Limits of the stability of hexagonal phases upon uniaxial loading
In modern studies, experimental methods for estimating nonlinear elastic moduli are often replaced with calculations of these quantities in mathematical simulation. However, different reliable models and experiments give different values of nonlinear elastic moduli. This work proposes a poßsible sol...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Gufan, M A [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2017 |
|---|
| Rechteinformationen: |
Nutzungsrecht: © Allerton Press, Inc. 2017 |
|---|
| Schlagwörter: |
|---|
| Übergeordnetes Werk: |
Enthalten in: Bulletin of the Russian Academy of Sciences. Physics - New York, NY : Allerton Press, 1992, 81(2017), 6, Seite 768-778 |
|---|---|
| Übergeordnetes Werk: |
volume:81 ; year:2017 ; number:6 ; pages:768-778 |
| Links: |
|---|
| DOI / URN: |
10.3103/S1062873817060119 |
|---|
| Katalog-ID: |
OLC199580097X |
|---|
| LEADER | 01000caa a2200265 4500 | ||
|---|---|---|---|
| 001 | OLC199580097X | ||
| 003 | DE-627 | ||
| 005 | 20230715063253.0 | ||
| 007 | tu | ||
| 008 | 170901s2017 xx ||||| 00| ||eng c | ||
| 024 | 7 | |a 10.3103/S1062873817060119 |2 doi | |
| 028 | 5 | 2 | |a PQ20171125 |
| 035 | |a (DE-627)OLC199580097X | ||
| 035 | |a (DE-599)GBVOLC199580097X | ||
| 035 | |a (PRQ)p663-eff5696cfbd1f7f702e8f09a91e5f5c5584e68c7f9c74fc04e6508f79454cd470 | ||
| 035 | |a (KEY)0018054820170000081000600768limitsofthestabilityofhexagonalphasesuponuniaxiall | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 082 | 0 | 4 | |a 530 |q DNB |
| 100 | 1 | |a Gufan, M A |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Limits of the stability of hexagonal phases upon uniaxial loading |
| 264 | 1 | |c 2017 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a ohne Hilfsmittel zu benutzen |b n |2 rdamedia | ||
| 338 | |a Band |b nc |2 rdacarrier | ||
| 520 | |a In modern studies, experimental methods for estimating nonlinear elastic moduli are often replaced with calculations of these quantities in mathematical simulation. However, different reliable models and experiments give different values of nonlinear elastic moduli. This work proposes a poßsible solution to the problem of which sets of elastic moduli should be used to predict the properties of substances. Two sets of the second-({cαβ,γδ}), third-({cαβ,γδ}), and fourth-order elastic moduli ({cαβ,γδ,μη,τρ}) of hexagonal Gd crystal proposed in the literature are considered as examples. The elastic moduli are defined as partial derivatives of the nonequilibrium Landau potential ΦL {uαβ{ with respect to components of the tensor of homogeneous deformation of the crystal (Ü). Necessary information about the nonequilibrium Landau potential as a function of {uαβ{ is given in the second section. An analytical way of deriving relationships between generally independent values of nonlinear elastic moduli caused by symmetry is proposed in Sections 3 and 4. The approach is based on using the integral rational basis of invariants (IRBI), which have the form of polynomials {uaß{. Aspects of the theory of phase transitions based on IRBI are discussed in Section 3. The set of polynomials of the second, third, and fourth order included in the list of basic invariants {J i (P)}, and the form of Landau potential Φ({J i (P)}, are clearly defined. The forms of the chosen dependences {J i (P)} and (ΦL{J i (P)}) are defined in Section 4 to compare the results from different works. Once the forms of Landau potential ΦL{J i (P)} and ΦL{uαβ} are defined, they are compared. The comparison results allow derivation of the nontrivial relationships between the components of the third-C III and fourth-rank elastic moduli tensors C IV due Gd hexagonal symmetry. Two different sets of calculated elastic moduli of Gd crystals, found in two different works, are given in Section 5. The criteria for selecting the most suitable set of numerical values of elastic moduli are described in Sections 6 and 7. One criterion is a comparison of load limits calculated from isothermal Gd elastic moduli and experimentally determined numerical values of the limits of stability of a certain Gd phase. In the last section, we show how the criterion based on comparing the phase stability limits allows us to dertermine which sets of third-rank elastic moduli should be used in, e.g., predicting Raman spectra. | ||
| 540 | |a Nutzungsrecht: © Allerton Press, Inc. 2017 | ||
| 650 | 4 | |a Physics | |
| 650 | 4 | |a Nuclear Physics, Heavy Ions, Hadrons | |
| 650 | 4 | |a Modulus of elasticity | |
| 650 | 4 | |a Phase stability | |
| 650 | 4 | |a Invariants | |
| 650 | 4 | |a Mathematical models | |
| 650 | 4 | |a Stability criteria | |
| 650 | 4 | |a Polynomials | |
| 650 | 4 | |a Phase transformations | |
| 650 | 4 | |a Tensors | |
| 650 | 4 | |a Load limits | |
| 650 | 4 | |a Mathematical analysis | |
| 650 | 4 | |a Phase transitions | |
| 650 | 4 | |a Elastic limit | |
| 650 | 4 | |a Deformation mechanisms | |
| 650 | 4 | |a Materials elasticity | |
| 650 | 4 | |a Raman spectra | |
| 650 | 4 | |a Computer simulation | |
| 650 | 4 | |a Elastic properties | |
| 650 | 4 | |a Symmetry | |
| 650 | 4 | |a Deformation | |
| 650 | 4 | |a Derivation | |
| 700 | 1 | |a Gufan, Yu M |4 oth | |
| 700 | 1 | |a Karamurzov, B S |4 oth | |
| 700 | 1 | |a Novakovich, A A |4 oth | |
| 773 | 0 | 8 | |i Enthalten in |t Bulletin of the Russian Academy of Sciences. Physics |d New York, NY : Allerton Press, 1992 |g 81(2017), 6, Seite 768-778 |w (DE-627)131135384 |w (DE-600)1124898-1 |w (DE-576)032854463 |x 1062-8738 |7 nnns |
| 773 | 1 | 8 | |g volume:81 |g year:2017 |g number:6 |g pages:768-778 |
| 856 | 4 | 1 | |u http://dx.doi.org/10.3103/S1062873817060119 |3 Volltext |
| 912 | |a GBV_USEFLAG_A | ||
| 912 | |a SYSFLAG_A | ||
| 912 | |a GBV_OLC | ||
| 912 | |a SSG-OLC-PHY | ||
| 912 | |a SSG-OLC-OEU | ||
| 912 | |a SSG-OLC-HIS | ||
| 912 | |a GBV_ILN_70 | ||
| 951 | |a AR | ||
| 952 | |d 81 |j 2017 |e 6 |h 768-778 | ||
| author_variant |
m a g ma mag |
|---|---|
| matchkey_str |
article:10628738:2017----::iisfhsaiiyfeaoapaeuou |
| hierarchy_sort_str |
2017 |
| publishDate |
2017 |
| allfields |
