Burning and graphitization of optically levitated nanodiamonds in vacuum

A nitrogen-vacancy (NV−) centre in a nanodiamond, levitated in high vacuum, has recently been proposed as a probe for demonstrating mesoscopic centre-of-mass superpositions and for testing quantum gravity. Here, we study the behaviour of optically levitated nanodiamonds containing NV− centres at sub-atmospheric pressures and show that while they burn in air, this can be prevented by replacing the air with nitrogen. However, in nitrogen the nanodiamonds graphitize below ≈10 mB. Exploiting the Brownian motion of a levitated nanodiamond, we extract its internal temperature (Ti) and find that it would be detrimental to the NV− centre’s spin coherence time. These values of Ti make it clear that the diamond is not melting, contradicting a recent suggestion. Additionally, using the measured damping rate of a levitated nanoparticle at a given pressure, we propose a new way of determining its size.

Scientific RepoRts | 6:21633 | DOI: 10.1038/srep21633 a nitrogen environment down to 10 mB, but beyond that, it graphitizes. The source of heating is believed to be the absorption of 1064 nm trapping laser light by the impurities in diamond and the amorphous carbon on the surface. Lastly, exploiting the measured damping rate of a levitated object, we present a new way of determining its size in situ. Figure 1a shows a schematic of our experimental setup where we use a 0.80 numerical aperture (NA) microscope objective to focus a 1064 nm laser beam into a diffraction limited spot. The force resulting from the electric field gradient forms the basis of our dipole trap 20 . The balanced photodiode visible in Fig. 1a provides a voltage signal generated from the interference between the directly transmitted trapping laser light and the oscillator's position dependent scattered electromagnetic radiation 20 . Performing a Fourier transform on this voltage signal provides the measured spectral information as well as the damping rate of a levitated nanoparticle. We use this spectral information and damping rate to retrieve T i and the size of a nanodiamond.

Experimental Setup
In the regime where the oscillation amplitude of a trapped particle is small, the trapping potential of an optical tweezer can be approximated as harmonic 20 . Under this condition, the motion of a levitated object can be expressed as where x is the displacement of a trapped particle from the centre of the trap along the x-axis. M and γ CM , respectively, are the mass and the damping rate of a trapped particle while ω κ = /M 0 is the trap frequency and κ is the spring constant of the trap 20 . f(t) is a Gaussian random force exerted by the gas molecules on a trapped particle where k B is the Boltzmann constant, T CM is the CM temperature of a trapped particle, and δ(t 2 − t 1 ) is the Dirac delta function 20 . Similar analyses for the remaining two axes are also valid. After performing a Fourier transform and rearrangement, the power spectral density (PSD) of (1) can be written as We fit (2) with the experimental data. Figure 1b shows the PSDs corresponding to the measured voltage signals from a levitated nanodiamond for different trapping powers along with the respective fits (solid lines) of equation (2) at 20 mB. For the purpose of comparison, in Fig. 1b we have also included the relevant theoretical PSDs (dashed grey lines). In plotting the theoretical PSDs we have assumed that all parameters are identical to the measured PSDs except T CM which has been taken equal to 300 K. Figure 1c demonstrates the measured damping rate as a function of pressure at a constant trapping power of 180 mW. Later, we use this damping rate to find the size of a nanoparticle.

