Lattice dynamics of sapphire (corundum)

Bialas, H.; Stolz, H.

doi:10.1007/bf01325390

Cited by 49 publications

(13 citation statements)

References 12 publications

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“…In Al 2 O 3 , the value of ប eff at the creation of excitons and at their radiative decay corresponds to the acoustic branch of vibrations. The vibration spectrum of Al 2 O 3 was investigated by means of neutron scattering at 20 K. 38 Our experimental data testify to the excitation of the A emission not only at the direct formation of p 5 s excitons by 8.9-9.3-eV photons but also at the recombination of free electrons and free ͑mobile͒ holes. However, the effective cross section for the recombination of free electrons and holes in a regular lattice of Al 2 O 3 is significantly lower than that value for the e-h recombination near neutral Sc 3ϩ centers (Ϸ10 Ϫ15 cm Ϫ2 ).…”

Section: About Mechanisms Of Exciton Self-trapping In Al 2 Omentioning

confidence: 66%

Self-trapping and multiplication of electronic excitations inAl2O3and
Kirm
¹
,
Zimmerer
²
,
Feldbach
³

et al. 1999
Phys. Rev. B
114
2
65
1
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The processes of intrinsic and extrinsic luminescence excitation by synchrotron radiation of 4-40 eV or electron pulses have been studied in ␣-Al 2 O 3 single crystals at 8 K. The intrinsic A ͑7.6 eV͒ and E emissions ͑3.77 eV͒ can be effectively excited in the region of long-wavelength ͑8.85-9.1 eV͒ and short-wavelength ͑9.1-9.3 eV͒ components of exciton absorption doublet, respectively. Fast ͑ϳ6 and ϳ20 ns͒ and slow ͑ϳ150 ns͒ components of the A emission correspond to the creation of singlet and triplet p 5 s excitons. The efficiency of the A emission in the region of band-to-band transitions is low. The intensity of A emission sharply increases ͑approximately quadratically͒ with a rise of the excitation density by nanosecond electron pulses. In Al 2 O 3 :Sc, the 5.6-eV luminescence is caused by the decay of near-impurity electronic excitations ͑ϳ8.5 eV͒ as well as by the electron recombination with holes localized near Sc 3ϩ centers. The efficiency of 7.6-, 5.6-, and 3.8-eV emission sharply increases at the energy of exciting photons of hϾ25 eV. One photon of 26-29 and 30-37 eV causes the ionization of the 2p 6 or 2s 2 shell of the oxygen ion and provides the creation of two or three electron-hole pairs, respectively. Long-term investigations of ␣-Al 2 O 3 crystals did not lead to the detection of immobile self-trapped holes or electrons. The A emission excited at the direct photocreation of excitons or at the recombination of free electrons and free holes is interpreted by us as the radiative decay of self-shrunk excitons. The theoretical model of Sumi allows the existence of such immobile self-shrunk excitons even if an electron and a hole do not separately undergo the self-trapping. ͓S0163-1829͑99͒01825-1͔

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Section: About Mechanisms Of Exciton Self-trapping In Al 2 Omentioning

confidence: 66%

Self-trapping and multiplication of electronic excitations inAl2O3and
Kirm
¹
,
Zimmerer
²
,
Feldbach
³

et al. 1999
Phys. Rev. B
114
2
65
1
View full text Add to dashboard Cite

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“…The best agreement (1%) occurs for A120 3, for which vibrational data are completely determined [Barker, 1963;Porto and Krishnan, 1967;Bialas and Stolz, 1975;Kappus, 1975].…”

Section: Peaks Whereas the Brout Sum For Perovskite Involves 12 Modementioning

confidence: 99%

“…where C v is the heat capacity, and V in this case is per mole For solids with a large number of modes, dispersion is low rather than per unit cell. For silicates and most other (e.g., A120 3 data by Bialas and Stolz [1975]). The amount of compounds, Ks-KT is also about -2%.…”

Section: Introductionmentioning

confidence: 99%

Calculation of bulk modulus and its pressure derivatives from vibrational frequencies and mode Grüneisen Parameters: Solids with cubic symmetry or one nearest‐neighbor distance