10.3103/S1062873817060119 doi PQ20171125 (DE-627)OLC199580097X (DE-599)GBVOLC199580097X (PRQ)p663-eff5696cfbd1f7f702e8f09a91e5f5c5584e68c7f9c74fc04e6508f79454cd470 (KEY)0018054820170000081000600768limitsofthestabilityofhexagonalphasesuponuniaxiall DE-627 ger DE-627 rakwb eng 530 DNB Gufan, M A verfasserin aut Limits of the stability of hexagonal phases upon uniaxial loading 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In modern studies, experimental methods for estimating nonlinear elastic moduli are often replaced with calculations of these quantities in mathematical simulation. However, different reliable models and experiments give different values of nonlinear elastic moduli. This work proposes a poßsible solution to the problem of which sets of elastic moduli should be used to predict the properties of substances. Two sets of the second-({cαβ,γδ}), third-({cαβ,γδ}), and fourth-order elastic moduli ({cαβ,γδ,μη,τρ}) of hexagonal Gd crystal proposed in the literature are considered as examples. The elastic moduli are defined as partial derivatives of the nonequilibrium Landau potential ΦL {uαβ{ with respect to components of the tensor of homogeneous deformation of the crystal (Ü). Necessary information about the nonequilibrium Landau potential as a function of {uαβ{ is given in the second section. An analytical way of deriving relationships between generally independent values of nonlinear elastic moduli caused by symmetry is proposed in Sections 3 and 4. The approach is based on using the integral rational basis of invariants (IRBI), which have the form of polynomials {uaß{. Aspects of the theory of phase transitions based on IRBI are discussed in Section 3. The set of polynomials of the second, third, and fourth order included in the list of basic invariants {J i (P)}, and the form of Landau potential Φ({J i (P)}, are clearly defined. The forms of the chosen dependences {J i (P)} and (ΦL{J i (P)}) are defined in Section 4 to compare the results from different works. Once the forms of Landau potential ΦL{J i (P)} and ΦL{uαβ} are defined, they are compared. The comparison results allow derivation of the nontrivial relationships between the components of the third-C III and fourth-rank elastic moduli tensors C IV due Gd hexagonal symmetry. Two different sets of calculated elastic moduli of Gd crystals, found in two different works, are given in Section 5. The criteria for selecting the most suitable set of numerical values of elastic moduli are described in Sections 6 and 7. One criterion is a comparison of load limits calculated from isothermal Gd elastic moduli and experimentally determined numerical values of the limits of stability of a certain Gd phase. In the last section, we show how the criterion based on comparing the phase stability limits allows us to dertermine which sets of third-rank elastic moduli should be used in, e.g., predicting Raman spectra. Nutzungsrecht: © Allerton Press, Inc. 2017 Physics Nuclear Physics, Heavy Ions, Hadrons Modulus of elasticity Phase stability Invariants Mathematical models Stability criteria Polynomials Phase transformations Tensors Load limits Mathematical analysis Phase transitions Elastic limit Deformation mechanisms Materials elasticity Raman spectra Computer simulation Elastic properties Symmetry Deformation Derivation Gufan, Yu M oth Karamurzov, B S oth Novakovich, A A oth Enthalten in Bulletin of the Russian Academy of Sciences. Physics New York, NY : Allerton Press, 1992 81(2017), 6, Seite 768-778 (DE-627)131135384 (DE-600)1124898-1 (DE-576)032854463 1062-8738 nnns volume:81 year:2017 number:6 pages:768-778 http://dx.doi.org/10.3103/S1062873817060119 Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-OEU SSG-OLC-HIS GBV_ILN_70 AR 81 2017 6 768-778 |
| spelling |
10.3103/S1062873817060119 doi PQ20171125 (DE-627)OLC199580097X (DE-599)GBVOLC199580097X (PRQ)p663-eff5696cfbd1f7f702e8f09a91e5f5c5584e68c7f9c74fc04e6508f79454cd470 (KEY)0018054820170000081000600768limitsofthestabilityofhexagonalphasesuponuniaxiall DE-627 ger DE-627 rakwb eng 530 DNB Gufan, M A verfasserin aut Limits of the stability of hexagonal phases upon uniaxial loading 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In modern studies, experimental methods for estimating nonlinear elastic moduli are often replaced with calculations of these quantities in mathematical simulation. However, different reliable models and experiments give different values of nonlinear elastic moduli. This work proposes a poßsible solution to the problem of which sets of elastic moduli should be used to predict the properties of substances. Two sets of the second-({cαβ,γδ}), third-({cαβ,γδ}), and fourth-order elastic moduli ({cαβ,γδ,μη,τρ}) of hexagonal Gd crystal proposed in the literature are considered as examples. The elastic moduli are defined as partial derivatives of the nonequilibrium Landau potential ΦL {uαβ{ with respect to components of the tensor of homogeneous deformation of the crystal (Ü). Necessary information about the nonequilibrium Landau potential as a function of {uαβ{ is given in the second section. An analytical way of deriving relationships between generally independent values of nonlinear elastic moduli caused by symmetry is proposed in Sections 3 and 4. The approach is based on using the integral rational basis of invariants (IRBI), which have the form of polynomials {uaß{. Aspects of the theory of phase transitions based on IRBI are discussed in Section 3. The set of polynomials of the second, third, and fourth order included in the list of basic invariants {J i (P)}, and the form of Landau potential Φ({J i (P)}, are clearly defined. The forms of the chosen dependences {J i (P)} and (ΦL{J i (P)}) are defined in Section 4 to compare the results from different works. Once the forms of Landau potential ΦL{J i (P)} and ΦL{uαβ} are defined, they are compared. The comparison results allow derivation of the nontrivial relationships between the components of the third-C III and fourth-rank elastic moduli tensors C IV due Gd hexagonal symmetry. Two different sets of calculated elastic moduli of Gd crystals, found in two different works, are given in Section 5. The criteria for selecting the most suitable set of numerical values of elastic moduli are described in Sections 6 and 7. One criterion is a comparison of load limits calculated from isothermal Gd elastic moduli and experimentally determined numerical values of the limits of stability of a certain Gd phase. In the last section, we show how the criterion based on comparing the phase stability limits allows us to dertermine which sets of third-rank elastic moduli should be used in, e.g., predicting Raman spectra. Nutzungsrecht: © Allerton Press, Inc. 2017 Physics Nuclear Physics, Heavy Ions, Hadrons Modulus of elasticity Phase stability Invariants Mathematical models Stability criteria Polynomials Phase transformations Tensors Load limits Mathematical analysis Phase transitions Elastic limit Deformation mechanisms Materials elasticity Raman spectra Computer simulation Elastic properties Symmetry Deformation Derivation Gufan, Yu M oth Karamurzov, B S oth Novakovich, A A oth Enthalten in Bulletin of the Russian Academy of Sciences. Physics New York, NY : Allerton Press, 1992 81(2017), 6, Seite 768-778 (DE-627)131135384 (DE-600)1124898-1 (DE-576)032854463 1062-8738 nnns volume:81 year:2017 number:6 pages:768-778 http://dx.doi.org/10.3103/S1062873817060119 Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-OEU SSG-OLC-HIS GBV_ILN_70 AR 81 2017 6 768-778 |
