Nanodiamond

by Oliver A Williams (Editor)

Overview

The exceptional mechanical, optical, surface and biocompatibility properties of nanodiamond have gained it much interest. Exhibiting the outstanding bulk properties of diamond at the nanoscale in the form of a film or small particle makes it an inexpensive alternative for many applications.

Nanodiamond is the first comprehensive book on the subject. The book reviews the state of the art of nanodiamond films and particles covering the fundamentals of growth, purification and spectroscopy and some of its diverse applications such as MEMS, drug delivery and biomarkers and biosensing. Specific chapters include the theory of nanodiamond, diamond nucleation, low temperature growth, diamond nanowires, electrochemistry of nanodiamond, nanodiamond flexible implants, and cell labelling with nanodiamond particles.

Edited by a leading expert in nanodiamonds, this is the perfect resource for those new to, and active in, nanodiamond research and those interested in its applications.

Product Details

ISBN-13:	9781849736398
Publisher:	RSC
Publication date:	03/18/2014
Series:	Nanoscience & Nanotechnology Series , #31
Pages:	552
Product dimensions:	6.15(w) x 9.20(h) x (d)

About the Author

Oliver A. Williams received his PhD on the electronic properties of diamond from the UniversityCollege London, UK. He then moved to the Argonne National Laboratory, USA to work on nanocrystalline diamond. Following this he worked for the Institute for Materials Research in Belgium, an affiliated lab of IMEC vzw and then received the Fraunhofer Attract award at the Fraunhofer Institute for Applied Solid State Research in Freiburg to develop MEMS structures from nanocrystalline diamond before moving to Cardiff Universityas a Reader in Experimental Physics focusing on the growth and applications of nanodiamond.

Read an Excerpt

Nanodiamond

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By Oliver Williams

The Royal Society of Chemistry

Copyright © 2014 The Royal Society of Chemistry
All rights reserved.
ISBN: 978-1-84973-639-8

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CHAPTER 1

Distribution, Diffusion and Concentration of Defects in Colloidal Diamond

AMANDA S. BARNARD

CSIRO Materials Science and Engineering, 343 Royal Parade, Parkville, Victoria, 3052, Australia

Email: [e-mail]

1.1 Introduction

It is often convenient to think of nanodiamond as pure, and free of defects, but this is not necessarily realistic. Nanodiamonds can (and do) contain a variety of defects, whether we want them there or not. These include intrinsic point defects, such as lattice vacancies, and incidental impurities, such as nitrogen, which are a result of the synthesis and/or purification processes. In general, defects are always thermodynamically unstable, but the relative (in)stability of these defects, and hence the probability that they can be removed from the particle, can depend on the location of the defect within the particle. This is quite different to the case of bulk diamond, where all lattice sites are geometrically (and, therefore, energetically) equivalent.

There are of course, types of defects that are very useful, and are therefore introduced deliberately. Well known examples are the p-type or n-type dopants used in electronic applications, but there are other types of useful point defects that are not dopants. Collectively these are often referred to as "functional defects" (as they provide some functionality), and include the range of optically active defects and colour centres. The most simple defect in diamond is a single, neutral lattice vacancy, which is commonly referred to as a GR1 defect (where GR stands for general radiation). Vacancies are omnipresent in diamond, and so this defect has been extensively studied in various states.

Since nitrogen is also widespread in diamond, numerous studies have also focused on characterising and understanding the properties of different types of N-related defects, including the single substitutional nitrogen impurity, known as the C-centre. However, arguably, the most widely studied defect in nanocrystalline diamond is the paramagnetic nitrogen–vacancy complex (N–V), which forms when a vacancy (GR1) migrates to bind with a C-centre. The energy-level structure of the negatively charged N–V defect results in emissions characterised by a narrow zero-phonon line (ZPL) at 637 nm (the neutral N–V centre has a zero-phonon line at 575 nm) accompanied by a wide-structured side band of lower energy due to transition from the same excited state, but with formation of phonons localised on the defect. The optical emission from N–V centres in diamond nanocrystals has been shown to strongly depend on the crystal size, and the charge state is related to the temperature.

