We observed changes in morphology and internal strain state of commercial diamond nanocrystals during high-temperature annealing. Three nanodiamonds were measured with Bragg coherent x-ray diffraction imaging, yielding three-dimensional strain-sensitive images as a function of time/temperature. Up to temperatures of 800 °C, crystals with Gaussian strain distributions with a full-width-at-half-maximum of less than were largely unchanged, and annealing-induced strain relaxation was observed in a nanodiamond with maximum lattice distortions above this threshold. X-ray measurements found changes in nanodiamond morphology at temperatures above 600 °C that are consistent with graphitization of the surface, a result verified with ensemble Raman measurements.
Nanoscale quantum sensing has developed into a promising field with a wide range of applications both in physical and biological systems. Of potential quantum sensor technologies, the nitrogen-vacancy (NV) center in diamond has emerged as a frontrunner as it offers room temperature operation and optical addressability in a biologically inert material. The NV center itself can be described in terms of a single spin with energy levels well isolated within the diamond band-gap, which results in long spin coherence times (T2) at room temperature.1 The level structure of these defects is easily perturbed by changes in the local environment, and this sensitivity has enabled magnetometry with NV centers,2,3 as well as electric field sensing4 and thermometry.5,6 Additionally, the inherent atomic scale of the NV center defect also enables nanoscale metrology when NVs are contained in nanocrystals.7
Despite the promising applications demonstrated to date, a critical challenge remains: scaling the creation of diamond nanostructures with NV centers that maintain long spin coherence times. Commercial fluorescent diamond nanoparticles are promising in this regard as they are both inexpensive and scalable8,9 but typically contain inhomogeneous lattice strain fields due to residual stresses from their fabrication, typically by detonation or milling of inexpensive bulk material. The inhomogeneous distribution of strain within commercial nanodiamonds results in non-uniform behavior of the NV centers, which broadens the overall ensemble linewidth, reduces signal, and ultimately decreases sensing ability. Production of high quality nanodiamonds has been demonstrated via lithography of high quality bulk diamond with shallow NV centers incorporated using delta-doping growth techniques.10,11 These nanodiamonds yielded long spin coherence times and excellent sensitivity;12 however, their fabrication is not easily scalable. Alternatively, the crystal quality of readily available commercial nanodiamonds may be improved sufficiently for sensing applications by high-temperature annealing known to mobilize vacancies and alleviate crystal strain in bulk samples.11
In this work, we use x-ray Bragg coherent diffraction imaging (BCDI), a nondestructive strain-sensitive microscopy technique, to study the three-dimensional (3D) lattice distortions and morphology of single commercial diamond nanoparticles in situ during annealing. With this technique, we confirmed that as-fabricated commercial diamond nanocrystals contain inhomogeneous internal strain fields, as has been observed previously.13 Upon annealing to temperatures up to 800 °C, a nanocrystal with relatively broad distribution of strain showed a homogenization of its lattice structure as well as changes in morphology consistent with surface graphitization.14,15 Similar changes were not observed in less strained nanodiamonds.
BCDI is a hard x-ray imaging technique that reconstructs a strain-sensitive 3D image of individual sub-micron-sized crystals by inverting the diffracted x-ray intensity pattern measured about a Bragg peak of the crystal.16 The process is depicted schematically in Figure 1. The measurement involves illuminating a nanocrystal with a coherent x-ray beam in a geometry such that a Bragg condition is fulfilled. With an x-ray area detector, a series of coherent x-ray diffraction patterns about the Bragg peak are measured by rotating the crystal in the beam in a series of fine angular steps. The resulting 3D coherent Bragg peak intensity distribution is inverted to a real space image via iterative numerical phase retrieval algorithms.17 The phase of the resulting complex-valued 3D image is proportional to a component of the lattice displacement vector (which maps lattice distortions),18 and the amplitude of the reconstruction maps the morphology of the crystal volume scattering into the measured Bragg peak (referred to as the Bragg electron density).19 In this work, the reconstructed Bragg electron density represents the volume fraction of a diamond nanoparticle that retains the diamond lattice structure and original crystal orientation, and it is sensitive to the displacement of (111) diamond lattice planes (u111) relative to the average lattice parameter of the crystal at each temperature. Compressive/tensile strain along the 111 direction can be determined from u{111} via the spatial derivative .20 This imaging capability enables structural changes in individual nanocrystals to be mapped with nanometer-scale spatial resolution, picometer-scale sensitivity to lattice distortions, and strain resolution of .
