# Study on Heat Transfer Performance and Anti-Fouling Mechanism of Ternary Ni-W-P Coating
## 3 Results
### Transient States of Calcite, Aragonite, and Vaterite
The energy barriers of the transition state TSla, TSlb, and TSlc between free-state ions and their crystal phase are 0.66, 0.18, and 0.10 eV, respectively. During the banding process, the distance between Ca\({}^{2+}\) and [CO\({}_{3}\)]\({}^{2-}\) reduces. In addition, it is found that Ca\({}^{2+}\) attacked [CO\({}_{3}\)]\({}^{2-}\) and formed the multi-intermediate under different attacking sites when computing the TSla. Similarly, the calculations of the transition state for the intermediate of vaterite and aragonite show multi-intermediates. The frequency analysis and calculation of the reaction intermediates, as well as transition states were conducted to optimize structures. After the consequence shows only one imaginary frequency, the only one structure in the transition state of TSla, TSlb, TSlc, TS2, TS3, and TS4 were ascertained authentically and accurately. Meanwhile, during the process of crystal transition of calcite, aragonite, and vaterite, the crystal type of CaCO\({}_{3}\) will also change due to different pressure and temperature [50; 51; 52; 53; 54]. According to Figure 12b, it is a need to cross the corresponding energy barrier in the process of mutual transformation under the experimental conditions (328.15 K, 0.1 MPa). Additionally, the relative stretch length of the intermediate of Ca\({}^{2+}\) and [CO\({}_{3}\)]\({}^{2-}\) is 0.220 A, 0.027 A, and 0.095 A, respectively. In the previous research, the ternary Ni-W-P coating has the lower surface free energy based on the experimental results of contact angle Figure 12a [9; 10; 16]. With the decrease of W content, the surface free energy of Ni-W-P coating was also lower. Take the consequence of Figure 12b into consideration, as the free Ca\({}^{2+}\) and [CO\({}_{3}\)]\({}^{2-}\) are easy to transfer to the transition state TSlc with low energy barrier on the surface of Ni-W-P coatings with low surface energy, CaCO\({}_{3}\) is prone to nucleate into structure of aragonite-phase [55; 56]. Besides, because of the influence of high surface free energy on the surface of bare substrate and Ni-W-P coating with high W content, Ca\({}^{2+}\) and [CO\({}_{3}\)]\({}^{2-}\) in free state can cross high energy barrier and form calcite-phase CaCO  
Figure 11: Structure of three crystal calcium carbonate (**a1–3**) calcite; (**b1–3**) aragonite; (**c1–2**) vaterite; (**d1–3**) density of state of calcite, aragonite, and vaterite. fouiling [43], which is consistent with our previous mesoscopic results of the fouling crystal types on the surface of Ni-W-P coating. Refer to Figure 11, we can know that the crystal configuration of both calcite-phase and aragonite-phase is more stable than that of vaterite. In this case, vaterite belongs to the structure of unsteady state [43]. Thereupon, the vaterite transformed to calcite and aragonite can be regarded as the process of transforming the stable phase or the metastable phase to the unsteady state [48] and vaterite undoubted is the dissipative structure. The thermodynamic performance of vaterite is unstable [49], and it will be transformed into a more stable structure of aragonite or calcite phase in the subsequent reaction. Figure 12: (**a**) Contact angle and surface energy of uncoated specimen and the Ni-W-P coatings; (**b**) Energetic profile for potential energy surface of calcite, vaterite, and aragonite. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Species** & **Energy (eV)** & **Vibrational Frequency (cm\({}^{-1}\))** \\ \hline Ion state & \(-\)22.05315 & - \\ Calcite & \(-\)23.79033 & - \\ Vaterite & \(-\)24.09105 & - \\ Aragonite & \(-\)24.34573 & - \\ TS1a & \(-\)21.38945 & 1425.5 \\ TS1b & \(-\)21.86688 & 1405.0 \\ TS1c & \(-\)21.94878 & 1412.9 \\ TS2 & \(-\)23.69758 & 1411.9 \\ TS3 & \(-\)23.71231 & 1487.0 \\ TS4 & \(-\)23.77383 & 1474.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Energy and frequency of reaction of Ca\({}^{2+}\) and [CO\({}_{3}\)]\({}^{2-}\).