| allfields_unstemmed |
10.3103/S1062873817060119 doi PQ20171125 (DE-627)OLC199580097X (DE-599)GBVOLC199580097X (PRQ)p663-eff5696cfbd1f7f702e8f09a91e5f5c5584e68c7f9c74fc04e6508f79454cd470 (KEY)0018054820170000081000600768limitsofthestabilityofhexagonalphasesuponuniaxiall DE-627 ger DE-627 rakwb eng 530 DNB Gufan, M A verfasserin aut Limits of the stability of hexagonal phases upon uniaxial loading 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In modern studies, experimental methods for estimating nonlinear elastic moduli are often replaced with calculations of these quantities in mathematical simulation. However, different reliable models and experiments give different values of nonlinear elastic moduli. This work proposes a poßsible solution to the problem of which sets of elastic moduli should be used to predict the properties of substances. Two sets of the second-({cαβ,γδ}), third-({cαβ,γδ}), and fourth-order elastic moduli ({cαβ,γδ,μη,τρ}) of hexagonal Gd crystal proposed in the literature are considered as examples. The elastic moduli are defined as partial derivatives of the nonequilibrium Landau potential ΦL {uαβ{ with respect to components of the tensor of homogeneous deformation of the crystal (Ü). Necessary information about the nonequilibrium Landau potential as a function of {uαβ{ is given in the second section. An analytical way of deriving relationships between generally independent values of nonlinear elastic moduli caused by symmetry is proposed in Sections 3 and 4. The approach is based on using the integral rational basis of invariants (IRBI), which have the form of polynomials {uaß{. Aspects of the theory of phase transitions based on IRBI are discussed in Section 3. The set of polynomials of the second, third, and fourth order included in the list of basic invariants {J i (P)}, and the form of Landau potential Φ({J i (P)}, are clearly defined. The forms of the chosen dependences {J i (P)} and (ΦL{J i (P)}) are defined in Section 4 to compare the results from different works. Once the forms of Landau potential ΦL{J i (P)} and ΦL{uαβ} are defined, they are compared. The comparison results allow derivation of the nontrivial relationships between the components of the third-C III and fourth-rank elastic moduli tensors C IV due Gd hexagonal symmetry. Two different sets of calculated elastic moduli of Gd crystals, found in two different works, are given in Section 5. The criteria for selecting the most suitable set of numerical values of elastic moduli are described in Sections 6 and 7. One criterion is a comparison of load limits calculated from isothermal Gd elastic moduli and experimentally determined numerical values of the limits of stability of a certain Gd phase. In the last section, we show how the criterion based on comparing the phase stability limits allows us to dertermine which sets of third-rank elastic moduli should be used in, e.g., predicting Raman spectra. Nutzungsrecht: © Allerton Press, Inc. 2017 Physics Nuclear Physics, Heavy Ions, Hadrons Modulus of elasticity Phase stability Invariants Mathematical models Stability criteria Polynomials Phase transformations Tensors Load limits Mathematical analysis Phase transitions Elastic limit Deformation mechanisms Materials elasticity Raman spectra Computer simulation Elastic properties Symmetry Deformation Derivation Gufan, Yu M oth Karamurzov, B S oth Novakovich, A A oth Enthalten in Bulletin of the Russian Academy of Sciences. Physics New York, NY : Allerton Press, 1992 81(2017), 6, Seite 768-778 (DE-627)131135384 (DE-600)1124898-1 (DE-576)032854463 1062-8738 nnns volume:81 year:2017 number:6 pages:768-778 http://dx.doi.org/10.3103/S1062873817060119 Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-OEU SSG-OLC-HIS GBV_ILN_70 AR 81 2017 6 768-778 |
| allfieldsGer |
10.3103/S1062873817060119 doi PQ20171125 (DE-627)OLC199580097X (DE-599)GBVOLC199580097X (PRQ)p663-eff5696cfbd1f7f702e8f09a91e5f5c5584e68c7f9c74fc04e6508f79454cd470 (KEY)0018054820170000081000600768limitsofthestabilityofhexagonalphasesuponuniaxiall DE-627 ger DE-627 rakwb eng 530 DNB Gufan, M A verfasserin aut Limits of the stability of hexagonal phases upon uniaxial loading 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In modern studies, experimental methods for estimating nonlinear elastic moduli are often replaced with calculations of these quantities in mathematical simulation. However, different reliable models and experiments give different values of nonlinear elastic moduli. This work proposes a poßsible solution to the problem of which sets of elastic moduli should be used to predict the properties of substances. Two sets of the second-({cαβ,γδ}), third-({cαβ,γδ}), and fourth-order elastic moduli ({cαβ,γδ,μη,τρ}) of hexagonal Gd crystal proposed in the literature are considered as examples. The elastic moduli are defined as partial derivatives of the nonequilibrium Landau potential ΦL {uαβ{ with respect to components of the tensor of homogeneous deformation of the crystal (Ü). Necessary information about the nonequilibrium Landau potential as a function of {uαβ{ is given in the second section. An analytical way of deriving relationships between generally independent values of nonlinear elastic moduli caused by symmetry is proposed in Sections 3 and 4. The approach is based on using the integral rational basis of invariants (IRBI), which have the form of polynomials {uaß{. Aspects of the theory of phase transitions based on IRBI are discussed in Section 3. The set of polynomials of the second, third, and fourth order included in the list of basic invariants {J i (P)}, and the form of Landau potential Φ({J i (P)}, are clearly defined. The forms of the chosen