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The Effect of Long Range Order on Elastic Properties of Alloys
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Applied Material Physics. (Applied Material Science)ORCID iD: 0000-0003-0961-6621
2014 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Ab initio alloy theory, formulated within the exact muffin-tin orbitals method in combination with the coherent-potential approximation, is used to determine the effect of long range order on the elastic properties. The lattice parameters and single-crystal elastic constants of Cu3Au are calculated for different partially ordered structures ranging from the fully ordered L12 to the random face centered cubic lattice. Special attention is put on the chemical and magnetic effects and on the interplay between these two degrees of freedom.

For non-magnetic Cu3Au, it was found that the lattice parameters and single-crystal elastic constants follow a clear trend with the degree of chemical order: namely, C11 and C12 decrease slightly, whereas C44 remains nearly constant with increasing disorder. As none of the single-crystal elastic constants were modified significantly due to the long-range-order, the polycrystalline elastic moduli of Cu3Au also keep nearly constant upon ordering. The Debye temperature does not show a strong chemical order dependence either. Using the calculated Debye temperatures, we find that for the entropy change upon order-disorder transition varies between −0.018 kB and 0.022 kB, the upper value being surprisingly close to 0.023 kB observed in experiments.

However, some of the elastic constants of ferromagnetic Ni3Fe, adopting the same crystal lattice as Cu3Au, were affected considerably. For the lattice parameter a, the main effect of magnetism is concentrated in the chemically dis-ordered region, with long-range order parameter S below ∼ 0.6 and the effect gradually disappears with increasing S. In the ferromagnetic state, the lattice parameter is almost constant as a function of the degree of order. Out of the three single-crystal elastic constants, only C11 and C12 are found to be affected by magnetism in the ordered state, however, their combined effect results in a nearly constant bulk modulus as a function of S. C44 changes slightly with S and magnetic state. The tetragonal shear elastic constant C´ , the Young’s modulus E and the shear modulus G increase significantly with the degree of order in the ferromagnetic state, but the effect becomes weak as the system approaches the random regime. Especially the C´ shear elastic constant depends strongly on the magnetic state and the degree of order. As a result, the Zener anisotropy ratio C44/C´ and the Possion’s ratio are strongly affected by the long-range order in the ferromagnetic state. Nevertheless, the actual values for the Pugh ratio and the Cauchy pressure remain far from their critical values, indicating that the ductility of Ni3Fe is not influenced by the chemical/magnetic ordering. Interestingly, the ferromagnetic L12 system possesses ∼5.4% larger elastic Debye temperature than the paramagnetic one, which in turn has similar ΘD as the chemically disordered face centered cubic phase being in either ferro-or paramagnetic state. The implications of the chemical/magnetic order on the mechanical properties and order-disorder transition is discussed.

 

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. , vi, 42 p.
Keyword [en]
long-range order, elastic constant, alloys, magnetic
National Category
Condensed Matter Physics
Research subject
Industrial Engineering and Management
Identifiers
URN: urn:nbn:se:kth:diva-152529ISBN: 978-91-7595-276-5 (print)OAI: oai:DiVA.org:kth-152529DiVA: diva2:750197
Presentation
2014-10-03, konferensrummet, Materialvetenskap, Kungliga Tekniska Högskolan, Brinellvägen 23, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20140929

Available from: 2014-09-29 Created: 2014-09-26 Last updated: 2014-09-30Bibliographically approved
List of papers
1. The effect of long-range order on the elastic properties of Cu3Au
Open this publication in new window or tab >>The effect of long-range order on the elastic properties of Cu3Au
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2013 (English)In: Journal of Physics: Condensed Matter, ISSN 0953-8984, E-ISSN 1361-648X, Vol. 25, no 8, 085401- p.Article in journal (Refereed) Published
Abstract [en]

Ab initio calculations, based on the exact muffin-tin orbitals method are used to determine the elastic properties of Cu-Au alloys with Au/Cu ratio 1/3. The compositional disorder is treated within the coherent potential approximation. The lattice parameters and single-crystal elastic constants are calculated for different partially ordered structures ranging from the fully ordered L1(2) to the random face centered cubic lattice. It is shown that the theoretical elastic constants follow a clear trend with the degree of chemical order: namely, C-11 and C-12 decrease, whereas C-44 remains nearly constant with increasing disorder. The present results are in line with the experimental findings that the impact of the chemical ordering on the fundamental elastic parameters is close to the resolution of the available experimental and theoretical tools.

