Potential-induced breathing model for the elastic moduli and high-pressure behavior of the cubic alkaline-earth oxides

Mehl, Michael J.; Hemley, Russell J.; Boyer, L. L.

doi:10.1103/physrevb.33.8685

Cited by 193 publications

(75 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The purpose of the point charges is to better simulate the crystal environment by generating the correct crystalline electrostatic Madelung potential in the QM region. The correct Madelung potential also plays a key role in stabilizing the O 2− ion, as has been shown in Gordon-Kim 37 type models, 38,39 where the internal energy of ionic systems is determined from the energy of overlapping ionic charge densities. The finite point charge distribution is determined using the EWALD program, 30 as follows.…”

Section: Madelung Potential: Point Chargesmentioning

confidence: 91%

High sensitivity of O17 NMR to p-d hybridization in transition metal perovskites: First principles calculations of large anisotropic chemical shielding

Pechkis

Krakauer

2009

The Journal of Chemical Physics

View full text Add to dashboard Cite

A first principles embedded cluster approach is used to calculate O chemical shielding tensors, σ, in prototypical transition metal oxide ABO3 perovskite crystals. Our principal findings are 1) a large anisotropy ofσ between deshielded σx ≃ σy and shielded σz components (z along the Ti-O bond); 2) a nearly linear variation, across all the systems studied, of the isotropic σiso and uniaxial σax components, as a function of the B-O-B bond asymmetry. We show that the anisotropy and linear variation arise from large paramagnetic contributions to σx and σy due to virtual transitions between O(2p) and unoccupied B(nd) states. The calculated isotropic δiso and uniaxial δax chemical shifts are in good agreement with recent BaTiO3 and SrTiO3 single crystal 17 O NMR measurements. In PbTiO3 and PbZrO3, calculated δiso are also in good agreement with NMR powder spectrum measurements. In PbZrO3, δiso calculations of the five chemically distinct sites indicate a correction of the experimental assignments. The strong dependence ofσ on covalent O(2p)-B(nd) interactions seen in our calculations indicates that 17 O NMR spectroscopy, coupled with first principles calculations, can be an especially useful tool to study the local structure in complex perovskite alloys.

show abstract

Section: Madelung Potential: Point Chargesmentioning

confidence: 91%

High sensitivity of O17 NMR to p-d hybridization in transition metal perovskites: First principles calculations of large anisotropic chemical shielding

Pechkis

Krakauer

2009

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…±ÂÓÐÑÇ ÍÑÓÑÕÍÑAEÇÌ-ÔÕÄÖáÜÇÇ ÄÊÂËÏÑAEÇÌÔÕÄËÇ ËÑÐÑÄ ÑÒÓÇAEÇÎâÇÕÔâ ÓÂÊÐÑ-ÔÕßá ÄÞÓÂÉÇÐËâ (3.11) Ë ÄÊÂËÏÑAEÇÌÔÕÄËâ ÕÑÚÇÚÐÞx ËÑÐÑÄ Ë ÏÑÉÇÕ ÃÞÕß ÒÑÎÖÚÇÐÑ ÚËÔÎÇÐÐÞÏË ÏÇÕÑAEÂÏË. £ ÓÇÊÖÎßÕÂÕÇ ÒÑÎÐÖá àÐÇÓÅËá ÍÓËÔÕÂÎÎÂ ÏÑÉÐÑ ÊÂÒËÔÂÕß Ä ÔÎÇAEÖáÜÇÏ ÄËAEÇ: [18]. ±ÑÎÐÂâ àÐÇÓÅËâ ÍÓËÔÕÂÎÎÂ Ä àÕÑÏ ÒÓËÃÎËÉÇÐËË ËÏÇÇÕ ÄËAE …”