dependences {J i (P)} and (ΦL{J i (P)}) are defined in Section 4 to compare the results from different works. Once the forms of Landau potential ΦL{J i (P)} and ΦL{uαβ} are defined, they are compared. The comparison results allow derivation of the nontrivial relationships between the components of the third-C III and fourth-rank elastic moduli tensors C IV due Gd hexagonal symmetry. Two different sets of calculated elastic moduli of Gd crystals, found in two different works, are given in Section 5. The criteria for selecting the most suitable set of numerical values of elastic moduli are described in Sections 6 and 7. One criterion is a comparison of load limits calculated from isothermal Gd elastic moduli and experimentally determined numerical values of the limits of stability of a certain Gd phase. In the last section, we show how the criterion based on comparing the phase stability limits allows us to dertermine which sets of third-rank elastic moduli should be used in, e.g., predicting Raman spectra. Nutzungsrecht: © Allerton Press, Inc. 2017 Physics Nuclear Physics, Heavy Ions, Hadrons Modulus of elasticity Phase stability Invariants Mathematical models Stability criteria Polynomials Phase transformations Tensors Load limits Mathematical analysis Phase transitions Elastic limit Deformation mechanisms Materials elasticity Raman spectra Computer simulation Elastic properties Symmetry Deformation Derivation Gufan, Yu M oth Karamurzov, B S oth Novakovich, A A oth Enthalten in Bulletin of the Russian Academy of Sciences. Physics New York, NY : Allerton Press, 1992 81(2017), 6, Seite 768-778 (DE-627)131135384 (DE-600)1124898-1 (DE-576)032854463 1062-8738 nnns volume:81 year:2017 number:6 pages:768-778 http://dx.doi.org/10.3103/S1062873817060119 Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-OEU SSG-OLC-HIS GBV_ILN_70 AR 81 2017 6 768-778 |
| allfieldsSound |
10.3103/S1062873817060119 doi PQ20171125 (DE-627)OLC199580097X (DE-599)GBVOLC199580097X (PRQ)p663-eff5696cfbd1f7f702e8f09a91e5f5c5584e68c7f9c74fc04e6508f79454cd470 (KEY)0018054820170000081000600768limitsofthestabilityofhexagonalphasesuponuniaxiall DE-627 ger DE-627 rakwb eng 530 DNB Gufan, M A verfasserin aut Limits of the stability of hexagonal phases upon uniaxial loading 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In modern studies, experimental methods for estimating nonlinear elastic moduli are often replaced with calculations of these quantities in mathematical simulation. However, different reliable models and experiments give different values of nonlinear elastic moduli. This work proposes a poßsible solution to the problem of which sets of elastic moduli should be used to predict the properties of substances. Two sets of the second-({cαβ,γδ}), third-({cαβ,γδ}), and fourth-order elastic moduli ({cαβ,γδ,μη,τρ}) of hexagonal Gd crystal proposed in the literature are considered as examples. The elastic moduli are defined as partial derivatives of the nonequilibrium Landau potential ΦL {uαβ{ with respect to components of the tensor of homogeneous deformation of the crystal (Ü). Necessary information about the nonequilibrium Landau potential as a function of {uαβ{ is given in the second section. An analytical way of deriving relationships between generally independent values of nonlinear elastic moduli caused by symmetry is proposed in Sections 3 and 4. The approach is based on using the integral rational basis of invariants (IRBI), which have the form of polynomials {uaß{. Aspects of the theory of phase transitions based on IRBI are discussed in Section 3. The set of polynomials of the second, third, and fourth order included in the list of basic invariants {J i (P)}, and the form of Landau potential Φ({J i (P)}, are clearly defined. The forms of the chosen dependences {J i (P)} and (ΦL{J i (P)}) are defined in Section 4 to compare the results from different works. Once the forms of Landau potential ΦL{J i (P)} and ΦL{uαβ} are defined, they are compared. The comparison results allow derivation of the nontrivial relationships between the components of the third-C III and fourth-rank elastic moduli tensors C IV due Gd hexagonal symmetry. Two different sets of calculated elastic moduli of Gd crystals, found in two different works, are given in Section 5. The criteria for selecting the most suitable set of numerical values of elastic moduli are described in Sections 6 and 7. One criterion is a comparison of load limits calculated from isothermal Gd elastic moduli and experimentally determined numerical values of the limits of stability of a certain Gd phase. In the last section, we show how the criterion based on comparing the phase stability limits allows us to dertermine which sets of third-rank elastic moduli should be used in, e.g., predicting Raman spectra. Nutzungsrecht: © Allerton Press, Inc. 2017 Physics Nuclear Physics, Heavy Ions, Hadrons Modulus of elasticity Phase stability Invariants Mathematical models Stability criteria Polynomials Phase transformations Tensors Load limits Mathematical analysis Phase transitions Elastic limit Deformation mechanisms Materials elasticity Raman spectra Computer simulation Elastic properties Symmetry Deformation Derivation Gufan, Yu M oth Karamurzov, B S oth Novakovich, A A oth Enthalten in Bulletin of the Russian Academy of Sciences. Physics New York, NY : Allerton Press, 1992 81(2017), 6, Seite 768-778 (DE-627)131135384 (DE-600)1124898-1 (DE-576)032854463 1062-8738 nnns volume:81 year:2017 number:6 pages:768-778 http://dx.doi.org/10.3103/S1062873817060119 Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-OEU SSG-OLC-HIS GBV_ILN_70 AR 81 2017 6 768-778 |
| language |
English |
| source |
Enthalten in Bulletin of the Russian Academy of Sciences. Physics 81(2017), 6, Seite 768-778 volume:81 year:2017 number:6 pages:768-778 |
| sourceStr |
Enthalten in Bulletin of the Russian Academy of Sciences. Physics 81(2017), 6, Seite 768-778 volume:81 year:2017 number:6 pages:768-778 |
| format_phy_str_mv |
Article |
| institution |
findex.gbv.de |
| topic_facet |
Physics Nuclear Physics, Heavy Ions, Hadrons Modulus of elasticity Phase stability Invariants Mathematical models Stability criteria Polynomials Phase transformations Tensors Load limits Mathematical analysis Phase transitions Elastic limit Deformation mechanisms Materials elasticity Raman spectra Computer simulation Elastic properties Symmetry Deformation Derivation |
| dewey-raw |
530 |
| isfreeaccess_bool |
false |
