# On the Morphology of Group II Metal Fluoride Nanocrystals at Finite Temperature and Partial Pressure of HF

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## Abstract

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## 1. Introduction

## 2. Results

#### 2.1. Bulk Calculations

#### 2.2. Clean Surfaces

#### 2.3. Crystal Shapes at Thermodynamic Equilibrium

#### 2.4. Comparison Experimental Found Crystal Shapes

## 3. Material and Methods

#### 3.1. Computational Details

#### 3.2. Synthesis of Nanoparticles

## 4. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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Sample Availability: Not available. |

**Figure 1.**Primitive unit cells of relaxed symmetric slabs of CaF${}_{2}$ surfaces. For the (111) surface, six layers are used, for the (110) surface, six layers, each consisting of a CaF${}_{2}$-unit, and for the (100), 15 layers are used. Fluorides are drawn in red and calcium in blue.

**Figure 2.**Variation of the surface energy as a function of the pressure of HF for the three low index surfaces of CaF${}_{2}$ at 300 K.

**Figure 3.**The effect of temperature on the morphology and composition of the CaF${}_{2}$ crystal at four pressure conditions—surface (111) in red and (100) in green. The clean surfaces are indicated by empty planes, the dotted planes correspond to 100% HF coverage, wavy lines to 50% HF coverage and dashed planes to 25% HF coverage.

**Figure 4.**The effect of temperature on the morphology and composition of the SrF${}_{2}$ crystal at four pressure conditions—surface (111) in red and (100) in green. The clean surfaces are indicated by empty planes, the dotted planes correspond to 100% HF coverage, wavy lines to 50% HF coverage and dashed planes to 25% HF coverage.

**Figure 5.**The effect of temperature on the morphology and composition of the BaF${}_{2}$ crystal at four pressure conditions—surface (111) in red and (100) in green. The clean surfaces are indicated by empty planes, the dotted planes correspond to 100% HF coverage, wavy lines to 50% HF coverage and dashed planes to 25% HF coverage.

**Table 1.**Optimized lattice constant a${}_{0}$ (Å), bulk modulus B (GPa), cohesive energy E${}_{coh}$ (eV) and lattice energy E${}_{lat}$ (eV) for CaF${}_{2}$, SrF${}_{2}$ and BaF${}_{2}$ calculated at the PBE level. The energy values are counterpoise corrected. Experimental values are given for comparison.

CaF${}_{2}$ | SrF${}_{2}$ | BaF${}_{2}$ | ||||
---|---|---|---|---|---|---|

Calc. | Exp. | calc. | Exp. | Calc. | Exp. | |

a (Å) | 5.50 | 5.46 | 5.84 | 5.8 | 6.24 | 6.20 |

B (GPa) | 82 | 83 | 62 | 69 | 62 | 57 |

E${}_{coh}$ (eV) | −16.88 | −16.08 | −17.01 | −15.95 | −17.90 | −16.01 |

E${}_{lat}$ (eV) | −26.89 | −27.46 | −25.35 | −26.03 | −23.90 | −24.58 |

**Table 2.**PBE-calculated vacuum surface energies for the low-index surfaces of CaF${}_{2}$, SrF${}_{2}$ and BaF${}_{2}$.

Surface | Surface Energy in (J/m${}^{2}$) | ||
---|---|---|---|

CaF${}_{2}$ | SrF${}_{2}$ | BaF${}_{2}$ | |

111 | 0.47 | 0.45 | 0.39 |

110 | 0.71 | 0.67 | 0.57 |

100 | 0.95 | 0.98 | 0.86 |

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**MDPI and ACS Style**

Kaawar, Z.; Mahn, S.; Kemnitz, E.; Paulus, B.
On the Morphology of Group II Metal Fluoride Nanocrystals at Finite Temperature and Partial Pressure of HF. *Molecules* **2017**, *22*, 663.
https://doi.org/10.3390/molecules22040663

**AMA Style**

Kaawar Z, Mahn S, Kemnitz E, Paulus B.
On the Morphology of Group II Metal Fluoride Nanocrystals at Finite Temperature and Partial Pressure of HF. *Molecules*. 2017; 22(4):663.
https://doi.org/10.3390/molecules22040663

**Chicago/Turabian Style**

Kaawar, Zeinab, Stefan Mahn, Erhard Kemnitz, and Beate Paulus.
2017. "On the Morphology of Group II Metal Fluoride Nanocrystals at Finite Temperature and Partial Pressure of HF" *Molecules* 22, no. 4: 663.
https://doi.org/10.3390/molecules22040663