Defects, such as GR1 centres and N–V centres, are mobile within diamond, and may migrate if a driving force is sufficient to overcome the kinetic energy barriers associated with diffusion. The diffusion of an N–V centre is vacancy assisted, and the rate-limiting step is the C–N exchange energy. During this migration, if an N–V centre interacts with another single nitrogen atom (or a migrating vacancy interacts with a nitrogen dimer, known as an A-centre), then an H3 centre is formed. The H3 centre consists of two N atoms surrounding a vacancy. It is one of the most studied in diamond, and may be formed abundantly by irradiation with 1 to 2 MeV electrons to doses of 1018–1020 electrons cm-2, and annealing at 1200 K for 20 h in a vacuum. If we continue this logical progression, then if an N–V centre migrates to an A-centre, or alternatively an H3 centre migrates to a C-centre (which is far less likely), then an N3 centre may be formed. The N3 centre consists of three nitrogen atoms surrounding a vacancy (whereas a vacancy completely surrounded by four N atoms is known as a B-centre). Both the H3 and N3 provide photoluminescence and cathodoluminescence, are known to be thermally stable, and exhibit high quantum efficiency up to temperatures in excess of 500 K.

A summary of the point group symmetry, zero phonon line (ZPL), central wavelength (λ0) and photoacoustic imaging quantum yield for the GR1, N–V, H3 and N3 defects is provided in Table 1.1, where we can see that the quantum yield for each of these defects is quite different. The quantum yield is defined as the number of photons emitted via photoluminescence versus the number of photons absorbed during excitation. The N–V and H3 defects are the most efficient, which somewhat explains their popularity in the scientific community. In addition to the quantum yield the wavelength itself is very important as it determines the penetration depth of the irradiation. The penetration depth for 532 nm light is 0.6 mm, for 670 nm is 2.4 mm, and for 750 nm is 2.6 mm. This is insufficient to penetrate human skin, irrespective of the quantum yield.

To be able to effectively exploit any of these functional defects, we need to draw upon a reliable understanding of the thermochemical stability of the defect within the host particle, in addition to the photostability. The optical properties of each of these defects are intrinsically linked to the physical structure of the defect within the lattice as this determines the energy levels of the excited states. In conventional experiments this can be difficult to probe as information on the physical (or structural) stability must be extracted indirectly by measuring the optical spectra, and if the emission decays, blinks or disappears any underlying physiochemical explanations will be obscured. In contrast, by using computer simulations the stability and properties of different configurations can be accessed directly. It is possible to establish the structure of a defect definitively, irrespective of the location within the particle, and the thermochemical stability can be determined unambiguously.

In this chapter a collection of computational studies examining the stability of a range of different defects will be briefly reviewed, with a focus on how the stability of the host nanodiamond affects the stability of the defect.

1.2 Defect-free Diamond Nanoparticles

Before beginning an exploration of defective diamond nanoparticles, it is firstly important to select the right host structures to use, and develop a general understanding of issues related to other "defects" intrinsic to diamond nanoparticles: the surfaces, edges, and corners.

To determine the lowest energy shape for nanodiamonds enclosed by low-index surfaces, Barnard and Sternberg used the density functional-based tight-binding method with self-consistent charges (SCC-DFTB) to simulate a set of nineteen different diamond nanoparticle structures ranging from 1 nm to 3.3 nm in diameter (142 to 1798 atoms). This method was selected as it had previously been shown to provide good agreement with higher level quantum chemical methods for all-carbon systems, and is capable of accommodating sizes much larger than those accessible to the purely first principles methods (mentioned above). Within this structure set there were four subsets consisting of octahedral, truncated octahedral, cuboctahedral, and cuboid shapes, respectively. The complete octahedral subset contains C286, C455, C680, C969, C1330, and C1771 structures enclosed entirely (100%) with {111} surfaces. The truncated octahedral subset contains C268, C548, C837, C1198, and C1639 structures enclosed with ~76% {111} surfaces and ~24% {100} surfaces. The cuboctahedral subset contains C142, C323, C660, and C1276 structures enclosed with ~36% {111} surfaces and ~64% {100} surfaces. The final subset of cuboid structures contains C259, C712, C881, and C1798 with ~34% {100} surfaces and ~66% {110} surfaces. All of the structures were fully relaxed using the conjugate gradient scheme to minimise the total energy.

In this article the authors systematically modelled the evolution of the core–shell structure for octahedral, truncated octahedral, cuboctahedral, and cuboid shapes over this size range, including explicit examination of the fraction of sp3, sp2+x and sp2-bonded atoms, and their location. This can be seen in the figure plate provided in Figure 1.1, which is based on a combination of visualisation modes, employing a simple ball method for the sp2 and sp2+x hybridised atoms (where 0 < x< 1), and the polyhedron method for the tetrahedrally coordinated sp hybridised atoms (each of which is surrounded by a coordination tetrahedron spanned by the four neighbours of the central atom). In this figure the diamond-like regions appear as collections of interpenetrating tetrahedra, and sp2 and sp2+x atoms participating in the fullerenic (or graphitic) regions appear as simple spheres decorating the outer surface of the diamond-like regions (connecting bonds not shown). This was designed to make the shape and extent of the diamond-like cores easily discernible, at the expense of detail in the shell region (which is more prevalently displayed in other works).