| container_title |
Bulletin of the Russian Academy of Sciences. Physics |
| authorswithroles_txt_mv |
Gufan, M A @@aut@@ Gufan, Yu M @@oth@@ Karamurzov, B S @@oth@@ Novakovich, A A @@oth@@ |
| publishDateDaySort_date |
2017-01-01T00:00:00Z |
| hierarchy_top_id |
131135384 |
| dewey-sort |
3530 |
| id |
OLC199580097X |
| language_de |
englisch |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a2200265 4500</leader><controlfield tag="001">OLC199580097X</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230715063253.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">170901s2017 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.3103/S1062873817060119</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">PQ20171125</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC199580097X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)GBVOLC199580097X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(PRQ)p663-eff5696cfbd1f7f702e8f09a91e5f5c5584e68c7f9c74fc04e6508f79454cd470</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(KEY)0018054820170000081000600768limitsofthestabilityofhexagonalphasesuponuniaxiall</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="q">DNB</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Gufan, M A</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Limits of the stability of hexagonal phases upon uniaxial loading</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2017</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">In modern studies, experimental methods for estimating nonlinear elastic moduli are often replaced with calculations of these quantities in mathematical simulation. However, different reliable models and experiments give different values of nonlinear elastic moduli. This work proposes a poßsible solution to the problem of which sets of elastic moduli should be used to predict the properties of substances. Two sets of the second-({cαβ,γδ}), third-({cαβ,γδ}), and fourth-order elastic moduli ({cαβ,γδ,μη,τρ}) of hexagonal Gd crystal proposed in the literature are considered as examples. The elastic moduli are defined as partial derivatives of the nonequilibrium Landau potential ΦL {uαβ{ with respect to components of the tensor of homogeneous deformation of the crystal (Ü). Necessary information about the nonequilibrium Landau potential as a function of {uαβ{ is given in the second section. An analytical way of deriving relationships between generally independent values of nonlinear elastic moduli caused by symmetry is proposed in Sections 3 and 4. The approach is based on using the integral rational basis of invariants (IRBI), which have the form of polynomials {uaß{. Aspects of the theory of phase transitions based on IRBI are discussed in Section 3. The set of polynomials of the second, third, and fourth order included in the list of basic invariants {J i (P)}, and the form of Landau potential Φ({J i (P)}, are clearly defined. The forms of the chosen dependences {J i (P)} and (ΦL{J i (P)}) are defined in Section 4 to compare the results from different works. Once the forms of Landau potential ΦL{J i (P)} and ΦL{uαβ} are defined, they are compared. The comparison results allow derivation of the nontrivial relationships between the components of the third-C III and fourth-rank elastic moduli tensors C IV due Gd hexagonal symmetry. Two different sets of calculated elastic moduli of Gd crystals, found in two different works, are given in Section 5. The criteria for selecting the most suitable set of numerical values of elastic moduli are described in Sections 6 and 7. One criterion is a comparison of load limits calculated from isothermal Gd elastic moduli and experimentally determined numerical values of the limits of stability of a certain Gd phase. In the last section, we show how the criterion based on comparing the phase stability limits allows us to dertermine which sets of third-rank elastic moduli should be used in, e.g., predicting Raman spectra.</subfield></datafield><datafield tag="540" ind1=" " ind2=" "><subfield code="a">Nutzungsrecht: © Allerton Press, Inc. 2017</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Physics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nuclear Physics, Heavy Ions, Hadrons</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Modulus of elasticity</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Phase stability</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Invariants</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical models</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stability criteria</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Polynomials</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Phase transformations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Tensors</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Load limits</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Phase transitions</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Elastic limit</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Deformation mechanisms</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Materials elasticity</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Raman spectra</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computer simulation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Elastic properties</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Symmetry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Deformation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Derivation</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Gufan, Yu M</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Karamurzov, B S</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Novakovich, A A</subfield><subfield code="4">oth</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Bulletin of the Russian Academy of Sciences. Physics</subfield><subfield code="d">New York, NY : Allerton Press, 1992</subfield><subfield code="g">81(2017), 6, Seite 768-778</subfield><subfield code="w">(DE-627)131135384</subfield><subfield code="w">(DE-600)1124898-1</subfield><subfield code="w">(DE-576)032854463</subfield><subfield code="x">1062-8738</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:81</subfield><subfield code="g">year:2017</subfield><subfield code="g">number:6</subfield><subfield code="g">pages:768-778</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">http://dx.doi.org/10.3103/S1062873817060119</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-OEU</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-HIS</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">81</subfield><subfield code="j">2017</subfield><subfield code="e">6</subfield><subfield code="h">768-778</subfield></datafield></record></collection>
