#
Small Polaron Hopping in Fe:LiNbO_{3} as a Function of Temperature and Composition

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## Abstract

**:**

## 1. Introduction

## 2. Experiment

#### 2.1. Samples

#### 2.2. Transient Absorption

## 3. Monte Carlo Simulations

#### 3.1. Decay Model

#### 3.2. Simulation Code

## 4. Results and Discussion

#### 4.1. Activation Energies Deduced via TAS

#### 4.2. Hopping Regimes’ Landscapes Inspected by Monte Carlo Simulations

#### 4.2.1. Free Polaron Transport

#### 4.2.2. Bound Polaron Transport

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Typical experimental results of TA spectroscopy on the sample Fe:LN 0.1 mol %. (

**a**) Room temperature; (

**b**) Low temperature.

**Figure 2.**Arrhenius plot of the mean decay time of the signal at 785 nm, calculated using the parameters of the Kohlrausch, Williams and Watts (KWW) fit of the Transient Absorption Spectroscopy (TAS) data. The plots evidence a change in the transport mechanism around $200\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$. The high temperature regime is described by an activation energy of [U ∼ 0.42] eV and is well matched by numerical simulations in sample Fe:LN 0.02 mol %.

Final site | ||||

Energy in eV | Free (FP) | Antisite (GP) | Fe | |

Free (FP) | 0.273 | 0.156 | 0.003 | |

Initial site | Antisite (GP) | 0.551 | 0.375 | 0.038 |

Fe | 1.378 | 1.018 | 0.350 |

**Figure 4.**(

**Left**) Fraction of hops as a free polaron ${N}_{FP-FP}/{N}_{tot}$ as a function of temperature and $\left[{\mathrm{Nb}}_{\mathrm{Li}}\right]$ concentration for an undoped sample $\left(\left[\mathrm{Fe}\right]=0\right)$. (

**Right**) Total number of hops ${N}_{FP-FP}$ as a function of the temperature and $\left[\mathrm{Fe}\right]$ concentration for a stoichiometric sample ($\left[{\mathrm{Nb}}_{\mathrm{Li}}\right]=0$).

**Figure 5.**(

**Left**) ${N}_{GP-GP}/{N}_{tot}$ as a function of temperature and antisite concentration for an undoped sample ($\left[\mathrm{Fe}\right]=0$). (

**Right**) ${N}_{GP-GP}$ as a function of the temperature and $\left[\mathrm{Fe}\right]$ concentration for a congruent sample ($\left[{\mathrm{Nb}}_{\mathrm{Li}}\right]=19\times {10}^{25}\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-3}$). Free polaron contribution has been disregarded for simplicity. Note the different temperature range in the two plots.

**Table 1.**Defect concentrations for the samples under study determined by optical absorption (see the text).

$(\times {10}^{24}\phantom{\rule{0.222222em}{0ex}}{\mathbf{m}}^{-3})$ | [Fe] | [$\mathbf{Fe}{}^{2+}$] | [$\mathbf{Fe}{}^{3+}$] | [$\mathbf{Fe}{}^{2+}$]/[$\mathbf{Fe}{}^{3+}$] | [$\mathbf{Nb}{}_{\mathbf{Li}}$] |
---|---|---|---|---|---|

Fe:LN 0.02 mol % | 3.8 | 0.1 | 3.7 | 0.04 | 190.9 |

Fe:LN 0.05 mol % | 9.5 | 0.8 | 7.9 | 0.1 | 190.9 |

Fe:LN 0.1 mol % | 18.90 | 13.7 | 5.2 | 2.62 | 190.9 |

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**MDPI and ACS Style**

Vittadello, L.; Bazzan, M.; Messerschmidt, S.; Imlau, M.
Small Polaron Hopping in Fe:LiNbO_{3} as a Function of Temperature and Composition. *Crystals* **2018**, *8*, 294.
https://doi.org/10.3390/cryst8070294

**AMA Style**

Vittadello L, Bazzan M, Messerschmidt S, Imlau M.
Small Polaron Hopping in Fe:LiNbO_{3} as a Function of Temperature and Composition. *Crystals*. 2018; 8(7):294.
https://doi.org/10.3390/cryst8070294

**Chicago/Turabian Style**

Vittadello, Laura, Marco Bazzan, Simon Messerschmidt, and Mirco Imlau.
2018. "Small Polaron Hopping in Fe:LiNbO_{3} as a Function of Temperature and Composition" *Crystals* 8, no. 7: 294.
https://doi.org/10.3390/cryst8070294