Levitated Nanodiamonds in Vacuum
To study the behaviour of diamond below atmospheric pressure, after levitating a nanodiamond with the minimum possible trapping power (180 mW), we gradually take it to different levels of vacuum whilst continuously monitoring its scattering intensity (size) using a camera. Figure 2a shows a typical plot of scattering intensity versus pressure (pink circles) from a levitated nanodiamond (for more data points see supplementary information Fig. S1). It can be observed that as we evacuate the trapping chamber, the scattering intensity diminishes: a levitated nanodiamond shrinks in size as the pressure is reduced. We attribute this reduction in size to the removal of physisorbed water and organic substances such as the carboxyl groups (nanodiamonds as obtained from the supplier are in water and are coated with carboxyl groups for stabilization) present on the surface of nanodiamonds down to 20 mB where the temperature reaches ≈ 450 K (see Fig. 3). Physisorbed water and organic impurities normally disappear 21 at or below 473 K. This is further confirmed when we keep a levitated nanodiamond in a vacuum of less than 10 mB for an extended period of time (about an hour) and take it to back to atmospheric pressure (red squares in Fig. 2a) and bring it down to the low pressures again. In the second round of evacuation, the scattering intensity remains constant down to 10 mB. This unaltered scattering intensity in the second round of evacuation indicates the absence of substances which evaporate/burn at relatively lower temperatures.
The reduction in size below 10 mB is attributed to the burning of amorphous carbon or diamond. Amorphous carbon is generally found as an outer layer on the surface of nanodiamonds [21][22][23] . The burning temperature of amorphous carbon 21 at atmospheric pressure varies between 573-723 K while the oxidation temperature of nanodiamonds 21,22,24 ranges from 723-769 K. Also, the exact oxidation temperature of nanodiamonds depend on the surface quality, the crystallographic faces, and the densities of impurities in nanodiamonds 21,22,24 . To confirm the presence of amorphous carbon as well as diamond in the nanoparticles that we have used in our experiments, we performed Raman spectroscopy using a 785 nm laser. At this wavelength amorphous carbon is more sensitive than diamond 25 . Figure 2b presents the relevant data. This figure clearly shows the presence of amorphous carbon and diamond peaked at ≈ 1400 cm −1 and at ≈ 1335 cm −1 , respectively 23,[25][26][27] . Given that amorphous carbon is a strongly absorbing material [28][29][30][31] , trapping light (1064 nm) absorption and hence raised T i and consequent burning in an air environment is highly probable. This burning of nanodiamond in air can potentially be a major hurdle in applications where vacuum is inevitable.
Based on the idea that an oxygen-less environment may be a cure to this problem, we have studied the behaviour of levitated nanodiamonds in a nitrogen environment. This is shown in Fig. 2a as blue crosses for a constant Figure 2. (a) Normalized scattering intensity as a function of pressure. Pink circles are for a nanodiamond as we take it to low pressures from atmospheric conditions for the first time and red squares are for the same nanodiamond but when we take it back to atmospheric pressure after keeping it at ≤ 10 mB for about an hour. Similarly, green dots are for the same nanodiamond used in the previous two steps but when we take it to low pressures for the 2 nd time from atmospheric pressure. Trapping power was 180 mW. Above 20 mB physisorbed water/organic substances evaporate/burn while below this pressure diamond or amorphous carbon burns. In the second round of evacuation a nanodiamond maintains its size down to ≈ 10 mB due to the absence of water and the organic substances on the surface. Blues crosses are the scattering intensities of a nanodiamond in a nitrogen environment. Trapping power was ≈ 300 mW. Down to 10 mB its size remains unchanged while below this pressure, due to elevated temperature, it graphitizes. (b) Raman spectrum of nanodiamonds under 785 nm laser excitation.
trapping power of 300 mW. It can be observed that at pressures > 10 mB the scattering intensity hence the size of a nanodiamond remains unchanged; even though temperature is quite high (see Fig. 3). This is due to the fact that for burning to occur, a nanodiamond requires oxygen which is absent in a nitrogen rich environment. However, if the pressure is reduced below 10 mB, the scattering intensity of the nanodiamond gradually diminishes. Given that there is almost no oxygen in the chamber and the reduced pressure means less cooling due to gas molecules and hence higher internal temperature, we believe this is the onset of graphitization of the nanodiamond. At atmospheric pressure graphitization of nanodiamonds starts in the temperature range 943-1073 K and depends on the surface quality of nanodiamonds 24,26 . Since we are operating at sub-atmospheric pressures, graphitization at a lower temperature is most likely to happen. Lastly, it is noteworthy that irrespective of an air or a nitrogen environment, below 5 mB levitated nanodiamonds rapidly shrink in size and by ≈ 2 mB completely disappear from the trap.

