Tellurite And Fluorotellurite Glasses For Active And Passive
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Tellurite And Fluorotellurite Glasses For Active And Passive

Tellurite And Fluorotellurite Glasses For Active And Passive Tellurite And Fluorotellurite Glasses For Active And Passive

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10.06.2013 Views

6. Optical properties; MDO 175 Potential energy h ω h ω h ω h ω h ω h ω h ω h ω h ω 1/2 h ω re Distance υ = 1 υ = 0 υ = 3 υ = 2 υ = 5 υ = 4 υ = 7 υ = 6 Fig. (6.3): Variation in potential energy with distance between two nuclei, using the harmonic oscillator model [2]. Quantum mechanical theory states that the molecule can only occupy discrete energy levels, given by the quantum number, υ (an integer). The energy of a particular level is given by equation (6.14) [2]. υ = 9 υ = 8 1 h k 1 E υ = ( υ + ) ≡ ( υ + ) hω (6.14) 2 2π µ 2 where µ = reduced mass = m1m2 m + m 1 2 1 k , mi = mass of atom i, and ω = . At the lowest 2π µ 1 vibrational energy (υ = 0), the molecule still has energy, E0 = hω . Higher energy 2 levels (1, 2, 3…), are separated by energy hω [2]. For diatomic molecules, the force constant of the bond can be calculated relatively easily from vibrational spectra.

6. Optical properties; MDO 176 Absorption results from the excitation of the molecule from υ = 0 to υ = 1, and so on, by the incident radiation. This gives ∆E = hω, and k can be obtained by rearranging equation (6.14) [2]. The anharmonic oscillator The parabolic potential well shown by equation (6.13) and fig. (6.3) is not an accurate model of the variation in force experienced by a diatomic molecule. Equation (6.13) represents a symmetric potential well, whereas in reality it would be asymmetric [2]. As the nuclei come together, they repel each other and the potential energy will rise exponentially, similar to the harmonic oscillator. However, as the nuclei are pulled apart, the potential energy will level off as dissociation occurs, resulting in an asymmetric potential well. An empirical equation known as the Morse potential, can be used to model this behaviour. This is shown by equation (6.15) [2]. E −κq 2 p = Ed ( 1− e ) (6.15) where Ed = depth of the potential well, and κ = curvature of bottom of the potential well. This is graphically illustrated in fig. (6.4).

6. Optical properties; MDO 175<br />

Potential energy<br />

h ω<br />

h ω<br />

h ω<br />

h ω<br />

h ω<br />

h ω<br />

h ω<br />

h ω<br />

h ω<br />

1/2 h ω<br />

re<br />

Distance<br />

υ = 1<br />

υ = 0<br />

υ = 3<br />

υ = 2<br />

υ = 5<br />

υ = 4<br />

υ = 7<br />

υ = 6<br />

Fig. (6.3): Variation in potential energy with distance between two nuclei, using the<br />

harmonic oscillator model [2].<br />

Quantum mechanical theory states that the molecule can only occupy discrete energy<br />

levels, given by the quantum number, υ (an integer). The energy of a particular level is<br />

given by equation (6.14) [2].<br />

υ = 9<br />

υ = 8<br />

1 h k 1<br />

E υ = ( υ + ) ≡ ( υ + ) hω<br />

(6.14)<br />

2 2π<br />

µ 2<br />

where µ = reduced mass =<br />

m1m2<br />

m + m<br />

1<br />

2<br />

1 k<br />

, mi = mass of atom i, and ω = . At the lowest<br />

2π<br />

µ<br />

1<br />

vibrational energy (υ = 0), the molecule still has energy, E0<br />

= hω<br />

. Higher energy<br />

2<br />

levels (1, 2, 3…), are separated by energy hω [2]. <strong>For</strong> diatomic molecules, the force<br />

constant of the bond can be calculated relatively easily from vibrational spectra.

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