#
Structural and Electrochemical Properties of F-Doped RbTiOPO_{4} (RTP:F) Predicted from First Principles

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results and Discussion

#### 3.1. Crystallographic and Electric Properties of Stoichiometric RTP:F

#### 3.2. Electrochemical Performance of RTP:F

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) The crystal structure of F-doped RbTiOPO${}_{4}$ (RTP:F) is shown to illustrate the KTP-type crystal structure. The green atoms correspond to the fluorine (F) atoms located at the lattice sites O(9) and O(10). Chains of TiO${}_{4}$F${}_{2}$ octahedra and PO${}_{4}$ tetrahedra cross the crystal along the $\left[100\right]$ and $\left[010\right]$ crystal directions. The Rb ions, on the other hand, form a positively charged sublattice. (

**b**) Visualization of the difference between F $\widehat{\mathrm{T}\mathrm{i}\left(1\right)}$ F and F $\widehat{\mathrm{T}\mathrm{i}\left(2\right)}$ F bond angles.

**Figure 2.**(

**a**) Geometry (l.h.s.) and pDOS (r.h.s.) of the stoichiometric RTP:F unit cell after geometry relaxation. The Ti(1) and T(2) states are depicted in red and blue, respectively. Notably, they are clearly separated from each other. (

**b**–

**i**) Geometries and pDOS of Rb${}_{1-x}$TiPO${}_{4}$F after the deintercalation of different concentrations $x=0.125$–$1.000$ of Rb. The yellow isosurfaces represent the spin-density difference of the spin-up and the spin-down channel, clearly showing the localization of the occupied defect states at the Ti sites and their consequent oxidation from Ti${}^{+3}$ to Ti${}^{+4}$ upon the deintercalation of Rb. Note that for $x\le 0.5$ (i.e., structures (

**b**–

**e**)) only Ti(1) have been oxidized. ${E}_{F}$ indicates the Fermi level position.

**Figure 3.**(

**a**) Average voltage $\overline{V}$ of the RTP:F cathode as predicted under the application of different levels of theory: The red solid and the grey dashed curve are obtained using the PBEsol$+U$ formalism, whereby the latter implies the DFT ground-state energy of a local minimum of the stoichiometric unit cell. The remaining orange, blue, and green voltage curves are obtained under the application of hybrid functionals, i.e., PBE0, HSE, and B3LYP, respectively. (

**b**) Volume shrinkage of the cathode upon the deintercalation of Rb (calculated using the PBEsol$+U$ formalism).

**Table 1.**Lattice constants ($a,\phantom{\rule{4pt}{0ex}}b$, and c) and unit-cell volumes (V) of different KTP-type compounds.

Compound | a [Å] | b [Å] | c [Å] | V [Å${}^{3}$] | |
---|---|---|---|---|---|

KTiOPO${}_{4}$ | 12.819 | 6.399 | 10.584 | 868.2 | Exp. [45] |

12.860 | 6.432 | 10.616 | 876.7 | PBEsol [67] | |

KTiPO${}_{4}$F | 13.002 | 6.434 | 10.764 | 900.5 | Exp. [17] |

13.30 | 6.56 | 11.04 | 894.9 | PBE$+U$ [17] | |

RbTiOPO${}_{4}$ | 12.952 | 6.500 | 10.558 | 888.9 | Exp. [66] |

12.986 | 6.521 | 10.568 | 894.9 | PBEsol [65] | |

RbTiPO${}_{4}$F | 13.236 | 6.616 | 10.945 | 958.5 | PBEsol$+U$, This work |

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Bocchini, A.; Xie, Y.; Schmidt, W.G.; Gerstmann, U.
Structural and Electrochemical Properties of F-Doped RbTiOPO_{4} (RTP:F) Predicted from First Principles. *Crystals* **2024**, *14*, 5.
https://doi.org/10.3390/cryst14010005

**AMA Style**

Bocchini A, Xie Y, Schmidt WG, Gerstmann U.
Structural and Electrochemical Properties of F-Doped RbTiOPO_{4} (RTP:F) Predicted from First Principles. *Crystals*. 2024; 14(1):5.
https://doi.org/10.3390/cryst14010005

**Chicago/Turabian Style**

Bocchini, Adriana, Yingjie Xie, Wolf Gero Schmidt, and Uwe Gerstmann.
2024. "Structural and Electrochemical Properties of F-Doped RbTiOPO_{4} (RTP:F) Predicted from First Principles" *Crystals* 14, no. 1: 5.
https://doi.org/10.3390/cryst14010005