|
| author |
Gufan, M A |
| spellingShingle |
Gufan, M A ddc 530 misc Physics misc Nuclear Physics, Heavy Ions, Hadrons misc Modulus of elasticity misc Phase stability misc Invariants misc Mathematical models misc Stability criteria misc Polynomials misc Phase transformations misc Tensors misc Load limits misc Mathematical analysis misc Phase transitions misc Elastic limit misc Deformation mechanisms misc Materials elasticity misc Raman spectra misc Computer simulation misc Elastic properties misc Symmetry misc Deformation misc Derivation Limits of the stability of hexagonal phases upon uniaxial loading |
| authorStr |
Gufan, M A |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)131135384 |
| format |
Article |
| dewey-ones |
530 - Physics |
| delete_txt_mv |
keep |
| author_role |
aut |
| collection |
OLC |
| remote_str |
false |
| illustrated |
Not Illustrated |
| issn |
1062-8738 |
| topic_title |
530 DNB Limits of the stability of hexagonal phases upon uniaxial loading Physics Nuclear Physics, Heavy Ions, Hadrons Modulus of elasticity Phase stability Invariants Mathematical models Stability criteria Polynomials Phase transformations Tensors Load limits Mathematical analysis Phase transitions Elastic limit Deformation mechanisms Materials elasticity Raman spectra Computer simulation Elastic properties Symmetry Deformation Derivation |
| topic |
ddc 530 misc Physics misc Nuclear Physics, Heavy Ions, Hadrons misc Modulus of elasticity misc Phase stability misc Invariants misc Mathematical models misc Stability criteria misc Polynomials misc Phase transformations misc Tensors misc Load limits misc Mathematical analysis misc Phase transitions misc Elastic limit misc Deformation mechanisms misc Materials elasticity misc Raman spectra misc Computer simulation misc Elastic properties misc Symmetry misc Deformation misc Derivation |
| topic_unstemmed |
ddc 530 misc Physics misc Nuclear Physics, Heavy Ions, Hadrons misc Modulus of elasticity misc Phase stability misc Invariants misc Mathematical models misc Stability criteria misc Polynomials misc Phase transformations misc Tensors misc Load limits misc Mathematical analysis misc Phase transitions misc Elastic limit misc Deformation mechanisms misc Materials elasticity misc Raman spectra misc Computer simulation misc Elastic properties misc Symmetry misc Deformation misc Derivation |
| topic_browse |
ddc 530 misc Physics misc Nuclear Physics, Heavy Ions, Hadrons misc Modulus of elasticity misc Phase stability misc Invariants misc Mathematical models misc Stability criteria misc Polynomials misc Phase transformations misc Tensors misc Load limits misc Mathematical analysis misc Phase transitions misc Elastic limit misc Deformation mechanisms misc Materials elasticity misc Raman spectra misc Computer simulation misc Elastic properties misc Symmetry misc Deformation misc Derivation |
| format_facet |
Aufsätze Gedruckte Aufsätze |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
nc |
| author2_variant |
y m g ym ymg b s k bs bsk a a n aa aan |
| hierarchy_parent_title |
Bulletin of the Russian Academy of Sciences. Physics |
| hierarchy_parent_id |
131135384 |
| dewey-tens |
530 - Physics |
| hierarchy_top_title |
Bulletin of the Russian Academy of Sciences. Physics |
| isfreeaccess_txt |
false |
| familylinks_str_mv |
(DE-627)131135384 (DE-600)1124898-1 (DE-576)032854463 |
| title |
Limits of the stability of hexagonal phases upon uniaxial loading |
| ctrlnum |
(DE-627)OLC199580097X (DE-599)GBVOLC199580097X (PRQ)p663-eff5696cfbd1f7f702e8f09a91e5f5c5584e68c7f9c74fc04e6508f79454cd470 (KEY)0018054820170000081000600768limitsofthestabilityofhexagonalphasesuponuniaxiall |
| title_full |
Limits of the stability of hexagonal phases upon uniaxial loading |
| author_sort |
Gufan, M A |
| journal |
Bulletin of the Russian Academy of Sciences. Physics |
| journalStr |
Bulletin of the Russian Academy of Sciences. Physics |
| lang_code |
eng |
| isOA_bool |
false |
| dewey-hundreds |
500 - Science |
| recordtype |
marc |
| publishDateSort |
2017 |
| contenttype_str_mv |
txt |
| container_start_page |
768 |
| author_browse |
Gufan, M A |
| container_volume |
81 |
| class |
530 DNB |
| format_se |
Aufsätze |
| author-letter |
Gufan, M A |
| doi_str_mv |
10.3103/S1062873817060119 |
| dewey-full |
530 |
| title_sort |
limits of the stability of hexagonal phases upon uniaxial loading |
| title_auth |
Limits of the stability of hexagonal phases upon uniaxial loading |
| abstract |
In modern studies, experimental methods for estimating nonlinear elastic moduli are often replaced with calculations of these quantities in mathematical simulation. However, different reliable models and experiments give different values of nonlinear elastic moduli. This work proposes a poßsible solution to the problem of which sets of elastic moduli should be used to predict the properties of substances. Two sets of the second-({cαβ,γδ}), third-({cαβ,γδ}), and fourth-order elastic moduli ({cαβ,γδ,μη,τρ}) of hexagonal Gd crystal proposed in the literature are considered as examples. The elastic moduli are defined as partial derivatives of the nonequilibrium Landau potential ΦL {uαβ{ with respect to components of the tensor of homogeneous deformation of the crystal (Ü). Necessary information about the nonequilibrium Landau potential as a function of {uαβ{ is given in the second section. An analytical way of deriving relationships between generally independent values of nonlinear elastic moduli caused by symmetry is proposed in Sections 3 and 4. The approach is based on using the integral rational basis of invariants (IRBI), which have the form of polynomials {uaß{. Aspects of the theory of phase transitions based on IRBI are discussed in Section 3. The set of polynomials of the second, third, and fourth order included in the list of basic invariants {J i (P)}, and the form of Landau potential Φ({J i (P)}, are clearly defined. The forms of the chosen dependences {J i (P)} and (ΦL{J i (P)}) are defined in Section 4 to compare the results from different works. Once the forms of Landau potential ΦL{J i (P)} and ΦL{uαβ} are defined, they are compared. The comparison results allow derivation of the nontrivial relationships between the components of the third-C III and fourth-rank elastic moduli tensors C IV due Gd hexagonal symmetry. Two different sets of calculated elastic moduli of Gd crystals, found in two different works, are given in Section 5. The criteria for selecting the most suitable set of numerical values of elastic moduli are described in Sections 6 and 7. One criterion is a comparison of load limits calculated from isothermal Gd elastic moduli and experimentally determined numerical values of the limits of stability of a certain Gd phase. In the last section, we show how the criterion based on comparing the phase stability limits allows us to dertermine which sets of third-rank elastic moduli should be used in, e.g., predicting Raman spectra. |