Hofmeister¹

1991

J. Geophys. Res.

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The bulk modulus KT can be related to structural parameters and to the sum of the squares of the vibrational frequencies. ∑vi2, for N‐atom crystals of cubic symmetry or for any symmetry that contains only one nearest‐neighbor distance. Required assumptions are the existence of (1) electrostatic forces exclusively between atoms at equivalent positions in the primitive unit cell, (2) pair‐wise central repulsive potentials between all other atoms, and (3) rigid ions. Including pressure in the derivation requires a more stringent version of point 2, namely, (4) that the structure scales isotropically upon compression. This leads to structurally independent formulas for the pressure derivatives of bulk modulus at 1 atm: the only variables are KT and sums involving vi2 and the first or second pressurderivative of vi, i.e., the mode Grüneisen parameters. Implicit in all equations is the independence of the sums on wave vector. Thus, knowledge of zone center phonons (mostly infrared and Raman bands) is sufficient to calculate elastic properties. Investigating these relationships for 45 minerals with 10 different structures shows that KT(0) is predicted within 7% of experiment for 21 solids, all of which should lack strong interactions between atoms at equivalent sites in the Bravais unit cell (i.e., rutile, corundum, ilmenite, and spinel structures). The accuracy of the model strongly depends on the accuracy of the sum ∑vi2. Agreement for B1, B2, fluorite, and wurtzite structures is moderate to poor, as expected, because these structures place like atoms as second nearest neighbors and can thus violate assumption 1. For rocksalt, agreement varies, depends on the size of the cation, not on the polarizability (i.e. the ionic rigidity) as inferred earlier. Calculated KT for the garnets is 1.367 time experimental KT, instead of unity, which is related to the structure not scaling perfectly with pressure. Agreement is variable (3–20%) for the perovskite structure with large discrepancies associated with ill‐constrained sums. However, for all structures, the relative size of KT is predicted, so that the theory can be used for systematics for all minerals with the proper symmetry, reguardless of whether the assumptions are satisified. For all of the above mentioned structures, K′o and K″o are predicted within the experimental uncertainties from the available spectroscopic measurements of 13 solids for K′o and 6 solids for K″o at pressure. Based on this, the good agreement for ilmenite, which does not meet the symmetry requirements, and the structural independence of the formulas, the relations involving K′o and K″o are inferred to hold for structures more complex than cubic or AXBY.

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“…Second, the estimate for the energy of the local E g ͑O h ͒ phonon in the excited 2 E͑C 3v ͒ state of 200 cm −1 is quite small. Values around 400 cm −1 , where the peaks in the density of states of the E-mode phonons in corundum crystal occur, 28,29 may be more appropriate. For these higher values of the phonon energy, the displacement of the potential minimum in the E space will be approximately 30% smaller.…”

