In this chapter, we will discuss the key features of nanodiamonds that are relevant to the development of fluorescent nanodiamonds (FNDs) and their many uses in biotechnology and beyond. Up till now, we have surveyed nanotechnology in previous chapters starting with its historical development and focusing, in particular, on the nanocarbon materials. With a general introduction to nanodiamonds (Chapter 2), we have learned some methods commonly used to prepare man‐made diamonds and the fundamental properties shared by all diamonds and nanodiamonds alike. In this and the following two chapters, we are about to find out that nanodiamonds can glow (Chapter 3), support (Chapter 4), and is safe to use (Chapter 5). These unique features have made nanodiamonds a superior material for a fast‐growing list of applications at present time and in the coming future.

First comes an optical property that puts a touch of color on diamond. After all, who can turn away from the speckles of a diamond with an irresistible color destined to capture our hearts? It is only fitting to start with color centers in diamond.

Color centers are crystal defects that absorb light in a spectral region where the crystal itself has no absorption [1]. The term “color center” is derived from the German word Farbenzentren, which was first discovered in alkali halide crystals by Pohl and coworkers in the 1930s [2]. It has later been confirmed both experimentally and theoretically that the Farbenzentren (or F‐center) is a crystalline vacancy with captured unpaired electron(s) that absorbs light in the visible region, thus giving various colors to the crystals. Similar to the F‐centers in alkali halides, color centers can be found in diamond as well [3], although their formation occurs under far more extreme conditions due to the chemical inertness and mechanical rigidity of the material (Chapter 2). This chapter begins with an introduction to the optical properties of diamond, followed by a brief review of the history of diamond coloration by radiation damage and a comprehensive discussion of some important spectral characteristics of vacancy‐related color centers.

3.1 Nitrogen Impurities

As discussed in the previous chapter, a pure diamond is optically transparent with its transmittance extending from 225 to 2000 nm (Figure 2.2). The diamond crystal shows only infrared (IR) absorption bands at 2–7 μm resulting from two‐ and three‐phonon excitation processes [4]. The absence of one‐phonon absorption is due to the high symmetry of diamond’s crystal structure, of which C–C vibrations are IR‐inactive. Such vibrational modes, alternatively, appear as a sharp Raman scattering peak at 1332 cm⁻¹ (or 7.508 μm), serving as a fingerprint for easy identification of diamond from other carbon‐based materials [5]. Therefore, for any colored diamond, its optical absorption and emission must be contributed by impurities and structural defects in the crystal matrix.

Nitrogen is the major impurity in diamond [6]. The nitrogen concentration of diamond is typically measured by inert gas fusion analysis [7], which involves fusing the sample material in a graphite crucible at high temperatures and then determining the amount of the nitrogen gas released by a mass spectrometer. Quantitative as is, the method is destructive. IR absorption spectroscopy, on the other hand, is nondestructive and it has been applied as a tool to characterize the nitrogen concentrations [8]. Figure 3.1a presents a typical IR spectrum of type Ib bulk diamond, obtained by direct absorption methods [9]. Two prominent features are observed at 1130 and 1344 cm⁻¹ and they are attributed to the localized vibrational modes of C─N bonds [10, 11]. Studies have established the correlations between the absorption coefficients (μ in units of cm⁻¹) of these two bands and the concentration ([N⁰] in units of ppm) of neutral nitrogen atoms dispersed in diamond, giving [10–12]

(3.1)

Similarly, for type Ia bulk diamond, a prominent feature is found at 1282 cm⁻¹ (Figure 3.1b) [13], which is related to the localized vibrational modes of the –N–C–N– moieties in the N aggregates, N_A, whose concentrations can be estimated as [14]

(3.2)

In both cases, the absorption coefficient is defined as

(3.3)

where A is the measured absorbance at the specified wavenumber and L is the sample thickness (in cm).