| abstractGer |
In modern studies, experimental methods for estimating nonlinear elastic moduli are often replaced with calculations of these quantities in mathematical simulation. However, different reliable models and experiments give different values of nonlinear elastic moduli. This work proposes a poßsible solution to the problem of which sets of elastic moduli should be used to predict the properties of substances. Two sets of the second-({cαβ,γδ}), third-({cαβ,γδ}), and fourth-order elastic moduli ({cαβ,γδ,μη,τρ}) of hexagonal Gd crystal proposed in the literature are considered as examples. The elastic moduli are defined as partial derivatives of the nonequilibrium Landau potential ΦL {uαβ{ with respect to components of the tensor of homogeneous deformation of the crystal (Ü). Necessary information about the nonequilibrium Landau potential as a function of {uαβ{ is given in the second section. An analytical way of deriving relationships between generally independent values of nonlinear elastic moduli caused by symmetry is proposed in Sections 3 and 4. The approach is based on using the integral rational basis of invariants (IRBI), which have the form of polynomials {uaß{. Aspects of the theory of phase transitions based on IRBI are discussed in Section 3. The set of polynomials of the second, third, and fourth order included in the list of basic invariants {J i (P)}, and the form of Landau potential Φ({J i (P)}, are clearly defined. The forms of the chosen dependences {J i (P)} and (ΦL{J i (P)}) are defined in Section 4 to compare the results from different works. Once the forms of Landau potential ΦL{J i (P)} and ΦL{uαβ} are defined, they are compared. The comparison results allow derivation of the nontrivial relationships between the components of the third-C III and fourth-rank elastic moduli tensors C IV due Gd hexagonal symmetry. Two different sets of calculated elastic moduli of Gd crystals, found in two different works, are given in Section 5. The criteria for selecting the most suitable set of numerical values of elastic moduli are described in Sections 6 and 7. One criterion is a comparison of load limits calculated from isothermal Gd elastic moduli and experimentally determined numerical values of the limits of stability of a certain Gd phase. In the last section, we show how the criterion based on comparing the phase stability limits allows us to dertermine which sets of third-rank elastic moduli should be used in, e.g., predicting Raman spectra. |
| abstract_unstemmed |
In modern studies, experimental methods for estimating nonlinear elastic moduli are often replaced with calculations of these quantities in mathematical simulation. However, different reliable models and experiments give different values of nonlinear elastic moduli. This work proposes a poßsible solution to the problem of which sets of elastic moduli should be used to predict the properties of substances. Two sets of the second-({cαβ,γδ}), third-({cαβ,γδ}), and fourth-order elastic moduli ({cαβ,γδ,μη,τρ}) of hexagonal Gd crystal proposed in the literature are considered as examples. The elastic moduli are defined as partial derivatives of the nonequilibrium Landau potential ΦL {uαβ{ with respect to components of the tensor of homogeneous deformation of the crystal (Ü). Necessary information about the nonequilibrium Landau potential as a function of {uαβ{ is given in the second section. An analytical way of deriving relationships between generally independent values of nonlinear elastic moduli caused by symmetry is proposed in Sections 3 and 4. The approach is based on using the integral rational basis of invariants (IRBI), which have the form of polynomials {uaß{. Aspects of the theory of phase transitions based on IRBI are discussed in Section 3. The set of polynomials of the second, third, and fourth order included in the list of basic invariants {J i (P)}, and the form of Landau potential Φ({J i (P)}, are clearly defined. The forms of the chosen dependences {J i (P)} and (ΦL{J i (P)}) are defined in Section 4 to compare the results from different works. Once the forms of Landau potential ΦL{J i (P)} and ΦL{uαβ} are defined, they are compared. The comparison results allow derivation of the nontrivial relationships between the components of the third-C III and fourth-rank elastic moduli tensors C IV due Gd hexagonal symmetry. Two different sets of calculated elastic moduli of Gd crystals, found in two different works, are given in Section 5. The criteria for selecting the most suitable set of numerical values of elastic moduli are described in Sections 6 and 7. One criterion is a comparison of load limits calculated from isothermal Gd elastic moduli and experimentally determined numerical values of the limits of stability of a certain Gd phase. In the last section, we show how the criterion based on comparing the phase stability limits allows us to dertermine which sets of third-rank elastic moduli should be used in, e.g., predicting Raman spectra. |
| collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-OEU SSG-OLC-HIS GBV_ILN_70 |
| container_issue |
6 |
| title_short |
Limits of the stability of hexagonal phases upon uniaxial loading |
| url |
http://dx.doi.org/10.3103/S1062873817060119 |
| remote_bool |
false |
| author2 |
Gufan, Yu M Karamurzov, B S Novakovich, A A |
| author2Str |
Gufan, Yu M Karamurzov, B S Novakovich, A A |
| ppnlink |
131135384 |
| mediatype_str_mv |
n |
| isOA_txt |
false |
| hochschulschrift_bool |
false |
| author2_role |
oth oth oth |
| doi_str |
10.3103/S1062873817060119 |
| up_date |
2024-07-03T22:48:18.273Z |
| _version_ |