A schematic of the experimental in situ BCDI setup is shown in (a). A silicon substrate with drop-cast commercial nanodiamonds was placed on a heating stage and covered with an x-ray-transparent gas flow cell to maintain a helium atmosphere. The sample was illuminated with a coherent synchrotron x-ray beam at an incident angle that satisfies a {111} Bragg reflection of an individual nanodiamond crystal. The single nanocrystal produces a coherent x-ray diffraction pattern that is measured with an area detector. The sample angle is scanned in fine increments ( in steps), yielding a series of 2D patterns that are assembled to yield a 3D coherent Bragg peak intensity distribution (b) that is rich with fringes that encode the morphology and internal lattice distortions of the crystal. This information is inverted to a real-space 3D image of the crystal via iterative phase retrieval methods (c). The resulting reconstructions can be visualized as a 3D surface with coloring representing near-surface displacement of (111) lattice planes u111 or as a cut through the particle that shows the interior lattice displacements. The units of u111 are relative to the average lattice parameter of the crystal. Compressive/tensile strain can be determined by spatial differentiation of the lattice displacement field via .
A schematic of the experimental in situ BCDI setup is shown in (a). A silicon substrate with drop-cast commercial nanodiamonds was placed on a heating stage and covered with an x-ray-transparent gas flow cell to maintain a helium atmosphere. The sample was illuminated with a coherent synchrotron x-ray beam at an incident angle that satisfies a {111} Bragg reflection of an individual nanodiamond crystal. The single nanocrystal produces a coherent x-ray diffraction pattern that is measured with an area detector. The sample angle is scanned in fine increments ( in steps), yielding a series of 2D patterns that are assembled to yield a 3D coherent Bragg peak intensity distribution (b) that is rich with fringes that encode the morphology and internal lattice distortions of the crystal. This information is inverted to a real-space 3D image of the crystal via iterative phase retrieval methods (c). The resulting reconstructions can be visualized as a 3D surface with coloring representing near-surface displacement of (111) lattice planes u111 or as a cut through the particle that shows the interior lattice displacements. The units of u111 are relative to the average lattice parameter of the crystal. Compressive/tensile strain can be determined by spatial differentiation of the lattice displacement field via .
We utilized BCDI to measure changes in the 3D Bragg electron density and the lattice strain distribution of individual nanodiamonds as a function of time and temperature during annealing and strain relaxation. The samples used in this study were commercially available fluorescent nanodiamond crystals from Adamas Nanotechnologies. They were fabricated via milling of bulk diamond, yielding particles with diameters ranging from 50 to 500 nm. To study these crystals with BCDI, they were drop-cast onto a (100)-surface-oriented silicon substrate. This process provided an area coverage of nanocrystals with the diverse lattice orientations appropriate for BCDI experiments. To ensure that the nanocrystals adhered to the substrates, the Si substrates were coated with a thin layer of silica via sol-gel polymerization of tetraethyl orthosilicate (TEOS).21 BCDI measurements were performed at the Advanced Photon Source Sector 34-ID-C synchrotron beamline using a mirror-focused monochromatic 9 keV coherent x-ray beam. A custom-built substrate heater enclosed in an x-ray transparent gas flow cell was used to heat the nanodiamond samples during BCDI measurements. BCDI measurements were performed at a {111} Bragg peak of three individual nanodiamond crystals at various temperatures in an environment of flowing high-purity helium. One suitable crystal was identified per substrate, and that nanodiamond was imaged at a series of temperatures. At room temperature, the (111) lattice parameter of the nanodiamonds measured in this work was found to be , agreeing with the nominal corresponding lattice spacing in bulk diamond of .22 Starting from 20 °C, the temperature was increased with a ramp rate of C/min. At different temperatures in the annealing process, the temperature was held constant for ∼70 min in order to measure 3D BCDI data sets, then the temperature ramp was resumed. This single-particle imaging experiment was repeated on three crystals (referred to as Crystals 1, 2, and 3) with different initial strain distributions and sizes (150–350 nm diameter). The thermal annealing history of these nanodiamond crystals is shown in Figure 2(c).