Though useful in quantifying [N⁰] and [N_A] in bulk diamonds, Eqs. (3.1) and (3.2) are not suited for diamond powders because the sample thickness L (and, thus, absorption coefficient μ) is ill‐defined. A way to circumvent this problem is to use the two‐photon absorption band of diamond at approximately 5 μm as the internal standard (Figure 3.1) [15]. The absorption band shows a characteristic dip at 2120 cm⁻¹ and the depth of this dip is directly proportional to the effective sample thickness. Su et al. [16] have reported that the [N⁰] in type Ib diamond powders can be estimated by

(3.4)

where Δμ₁₁₃₀ is the absorption coefficient difference corresponding to the height of the hump at 1130 cm⁻¹ (the “mountain”) and Δμ₂₁₂₀ is the absorption coefficient difference between the linear line drawn across the two peaks at 2033 and 2160 cm⁻¹ and the dip at 2120 cm⁻¹ (the “valley”) (Figure 3.1). Hence, Δμ₁₁₃₀/Δμ₂₁₂₀ is the mountain/valley ratio. Similarly, for type Ia diamond, one has

(3.5)

where Δμ₁₂₈₂ is the absorption coefficient difference corresponding to the height of the peak at 1282 cm⁻¹.

The major advantage of using these modified equations is that the measured [N⁰] or [N_A] is independent of the sample thickness since it involves only relative absorbance in the calculations. Additionally, as a ratio, the result is virtually free of any baseline shift typical of every spectrum obtained experimentally. The method is readily applicable for diamond crystallites measured by diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) [17], a technique widely used to determine IR photons scattered from fine particles [18]. For instance, with DRIFTS, the nitrogen content of submillimeter diamond crystallites prepared under high‐pressure and high‐temperature conditions was successfully measured to be [N⁰] = 100–300 ppm [16], classified as type Ib diamonds. The method also confirmed that increasing the nitrogen content to more than 600 ppm could be achieved by doping the solvent catalyst with inorganic nitrogen‐containing substances in high concentrations [19].

3.2 Crystal Defects

Crystal defects are the second source responsible for diamond color. The discovery of diamond coloration through radiation damage can be traced back to the turn of the twentieth century. In 1896, French scientist Henri Becquerel accidentally discovered radioactivity while performing phosphorescence experiments with uranium salts. Inspired by this finding as well as the discovery of X‐ray by Wilhelm Röntgen in 1895, Marie and Pierre Curie continued the studies for different uranium minerals and eventually discovered two new elements, polonium (Po, Z = 84) and radium (Ra, Z = 88) in 1898. Becquerel and the Curies shared the Nobel Prize in 1903 for their work in discovering spontaneous radioactivity and the new radiation phenomena [20]. A year later, in a paper presented to the Royal Society of London, the English scientist William Crookes reported that the exposure of diamonds to radiation generated by radium bromide for several months could give the gem a bluish green to green color. The discovery, also by serendipity, had caused considerable interest and excitement in the gemological community because the color alternations were permanent, unlike painting or coating on the gems in the early days for added market value [21].

So, what has caused diamond to change color?

Radium bromide used by Crookes contains radium, which is a highly radioactive element. It is now known that all isotopes of radium are radioactive and the most stable isotope is Ra‐226 with a half‐lifetime of 1600 years [22]. The isotope slowly decays to radon, which is a stable inert gas, emitting alpha particles along with the process. Research studies by physicists during the time period between 1910 and 1940 had concluded that the color change of diamond was mainly due to the alpha radiation from radium. The color appeared to be confined to a shallow layer on the diamond’s surface. More studies of the effect found that the green or blue‐green color could be changed further to various shades of color ranging from yellow to brown by thermal annealing. It was this permanent color enhancement through irradiation combined with high‐pressure high‐temperature annealing that opened the modern era of diamond treatment. An excellent review on the historical accounts of diamond treatments has been given by Overton and Shigley [21].

Alpha particles are not the only type of radiation useful for treating diamonds. Exposure to high‐energy sources such as electrons, neutrons, protons, helium ions, or gamma rays can also change the diamond color in a similar fashion [23]. It is well understood now that the color change is due to structural damages that occur when the radiation passes through the diamond crystalline. Specifically, the penetrating particles collide with the diamond lattice, knocking off the carbon atoms from their originally occupied positions to create vacant sites in the lattice matrix. Since the vacancies can exist in both neutral and negatively charged states, they give rise to a broad range of absorption in the visible and near‐infrared regions of the spectrum, yielding a blue‐to‐green color (Figure 3.2). Subsequent heating of the irradiated diamonds above 500 °C in an inert atmosphere changes the blue green color to yellow, brownish, or other hues [21]. More details are discussed later in this chapter.

