^{1}

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^{1}

^{2}

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Contact angles of water droplet on as-grown Z, +X, –X, and m faces of synthetic quartz crystals with growth term of 20 and 48 days, and polished Z, +X, –X, Y, and 45 ° cut faces of synthetic quartz crystal were observed. The average of the contact angles on as-grown Z, +X, and –X faces increased with the growth term, and they were larger than that on polished Z, +X, and –X faces. On the other hand, the average of the contact angles of water on m face decreased with the growth term, and they were smaller than that on polished Y cut face. Growth rate of the faces of synthetic crystals was measured and the order of growth rate was, m < –X < +X < Z. Specific surface free energy (SSFE) was calculated using Neumann’s equation. The SSFE of polished face was in the order of, m < –X < +X < Z, which corresponds to the order of the growth rate. The SSFE was larger for the face with larger growth rate.

Specific surface free energy (SSFE) is significant value to discuss crystal growth thermodynamically, and SSFE is well discussed theoretically. However, experimental determination of SSFE of crystal is very few. One of the experimental trials to determine the surface energy of quartz crystal was performed by Brace and Walsh [

crystals, and reported that the crystals satisfy Wulff’s relationship, that is, SSFE is proportional to the grown length of the crystals. We also determined the SSFE of as-grown face of synthetic quartz crystal [

A single crystal of synthetic quartz was grown at NDK Co., Ltd., by the industrial hydrothermal method using NaOH solution [

Water droplet was dropped on the face of crystal using a micropipet. The droplets sized −0.5 mm^{3} were observed using a digital camera (Canon ET-67B). The details of the measurement are described elsewhere [

The relationship between the surface tension and the contact angle is indicated by Young’s equation as the following:

where

where ^{2}/mJ)^{2}. Combining Equation (2) with Equation (1) yields

In this equation, only

The contact angles of the water droplets had a wide distribution on each face of the crystal. The measured contact angles of water droplets on the as-grown Z and polished Z cut face are shown in

with growth term of 20 and 48 days were 22 ± 2, 39 ± 6, and 47 ± 7 degree, respectively. Average of contact angle of as-grown Z face of 20 and 48 days grown is larger than that of polished Z cut face. The distribution of the contact angles is wider for the as-grown Z face than that of the polished Z cut face. The observed contact angle and the calculated SSFE summarized in

Calculated SSFEs for Z cut, 20 and 48 days grown Z faces are 68 ± 1, 58 ± 4, and 53 ± 5 mN/m, respectively. Because the sample crystals were grown from Z cut plate, the SSFE of polished Z cut face is considered to be the SSFE of the seed crystal. The relationship between the average of SSFE and growth time is shown in

faces | Contact angles (degree) | SSFE (mN/m) |
---|---|---|

Polished Z cut | 22 ± 2 | 68 ± 1 |

As-grown Z (20 days) | 39 ± 6 | 58 ± 4 |

As-grown Z (48 days) | 47 ± 7 | 53 ± 5 |

Polished +X cut | 26 ± 3 | 65 ± 1 |

As-grown +X (20 days) | 48 ± 7 | 52 ± 5 |

As-grown +X (48 days) | 54 ± 6 | 48 ± 5 |

Polished –X cut | 34 ± 3 | 61 ± 2 |

As-grown –X (20 days) | 39 ± 6 | 58 ± 4 |

As-grown –X (48 days) | 55 ± 4 | 47 ± 3 |

Polished Y cut | 82 ± 5 | 27 ± 4 |

As-grown m (20 days) | 53 ± 10 | 48 ± 7 |

As-grown m (48 days) | 42 ± 6 | 56 ± 4 |

Polished 45˚ cut | 33 ± 4 | 62 ± 2 |

The distributions of the contact angles of water droplets on +X face are shown in

Calculated SSFEs for polished +X cut, 20 and 48 days grown +X faces are 65 ± 1, 52 ± 5, and 48 ± 5 mN/m, respectively, and for polished –X cut, 20 and 48 days grown –X faces are 61 ± 2, 58 ± 4, and 47 ± 3 mN/m, respectively. The crystal was grown from Z cut plate, and Z cut plate has very narrow X and Y faces and it was

difficult to observe the contact angle of water on X or Y face of Z cut plate. Here, we postulated that the SSFE of polished X and Y cut face is regarded to the SSFE of X and Y face of the seed crystal. The relationship between the average of SSFE of ±X faces and growth term of each face is shown in

The distributions of contact angles of water on the as-grown m and polished Y cut face are shown in

Calculated SSFE of polished Y cut face and m face of 20 and 48 days grown were 27 ± 4, 48 ± 7, and 56 ± 4 mN/m, respectively. The m face has growth hillocks with six vicinal faces. Each vicinal face shows the different step roughness. Because the flat m face, that is, polished Y cut face has the smallest SSFE, the SSFE of other faces of hillocks is larger than that of Y cut face. The SSFE of polished Y cut face can be regarded as that of seed crystal. The relationship between the SSFE and growth term is shown in

The distribution of contact angles of water on the 45˚ cut face is shown in

m | –X | +X | Z | |
---|---|---|---|---|

20 days | 0.025 | 0.10 | 0.29 | 0.39 |

48 days | 0.018 | 0.095 | 0.24 | 0.28 |

The growth rates of each face of 20 and 48 days grown crystal are summarized in

Although the polished faces are flat enough by optical observation, there should be roughness in atomic scale. If the surface is ideally flat and uniform, the SSFE should be unique, and no distribution could be observed. However, the average value of SSFE of each polished face has obvious difference and reflects the difference of growth rate of each face.