# Mechanical Properties of a Diamond Schwarzite: From Atomistic Models to 3D-Printed Structures

**Authors:** Levi C. Felix, Vladimir Gaal, Cristiano F. Woellner, Varlei Rodrigues, Douglas S. Galvao  
**arXiv:** [2001.03430](https://arxiv.org/abs/2001.03430)  
**Date:** 2020-01-10  
**Summary page:** https://www.summarizepaper.com/en/paper/2001.03430v1/

## Key points

- Triply Periodic Minimal Surfaces (TPMS) are optimal geometries for structural applications in materials science
- TPMS possess locally minimized surface area under the constraint of periodic boundary conditions
- Different families of surfaces were obtained with different topologies satisfying such conditions, including Primitive (P), Gyroid (G) and Diamond (D) surfaces
- Schwarzites are 3D crystalline porous carbon nanocrystals exhibiting the shape of TPMS, proposed by Mackay and Terrones in 1991
- The complex topology of schwarzites poses serious limitations on their synthesis with conventional nanoscale fabrication methods like Chemical Vapour Deposition (CVD)
- Additive Manufacturing (AM) techniques like 3D Printing can be employed to fabricate TPMS structures
- An optimized atomic model of a schwarzite structure from the D family was used to generate a surface mesh which was subsequently 3D-printed through Fused Deposition Modelling (FDM) using thermoplastic PolyLactic Acid (PLA) polymer filaments
- Mechanical properties under uniaxial compression were investigated for both the atomic model and the 3D-printed one
- Fully atomistic Molecular Dynamics (MD) simulations were carried out to investigate the uniaxial compression behavior of the D8bal atomic model
- The mechanical testings performed on the 3D-printed schwarzite showed deformation mechanisms similar to those observed in MD simulations, suggesting a scale-independent mechanical behavior dominated by structural topology.
- This study demonstrates that AM techniques can be utilized to fabricate complex TPMS structures like schwarzites for potential use in structural applications.
- The findings also shed light on how structural topology can influence mechanical behavior at different scales.

## Summary

In recent years, Triply Periodic Minimal Surfaces (TPMS) have been found to be optimal geometries for structural applications in materials science. TPMS are surfaces that possess locally minimized surface area under the constraint of periodic boundary conditions. Different families of surfaces were obtained with different topologies satisfying such conditions, including Primitive (P), Gyroid (G) and Diamond (D) surfaces. Proposed by Mackay and Terrones in 1991, schwarzites are 3D crystalline porous carbon nanocrystals exhibiting the shape of TPMS. However, the complex topology of schwarzites poses serious limitations on their synthesis with conventional nanoscale fabrication methods, such as Chemical Vapour Deposition (CVD). To overcome this challenge, Additive Manufacturing (AM) techniques, such as 3D Printing, can be employed to fabricate TPMS structures. In this study, an optimized atomic model of a schwarzite structure from the D family (D8bal) was used to generate a surface mesh which was subsequently 3D-printed through Fused Deposition Modelling (FDM) using thermoplastic PolyLactic Acid (PLA) polymer filaments. Mechanical properties under uniaxial compression were investigated for both the atomic model and the 3D-printed one. Fully atomistic Molecular Dynamics (MD) simulations were also carried out to investigate the uniaxial compression behavior of the D8bal atomic model. The mechanical testings performed on the 3D-printed schwarzite showed deformation mechanisms similar to those observed in MD simulations. These results suggest a scale-independent mechanical behavior dominated by structural topology. Overall, this study demonstrates that AM techniques can be utilized to fabricate complex TPMS structures like schwarzites for potential use in structural applications. The findings also shed light on how structural topology can influence mechanical behavior at different scales.