Based on these results it was determined that there is a relationship between the size of the particle and the fraction of diamond-like and/or fullerenic carbon, but that it depended significantly on the overall shape. In shapes when there is greater than 76% {111} surface area, nanodiamonds are likely to prefer a core–shell (bucky-diamond) structure, and the core/shell ratio depends on the overall size. The authors noted a distinct cross-over between predominately sp2 and predominantly sp3 structures at ~1100 atoms. If there is less than 76% {111} surface area, particles are likely to be stable in the diamond structure with a thin (either single or double layer) shell down to approximately 600 atoms (which is discussed below). It was presumed that a type of confinement by multiple layers is responsible for inhibiting relaxation of sp3-bonded atoms into a sp2-bonded shell, and promoting the stability of diamond-like cores at the centre of the structures with a high fraction of {111} surface area.

The reconstruction of the {111} surfaces on smaller (<2.5 nm) nanodiamonds lowers the surface energy (as the anti-bonding electrons become part of the aromatic character of the fullerenic shell), but introduces considerable surface stress. This was explicitly investigated by Barnard et al. using a simple thermodynamic theory to compare nanodiamonds and fullerenes directly. By treating only dehydrogenated nanodiamonds (i.e., nanodiamond structures consisting of mostly [sp.sup.3]-bonded atoms as opposed to bucky-diamond), a direct comparison with fullerenes was made. The method was based on the enthalpy of formation as a function of size, expressed in terms of the bond energies for diamond-like and fullerenic particles, the surface dangling bond energy, the number of carbon atoms, the number of dangling bonds on the surface of the particle, and the standard heat of formation of carbon at T = 298.15 K.

In the case of fullerenes the closed shell eliminates the dependence on the effective surface-to-volume ratio and, therefore, the size dependence. Thus, a term for the strain energy that vanishes in the graphene limit was added by first making the assumption that a fullerene may be approximated as a homogeneous and isotropic elastic sphere. This was derived by considering the bending and stretching of a suitable elastic sheet in terms of the bending energy per unit area, the bending modulus of the sheet, and the mean radius of curvature. A spherical model was assumed and an expression for the strain energy per carbon atom for fullerenes that is proportional to the inverse of the square of the radius of curvature was derived. Using this model the cross-over in the enthalpy of formation of dehydrogenated (stable) nanodiamond crystals and fullerenes was found to be at ~1100 atoms, which is approximately equivalent to cubic nanodiamond crystals of 1.9 nm in diameter. An important point in this work was the selection of the chemical reservoir and the frame of reference. The model used a reservoir of free (isolated) C atoms, and included the formation enthalpy of a dangling bond so that the nanoparticles were assumed to be in mutual equilibrium with a continuous diamond or graphitic surface, not the bulk.

To investigate the cases where carbon nanoparticles may contain both sp2 and sp3 bonding simultaneously, Barnard et al. addressed the stability of multi-shell carbon nanoparticles using the same model described above for comparing the stability of nanodiamonds and fullerenes, and applied it to bucky-diamond and carbon onions. The onions were treated as nested fullerenes by adding a term for the van der Waals attraction (0.056 eV) to the expression used to describe fullerenes. The bucky-diamonds were treated in the same manner as nanodiamonds, although, obviously, the dangling-bond-to-carbon-atom ratio is different for nanodiamonds and bucky-diamonds (of similar diameter) due to the formation of the graphitised fullerenic outer shells.

The enthalpy of formation (as a function of particle size) for bucky-diamonds and carbon onions was calculated, and extrapolated along with the nanodiamond and fullerene results mentioned above. From this comparison three main conclusions were drawn. First, the [sp.sup.2]-bonded onion and fullerene results were indistinguishable (within uncertainties) below approximately 2000 atoms. Second, the enthalpy of formation of a bucky-diamond is more akin to carbon onions than to nanodiamonds. Finally, in the region from ~500 to ~1850 atoms the results predicted that a thermodynamic coexistence region is formed, within which bucky-diamonds coexist (within uncertainties) with the other carbon nanoparticles. This region was then further broken into three sub-regions. From ~1.4 nm to 1.7 nm the enthalpy of formation of bucky-diamonds was found to be indistinguishable from that of fullerenes (within uncertainties), although carbon onions represent the most stable form of nanocarbon. Between ~1.7 nm and 2.0 nm bucky-diamonds and carbon onions coexist (within uncertainties), and bucky-diamond was found to coexist with nanodiamond (within uncertainties) between ~2.0 nm and 2.2 nm. Further, the intersection of the bucky-diamonds and carbon onions stability was found to be very close to the intersection for nanodiamonds and fullerenes at ~1100 atoms, suggesting that at approximately 1100 atoms an sp3-bonded core becomes more favourable than an sp2-bonded core, irrespective of surface structure. Once again, the model used in this study assumed a reservoir of free (isolated) C atoms, and the nanoparticles were assumed to be in mutual equilibrium with a continuous diamond or graphitic surface.