Section: ®çõñAe ×öðíùëñðâîâ òîñõðñôõë ë Aeëðâïëíâ óçûçõíëunclassified

Ab initio calculations of lattice dynamics of crystals

Savrasov¹,

Maksimov²

1995

Usp. Fiz. Nauk

View full text Add to dashboard Cite

£ ÔËÎÖ ÖÔÎÑÄËâ àÍÔÕÓÇÏÂÎßÐÑÔÕË ×ÖÐÍÙËÑÐÂÎÂ ÒÑÎÐÑÌ àÐÇÓÅËË (3.1) ÄÕÑÓÑÇ ÔÎÂÅÂÇÏÑÇ Ä (3.5) ÑÃÓÂÜÂÇÕÔâ Ä ÐÖÎß. ±ÑÔÍÑÎßÍÖ Ä ÄÞÓÂÉÇÐËË AEÎâ ÒÑÎÐÑÌ àÐÇÓÅËË (3.1) âÄÐÞÏ ÑÃÓÂÊÑÏ ÑÕ R ÊÂÄËÔËÕ ÎËÛß ÄÕÑÓÑÇ ÔÎÂÅÂÇÏÑÇ, ÑÒËÔÞ-ÄÂáÜÇÇ ÄÊÂËÏÑAEÇÌÔÕÄËÇ Ô ÄÐÇÛÐËÏ ÒÑÎÇÏ, ÏÞ ËÏÇÇÏÂÍËÏ ÑÃÓÂÊÑÏ, ×ÑÓÏÂÎßÐÞÇ ÄÞÓÂÉÇÐËâ AEÎâ àÎÇÍÕÓÑÐ-ÐÑÅÑ ÄÍÎÂAEÂ Ä ÔËÎÖ Ë AEËÐÂÏËÚÇÔÍÖá ÏÂÕÓËÙÖ, ÒÑÎÖÚÇÐÐÞÇ Ä ÓÂÏÍÂx ÏÐÑÅÑÚÂÔÕËÚÐÑÅÑ ÒÑAExÑAEÂ (×ÑÓÏÖÎÞ (2.5) Ë (2.7)) Ë ÏÇÕÑAEÑÏ ×ÖÐÍÙËÑÐÂÎÂ ÒÎÑÕÐÑÔÕË (3.6) Ë (3.8), ÒÑÎÐÑÔÕßá ËAEÇÐÕËÚÐÞ. ¿ÕÑ Ë ÐÇÖAEËÄËÕÇÎßÐÑ, ÒÑÔÍÑÎßÍÖ Ä ÑÃÑËx ÏÇÕÑAEÂx ÏÞ ËÔxÑAEËÎË ËÊ ÓÂÔÔÏÑÕÓÇÐËâ àÐÇÓÅËË àÎÇÍÕÓÑÐÑÄ Ä ÊÂAEÂÐÐÑÏ ÒÑÎÇ âAEÇÓ Ë ÇÇ ËÊÏÇÐÇÐËâ ÒÑAE AEÇÌÔÕÄËÇÏ Ëx ÔÏÇÜÇÐËâ. ²ÂÊÎËÚËÇ àÕËx ÒÑAExÑAEÑÄ ÊÂÍÎá-ÚÂÇÕÔâ Ä ÏÇÕÑAEÂx ÓÂÔÚÇÕÂ àÐÇÓÅËË, ÓÂÔÒÓÇAEÇÎÇÐËâ ÒÎÑÕÐÑ-ÔÕË Ë ËÊÏÇÐÇÐËâ àÕËx ÄÇÎËÚËÐ.