Researchers in Japan mapped stress fields around atomic flaws in diamond, confirming an 80-year-old theory. Led by Tokuyuki Teraji, the team used nitrogen-vacancy centers to measure these tiny defects. Teraji said, "We realized that 'stress imaging' within the diamond crystal is essential for achieving even higher crystal quality." This helps manufacturers.
For the first time, researchers in Japan have directly mapped several components of the stress field surrounding an atomic-scale flaw in the crystal structure of diamond. Led by Tokuyuki Teraji at Japan's National Institute for Materials Science, the team achieved its result using nitrogen-vacancy (NV) centers in diamond, whose spin states respond differently to stress depending on how they are oriented relative to the stress field.
Published in Applied Physics Letters, the technique validates an 80-year-old theory about how miniature stress fields are distributed in diamond. It could also help improve the processes used to manufacture the high-quality diamond demanded by emerging technologies.
Atomic-scale flaws
Even in otherwise orderly crystals like diamond, atomic-scale flaws can always be found, where neighboring rows of atoms are misaligned with each other. Named "dislocations," these flaws create minute stress fields which ripple out through the surrounding atoms. Across the whole lattice, they can strongly affect the material's mechanical, electrical and magnetic properties.
More than 80 years ago, physicists used elasticity theory to derive a mathematical description of these stress fields, known as a "stress tensor," which defines the stress at any given point surrounding a dislocation.
Since then, this description has underpinned our understanding of how dislocations behave, from the energy they store to the forces they exert on each other. However, measuring these microscopic stress fields directly has proven far more challenging: existing techniques can capture only some aspects of the stress, so the theory has never been fully tested.
Recently, this difficulty has become more pressing in the design of next-generation power and quantum devices. Many of these technologies rely on growing high-quality crystals in the lab: a process that demands exquisite control. Without a reliable way to measure dislocation stress fields directly, uncertainties can arise about how these defects affect a crystal's properties, preventing materials from reaching their full potential.
Fluorescing stress fields
In the study, Teraji's team used NV centers as tiny sensors of the stress surrounding a dislocation. These defects form when a carbon atom in the diamond lattice is replaced by a nitrogen atom, sitting next to an empty lattice site.
"We realized that 'stress imaging' within the diamond crystal is essential for achieving even higher crystal quality," Teraji says. "To achieve this, we adopted an approach that combined the optimization of quantum sensing technology with the adjustment of the nitrogen concentration within the crystal."
NV centers are especially useful in quantum sensing since the spin states of unpaired electrons associated with them are highly sensitive to their local environments, including mechanical stress. They are also highly stable, retaining their quantum information for a long time, even at room temperature.
In addition, their spin states can be easily read out optically. When illuminated with laser light, NV centers fluoresce more or less brightly depending on their spin state. By applying microwaves, researchers can flip this spin—but only when the microwave frequency matches the NV center's resonant frequency, causing a measurable dip in brightness.
Revealing distributions
To exploit this behavior, Teraji's team considered how these resonant frequencies would change in response to a dislocation's stress field. Within the diamond lattice, NV centers can sit in four possible orientations. Crucially, their resonant frequencies shift depending on the direction of the applied stress relative to the axis running from nitrogen atom to vacancy. For NV centers sitting in the same stress field, this should create subtly different shifts for each orientation, allowing separate components of the stress tensor to be untangled.
To detect these shifts, the researchers first grew a thin, high-quality diamond film using chemical vapor deposition, then located a region where the stress field was dominated by a single 45° dislocation.
They grew the film from carbon enriched in the carbon-12 isotope, which boosts the coherence of NV spin states. In addition, they fine-tuned the concentration of nitrogen in the film to maximize the brightness of the NV centers' fluorescence, without sacrificing the coherence of their spin states.
Using a confocal microscope, they then subjected NV centers across the film to pairs of microwave pulses, separated by a carefully chosen interval. This technique allowed them to measure resonant frequencies with extreme precision from the resulting fluorescence brightness, detecting stress to within around 1 megapascal: roughly 10 times more precise than conventional methods.
From these measurements, they mapped four separate components of the stress tensor around the dislocation. "The measurements revealed a point-symmetric stress distribution centered around the dislocation, successfully detecting small stress variations," Teraji explains.
By fitting this data using elasticity theory, the team extracted values for diamond's elastic properties that closely matched established values for bulk diamond, confirming close agreement with the theoretically calculated stress tensor. "This provided the world's first direct experimental validation of the analytical stress tensor around a single dislocation predicted by elasticity theory," Teraji adds.
Probing real defects
Based on its results, Teraji's team is hopeful that its combination of fine-tuned diamond fabrication and direct stress measurement could lead to important new advances in emerging technologies.
"This combined approach allows for the quantitative evaluation and fitting of local stress fields around microscopic defects that degrade device performance," Teraji says. "Consequently, it provides direct guidelines for further optimizing crystal growth processes and improving the reliability of next-generation power and quantum devices."
With the ability to directly measure the stress fields of individual dislocations, and even distinguish single dislocations from bundles of them, its technique could ultimately provide a powerful new framework for analyzing crystal defects.