At the previous webinar, 'MatSQ 109: A New Paradigm of Materials Research - Machine Learning(CGCNN)' covered 'How to calculate bulk modulus' for preparing the machine learning training set.
The bulk modulus, the value representing the resistance to stress in a solid, is one of the material's fundamental properties. The previous weekly tip #16 deals with the details of the bulk modulus.
In this module tip, we'll learn how to calculate bulk modulus using the newly released functions, such as the 'High throughput' module, the 'Range' option of the strain menu, and the 'Murnaghan' option of the 'Curve Fitting Tools' module.
You should prepare a structure set with a series of different volumes for calculating bulk modulus.
The 'Range' tab of the 'Strain' menu enables modeling easily the series of the structure set for bulk modulus calculation.
In first, select the axis that will be strained. If you choose all axes, it gives the same strain to all axes considering hydrostatic pressure.
The 'Strain Range' can determine strain rate. After applying minimum/maximum strain rate and interval, the Structure List' adds all strained structures.
2. High throughput Calculation
Now you can easily perform the Quantum Espresso high throughput calculation using the new 'High Throughput' module.
If you connect the 'High Throughput' module and the 'Structure Builder' module, the setting UI for high throughput calculations appears.
The 'Default' tab allows modifying and applying the entire input script and pseudopotential. Copy-and-paste from the Quantum Espresso (General) module makes the input script setting easy.
After finishing all settings, click the 'Update' button on the right-top side. Then all input scripts contained in every high throughput job are changed.
This 'Calculations' can change each job, for example, modifying the input script and pseudopotential and checking each structure.
You don't need to change any part for calculating bulk modulus because the bulk modulus calculation should use the same input script for different models.
After finishing the calculation settings, set the 'Job Submit' part and lick the 'Start Job!' button. It may take some time because it submits all high throughput job sequentially. The top side dashboard shows the submitted jobs.
3. Data Checking
Import all high throughput results using the 'Correlation' module, after all high throughput jobs finishing. And then copy the Volume and Final energy data.
4. Curve Fitting Tools
On the 'Curve Fitting Tools' module, you can fit the Volume vs Energy data obtained from the high throughput with the desired equation.
Select the desired trend line type at the 'Type of Fitting' option. For obtaining the bulk modulus, select the 'Murnaghan' option.
When you select the Murnaghan option, the following Murnaghan equation is automatically entered. The Murnaghan equation is the representative equation of state for modeling material's behavior under high-pressure conditions.
(V: Volume, B0: Bulk modulus, B'0: Pressure Derivative of the Bulk modulus, V0: Equilibrium Volume)
For the cubic system case, you can obtain the most stable lattice parameter by calculating the cube root of equilibrium volume.
However, the equation has some difference from that in the previous post, Weekly Tip #16. The equation in Weekly Tip #16 is the 'Birch's equation' considering up to the 4th term. Therefore, there is some difference in results even using the same input. When the data from Weekly Tip #16 is applied to the Curve Fitting Tools module, the following results are displayed.
We can find some differences from the 15.94 GPa obtained using the formula in Weekly Tip #16.
However, this is only a difference in methodology, and it is difficult to conclude which is the more accurate method. In practice, there is an example of comparing bulk modulus results obtained using different methodologies.[1-3]
In this module tip, we learned how to calculate the bulk modulus using the newly released feature.
The High throughput module can be a powerful tool depending on how we use it. For example, when performing a convergence test, the structure can be modeled using the optimal lattice constant obtained through bulk modulus calculation. And next, connect the high throughput module to that structure and then change the input script for each job at the Calculations part.
In addition, the Correlation and Curve Fitting Tools modules can also play a useful role in analyzing your research data.
Perform high throughput calculations and post-process with new features in Materials Square!
Tutorial Video in Webinar
Do you need more Information?
 Katsura, T., & Tange, Y. (2019). A Simple Derivation of the Birch-Murnaghan Equations of State (EOSs) and Comparison with EOSs Derived from Other Definitions of Finite Strain. Minerals, 9(12), 745.
 Singh, B. P. (2005). A comparison of equations of state including the generalized Rydberg EOS. Physica B: Condensed Matter, 369(1-4), 111-116.
 Kumar, M., & Bedi, S. S. (1996). A comparative study of birch and kumar equations of state under high pressure NaCl as an example. physica status solidi (b), 196(2), 303-307.