As we can see from these examples, advances have been made in understanding the relative stability of sp2- and sp3-bonded particles at the nanoscale, and the basic structure of diamond nanoparticles has been established. These studies have clearly identified the two important size regimes, where (depending upon the phases under consideration) sp2-to-sp3 or sp3-to-sp2 phase transitions may be readily expected. In the case of larger particles the cross-over in stability between nanodiamond and nanographite may be expected at around 5 nm to 10 nm in diameter, and for smaller particles, the crossover between nanodiamond and fullerenic particles may be expected at 1.5 nm to 2 nm. They have also identified the lowest energy morphology (the truncated octahedron) in this size regime.

Based on these results, it is acceptable to use a single, model nanodiamond for exploring the stability of different point defects, provided it is a truncated octahedral (and, therefore, provides a range of both diamond-like and graphitised facets, if unpassivated), and sufficiently large to transcend the quantum confinement regime and (at least) occupy the coexistence regime from ~500 to ~1850 atoms. It is important that the model structure meets these criteria so as to ensure that all of the possible local bonding environments are included because the stability of a given defect will be sensitive to these issues.

1.3 Modelling Defects in Diamond Nanoparticles

In the following sections the thermodynamic stability (potential energy surface) and kinetic stability (probability of observation) will be reviewed for the GR1, N–V0, H3, and N3 defects in model nanodiamonds. The particles used in the studies reviewed in this chapter are a C837 truncated octahedral bucky-diamond and a hydrogenated C837H252 truncated octahedral nanodiamond, each displaying six {100} facets and eight {111} facets.

All of the calculations were originally performed using SCC-DFTB, which is a two-centre approach to density functional theory (DFT), where the Kohn–Sham density functional is expanded to second order around a reference electron density. In this approach the reference density is obtained from self-consistent density functional calculations of weakly confined neutral atoms, and the confinement potential is optimised to anticipate the charge density and effective potential in molecules and solids. A minimal valence basis is established and one- and two-centre tight-binding matrix elements are explicitly calculated within DFT. A universal short-range repulsive potential accounts for double counting terms in the Coulomb and exchange-correlation contributions, as well as the internuclear repulsion, and self-consistency is included at the level of Mulliken charges. This method was selected in these studies as it is more computationally efficient than DFT when such a large number of individual calculations are required.

(Continues...)

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Excerpted from Nanodiamond by Oliver Williams. Copyright © 2014 The Royal Society of Chemistry. Excerpted by permission of The Royal Society of Chemistry.
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Table of Contents

Distribution, Diffusion and Concentration of Defects in Colloidal Diamond;
Detonation Nanodiamonds: Synthesis, Properties and Applications;
The Chemistry of Nanodiamond;
Nanodiamond Purification;
Pure Nanodiamonds Produced by Laser Assisted Technique;
Electrochemistry of Nanodiamond Particles;
Nanodiamonds for Drug Delivery and Diagnostics;
Biophysical Interaction of Nanodiamonds with Biological Entities in-vivo;
Neuron Growth on Nanodiamond;
Diamond Nucleation and Seeding Techniques: Two Complementary Strategies for Growth of Ultra-Thin Diamond Film;
The Microstructures of Polycrystalline Diamond, Ballas and Nanocrytalline Diamond;
Low-Temperature Growth of Nanocrystalline Diamond Films in Surface-Wave Plasma;
Low Temperature Diamond Growth;
p-Type and n-Type Conductivity in Nanodiamond Films;
Electrochemistry of Nanocrystalline and Microcrystalline Diamond;
Superconductivity in Nanostructured Boron Doped Diamond and its Application to Device Fabrication;
Diamond Nano-Electro-Mechanical Systems;
Diamond Based Resonators for Chemical Detection ;
All-Diamond Electrochemical Devices: Fabrication, Properties and Applications;
Electron Field Emission from Diamond;