±ÓÇÉAEÇ ÚÇÏ ÒÇÓÇxÑAEËÕß Í ÑÃÔÖÉAEÇÐËá ÔÑÄÓÇÏÇÐÐÞx Ë ÐÂËÃÑÎÇÇ ÒÑÔÎÇAEÑÄÂÕÇÎßÐÞx ÏÇÕÑAEÑÄ ÓÂÔÚÇÕÂ Ä ÓÂÏÍÂx ÕÇÑÓËË ×ÖÐÍÙËÑÐÂÎÂ ÒÎÑÕÐÑÔÕË, ÏÞ ÍÓÂÕÍÑ ÓÂÔÔÏÑÕÓËÏ ÐÇÔÍÑÎßÍÑ ÒÓÑÔÕÇÌÛËx, ÐÑ ÄÇÔßÏÂ à××ÇÍÕËÄÐÞx ÒÑAE-xÑAEÑÄ Í ÕÇÑÓËË AEËÐÂÏËÍË ÓÇÛÇÕÍË, ÑÔÐÑÄÂÐÐÞx ÐÂ ÒÓÑÔÕÞx ÒÓËÃÎËÉÇÐËâx AEÎâ ×ÖÐÍÙËÑÐÂÎÂ (3.2). ²ÂÔÔÏÑÕ-ÓËÏ ÔÎÂÃÑÐÇÑAEÐÑÓÑAEÐÖá àÎÇÍÕÓÑÐÐÖá ÔËÔÕÇÏÖ. £ àÕÑÏ ÔÎÖÚÂÇ AEÎâ ×ÖÐÍÙËÑÐÂÎÂ ÒÎÑÕÐÑÔÕË (3.2) ÏÑÉÐÑ ËÔÒÑÎß-ÊÑÄÂÕß ÕÂÍ ÐÂÊÞÄÂÇÏÑÇ ÎÑÍÂÎßÐÑÇ ÒÓËÃÎËÉÇÐËÇ: ÅAEÇ Ä ÍÂÚÇÔÕÄÇ Efrrg ËÔÒÑÎßÊÖÇÕÔâ ÎÑÍÂÎßÐÑÇ ÒÓËÃÎË-ÉÇÐËÇ´ÑÏÂÔÂë ¶ÇÓÏËë¥ËÓÂÍÂ. ±ÂÓÐÑÇ ÍÑÓÑÕÍÑAEÇÌ-ÔÕÄÖáÜÇÇ ÄÊÂËÏÑAEÇÌÔÕÄËÇ ËÑÐÑÄ ÑÒÓÇAEÇÎâÇÕÔâ ÓÂÊÐÑ-ÔÕßá ÄÞÓÂÉÇÐËâ (3.11) Ë ÄÊÂËÏÑAEÇÌÔÕÄËâ ÕÑÚÇÚÐÞx ËÑÐÑÄ Ë ÏÑÉÇÕ ÃÞÕß ÒÑÎÖÚÇÐÑ ÚËÔÎÇÐÐÞÏË ÏÇÕÑAEÂÏË. £ ÓÇÊÖÎßÕÂÕÇ ÒÑÎÐÖá àÐÇÓÅËá ÍÓËÔÕÂÎÎÂ ÏÑÉÐÑ ÊÂÒËÔÂÕß Ä ÔÎÇAEÖáÜÇÏ ÄËAEÇ: ©AEÇÔß E xc frrg ì ÒÑÎÐÂâ ÑÃÏÇÐÐÑ-ÍÑÓÓÇÎâÙËÑÐÐÂâ àÐÇÓ-ÅËâ, ÄÍÎáÚÂáÜÂâ ÄÍÎÂAEÞ ÍÂÍ ÑÕ ÒÑÕÇÐÙËÂÎßÐÑÌ, ÕÂÍ Ë ÑÕ ÍËÐÇÕËÚÇÔÍÑÌ àÐÇÓÅËÌ: ±ÑÎÐÂâ àÐÇÓÅËâ ÔËÔÕÇÏÞ ÄÊÂËÏÑAEÇÌÔÕÄÖáÜËx àÎÇÍÕÓÑ-ÐÑÄ ÔÎÇAEÖáÜËÏ ÑÃÓÂÊÑÏ ÄÞÓÂÉÂÇÕÔâ ÚÇÓÇÊ ÓÇÛÇÐËâ ÖÓÂÄÐÇÐËâ (3.23): ËÏÇáÜËx ÄÑÎÐÑÄÞÇ ÄÇÍÕÑÓÞ q Ë Àq, Õ.Ç.