Selected BCDI reconstructions of nanodiamond Crystals 1 and 2 are shown in (a) and (b), respectively, at different stages during annealing. The thermal annealing history of the three nanodiamonds in this study is shown in (c). BCDI data were recorded at each temperature plateau in (c) for the respective particles. The shape of the nanodiamond reconstructions shown here is colored according to the near-surface displacement of (111) diamond lattice planes (u111).
Selected BCDI reconstructions of nanodiamond Crystals 1 and 2 are shown in (a) and (b), respectively, at different stages during annealing. The thermal annealing history of the three nanodiamonds in this study is shown in (c). BCDI data were recorded at each temperature plateau in (c) for the respective particles. The shape of the nanodiamond reconstructions shown here is colored according to the near-surface displacement of (111) diamond lattice planes (u111).
The images from several selected temperatures from two of the particles are shown in Figure 2. From these images, changes in the volume and internal lattice strain of the diamond particles can be quantified as a function of temperature. Figure 3 shows probability histograms of the magnitude of strain per pixel in the 3D images of the three measured nanodiamonds over the course of the anneal, and Figure 4 (left panel) shows the full-width-at-half-max (FWHM) of a Gaussian curve fit to these probability distributions as a function of temperature. From these figures, we observe that at 20 °C, Crystal 1 has a broader strain distribution as compared to Crystals 2 and 3. Upon annealing, the strain distribution of Crystal 1 narrows with temperature, indicating an improvement in the homogeneity of the lattice structure. On the other hand, the strain distributions of Crystals 2 and 3 did not change substantially with temperature. Additionally, the volume fraction of diamond in Crystal 1 decreased during the latter stages of the anneal but remained constant in Crystals 2 and 3 (Figure 4 (right panel)). These trends can also be seen when visually comparing the shape and near-surface lattice distortions of Crystals 1 and 2 in Figures 2(a) and 2(b).
Probability distributions of strain magnitude () per pixel for the temperature series of three crystals are shown. The initial state of Crystal 1 at 20 °C is characterized by a relatively broader distribution that sharpens upon annealing. The strain distributions of Crystals 2 and 3 are initially sharper and do not change significantly with temperature. The above distributions were fitted to a normal Gaussian distribution function, and the FWHM of this fit is shown in Figure 4.
Probability distributions of strain magnitude () per pixel for the temperature series of three crystals are shown. The initial state of Crystal 1 at 20 °C is characterized by a relatively broader distribution that sharpens upon annealing. The strain distributions of Crystals 2 and 3 are initially sharper and do not change significantly with temperature. The above distributions were fitted to a normal Gaussian distribution function, and the FWHM of this fit is shown in Figure 4.
(Left) FWHM values of the measured strain distributions in Figure 4 are shown, obtained via least squares fitting of a Gaussian normal distribution function. (Right) The volume of the crystals as a function of temperature is shown.
(Left) FWHM values of the measured strain distributions in Figure 4 are shown, obtained via least squares fitting of a Gaussian normal distribution function. (Right) The volume of the crystals as a function of temperature is shown.
The reduction of the crystalline volume of Crystal 1 suggests a surface etching process. One possible etching mechanism is high-temperature surface graphitization14,15 that would reduce the volume fraction of diamond in the nanoparticle and that has been previously observed in diamond annealed under conditions similar to our experiment.23 To verify the presence of surface graphite, Raman spectroscopy was performed on samples prepared in this work. Figure 5 shows Raman spectra from three different substrates: a bare Si substrate, a Si substrate with drop-cast nanodiamonds treated with TEOS, and a post-annealed nanodiamond-coated Si substrate used in this study. The post-annealed nanodiamond sample shows a clear peak at a wavenumber of cm−1, a signature associated with surface graphitization of diamond.9 The sharp feature at 1332 cm−1 originates from the nanodiamonds. The other prominent features in the spectra are from the Si substrate.
Raman spectra of two control samples (TEOS-treated ND and bare Si) and one sample substrate after in situ BCDI imaging (post-anneal ND) measured with 780 nm excitation are shown in (a). The feature at 520 cm−1 and between 900 and 1000 cm−1 is due to the silicon substrate. The sharp feature at 1332 cm−1 is from the lattice of the diamond nanoparticles. The broad peak at cm−1 is a signature of surface graphitization in diamond. (b) shows a cut of the lattice displacement field and strain state in the center of Crystal 1 at 750°. The initial state of Crystal 1 is shown in (c) along with a black outline of the final morphology of the crystal observed at 750 °C.