1803599896464326659 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a2200265 4500</leader><controlfield tag="001">OLC199580097X</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230715063253.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">170901s2017 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.3103/S1062873817060119</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">PQ20171125</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC199580097X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)GBVOLC199580097X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(PRQ)p663-eff5696cfbd1f7f702e8f09a91e5f5c5584e68c7f9c74fc04e6508f79454cd470</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(KEY)0018054820170000081000600768limitsofthestabilityofhexagonalphasesuponuniaxiall</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="q">DNB</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Gufan, M A</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Limits of the stability of hexagonal phases upon uniaxial loading</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2017</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">In modern studies, experimental methods for estimating nonlinear elastic moduli are often replaced with calculations of these quantities in mathematical simulation. However, different reliable models and experiments give different values of nonlinear elastic moduli. This work proposes a poßsible solution to the problem of which sets of elastic moduli should be used to predict the properties of substances. Two sets of the second-({cαβ,γδ}), third-({cαβ,γδ}), and fourth-order elastic moduli ({cαβ,γδ,μη,τρ}) of hexagonal Gd crystal proposed in the literature are considered as examples. The elastic moduli are defined as partial derivatives of the nonequilibrium Landau potential ΦL {uαβ{ with respect to components of the tensor of homogeneous deformation of the crystal (Ü). Necessary information about the nonequilibrium Landau potential as a function of {uαβ{ is given in the second section. An analytical way of deriving relationships between generally independent values of nonlinear elastic moduli caused by symmetry is proposed in Sections 3 and 4. The approach is based on using the integral rational basis of invariants (IRBI), which have the form of polynomials {uaß{. Aspects of the theory of phase transitions based on IRBI are discussed in Section 3. The set of polynomials of the second, third, and fourth order included in the list of basic invariants {J i (P)}, and the form of Landau potential Φ({J i (P)}, are clearly defined. The forms of the chosen dependences {J i (P)} and (ΦL{J i (P)}) are defined in Section 4 to compare the results from different works. Once the forms of Landau potential ΦL{J i (P)} and ΦL{uαβ} are defined, they are compared. The comparison results allow derivation of the nontrivial relationships between the components of the third-C III and fourth-rank elastic moduli tensors C IV due Gd hexagonal symmetry. Two different sets of calculated elastic moduli of Gd crystals, found in two different works, are given in Section 5. The criteria for selecting the most suitable set of numerical values of elastic moduli are described in Sections 6 and 7. One criterion is a comparison of load limits calculated from isothermal Gd elastic moduli and experimentally determined numerical values of the limits of stability of a certain Gd phase. In the last section, we show how the criterion based on comparing the phase stability limits allows us to dertermine which sets of third-rank elastic moduli should be used in, e.g., predicting Raman spectra.</subfield></datafield><datafield tag="540" ind1=" " ind2=" "><subfield code="a">Nutzungsrecht: © Allerton Press, Inc. 2017</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Physics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nuclear Physics, Heavy Ions, Hadrons</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Modulus of elasticity</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Phase stability</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Invariants</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical models</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stability criteria</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Polynomials</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Phase transformations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Tensors</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Load limits</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Phase transitions</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Elastic limit</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Deformation mechanisms</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Materials elasticity</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Raman spectra</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computer simulation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Elastic properties</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Symmetry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Deformation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Derivation</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Gufan, Yu M</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Karamurzov, B S</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Novakovich, A A</subfield><subfield code="4">oth</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Bulletin of the Russian Academy of Sciences. Physics</subfield><subfield code="d">New York, NY : Allerton Press, 1992</subfield><subfield code="g">81(2017), 6, Seite 768-778</subfield><subfield code="w">(DE-627)131135384</subfield><subfield code="w">(DE-600)1124898-1</subfield><subfield code="w">(DE-576)032854463</subfield><subfield code="x">1062-8738</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:81</subfield><subfield code="g">year:2017</subfield><subfield code="g">number:6</subfield><subfield code="g">pages:768-778</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">http://dx.doi.org/10.3103/S1062873817060119</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-OEU</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-HIS</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">81</subfield><subfield code="j">2017</subfield><subfield code="e">6</subfield><subfield code="h">768-778</subfield></datafield></record></collection>
|
| score |
7.3985224 |