Section: Fit To the Transient Xanes Spectrummentioning

confidence: 99%

Local structural changes in excitedTi3+:Al2O3studied by time-resolved XANES

et al. 2009

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Transient changes in the local structure of optically excited Ti 3+ ions in a Al 2 O 3 single crystal are studied by time-resolved x-ray absorption spectroscopy. A model considering coupling of the excited 2 E͑C 3v ͒ electronic state of the Ti 3+ ion to the approximate A 1g ͑O h ͒ and E g ͑O h ͒ local vibrational modes of the TiO 6 octahedron is constructed to fit the experimental data. We determine the magnitude of the A 1g ͑O h ͒ mode and give an estimate of the E g ͑O h ͒ Jahn-Teller distortion although this analysis does not distinguish between compression and elongation of the oxygen octahedron. Assuming a compressed octahedron, the E g ͑O h ͒ distortion is found to be 0.14Ϯ 0.02 Å with an A 1g ͑O h ͒ mode of 0.066Ϯ 0.006 Å. In the case of an elongated octahedron the E g ͑O h ͒ distortion is −0.195Ϯ 0.017 Å with an A 1g ͑O h ͒ mode of 0.052Ϯ 0.002 Å. DOI: 10.1103/PhysRevB.80.134301 PACS number͑s͒: 61.05.cj, 78.47.Ϫp, 63.20.kd, 71.70.Ej Electronic excitation of impurity ions in crystals is often accompanied by transient changes in the local structure of the host. These changes are most commonly studied by optical spectroscopy, yielding indirect and sometimes incomplete information. Quantitative information about the shortand medium-range organization of atoms can be provided by x-ray absorption spectroscopy ͑XAS͒. The element specificity of this method is ideal for the study of substitutional impurity centers in solids. In the case of very dilute impurities, collecting extended x-ray absorption fine-structure ͑EX-AFS͒ spectra with a good signal-to-noise ratio can be a challenging task. In such cases, the larger features of x-ray absorption near-edge structure ͑XANES͒ are often exploited to yield information about the local structure. Analysis of XANES spectra is, however, not straightforward because of the photoelectron multiple-scattering processes that contribute significantly to the near-edge region. Pump-probe methods can be used to study the transient XAS created in the course of chemical reactions or due to electronic excitation of solids.1 This technique has been successfully applied to investigate the electronic and geometric modifications of photoexcited chemicals in solution although progress in this field is limited due to the limited short x-ray pulse flux available at current sources. [2][3][4][5][6] To evaluate the quality of information that we obtain from the analysis of transient XAS data of dilute laser-excited impurities in crystalline solids, we have chosen Ti 3+ :Al 2 O 3 as a model system. Ti 3+ :Al 2 O 3 has been studied extensively from analysis of optical, magnetic, Raman, and neutron data as an example of a crystal with a strong Jahn-Teller ͑JT͒ electronlattice coupling in the excited 2 E͑C 3v ͒ state. The electronic level structure of the Ti 3+ ion in Al 2 O 3 is sketched in Fig. 1 To quantify the distortion of the local structure when the Ti 3+ ion is in the excited 2 E 3/2 ͑C 3v ‫ء‬ ͒ state, we performed timeresolved laser pump/x-ray probe measurements. The setup and the expe...

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Lattice dynamics of sapphire (corundum)

Cited by 49 publications

References 12 publications

Self-trapping and multiplication of electronic excitations inAl2O3and
Kirm
¹
,
Zimmerer
²
,
Feldbach
³

et al. 1999
Phys. Rev. B
114
2
65
1
View full text Add to dashboard Cite

Self-trapping and multiplication of electronic excitations inAl2O3and
Kirm
¹
,
Zimmerer
²
,
Feldbach
³

et al. 1999
Phys. Rev. B
114
2
65
1
View full text Add to dashboard Cite

Calculation of bulk modulus and its pressure derivatives from vibrational frequencies and mode Grüneisen Parameters: Solids with cubic symmetry or one nearest‐neighbor distance

Local structural changes in excitedTi3+:Al2O3studied by time-resolved XANES

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Lattice dynamics of sapphire (corundum)

Cited by 49 publications

References 12 publications

Self-trapping and multiplication of electronic excitations inAl2O3andKirm1, Zimmerer2, Feldbach3 et al. 1999Phys. Rev. B1142651View full textAdd to dashboardCite

Self-trapping and multiplication of electronic excitations inAl2O3andKirm1, Zimmerer2, Feldbach3 et al. 1999Phys. Rev. B1142651View full textAdd to dashboardCite

Calculation of bulk modulus and its pressure derivatives from vibrational frequencies and mode Grüneisen Parameters: Solids with cubic symmetry or one nearest‐neighbor distance

Local structural changes in excitedTi3+:Al2O3studied by time-resolved XANES

Contact Info

Product

Resources

About

Self-trapping and multiplication of electronic excitations inAl2O3and
Kirm
¹
,
Zimmerer
²
,
Feldbach
³

et al. 1999
Phys. Rev. B
114
2
65
1
View full text Add to dashboard Cite

Self-trapping and multiplication of electronic excitations inAl2O3and
Kirm
¹
,
Zimmerer
²
,
Feldbach
³

et al. 1999
Phys. Rev. B
114
2
65
1
View full text Add to dashboard Cite