Raman spectra of two control samples (TEOS-treated ND and bare Si) and one sample substrate after in situ BCDI imaging (post-anneal ND) measured with 780 nm excitation are shown in (a). The feature at 520 cm−1 and between 900 and 1000 cm−1 is due to the silicon substrate. The sharp feature at 1332 cm−1 is from the lattice of the diamond nanoparticles. The broad peak at cm−1 is a signature of surface graphitization in diamond. (b) shows a cut of the lattice displacement field and strain state in the center of Crystal 1 at 750°. The initial state of Crystal 1 is shown in (c) along with a black outline of the final morphology of the crystal observed at 750 °C.
Though the Raman spectra were the ensemble measurement of thousands of diamond particles, the picture of diamond surface graphitization during annealing is consistent with a reduction in the Bragg diffracting volume of Crystal 1 measured with BCDI. Carbon that converts to graphite at the surface of a nanoparticle no longer shares the same lattice structure as diamond. Therefore, the graphite at the surface will not diffract into the measured diamond 111 Bragg peak, and the Bragg diffracting volume will shrink as graphitization proceeds.
In Crystal 1, surface etching via graphitization likely contributed to the observed structural homogenization. Figures 5(b) and 5(c) show a cut through the center of Crystal 1 at 750 °C, as compared to its initial state. The outline of the particle at high temperature (black contour in Figure 5(c)) is superimposed on the images of the initial lattice distortion and strain state in order to highlight the volume change of diamond. The volume of the nanodiamond that was etched away contained regions with relatively high levels of strain, and its removal aided in homogenizing the lattice structure.
Additionally, within the outline of Crystal 1 at 750 °C, we observed a decrease in the magnitude of the lattice displacement field and strain, especially in more highly distorted regions. One possible mechanism for this is vacancy diffusion that leads to improvements in crystal quality via recombination of vacancies with interstitial defects or vacancy annihilation at the surface. In this crystal, we did not observe any dislocations (line defects), which can easily be identified with BCDI.20 Thus, the mechanisms for strain relaxation in this particle are twofold: (1) exfoliation of strained exterior volumes of the diamond via graphitization and (2) a homogenization of the lattice structure within the remaining crystal volume by defect annihilation.
The graphitization and strain annealing observed in Crystal 1 were not evident in Crystals 2 and 3. We explain this observation by proposing that the thermal anneal applied in this study was sufficient to activate graphitization and enable vacancy annihilation only in highly strained volumes of material that contain higher point defect populations. Inducing structural homogenization in more perfect crystals (as in Crystals 2 and 3) may require longer annealing times and/or higher temperatures. In addition, we note that at 750 °C, the FWHM of the strain distribution of Crystal 1 dropped no further than those of Crystals 2 and 3, possibly suggesting a limit of “healing” of the crystal via annealing under the conditions of this study.
In conclusion, we presented experimental in situ observations of changes in morphology and internal strain state of commercial diamond nanocrystals during high-temperature annealing in a helium atmosphere, and we find that improvements in the homogeneity of the crystal lattice depend on the initial strain state. This work paves the way for developing efficient methods by which we optimize the structure of commercial nanodiamonds such that their internal strain is reduced to suitable levels for NV sensing applications —a critical step towards for the transfer of NV technology towards large-scale applications. Additionally, in situ BCDI measurements of this kind may be applied to other strain sensitive defects in diamond24 or similar challenges in other nanoparticle systems for quantum sensing such as SiC.
BCDI measurements and sample preparation of nanocrystalline diamond were supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. Raman measurements were supported by the Air Force Office of Scientific Research and by the Army Research Office OSU-MURI (Ohio State University–Multidisciplinary University Research Initiative). C.P.A. was supported by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program. We made use of shared Raman spectroscopy facilities supported by the NSF MRSEC Program under DMR-0820054. Use of the Advanced Photon Source was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. The authors thank P. C. Jerger, P. J. Mintun, C. G. Yale, and B. Zhou for useful discussion.