3.3 Vacancy‐Related Color Centers

3.3.1 GR1 and ND1

Systematic investigations of radiation damage in natural and synthetic diamonds were first carried out in the 1950s [24, 25]. Since then, a wealth of information has been collected through optical spectroscopy and electron paramagnetic resonance studies for the color centers [3, 26]. Nearly all radiation‐damaged diamonds show an absorption band associated with the neutral vacancy defect (cf., Figure 3.3a for the molecular structure [27]), designated as V⁰, in their ultraviolet‐visible (UV‐Vis) spectra [28]. The neutral vacancy, known as the GR1 center where GR stands for “general radiation” (Table 3.1), is one of the best characterized optical defects in diamond [8]. It has a T_d point symmetry and exhibits a narrow zero‐phonon line (ZPL) at 741 nm (or 1.673 eV) accompanied by a broad phonon sideband of a maximum around 620 nm in the UV‐Vis absorption spectrum (Figure 3.4a and b). When exposed to orange‐red light, the center emits near‐infrared photoluminescence at approximately 800 nm (Figure 3.5) [29] with a quantum yield of only 1.4% at low temperature (Table 3.2) [30]. Although GR1 is not a good chromophore for fluorescence imaging because of such a low quantum yield, it can be produced with a high number density (>100 ppm) by extensive irradiation without the need of thermal annealing. Davies [8] has provided a calibration constant that correlates the concentration ([V⁰] in cm⁻³) of the neutral vacancy and the integrated absorption coefficient (A_GR1 in cm⁻¹) of its ZPL at 80 K to be (Table 3.3):

(3.6)

Letter	Significance	Range
GR	General radiation (induced in all diamonds by irradiation)	GR1 (1.67 eV) to GR8 (3.00 eV)
H	Heat treatment (preceded by irradiation)	H1 (0.18 eV) to H18 (3.56 eV)
N	Natural diamond	N1 (1.50 eV) to N9 (5.26 eV)

Center	Point group	ZPL (nm)	τ (ns)	QE (%)	References
V0 (GR1)	T d	741	2.55	1.4	[29, 30]
V− (ND1)	T d	394	—	—	[24]
NV−	C 3v	637	11.6	99	[33, 34, 57]
NV0	C 3v	575	19	—	[32, 35]
N–V–N (H3)	C 2v	503	16	95	[43, 44]
N3+V (N3)	C 3v	415	41	29	[44, 46]
SiV−	D 3d	738	1.28	—	[48, 49]

^aListed are zero‐phonon line (ZPL), emission lifetime (τ), and quantum efficiency (QE) at low temperatures.

Line	Calibration
1	A GR1 = (1.2 ± 0.3) × 10−16 [V0]
2	A ND1 = (4.8 ± 0.2) × 10−16 [V−]
3	A NV− = (1.4 ± 0.35) × 10−16 [NV−]
4	A H3 = (1.0 ± 0.35) × 10−16 [H3]
5	A N3 = (8.6 ± 2) × 10−17 [N3]

Aside from V⁰, the vacancy defect can also exist in the negatively charged form, designated as V⁻ or ND1 [24]. The V⁻ center shows a sharp ZPL at 3.149 eV (394 nm), which appears only when a substantial amount of nitrogen is present in the diamond lattice. In type Ia diamonds, the ND1 center has a peak intensity comparable to that of GR1 but can barely be detectable in type IIa diamonds (Figure 3.4a and b). There is no distinct photoluminescence band associated with ND1. It has been reported that intense UV illumination of the ND1 band results in a reduction of its absorption strength but concurrently increases the GR1 band intensity [31], presumably due to the release of the trapped electrons from the vacancies. However, heating of the samples in the dark can reverse these changes, suggesting the occurrence of some interesting ionization‐recombination processes. More about this process is given later.