Internal Temperature of a Levitated Nanodiamond
Even though the nanodiamonds that we use in our experiments contain NV − centres, most of them do not fluoresce upon levitation -consistent with the results of a previous study 32 by Neukirch et al. It has been shown that the resonant frequency of optically-detected magnetic resonance from the fluorescing levitated nanodiamonds can reveal the internal temperature 32 , but in this article we instead use a Brownian motion based temperature determination technique developed by Millen et al. in ref. 33. According to this technique, the interaction between two thermal baths -one consisting of the impinging gas molecules while the other is composed of the emerging gas molecules, is mediated by a levitated object whose internal temperature is higher than that of the impinging gas molecules. The temperature of the impinging gas molecules is T imp while that of the emerging gas molecules is T em . T CM can be expressed as ( ) where γ imp and γ em are the damping rates due to the impinging and emerging gas molecules, respectively 33 . Using this methodology and assuming a full accommodation (T i = T em ), in Fig. 3 we present T i obtained from the same nanodiamond used in Fig. 2 as a function of trapping power in air (blue circles) at 20 mB. In measuring T i we have assumed that a levitated nanodiamond is at room temperature at ≈ 150 mB (see supplementary info Fig. S2). This assumption is also supported by the optically detected magnetic resonance based temperature measurements performed on nanodiamonds by Hoang et al. using a similar setup to ours 34 . Also, since fitting uncertainties increase with the increasing pressure, T i has been plotted as a function of trapping power at a constant pressure and it was measured during the 2 nd round of evacuation at which a levitated nanodiamond maintains its size. Constancy in size/mass is a requirement of the PSD analysis. From Fig. 3 one can see that the internal temperature reaches ≈ 750 K at 380 mW of trapping power in air. This is well within the reported burning temperature of amorphous carbon or diamond 21,22,24 . In Fig. 3 we have also included T i s obtained from a levitated nanodiamond submerged in a nitrogen environment. In this case T i reaches approximately 800 K at the maximum trapping power. At pressures below 20 mB, temperatures are expected to be higher given that the cooling due to gas molecules becomes less effective while the absorption remains constant. It is noteworthy that the fluorescence from NV − centres in diamond decreases significantly at temperatures beyond 550 K and by 700 K it reduces to 20% of the room temperature value 13 . Also, at T i = 700 K, NV − centre's fluorescence lifetime and the contrast between electron spin resonances reduce below 20% of the room temperature value 13 . At a temperature above 625 K, the spin coherence time of the NV − centre decreases as well 13 . Furthermore, the highest temperature that we have measured here, using trapping powers higher than those have been used by Neukirch et al. 32 , rules out the possibility of melting diamond as suggested in ref. 32. Diamond usually melts at temperatures ≥ 4000 K and requires pressure above atmospheric pressure 35 . A slight difference between the temperatures at a constant power such as at 300 mW in Fig. 3 between different environments can be attributed to the variation in surface qualities and the densities of impurities in different nanodiamonds 24,36 . Additionally, it has been demonstrated that bigger particles heat up rapidly compared to smaller particles under the same experimental conditions 33 . As a result, variation in the internal temperatures is expected unless all the attributes of different particles are identical. However, due to the inherent nature of levitated experiments, it is difficult to levitate particles with the same attributes in different runs of an experiment. This is further worsened by the polydispersity of nanoparticles. For example, the average size of the nanodiamonds that we have used in our experiment is quoted to be 100 nm by the manufacturer. A representative scanning electron microscope (SEM) image of this nanodiamond is shown in Fig. 4a. Nanodiamonds from a few tens of nanometers to a few hundred nanometers are visible. Consequently, trapping different sizes of nanodiamonds in different runs of an experiment is possible. Nevertheless, to be consistent throughout the experiment, we levitate nanodiamonds of similar size by monitoring their scattering intensities. Also, next we present a way of determining the size of an individual levitated object from the measured damping rate (γ CM ) that it encounters while oscillating inside the trap. For the purpose of following calculations, we assume that a levitated nanodiamond is of spherical shape.