³ÓÂÊÖ ÑÕÏÇÕËÏ ÄÇÔßÏÂ ÄÂÉÐÑÇ ÔÄÑÌÔÕÄÑ, ÍÑÕÑÓÑÏÖ ÖAEÑ-ÄÎÇÕÄÑÓâÇÕ ÄÐÇÛÐÇÇ ÄÑÊÏÖÜÇÐËÇ. ¦ÔÎË ÓÂAEËÖÔ-ÄÇÍÕÑÓ r ÒÑÎÖÚÂÇÕ ÒÓËÓÂÜÇÐËÇ, ÓÂÄÐÑÇ ÄÇÍÕÑÓÖ ÒÓËÏËÕËÄÐÑÌ ÕÓÂÐÔÎâÙËË, ÕÑ ÑÃÇ ÍÑÏÒÑÐÇÐÕÞ (3.27) ÒÓÇÑÃÓÂÊÖáÕÔâ ÍÂÍ ÄÑÎÐÞ ÃÎÑxÑÄÔÍÑÅÑ ÕËÒÂ:ÅAEÇ à××ÇÍÕÞ ÑÃÏÇÐÂ Ë ÍÑÓÓÇÎâÙËË ÓÂÔÔÏÂÕÓËÄÂáÕÔâ Ä ÒÓËÃÎËÉÇÐËË ÎÑÍÂÎßÐÑÌ ÒÎÑÕÐÑÔÕË. ±ÑAEÔÕÂÄËÏ ÔÇÌÚÂÔ ÄÞÓÂÉÇÐËÇ AEÎâ ÒÑÒÓÂÄÑÍ ÒÇÓÄÑÅÑ ÒÑÓâAEÍÂ (3.30) Ä ×ÑÓÏÖÎÖ (3.29).´ÑÅAEÂ ËÊÏÇÐÇÐËÇ ÒÎÑÕÐÑÔÕË ÄÞÓÂÉÂÇÕÔâ ÚÇÓÇÊ ÕÂÍ ÐÂÊÞÄÂÇÏÖá ×ÖÐÍÙËá ÔÕÂÕËÚÇÔÍÑÌ ÒÑÎâÓËÊÖÇ-ÏÑÔÕË ÐÇÊÂÄËÔËÏÞx àÎÇÍÕÓÑÐÑÄÍÂÍ ËÐÕÇÅÓÂÎ ÑÕ àÕÑÌ ×ÖÐÍÙËË Ë àÍÓÂÐËÓÑÄÂÐÐÑÅÑ ÄÑÊÏÖ-ÜÇÐËâ: ±ÑÔÎÇAEÐËÏ ÛÂÅÑÏ âÄÎâÇÕÔâ ÄÞÒÑÎÐÇÐËÇ ÔÖÏÏËÓÑÄÂ-ÐËâ ÒÑ ÓÇÛÇÕÍÇ ®´-ÑÓÃËÕÂÎÇÌ, ÙÇÐÕÓËÓÑÄÂÐÐÞx ÐÂ ÓÂÊÎËÚÐÞx yÊÎÂx, Ô ×ÂÊÑÄÞÏ ÔAEÄËÅÑÏ expikt AEÎâ ÕÑÅÑ, ÚÕÑÃÞ ÐÂÛË ÃÂÊËÔÐÞÇ ×ÖÐÍÙËË ÖAEÑÄÎÇÕÄÑÓâÎË ÕÇÑÓÇÏÇ ¢ÎÑxÂ. ¿ÕÑ ÏÑÉÐÑ ÔAEÇÎÂÕß AEÑÔÕÂÕÑÚÐÑ ÒÓÑÔÕÑ, ÒÓÑÄÑAEâ ÎËÛß ÔÖÏÏËÓÑÄÂÐËÇ AEÎâ ÔÕÓÖÍÕÖÓÐÞx ÍÑÐÔÕÂÐÕ (4.6), ÒÑÔÍÑÎßÍÖ ÔÍÑÐÔÕÓÖËÓÑÄÂÐÐÞÇ ÑÓÃËÕÂÎË ÖÉÇ ÄÇÊAEÇ ÒÓÇAE-ÔÕÂÄÎÇÐÞ ÍÂÍ ÑAEÐÑÙÇÐÕÓÑÄÞÇ ÓÂÊÎÑÉÇÐËâ. £ ËÕÑÅÇ ÃÂÊËÔ-ÐÞÇ ×ÖÐÍÙËË ÒÑÎÖÚÂáÕÔâ ÔÎÇAEÖáÜËÏË: ÐËÇ AEÎâ ÔÕÓÖÍÕÖÓÐÞx ÍÑÐÔÕÂÐÕ (4.6): ±ÇÓÄÑÇ Ë ÄÕÑÓÑÇ ÔÎÂÅÂÇÏÞÇ Ä (4.10), Â ÕÂÍÉÇ ÒÇÓÄÑÇ ÔÎÂÅÂÇÏÑÇ Ä (4.11) ÑÃÑÊÐÂÚÂáÕ ËÐÕÇÅÓÂÎÞ ÒÑ ®´-Ô×Ç-ÓÂÏ, Â AEÓÖÅËÇ ì ÒÑ ÏÇÉAEÑÖÊÇÎßÐÑÌ ÑÃÎÂÔÕË. ªÏÇÐÐÑ, ÂËÃÑÎÇÇ ...

