Electron Paramagnetic Resonance in Modern Carbon-Based Nanomaterials

Fundamentals of Electron Paramagnetic Resonance in Modern Carbon-based Materials

Sushil K. Misra*

Department of Physics, Concordia University, Montreal, H3G 1M8, Canada

Abstract

The advantages of using multifrequency Electron Paramagnetic Resonance (EPR) in studying carbon-based materials are discussed. The details of designing continuous-wave EPR spectrometers operating at different frequencies are presented. Designs of CW and pulse Electron Nuclear Double Resonance (ENDOR) spectrometers, which are very important techniques for studying precisely hyperfine interactions and local environment of paramagnetic ions in carbon-based materials are included. Analysis of EPR spectra, spin Hamiltonians, EPR lineshapes, evaluation of spin-Hamiltonian parameters, and simulation of single-crystal and powder spectra are also explained. A short review of carbon-based materials studied by EPR is given.

Keywords: Carbon-based materials, Continuous Wave EPR, Davies ENDOR, Electron spin echo (ESE), Electron Spin Echo Envelope Modulation (ESEEM), Evaluation of spin Hamiltonian parameters, Electron Nuclear Double Resonance (ENDOR), EPR, EPR lineshape, EPR spectrometer, High-frequency spectrometers, Hyperfine interaction, Hyperfine Sublevel Correlation Spectroscopy (HYSCORE), Mims ENDOR, Pulse EPR, Pulse ENDOR, Simulation of EPR spectrum, Spin Hamiltonian, Zeeman effect.

* Corresponding author Sushil K. Misra: Department of Physics, Concordia University, Montreal, H3G 1M8, Canada ; Tel: +01-514-482-3690; E-mail: [email protected]

ELECTRON ZEEMAN EFFECT: EPR RESONANCE CONDITION

In electron paramagnetic resonance (EPR), one observes the resonant absorption of microwave (mw) energy by an unpaired electron making a transition from a lower-energy state to a higher-energy state in the presence of an external magnetic field (The term EPR will be used throughout this chapter, although electron spin resonance (ESR) and electron magnetic resonance (EMR) are also used in the literature). These energy levels are due to the interaction of the electronic magnetic moment with the applied external magnetic field. An unpaired electron is equivalent to a small bar magnet due to its magnetic moment.

If it is aligned with Bext, then its energy is lower than when it is aligned opposite to the direction of Bext, as shown in Fig. (1). This effect is called the Zeeman Effect.

The unpaired electron possesses the spin 1/2, so its lower and higher energy states are designated by the electronic magnetic quantum numbers MS = –1/2 and MS = +1/2, respectively. Then expressed for the two values of MS the energies E of an unpaired electron in an external magnetic field, Bext, are:

where, the dimensionless constant, g, termed as g-factor, is expressed in terms of the gyromagnetic ratio, γ, as γ = gμB/ħ, where μB is the Bohr magneton (=9.274 × 10-24 J/T; 1 Tesla [T] = 10.000 Gauss) and ħ is the reduced Plank’s constant (= h/2π, with h = 6.626 x 10-34 J×s being Planck’s constant).

Fig. (1))

Lower (left) and higher (right) possible orientations of an unpaired electron’s magnetic moment in the external magnetic field, Bext (Adapted from [1] with the Permission from John Wiley and Sons).

Under the action of an oscillating mw radiation of frequency υ0 in Hertz, the resonance condition is satisfied when

where, B0 = hυ0/gμB, so that the energy level separation between the two energy levels represented by MS = ±1/2, is equal to hυ0. In that case, resonant absorption of mw radiation will take place for Bext = B0. This is shown in Fig. (2).

Fig. (2))

A plot showing the splitting due to Zeeman effect by the external magnetic field Bext (neglecting hyperfine splitting and higher order zero-field splitting terms) and resonant absorption of mw radiation as the magnetic field is swept; adapted from [1] with the Permission from John Wiley and Sons).

HYPERFINE SPLITTING

The energy of the unpaired electron is influenced by its local surrounding. For instance, if there is a nucleus possessing magnetic moment near an unpaired electron, the magnetic field seen by the unpaired electron at its site would change due to the interaction between the electron and nuclear spin, known as hyperfine interaction (HFI) [2]. In that case, the external magnetic field required to satisfy the resonance condition given by eq. (2) will shift from B0 accordingly. Therefore, if the effective local magnetic effect, B1, depending on the HFI constant, of the nucleus on the unpaired electron is in the direction of Bext, the resonance will occur at Bext < B0, and if B1 opposes Bext at the location of the unpaired electron, the absorption will occur at Bext > B0, for a given υ0 (more details on HFI terms in the spin Hamiltonian are given below).

EPR LINE SHAPES

There are three types of line shapes, i.e. EPR absorption line intensity versus the magnetic field, usually observed in EPR. They are (i) Lorentzian, (ii) Gaussian, and (iii) Dysonian. These line shapes are expressed as:

and

respectively, where y is the line intensity; x is the magnetic field; x0 is the resonance field; α is the fraction of the dispersion component added into the absorption signal for Dysonian line shape [3], and Δx is the linewidth. One obtains for the first-derivative absorption signal an expression, which is proportional to Y’max(ΔBpp)², where 2Y’max is the amplitude of the peak-to-peak derivative, whereas ΔBpp is the peak-to-peak linewidth.

When there exists superposition of many components which differ from spin to spin, the line shape becomes Gaussian; it is known as inhomogeneous broadening. In contrast, if there exists no variation the line shape from one spin to another spin, a Lorentzian line shape is observed; it is known as homogeneous broadening.

