Building on the Thermal Conductivity work of Mg₀.₅Ni₀.₅O, we use the Mg₀.₅Ni₀.₅O model to construct the Co₀.₂₅Ni₀.₇₅O model. In the Mg₀.₅Ni₀.₅O structure, there are 8000 atoms in total, consisting of 2000 Mg, 2000 Ni, and 4000 O. For the new Co₀.₂₅Ni₀.₇₅O model, we aim to adjust the composition to 1000 Co, 3000 Ni, and 4000 O. To achieve this, we randomly select 1000 Mg atoms and transform them into Co atoms, ensuring that the overall ratio of Co:Ni:O remains 1:3:4. See Co₀.₂₅Ni₀.₇₅O Model Creation Folder
However, due to structural differences between Mg₀.₅Ni₀.₅O and Co₀.₂₅Ni₀.₇₅O, we anticipate that the optimized force parameters for Mg₀.₅Ni₀.₅O may not directly apply to Co₀.₂₅Ni₀.₇₅O. Therefore, we will need to explore and optimize these parameters for each temperature range (300K - 500K) by conducting a new set of simulations. The details of our approach for optimizing force parameters across different temperatures can be found in the Establishing a Best Fit Line for Optimized Forces Across Temperatures section in the Mg₀.₅Ni₀.₅O README file.
Since the Co₀.₂₅Ni₀.₇₅O model is newly constructed rather than being derived from a trained model, it is necessary to first relax the system using an NPT (constant number of particles, pressure, and temperature) simulation. This allows the system to adjust its volume and achieve a stable, equilibrium state before further analysis.
The NPT run ensures the material reaches its natural volume under standard conditions (with pressure P set to 0) and adjusts its atomic arrangement to the conditions of the simulation. This step is critical for avoiding distortions in the structure, which could lead to inaccurate thermal conductivity results in subsequent simulations. Once the volume is relaxed, we can proceed with the NVT (constant number of particles, volume, and temperature) simulation for accurate thermal conductivity measurements.
We can plot the pressure from the thermo.out file to compare the system before and after relaxation. Below are the pressure plots without and with relaxation:
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| Pressure without relaxation | Pressure after relaxation |
We conducted short runs (1M steps) at 300K to quickly evaluate the effect of different force parameters on the thermal conductivity of Co₀.₂₅Ni₀.₇₅O. These shorter runs allowed us to explore force parameters and identify ranges that consistently stabilize thermal conductivity measurements. Once identified, these parameters can be further validated through longer simulations.
The plots below display the results for three different force parameters:
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Spectral Thermal Conductivity of 5 runs at 300K with F(Å⁻¹) = 0.0001 |
Thermal Conductivity at 300K with F(Å⁻¹) = 0.0001 |
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Spectral Thermal Conductivity of 5 runs at 300K with F(Å⁻¹) = 0.00011 |
Thermal Conductivity at 300K with F(Å⁻¹) = 0.00011 |
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Spectral Thermal Conductivity of 5 runs at 300K with F(Å⁻¹) = 0.00012 |
Thermal Conductivity at 300K with F(Å⁻¹) = 0.00012 |
The force parameters tested (0.0001 Å⁻¹, 0.00011 Å⁻¹, and 0.00012 Å⁻¹) produced consistent results across all short runs, showing minimal variation in thermal conductivity measurements. The low error bars indicate high repeatability and suggest that the optimized force parameters are stabilizing the system. Given the close agreement between the different runs, these force parameters are promising candidates for further exploration.
After identifying likely force parameters through short runs, we extended the simulation time to 10M steps to achieve more accurate and detailed results. Below are the results for force parameters ranging from 0.00008 Å⁻¹ to 0.00011 Å⁻¹:
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Spectral Thermal Conductivity of 5 runs at 300K with F(Å⁻¹) = 0.00008 |
Thermal Conductivity at 300K with F(Å⁻¹) = 0.00008 |
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Spectral Thermal Conductivity of 5 runs at 300K with F(Å⁻¹) = 0.00009 |
Thermal Conductivity at 300K with F(Å⁻¹) = 0.00009 |
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Spectral Thermal Conductivity of 5 runs at 300K with F(Å⁻¹) = 0.0001 |
Thermal Conductivity at 300K with F(Å⁻¹) = 0.0001 |
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Spectral Thermal Conductivity of 5 runs at 300K with F(Å⁻¹) = 0.00011 |
Thermal Conductivity at 300K with F(Å⁻¹) = 0.00011 |
These extended simulations confirm the findings from the short runs, with force parameters in the range of 0.00008 Å⁻¹ to 0.00011 Å⁻¹ yielding stable results. The optimal value for force parameters appears to be around 0.00008 Å⁻¹, as this produced the most consistent results with the least error.
We applied the same process at 500K to find the optimal force parameters. Below are the results for the force parameter of 0.00015 Å⁻¹:
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Spectral Thermal Conductivity of 5 runs at 500K with F(Å⁻¹) = 0.00015 |
Thermal Conductivity at 500K with F(Å⁻¹) = 0.00015 |
The graph above demonstrates a consistent trend in thermal conductivity ( k(w) ) with smaller error bars, using optimized force parameters. As expected, thermal conductivity decreases as temperature ( T(K) ) increases, consistent with the traditional Umklapp scattering trend seen in crystalline materials. In such materials, thermal conductivity typically follows an inverse relationship with temperature, ( \propto 1/T ).
When the thermal conductivity results across different temperatures were plotted together, a clear trend emerged. Similar to the behavior observed in Mg₀.₅Ni₀.₅O, increasing temperature generally results in a decrease in thermal conductivity. However, Co₀.₂₅Ni₀.₇₅O exhibits a significant increase in thermal conductivity, suggesting that the thermal properties of Co₀.₂₅Ni₀.₇₅O are more sensitive to temperature variations than Mg₀.₅Ni₀.₅O.
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3D Plot of Average Spectral Thermal Conductivity Across Temperatures Using Optimized Force Parameters
- The force parameters optimized for Mg₀.₅Ni₀.₅O were not directly applicable to Co₀.₂₅Ni₀.₇₅O, as Co₀.₂₅Ni₀.₇₅O was constructed by rearranging the Mg₀.₅Ni₀.₅O model rather than coming from a pre-trained model.
- Co₀.₂₅Ni₀.₇₅O demonstrates a decrease in thermal conductivity with increasing temperatures, following the traditional Umklapp scattering trend, similar to Mg₀.₅Ni₀.₅O.
- Co₀.₂₅Ni₀.₇₅O's thermal conductivity is significantly higher than that of Mg₀.₅Ni₀.₅O and J14 across the tested temperature range, suggesting that Co₀.₂₅Ni₀.₇₅O experiences less scattering, making it more thermally conductive at elevated temperatures.