Keyword
Coherent-Potential Approximation, Au-Cu Alloys, Mg Alloys, Constants, Energy, Metals, Gold, Transition, Pressure, Model
National Category
Other Physics Topics
Identifiers
urn:nbn:se:kth:diva-119452 (URN)10.1088/0953-8984/25/8/085401 (DOI)000314780400009 ()23360774 (PubMedID)2-s2.0-84873301825 (Scopus ID)
Funder
Swedish Research CouncilEU, European Research Council, 228074
Note

QC 20130315

Available from: 2013-03-15 Created: 2013-03-14 Last updated: 2017-12-06Bibliographically approved
2. Ab initio investigation of the elastic properties of Ni3Fe
Open this publication in new window or tab >>Ab initio investigation of the elastic properties of Ni3Fe
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2013 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 88, no 17, 174205- p.Article in journal (Refereed) Published
Abstract [en]

Ab initio alloy theory, formulated within the exact muffin-tin orbitals method in combination with the coherent-potential approximation, is used to determine the elastic properties of Ni-Fe alloys with Fe:Ni ratio 1:3. The interplay between magnetic and chemical effects is investigated by computing the lattice parameters and the single-and polycrystal elastic moduli for different partially ordered structures in the ferro-and paramagnetic states. It is found that the influence of long-range chemical order on the bulk properties strongly depends on the magnetic state. The largest magnetic-order-induced changes are obtained for the chemically ordered L1(2) phase. The ferromagnetic L1(2) system possesses similar to 5.4% larger elastic Debye temperature than the paramagnetic L1(2) phase, which in turn has a similar Theta(D) as the chemically disordered face-centered cubic phase in either the ferro-or paramagnetic state. It is concluded that magnetic ordering has a substantially larger impact on the bulk parameters of Ni3Fe than chemical ordering. The calculated trends are explained based on the electronic structure of nonmagnetic, ferromagnetic, and paramagnetic ordered and disordered phases.

Keyword
Single-Crystal Alloys, Coherent-Potential Approximation, Order-Disorder, Stiffness Coefficients, Configurational Order, Room-Temperature, Atomic Volume, Phase, Stability, Constants
National Category
Other Physics Topics
Identifiers
urn:nbn:se:kth:diva-139203 (URN)10.1103/PhysRevB.88.174205 (DOI)000327933500003 ()2-s2.0-84890386334 (Scopus ID)
Funder
Swedish Research CouncilEU, European Research Council
Note

QC 20140113

Available from: 2014-01-13 Created: 2014-01-08 Last updated: 2017-12-06Bibliographically approved
3. Large magneto-chemical-elastic coupling in highly magnetostrictive Fe-Ga alloys
Open this publication in new window or tab >>Large magneto-chemical-elastic coupling in highly magnetostrictive Fe-Ga alloys
2013 (English)In: Applied Physics Letters, ISSN 0003-6951, E-ISSN 1077-3118, Vol. 103, no 23, 231903- p.Article in journal (Refereed) Published
Abstract [en]

The strong softening of the tetragonal shear elastic constant (C') is the main reason for the second magnetostriction peak observed in Fe100-xGax alloys. Here, we study the coupling between chemical order and magnetism with the aim to understand the origin of the elastic softening. We demonstrate that C' strongly depends on the degree of order of Ga atoms in alpha-Fe. The B-2 type ordering proves to have an important role on the elastic softening for x < 19%, whereas the extreme shear lattice softening and the anomalous temperature dependence of C' are found to be due to the strong magnetochemical coupling in the DO3 phase.

Keyword
Chemical order, Degree of order, Elastic softening, Fe-Ga alloy, Shear elastic constants, Temperature dependence
National Category
Other Physics Topics
Identifiers
urn:nbn:se:kth:diva-140150 (URN)10.1063/1.4838657 (DOI)000328634900024 ()2-s2.0-84889823587 (Scopus ID)
Funder
Swedish Research CouncilEU, European Research Council, 228074
Note

QC 20140120

Available from: 2014-01-20 Created: 2014-01-17 Last updated: 2017-06-13Bibliographically approved

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