3.3.2 NV⁰ and NV⁻

Vacancies in diamond once produced by radiation damage are static at room temperature. They start to migrate when the irradiated diamond is heated above 500 °C. The activation energy barrier is 2.3 eV (or 53 kcal mol⁻¹) [28]. For type Ib diamond containing atomic nitrogen, while some of the vacancies are annihilated at the surface, the majority of them can form stable complexes (i.e. the nitrogen‐vacancy (NV) centers) with nitrogen atoms in the diamond matrix. Figure 3.4c shows a representative UV‐Vis absorption spectrum of a type Ib diamond after irradiation with 2‐MeV electrons and subsequent annealing at 800 °C under vacuum. The signature absorption band of V⁰ at 1.673 eV has disappeared nearly completely, replaced by a new feature emerging at 1.945 eV due to NV absorption. This large spectral change, a result of the combined irradiation and annealing treatments, shows up as a dramatic alteration in the diamond color from yellow to purple. Upon exposure to green light, these diamonds give off bright red emission vividly radiant in each and every way (Figure 3.6a). This red emission is possibly related to the extended red emission band detected in the interstellar medium as will be discussed in Chapter 14.

The NV center in diamond is a point defect comprising a substitutional nitrogen atom adjacent to a vacancy in a C_3v point group symmetry (Figure 3.3b). Similar to the vacancies GR1 and ND1, a NV center can exist in one of the two states: NV⁰ or NV⁻. The neutral form NV⁰ has a sharp ZPL at 575 nm (or 2.156 eV) [32], which is distinctively different from the ZPL at 637 nm (or 1.945 eV) of NV⁻ (Table 3.2) [33]. Both of the ZPLs are accompanied by broad phonon sidebands in the higher energy region of their absorption spectra (cf., Figure 3.4c for NV⁻ only). The corresponding emission bands peak approximately at 600 and 700 nm for NV⁰ and NV⁻, respectively (Figure 3.5), with the associated lifetimes of 11.6 ns [34] and 19 ns [35]. Compared to NV⁻, NV⁰ is significantly lower in concentration due to the transfer of electrons from N⁰ to NV⁰ during annealing [36, 37]:

(3.7)

In type Ib diamonds, since there exist about 100 ppm N⁰ in the crystal lattice, the reaction in Eq. (3.7) can readily occur at high temperatures, thus reducing the concentration of NV⁰ in the final products. For the NV⁻ center, its concentration (in cm⁻³) can be estimated based on the integrated absorption coefficient (in cm⁻¹) of the ZPL at 80 K by [8]

(3.8)

The charge transfer reaction as illustrated above can also be induced with electromagnetic radiation. This is recognized as photochromism, which describes a process where a chemical species can transform between two forms reversibly through the absorption of photons with each form having a distinct absorption spectrum [38]. For the NV centers in diamond, the relative concentrations of the two different forms, NV⁰ and NV⁻, may be changed by a shift of the Fermi level due to neutron irradiation [39] or laser illumination [40]. Figure 3.7 presents a schematic energy diagram of the photoinduced ionization and recombination of NV⁻ and NV⁰ with respect to the energy band gap (E_g = 5.5 eV) of diamond. Detailed spectroscopic investigations have shown that the ionization processes (1 and 2 in Figure 3.7) begin with one‐photon absorption by NV⁻, followed by the excitation of the same center with the second photon, which promotes the electron from the excited state of NV⁻ to the conduction band, creating NV⁰. For the charge recombination processes (3 and 4 in Figure 3.7), the NV⁰ center is first photoexcited, followed by energy transfer and capture of an electron from the valence band to form NV⁻. At the steady state, the NV⁻ population is close to 75% under continuous laser excitation in the 450–610 nm wavelength range [41].

3.3.3 H3 and N3

The nitrogen aggregates in type Ia (or natural) diamonds can take on several different forms in structures, which are identifiable based on their characteristic IR absorption bands [6, 11]. The smallest aggregate, known as the A center, consists of two adjacent lattice points occupied by two nitrogen atoms. They can combine with vacancies to form a stable nitrogen–vacancy complex, designated as H3 or N–V–N, with a C_2v point group symmetry (Figure 3.3c and Table 3.2). This color center has a ZPL at 503 nm, along with a broad phonon sideband around 470 nm (Figure 3.4d) [42, 43]. Similar to the cases of V⁰ and NV⁻, the concentration (in cm⁻³) of this center can be estimated from the integrated absorption coefficient (in cm⁻¹) of its ZPL at 80 K by [8]

