodynamics of the martensitic transformation in NiTi. ACTA ACUST UNITED AC 2007. [DOI: 10.1080/13642810108221985] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- P. D. Bogdanoff
- a Keck Laboratory of Engineering Materials , California Institute of Technology , Mail 138-78, Pasadena , California , 91125 , USA
| | - B. Fultz
- a Keck Laboratory of Engineering Materials , California Institute of Technology , Mail 138-78, Pasadena , California , 91125 , USA
- b E-mail:
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Delaire O, Fultz B. Charge redistribution and phonon entropy of vanadium alloys. PHYSICAL REVIEW LETTERS 2006; 97:245701. [PMID: 17280298 DOI: 10.1103/physrevlett.97.245701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2006] [Revised: 09/20/2006] [Indexed: 05/13/2023]
Abstract
The effects of alloying on the lattice dynamics of vanadium were investigated using inelastic neutron scattering. Phonon densities of states were obtained for bcc solid solutions of V with 3d, 4d, and 5d transition metal solutes, from which vibrational entropies of alloying were obtained. A good correlation is found between the vibrational entropy of alloying and the electronegativity of transition metal solutes across the 3d row and down columns of the periodic table. First-principles calculations on supercells matching the experimental compositions predicted a systematic charge redistribution in the nearest-neighbor shell around the solute atoms, also following the Pauling and Watson electronegativity scales. The systematic stiffening of the phonons is interpreted in terms of the modified screening properties of the electron density around the solutes.
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Affiliation(s)
- O Delaire
- W. M. Keck Laboratory, California Institute of Technology, Mail 138-78, Pasadena, California 91125, USA
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Nagel LJ, Fultz B, Robertson JL. Vibrational entropies of phases of Co3V measured by inelastic neutron scattering and cryogenic calorimetry. ACTA ACUST UNITED AC 2006. [DOI: 10.1080/13642819708202349] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- L. J. Nagel
- a Division of Engineering and Applied Science , Mail 138-78, California Institute of Technology , Pasadena , California , 91125 , USA
| | - B. Fultz
- a Division of Engineering and Applied Science , Mail 138-78, California Institute of Technology , Pasadena , California , 91125 , USA
| | - J. L. Robertson
- b Oak Ridge National Laboratory , PO Box 2008, Oak Ridge , Tennessee , 37831 , USA
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Delaire O, Swan-Wood T, Fultz B. Negative entropy of mixing for vanadium-platinum solutions. PHYSICAL REVIEW LETTERS 2004; 93:185704. [PMID: 15525182 DOI: 10.1103/physrevlett.93.185704] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2004] [Indexed: 05/24/2023]
Abstract
The phonon densities of states for pure vanadium and the solid solutions V-6.25% Ni, Pd, Pt were determined from inelastic neutron scattering measurements. The solute atoms caused a large stiffening of the phonons, resulting in large, negative vibrational entropies of mixing. For V-6.25%Pt, the negative vibrational entropy of mixing exceeds the conventional positive chemical entropy of mixing. This negative total entropy of mixing should extend to lower concentrations of Pt, and the effect on the bcc solvus line is discussed. The experimental data were inverted to obtain interatomic force constants by using a Born-von Kármán model with an iterative optimization algorithm. The stiffening of bonds responsible for the decrease of entropy was found to occur mainly in first-nearest-neighbor solute-host bonds, and correlates in part with the solute metallic radius.
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Affiliation(s)
- O Delaire
- California Institute of Technology, W. M. Keck Laboratory, mail 138-78, Pasadena, CA 91125, USA
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Wolverton C, Ololiņs V. Entropically favored ordering: the metallurgy of Al(2)Cu revisited. PHYSICAL REVIEW LETTERS 2001; 86:5518-5521. [PMID: 11415290 DOI: 10.1103/physrevlett.86.5518] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2000] [Indexed: 05/23/2023]
Abstract
The famous sequence of precipitates which form upon heat treating Al-Cu is part of nearly every metallurgical textbook. Numerous precipitation (and other) experiments have led to a long-standing belief that the energetic ground state of Al(2)Cu is the theta phase. Modern first-principles calculations at T = 0 K surprisingly predict the energy of the observed Al(2)Cu-theta phase to be higher than that of its metastable counterpart, theta('). We show that vibrational entropy reverses this energetic preference at T approximately 150--200 degrees C, resolves the apparent discrepancy between theory and experiment, and hence plays a critical (but previously unsuspected) role in the precipitation sequence.
