Atomistic simulation of the measurement of mechanical properties of gold nanorods by AFM

At a Glance

Metadata	Details
Publication Date	2017-11-20
Journal	Scientific Reports
Authors	Bernhard Reischl, Andrew L. Rohl, A. Kuronen, K. Nordlund
Institutions	University of Helsinki, Curtin University
Citations	8
Analysis	Full AI Review Included

Technical Documentation & Analysis: Atomistic Simulation of Nanorod Mechanical Properties

Documentation generated for 6CCVD (6ccvd.com) based on the research paper: Atomistic simulation of the measurement of mechanical properties of gold nanorods by AFM.

Executive Summary

This study utilizes large-scale Molecular Dynamics (MD) simulations to characterize the size- and orientation-dependent mechanical properties of gold nanorods, directly modeling a state-of-the-art Atomic Force Microscope (AFM) nanoindentation setup. The findings validate the necessity of high-rigidity diamond tips for nanoscale mechanics and demonstrate material science requirements for replicating such fundamental studies.

Direct Experimental Link: The simulation utilized a rigid, semi-spherical diamond tip ($R$ = 10 nm), explicitly matching commercially available Single Crystal Diamond (SCD) AFM probes (SCD Probe D300 series).
Orientation Dependence: Successfully quantified the Young’s Moduli ($E$) of gold nanorods, showing a strong dependence on crystallographic orientation: $E_{[110]}$ (140 ± 4 GPa) was significantly higher than $E_{[100]}$ (103 ± 2 GPa).
Oliver-Pharr Validation: The Oliver-Pharr method was applied successfully to the MD unloading curves, enabling direct comparison between atomistic simulation results and macroscopic experimental techniques, validating the methodology for nanoscale mechanical testing.
Incipient Plasticity Observed: Dislocations nucleated at extremely shallow depths ($d \le 0.5$ nm), proving that plastic deformation mechanisms (migration, annihilation) govern the mechanical response at the true nanoscale, requiring extremely stiff indenters.
Substrate Requirement: Explicitly including a silicon (100) substrate was necessary to model realistic stress-release pathways (ejection of dislocation loops), confirming the need for robust, low-deformation substrate materials in experiments.
6CCVD Relevance: The research highlights the critical role of highly rigid, high-purity Single Crystal Diamond (SCD) material, precisely dimensioned and polished, which is a core capability of 6CCVD.

Technical Specifications

The simulation extracted precise mechanical data and utilized highly specific geometric and physical parameters designed to replicate a real-world AFM nanoindentation experiment.

Parameter	Value	Unit	Context
Single Crystal Au Young’s Modulus ($E_{100}$)	103 ± 2	GPa	Oliver-Pharr result; (100) terminated nanorod
Single Crystal Au Young’s Modulus ($E_{110}$)	140 ± 4	GPa	Oliver-Pharr result; (110) terminated nanorod
Penta-Twinned Au Young’s Modulus ($E_{PT}$)	108 ± 2	GPa	Oliver-Pharr result
Tip Apex Radius ($R$)	10	nm	Semi-spherical Diamond tip (SCD Probe D300 model)
Maximum Indentation Depth ($d_{m}$)	2.7	nm	10% of nanorod diameter
Nanodrod Dimensions (L x D)	55 x 27	nm	Length x Diameter
Substrate Dimensions (Si 100)	120 x 80 x 15	nm³	Explicit Silicon substrate volume
Maximum Applied Force ($F_{max}$)	~1	µN	Force recorded at $d_{m}$ = 2.7 nm on SC Au nanorods
Indentation Step Size ($\Delta z$)	0.025	nm	Rigid shift increment during quasi-static MD
Simulation Temperature ($T$)	300	K	Maintained via Berendsen thermostat
Time Step ($\Delta t$)	0.71	fs	MD calculation time interval
Plastic Deformation Onset	< 0.5	nm	Indentation depth for first dislocation nucleation

Key Methodologies

The large-scale molecular dynamics (MD) simulation protocol was designed to minimize computational artifacts and maximize relevance to experimental AFM indentation setups.