(3.9)

For diamonds containing high‐density ensembles of H3 centers, bright green emission emerges when they are exposed to blue light around 470 nm (Figure 3.6b). The emission band peaks at 530 nm with a quantum efficiency of 0.95 and a lifetime of 16 ns (Table 3.2) [43]. The quantum efficiency remains high at temperatures exceeding 500 °C. Taking advantage of these remarkable photophysical properties, together with the high thermal conductivity and the non‐hygroscopic characteristic of the material, Rand and coworkers [44, 45] explored the possibility of using type Ia diamonds containing H3 as a high‐stability lasing medium for room‐temperature color center lasers. They measured a gain coefficient of 0.201 cm⁻¹ at 531 nm and an absorption cross‐section in the range of (1.4 − 2) × 10⁻¹⁷ cm² molecule⁻¹ at 488 nm, well suited for laser development.

N3 is another color center frequently discovered in natural diamonds after irradiation and annealing treatments (Table 3.2) [42]. Often produced alongside H3, this structural defect consists of three substitutional nitrogen atoms surrounding a vacancy, designated as N3 + V, in a point group symmetry of C_3v (Figure 3.3d). It has a ZPL at 415 nm and shows a photoluminescence sideband around 450 nm. The lifetime of this blue emission is 41 ns and the quantum efficiency is 0.29 (Table 3.2) [46], too low for any viable design of a new laser. The blue emission of this center is most commonly observed in natural diamonds when exposed to UV photons (wavelength < 225 nm), which excite electrons from the valence band to the conduction band [47].

3.4 The NV⁻ Center

Over the past six decades, the optical properties of vacancy‐related color centers in natural and synthetic diamonds have been extensively studied using various spectroscopic techniques [3]. Table 3.2 summarizes the spectroscopic properties of V⁰, V⁻, NV⁰, NV⁻, H3, N3, and SiV⁻ centers in bulk diamonds. Of these seven color centers, NV⁻ deserves special attention with an in‐depth discussion for its remarkable optical and magnetic properties. We will discuss in this section only some salient features of the center. Excellent reviews on its quantum optical and spectroscopic properties from both theoretical and experimental aspects can be found elsewhere [51–53].

The NV⁻ center consists of three carbons and one nitrogen surrounding an anionic vacancy in a tetrahedral configuration that belongs to a C_3v point group symmetry (cf., Table 3.4 for the character table). It is a six‐electron system: 1 e⁻ from each of the three carbons, 2 e⁻ from N, and 1 e⁻ of the vacancy. Linear combinations of atomic orbitals (LCAO) suggest a ground electronic configuration of a₁²a₁²e² [54]. The two electrons in the e‐orbital are unpaired, one in e_x and another one in e_y [55]. The unperturbed electronic energy structure of the center is ³A₂, a triplet ground state with the spin quantum numbers of m_s = 0 and ±1 in its magnetic sublevels (Figure 3.8). The two m_s = ±1 sublevels are degenerate in a zero magnetic field, and they are energetically higher than the m_s = 0 sublevel by 2.87 GHz, which is caused by the crystal field splitting arising from the spin–spin interactions between the unpaired electrons at the e_x and e_y levels [56]. In the presence of a weak external magnetic field, the degeneracy of the m_s = ±1 sublevels at the ground state of NV⁻ is lifted via the Zeeman effect. Under the circumstance that the magnetic field is aligned with the NV’s principal molecular axis passing through the C₃ rotation, the energy difference between these two levels is [53]

(3.10)

where g_e ∼ 2.003, μ_B = 14.00 MHz mT⁻¹ is the Bohr magneton, and B is the magnetic field strength (cf., Section 11.1 for further details).

In the optical region, the NV⁻ center shows a characteristic ZPL in both absorption and emission spectra at 637 nm. Uniaxial stress experiments confirmed that the ZPL originated from a transition of an “A” state to the “E” state of a trigonal center [32]. Since the spins must be conserved during optical transitions between the ground and excited states, one may designate the electronic transition as ³A₂ → ³E (Figure 3.8). Further studies found that the photoluminescence of the transition had a lifetime of 11.6 ns for a synthetic type Ib diamond [34] with a quantum yield close to 1 [57]. Moreover, the fluorescence intensity was exceptionally stable as the center acted like a pseudo‐atom in an inert and highly thermally conductive matrix. Gruber et al. [58] first reported that the NV⁻ centers were so stable that even under intensive laser excitation (>1 × 10⁶ W cm⁻²) over an extended period of time, they exhibited no sign of photobleaching. The high photostability allows facile detection of individual NV⁻ centers by fluorescence imaging, especially in biological systems, which constitutes one of the main themes of this book.