Determination of the Size of a Levitated Nanodiamond
The effective damping rate as shown in Fig. 1c can be expressed as γ CM = γ imp + γ em , where γ imp and γ em are the damping rates due to the impinging and emerging gas molecules, respectively 33  particle, the number density of gas molecules at pressure P, molecular mass, and the mean thermal velocity of impinging gas molecules, respectively 33 . N can further be expressed as N = N 0 P/P 0 , where N 0 is the number of gas molecules per cubic meter at atmospheric conditions and P 0 is the atmospheric pressure. On substitutions of various terms, one can express R as where M has been expressed as π ρ R 4 3 3 and ρ is the mass density of diamond. Given that the levitated nanodiamonds burn, equation (3) gives the ultimate size of a nanodiamond for which we previously found temperatures. That is, it is the size of the nanodiamond after the first round of evacuation. The actual size of a nanodiamond before burning can be found using scattering theory. The scattering intensity of a Rayleigh particle λ ( )  R is given by =   (3) and (4) of the trapped nanodiamond for which the internal temperatures were found in Fig. 3 in air as a function of pressure. minimum trapping power of 180 mW, Fig. 4b shows the radius of the trapped nanodiamond at various pressures in air. It can be observed that when the nanodiamond was initially trapped at atmospheric pressure, its diameter was ≈ 41 nm. Similarly, for the nitrogen case using the same parameters except γ cm = 2.22 × 10 5 radian and T i = 650 K, we get the ultimate diameter of the nanodiamond is ≈ 38 nm. Given the uncertainty in the shape of nanodiamonds as visible in Fig. 4a, the nanodiamonds that we have used to find T i s in air and nitrogen ambients are of similar size. This is also in good agreement with the technique (initial scattering intensities) that we have utilized to trap similar size nanodiamonds in different runs of an experiment. Furthermore, even though the actual dimensions of a nanodiamond will be different from R due to its asymmetric shape, the estimated size provided by our model is well within the distribution visible in the SEM image (Fig. 4a). Lastly, we believe that the method developed here for the determination of size of an individual particle can be used in any levitated experiment.

Conclusions
We have demonstrated that nanodiamonds burn in air while they graphitize in a nitrogen ambient by absorbing trapping laser (1064 nm) light as the cooling due to gas molecules becomes less effective with decreasing pressure. We believe that amorphous carbon, a strongly absorbing material, present on the surface of nanodiamonds is a key reason for this. We also think that purer nanodiamonds instead of the currently available HPHT synthesized nanodiamonds can be a cure to this problem. Our Brownian motion based analysis has shown that the internal temperature of a levitated nanodiamond can reach up to 800 K. This rules out the possibility of melting diamond which requires 35 a temperature ≥ 4000 K. Lastly, exploiting the damping rate that a particle encounters while in motion, we have developed a new way of determining its size. We consider that this new technique will be useful in present and future levitated experiments where the traditional electron microscopy and dynamic light scattering based size determinations are not suitable.

Methods
Nanodiamonds containing ≈ 500 NV − centres (ND-NV-100 nm) were bought from Adamas Nanotechnology Inc, USA. The average size of the nanodiamonds quoted by the manufacturer is 100 nm. To prevent agglomeration we sonicate as received nanodiamonds for ≈ 10 minutes in an ultrasonic bath and then put them into a nebulizer and inject them into the trapping chamber. The trapping chamber is continuously monitored by a CMOS camera (Thorlabs Inc). Once a nanodiamond is trapped, the trapping chamber is evacuated to study the behaviour of nanodiamonds in vacuum. Power spectral density data were collected using a balanced photodiode (Thorlabs Inc) and a Picoscope oscilloscope (Pico Technology, UK). In the case of nanodiamonds immersed in nitrogen, the trapping chamber was purged with nitrogen fifteen times.