System Construction: Three gold nanorod configurations (Single Crystal (100), Single Crystal (110), Penta-Twinned) were placed on an explicit, large Silicon (100) substrate (120 x 80 x 15 nm³).
AFM Tip Modeling: A rigid, semi-spherical diamond tip apex ($R$ = 10 nm) with [111] orientation aligned to the indentation direction was used, simulating a highly stable, non-deforming Single Crystal Diamond (SCD) probe.
Boundary Conditions: Periodic boundary conditions were applied in the x and y plane. The bottom four atomic layers (0.54 nm) of the silicon substrate were frozen to simulate bulk-like behavior.
Interaction Potentials: Atomic interactions were modeled using Tersoff-style potentials (Au-Au, C-C, Si-Si), Lennard-Jones (Au-C), and Morse potential (Au-Si), selected to accurately model interface bonding effects.
Quasi-Static Indentation Protocol: Indentation was performed by rigidly shifting the tip towards the sample in small increments ($\Delta z$ = -0.025 nm). Each shift was followed by a 10 ps equilibration period and 40 ps of force sampling to maintain quasi-static conditions.
Thermal Regulation: A Berendsen thermostat was applied to all moving atoms to maintain the system temperature at $T$ = 300 K.
Data Analysis: Young’s Moduli were derived by fitting the unloading force-distance curves ($d > 2.4$ nm) using a power law model ($F(d) = a(d - d_{0})^{m}$ with $m = 3/2$), then applying the established Oliver-Pharr method for direct comparison with experimental measurements.

6CCVD Solutions & Capabilities

This research confirms the fundamental requirement for ultra-hard, precision-engineered diamond materials—both for the indenter tip and potentially for advanced substrate development—in pioneering nanoscale mechanical measurements. 6CCVD is uniquely positioned to supply the materials necessary to replicate and advance this work.

Research Requirement	6CCVD Applicable Solutions	Customization Potential & Engineering Value
High-Rigidity AFM Indenter Tip	Applicable Materials: Optical Grade Single Crystal Diamond (SCD) wafers, specifically oriented (e.g., [111] alignment required by the simulation).	6CCVD provides low-defect SCD material (up to 500 µm thick) essential for crafting durable, high-fidelity indenter probes that eliminate tip deformation artifacts, matching the rigid tip assumption of the MD study.
Ultra-Low Surface Roughness ($< 0.1$ nm)	Polishing Capabilities: Industry-leading polishing; Ra < 1 nm for SCD and Ra < 5 nm for Inch-size PCD.	Surface quality is critical as dislocation nucleation is sensitive to atomic-scale roughness. Our superior polishing ensures smooth interfaces necessary for accurate mechanical contact modeling and fundamental studies on plasticity onset.
Custom Substrate Interfaces	Custom Dimensions and Materials: Large-area PCD plates (up to 125mm) or thinner SCD/BDD substrates.	While the simulation used Si, future experiments may require electrically conductive, highly rigid substrates. We offer large-area Polycrystalline Diamond (PCD) or Boron-Doped Diamond (BDD) with custom thickness (0.1 µm - 10 mm).
Precise Interconnects & Bonding	Metalization Services: Internal capability to deposit Au, Pt, Pd, Ti, W, Cu layers.	If experiments require monitoring electrical changes or creating high-stability bonding interfaces (like the Au-Si interface studied), 6CCVD can custom metalize diamond plates to precise thickness specifications.
Replication and Extension Support	Engineering Support: 6CCVD’s in-house PhD team can assist researchers with material selection, orientation optimization, and dimensional specifications for AFM nanoindentation and high-precision contact mechanics projects.	Partnership with 6CCVD ensures that experimental hardware matches the ideal parameters established in advanced atomistic simulations, accelerating R&D success in nanomechanics.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

Tech Support

Original Source

DOI: https://doi.org/10.1038/s41598-017-16460-9