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Research Papers: Radiative Heat Transfer

Absorption Spectra and Electron-Vibration Coupling of Ti:Sapphire From First Principles

[+] Author and Article Information
Hua Bao

Assistant Professor
University of Michigan-Shanghai Jiao Tong
University Joint Institute,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: hua.bao@sjtu.edu.cn

Xiulin Ruan

Associate Professor
School of Mechanical Engineering and
Birck Nanotechnology Center,
Purdue University,
West Lafayette, IN 47907
e-mail: ruan@purdue.edu

1Corresponding authors.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 25, 2015; final manuscript received November 30, 2015; published online January 12, 2016. Assoc. Editor: Zhuomin Zhang.

J. Heat Transfer 138(4), 042702 (Jan 12, 2016) (5 pages) Paper No: HT-15-1562; doi: 10.1115/1.4032177 History: Received August 25, 2015; Revised November 30, 2015

First-principles calculations are performed to study the absorption spectra and electron-vibration coupling of titanium-doped sapphire (Ti:Al2O3). Geometry optimization shows a local structure relaxation after the doping of Ti. Electronic band structure calculation shows that five additional dopant energy bands are observed around the band gap of Al2O3, and are attributed to the five localized d orbitals of the Ti dopant. The optical absorption spectra are then predicted by averaging the oscillator strength during a 4 ps first-principles molecular dynamics (MD) trajectory, and the spectra agree well with the experimental results. Electron-vibration coupling is further investigated by studying the response of the ground and excited states to the Eg vibrational mode, for which a configuration coordinate diagram is obtained. Stokes shift effect is observed, which confirms the red shift of emission spectra of Ti:sapphire. This work offers a quantitative understanding of the optical properties and crystal-field theory of Ti-doped sapphire. The first-principles calculation framework developed here can also be followed to predict the optical properties and study the electron-vibration coupling in other doped materials.

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Figures

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Fig. 1

The optimized structure for a doped 120 ion Ti:Al2O3 supercell

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Fig. 2

Electronic energy levels for the Ti-doped alumina supercell. The lower Ti 3d level is three-fold degenerate (D1, D2, and D3 denoted by the three circles) and the upper Ti 3d level is two-fold degenerate (D4 and D5 denoted by the two circles).

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Fig. 3

Charge density isosurfaces where the magnitude of the charge density is 3.4×10−10 e per unit cell. (a) The charge distribution of the D1 orbital. (b) The charge distribution of D4 orbital. It can be seen that these states are highly localized around the Ti dopant. The shape of the lobes around the Ti dopant resembles the typical d orbital.

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Fig. 4

Calculated absorption spectra at 300 K in this work (black solid line) and the experimental absorption spectra at room temperature [29] (dotted line) and emission spectra from Ref. [30] (dashed line)

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Fig. 5

The five different local vibrational modes of Ti octahedra

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Fig. 6

Configuration coordinate diagram for Eg vibrational mode

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Fig. 7

Fourier transform of transition energy during a 4 ps trajectory

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