With the magneto‐optical properties, the NV⁻ centers are amenable for analysis by optically detected magnetic resonance (ODMR), which is a double resonance technique that enables the transitions between spin sublevels to be detected by optical means. The technique is so powerful that it is capable of enhancing the sensitivity of spin resonance spectroscopy by several orders of magnitude. For the NV⁻ center in diamond, the origin of this effect lies in its unique electronic structure as discussed below.

In the electronic energy diagram of NV⁻ as illustrated in Figure 3.8, there exists a metastable singlet state, ¹A. The intersystem crossing (ISC) from ³E to this state is occasionally possible, depending on the sublevel of the excited state. Experimentally, it has been found that the ISC rate from the m_s = ±1 sublevel of the excited state to the singlet state is significantly higher than that from the m_s = 0 counterpart by non‐radiative energy transfer processes [59]. The singlet state then decays non‐radiatively to the m_s = 0 sublevel of the ground state. As a result, the optical pumping can preferentially populate the NV⁻ center in the m_s = 0 sublevel of the ground state, a process known as optically induced spin polarization. When a resonant microwave radiation of 2.87 GHz is applied, the electron spin will undergo the transition from m_s = 0 to ±1 sublevels of the ground state. Such a transition will reduce the fluorescence intensity by about 30% after several cycles of excitation, because the populations in the m_s = ±1 sublevels of the excited state return to the ground state through non‐radiative decays (Figure 3.8). That is to say, the information about the spins at the electronic ground states can be read out optically. Moreover, the spin states of the NV⁻ centers can be probed and manipulated individually by using continuous and/or pulsed microwave radiations for more advanced applications [53].

The ODMR detection of NV⁻ is so unique and significant that it is achievable at the single spin level even at room temperature [58], thanks to the excellent photostability of the center and the high quantum yield of the fluorescence emission. Furthermore, the Zeeman splitting of the ODMR bands of a single NV⁻ center can also be observed with high contrast (Figure 3.9) [60]. At present, the NV⁻ in diamond is the only known solid‐state system that allows detection and manipulation of the spin states of a single localized electron at room temperature. In addition to that, the NV⁻ center has an exceptionally long coherence time and as such its spin states have been reported to remain coherent for longer than 1 ms in isotope‐free bulk diamonds [61]. All these features combined together make diamonds hosting NV⁻ centers an extraordinary tool for ultra‐sensitive measurements of temperature, magnetic field, electric field, and mechanical stress at the nanometer scale [52]. First discovered in the 1950s, and throughout the years well into the twenty‐first century, the center has found remarkable applications in a wide range of research areas, including quantum information [62], quantum computing [63], nanoscale magnetometry [59, 64], high‐precision temperature sensing [65–67], and super‐resolution imaging [68].

Finally, the NV⁻ center is particularly appealing for use in biological imaging and tracking applications owing to its unmatchable physicochemical properties as summarized here [69–72]:

1. The NV⁻ centers can be produced as high‐density ensembles in nanoscale diamonds, which are biologically inert and photostable materials.
2. The emission band of NV⁻ peaks at 685 nm where the light has a long penetration depth through tissue, and more than 70% of the emitted photons lie in the near‐infrared window of bioimaging.
3. The fluorescence lifetime of NV⁻ is significantly longer than those of cell and tissue autofluorescence, allowing for time‐gated fluorescence imaging both in vitro and in vivo.
4. The fluorescence intensity of NV⁻ can be modulated by applying either sinusoidal magnetic field or sinusoidal microwave radiation to achieve background‐free detection in tissue imaging.

The combination of these outstanding features has attracted scientists to employ FNDs containing high‐density ensembles of the NV⁻ centers as bioimaging contrast agents. We will continue the discussion on the biological aspects of the applications in the following chapters of the book.

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