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Affiliation(s)
- C Wolverton
- Ford Research Laboratory, MD3028/SRL, Dearborn, Michigan 48121-2053, USA
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15
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Manley ME, Fultz B, McQueeney RJ, Brown CM, Hults WL, Smith JL, Thoma DJ, Osborn R, Robertson JL. Large harmonic softening of the phonon density of states of uranium. PHYSICAL REVIEW LETTERS 2001; 86:3076-3079. [PMID: 11290111 DOI: 10.1103/physrevlett.86.3076] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2000] [Indexed: 05/23/2023]
Abstract
Phonon density-of-states curves were obtained from inelastic neutron scattering spectra from the three crystalline phases of uranium at temperatures from 50 to 1213 K. The alpha-phase showed an unusually large thermal softening of phonon frequencies. Analysis of the vibrational power spectrum showed that this phonon softening originates with the softening of a harmonic solid, as opposed to vibrations in anharmonic potentials. It follows that thermal excitations of electronic states are more significant thermodynamically than are the classical volume effects. For the alpha-beta and beta-gamma phase transitions, vibrational and electronic entropies were comparable.
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Affiliation(s)
- M E Manley
- California Institute of Technology, Pasadena 91125, USA
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16
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Ozoliņs V, Asta M. Large vibrational effects upon calculated phase boundaries in Al-Sc. PHYSICAL REVIEW LETTERS 2001; 86:448-451. [PMID: 11177852 DOI: 10.1103/physrevlett.86.448] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2000] [Indexed: 05/23/2023]
Abstract
The fcc portion of the Al-Sc phase diagram is calculated from first principles including contributions to alloy free energies associated with ionic vibrations. It is found that vibrational entropy accounts for a 27-fold increase in the calculated solubility limits for Sc in fcc Al at high temperatures, bringing calculated and measured values into very good agreement. The present work gives a clear example demonstrating a large effect of vibrational entropy upon calculated phase boundaries in substitutional alloys.
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Affiliation(s)
- V Ozoliņs
- Sandia National Laboratories, MS 9161, P.O. Box 969, Livermore, California 94551-0969, USA
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Morgan D, Althoff JD, Fontaine D. Local environment effects in the vibrational properties of disordered alloys: An embedded-atom method study of Ni3Al and Cu3Au. ACTA ACUST UNITED AC 1998. [DOI: 10.1361/105497198770341752] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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Nagel LJ, Anthony L, Okamoto JK, Fultz B. An experimental study of the difference in vibrational entropy between ordered and disordered Fe3A1. ACTA ACUST UNITED AC 1997. [DOI: 10.1007/bf02665810] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Garbulsky GD, Ceder G. Contribution of the vibrational free energy to phase stability in substitutional alloys: Methods and trends. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:8993-9001. [PMID: 9982401 DOI: 10.1103/physrevb.53.8993] [Citation(s) in RCA: 55] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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20
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Mukherjee GD, Bansal C, Chatterjee A. Thermal expansion study of ordered and disordered Fe3Al: An effective approach for the determination of vibrational entropy. PHYSICAL REVIEW LETTERS 1996; 76:1876-1879. [PMID: 10060543 DOI: 10.1103/physrevlett.76.1876] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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21
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Asta M, Foiles SM. Embedded-atom-method effective-pair-interaction study of the structural and thermodynamic properties of Cu-Ni, Cu-Ag, and Au-Ni solid solutions. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:2389-2404. [PMID: 9983741 DOI: 10.1103/physrevb.53.2389] [Citation(s) in RCA: 24] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Fultz B, Anthony L, Nagel LJ, Nicklow RM, Spooner S. Phonon densities of states and vibrational entropies of ordered and disordered Ni3Al. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:3315-3321. [PMID: 9981449 DOI: 10.1103/physrevb.52.3315] [Citation(s) in RCA: 44] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Fultz B, Anthony L, Robertson JL, Nicklow RM, Spooner S, Mostoller M. Phonon modes and vibrational entropy of mixing in Fe-Cr. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:3280-3285. [PMID: 9981445 DOI: 10.1103/physrevb.52.3280] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Liu M, Finlayson TR, Smith TF. Thermal expansion of V3Si with controlled martensite-phase morphology. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:530-535. [PMID: 9979631 DOI: 10.1103/physrevb.52.530] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Anthony L, Nagel LJ, Okamoto JK, Fultz B. Magnitude and origin of the difference in vibrational entropy between ordered and disordered Fe3Al. PHYSICAL REVIEW LETTERS 1994; 73:3034-3037. [PMID: 10057265 DOI: 10.1103/physrevlett.73.3034] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Garbulsky GD, Ceder G. Effect of lattice vibrations on the ordering tendencies in substitutional binary alloys. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:6327-6330. [PMID: 10011623 DOI: 10.1103/physrevb.49.6327] [Citation(s) in RCA: 40] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Jurado M, Mañosa L, Planes A. Influence of configurational atomic order on the relative stability of bcc and close-packed structures in Cu-based alloys. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:3540-3543. [PMID: 10008791 DOI: 10.1103/physrevb.48.3540] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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