show abstract

“…MgO has been the subject of extensive theoretical and experimental investigations (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17) that have revealed the fundamental bonding properties in this class of materials. With the wealth of available data, MgO is often used as a test ground for new theories, new experiments, and even as a pressure calibration standard for high-pressure, high-temperature experimentation (18,19).…”

mentioning

confidence: 99%

Elasticity of MgO and a primary pressure scale to 55 GPa

Zha

Mao

Hemley

2000

Proc. Natl. Acad. Sci. U.S.A.

422

286

View full text Add to dashboard Cite

We have studied the elasticity and pressure-density equation of state of MgO in diamond cells to 55 GPa and have doubled the previous pressure limit of accurate elasticity determinations for crystals. Integrating single-crystal velocity data from Brillouin scattering measurements and density data from polycrystalline x-ray diffraction, we obtained the three principal elastic tensor elements (C11, C12, and C44) and various secondary elasticity parameters, including single-crystal elastic anisotropy, Cauchy relation, aggregate sound velocities, and Poisson's ratio, as functions of pressure. The present study also provides a direct determination of pressure without recourse to any prior pressure standard, thus creating a primary pressure scale. The commonly used ruby fluorescence pressure scale has thus been improved to 1% accuracy by the new MgO scale. E lasticity, the fourth-rank tensor defining the strain of crystalline solids under stress (1), contains key parameters relating the microscopic bonding properties to the macroscopic mechanical behaviors of the solid under compression. The study of elasticity under high pressure has wide applications in fields ranging from crystal physics to seismology (2). Direct experimental measurements of the tensor elements, however, have previously been limited to 32 GPa (3)-above this pressure our knowledge has been derived from theoretical predictions, extrapolations of lower pressure data, or indirect measurements with assumed stress͞strain conditions (4). In the present study, we extend measurements of the elasticity of MgO, an archetypal oxide with the simple NaCl-type (B1) crystal structure, to 55 GPa at 300 K.MgO has been the subject of extensive theoretical and experimental investigations (5-17) that have revealed the fundamental bonding properties in this class of materials. With the wealth of available data, MgO is often used as a test ground for new theories, new experiments, and even as a pressure calibration standard for high-pressure, high-temperature experimentation (18,19). Moreover, MgO is a major component in the Earth's lower mantle (20,21), and knowledge of its high-pressure behavior is crucial for understanding deep Earth geophysics. The crystal structure and volume compression of polycrystalline MgO samples without pressure media have been studied with x-ray diffraction in diamond cells up to 227 GPa (7,22, 23). MgO in the B1 structure is stable over the entire pressure range. Nonhydrostatic conditions in these measurements, however, may introduce systematic deviations in pressure of up to 10% in the pressure-density equations of state (22-24). Ultrasonic and Brillouin scattering studies of single-crystal MgO (8,16,25) have yielded detailed information on its elastic tensor, anisotropy, and aggregate shear and bulk moduli, but have been limited to a maximum pressure of 18.6 GPa. Evidence for nonhydrostaticity has also been found in previous Brillouin scattering experiments at pressures exceeding the hydrostatic limits of the pressure media used in these s...

show abstract

Potential-induced breathing model for the elastic moduli and high-pressure behavior of the cubic alkaline-earth oxides

Cited by 193 publications

References 42 publications

High sensitivity of O17 NMR to p-d hybridization in transition metal perovskites: First principles calculations of large anisotropic chemical shielding

High sensitivity of O17 NMR to p-d hybridization in transition metal perovskites: First principles calculations of large anisotropic chemical shielding

Ab initio calculations of lattice dynamics of crystals

Elasticity of MgO and a primary pressure scale to 55 GPa

Contact Info

Product

Resources

About