# Study on Heat Transfer Performance and Anti-Fouling Mechanism of Ternary Ni-W-P Coating
## 2 Experimental Section
### First Principle on Transformation of Calcite, Aragonite, and Vaterite  
Calcium carbonate is a salt that heat transmits via the vibration of atoms. Atoms in calcium carbonate crystals are bound together by interatomic forces. The interaction force between atoms can be obtained by derivation of atomic potential energy [33].  
\[F=-d\phi/dx \tag{12}\]  
where \(dx\) is the interatomic distance, A.  
While the distance between atoms is far, the nucleus of one atom is attracted by the electrons of the other atom. Whereas, when the atoms are close to each other, the electron orbits of different atoms will overlap. Atoms will always vibrate near their equilibrium positions. The motion of each atom is limited by the potential energy of its neighbors, while the differences of binding energy of the calcite, aragonite, and vaterite crystals in calcium carbonate fouling deposited on the heat transfer surface was seldom reported. Therefore, the interaction force between atoms and the density of states of them were studied respectively in this work.  
Material Studio 8.0 software was utilized for the simulation. Firstly, three models of calcite, aragonite, and vaterite were established and the numbers of atoms per cell were all 120. The primary growth surface (0 0 1) was utilized to build super-cell [34]. The geometry optimization in Dmol\({}^{3}\) module serves to minimize the energy of super-cell. Also, electronic exchange was disposed with the Perdew-Burke-Ernzerhof (PBE) [35; 36] functions of Generalized Gradient Approximation (GGA) when minimizing the energy between electrons. In the brillouin area, the k-space grid points are chosen with Monkhorst-Pack [37]. This is because the lower the coverage of the surface is, the stronger the interaction between the adsorbed material and the substrate surface is [38]. Linear synchronous transit (LST) and quadratic synchronous transit method (QST) in TS search module is utilized to calculate the intermediate state. Firstly, initial states (calcite, aragonite, vaterite) were established and the geometry optimization in Dmol\({}^{3}\) serves the relaxed geometry of them. Then LST/QST method in TS search was used to get the vibrational modes of the TS. Specifically, initial structure started from the low-energy reactants and guided by the tangent of the ST path at the current position. Then the structure marched along the response path (climbing step) hypothesized by LST/QST. The purpose is to make the structure of reactants reach the highest energy point of the hypothetical path (near the secondary region of the real transition state). When a certain criterion is satisfied, the exact transition state was calculated subsequently. When the transition state has only one imaginary frequency, the calculation of the corresponding transition state is completed as it has only one imaginary frequency [39]. Also, its vibration mode should be used to check whether the direction of vibration connects the reactant with the terminal state.  
After that, the frequency analysis and calculation of intermediate and transition states are carried out at the same level to verify the correctness and interconnection of them. Furthermore, the reaction path, transition state, and energy gradient change rule of calcite, aragonite, and vaterite are further studied. Transition state structures of calcium carbonate and their analysis will be researched in later articles.