A mixture of the absorptive and dispersive components of the susceptibility produces an asymmetric Dysonian line shape. This happens due to the non-uniform distribution of the mw electromagnetic field when the sample size is bigger than the skin depth. In addition to this, the movement of the paramagnetic centers also produces the asymmetry. The two terms in the Dysonian lineshape expression above (eq. (5)) take into account the clockwise and the anticlockwise circular polarizations of the mw radiation [3, 4]. The theory of Dysonian line shapes due to conduction electrons in metals is very complex.

An experimental EPR spectrum for anthracite reported by Tadyszak et al. [5] illustrates best the Dysonian lineshape when the sample becomes conducting as depicted in Fig. (3), showing a plot of the asymmetry parameter A/B, versus the reduced dimension for λ = d/δ = 3.5, where d is the sample thickness and δ is the skin depth. (Here A and B are the magnitudes of the amplitudes of the maxima of the first-derivative lineshape with respect to the baseline before and after the center of the lineshape). It can be seen from Fig. (3) that for smaller values of λ, the line becomes symmetric, e.g. for λ = 0.2. More details and references covering Dysonian line shape can be found in the treatise by Poole [6].

Fig. (3))

A plot of the asymmetry parameter (A/B) versus the reduced dimension λ = d/δ. here d and δ are, respectively, the sample thickness and the skin depth. (Adapted from [5]).

SPIN HAMILTONIAN

For a complete discussion, the reader is referred to Misra [7], the spin Hamiltonian (SH) is expressed as: , where in zero magnetic field

Here n is an even integer, which can take values between 0 and 6 (n ≤ 2S), for spin S ≤ 7/2, and m lies in the range 0 ≤|m|≤n for each n. The are called equivalent spin operators for the electron. They, along with their matrix elements for various spin values (≤ 7/2) are listed in [7]. The coefficients are determined by the crystal field symmetry at the site of the transition metal ion. In addition, the Zeeman terms depending on the external magnetic field, B, and the matrix, as well as the HFI terms depending on the HFI tensor are described by:

In eq. (7), g|| = gz; and A|| = Az; when there is symmetry about the z-axis.

Some special cases relevant to carbon containing materials are described as follows:

(i) For spin S = 1/2, I = 1/2, the EPR spectra are analyzed using the spin Hamiltonian .

(ii) When quadrupole nuclear interactions become important for the case of nuclear spin I > 1/2, e.g. low-spin Co²+ (S = 1/2, I = 7/2), the spin Hamiltonian for axial symmetry becomes

In the above equation Qʹ, Qʺ are the components parallel and perpendicular to the symmetry axis of the quadrupole interaction tensor, μn is the nuclear magneton, and gn is the nuclear g factor.

(iii) For S = 1; I > 1/2, the applicable spin Hamiltonian is:

In eq. (9), the parameters and are also denoted as D and E, respectively.

SIMULATION OF EPR SPECTRA

This section is devoted to simulation of EPR spectra, as adapted from Misra [8], where complete details are given. First, one needs to simulate single-crystal spectrum, which is then exploited to simulate polycrystalline spectrum.

Simulation of Single-crystal Spectrum

Simulation of EPR spectrum requires knowledge of both positions and intensities of EPR lines, as well as the line-shape function, F(Βri, B), where Βri denotes the resonance line positions for the various possible transitions i′↔i″, which can be Gaussian, Lorentzian, or a Dysonian appropriate to the sample. It is easier to calculate the line positions for the orientations of B parallel to the symmetry axes X, Y, Z by perturbation expressions, but for an arbitrary orientation of B, the task becomes more difficult; see [8] for specific details. P(i,θ,ϕ,νc) is the weight given to the various lines for the ith transition, which takes place between the levels i′ and i″, participating in resonance. Here, the mw frequency is νc and the orientation of B over the unit sphere is (θ, ϕ).

Thus, the single-crystal simulated spectrum can be expressed as:

In eq. (10), the summation is over all the lines observed for the particular orientation of B.

Transition Probability

The probability P(i,θ,ϕ,νc) of a transition, i, between the energy levels i' and i" is expressed as follows:

In eq. (11), Sα and B1α; (α = x,y,z) represent the components of the electron spin operator, S, and the modulation r.f. field B1. are the eigenvectors of the spin-Hamiltonian (SH) matrix, , corresponding to the energy levels Ei’ and Ei" participating in resonance [ ]. For more details of calculation see [8].

Lineshape function F(Bri, Bk)

The sum in Eq. (10) is performed to calculate the spectrum. P(i,θj,ϕj,νc) is considered centered at Br(i,θj,ϕj,νc) and the lineshape function F(Bri, Bk), is taken to be extended over the magnetic-field interval ±ΔB, as a function of ΔB1/2 (full-width at half-maximum, FWHM), which is characteristic of the lineshape, e.g. ΔB = ±10ΔB1/2, in order to obtain a good approximation for the Lorentzian lineshape.) The two most common line shapes are:

(i) Gaussian Lineshape, FG:

where Bri, σ, and KG = (1/BΔ)(ln2/π)¹/² are the resonant field value for the ith transition, the linewidth and the normalization constant for the lineshape, respectively. In the expression for KG, BΔ= (1/2) B1/2, where B1/2 is HWHM (half-width at half-maximum).

(ii) Lorentzian lineshape, FL:

where Γ is the Lorentzian linewidth (HWHM = (3)¹/²ΔBpp/2, with ΔBpp being the peak-to-peak first-derivative linewidth.

Simulation of a Polycrystalline Spectrum

In a polycrystalline material one can simulate the EPR spectrum by overlapping single-crystal spectra computed for external magnetic (Zeeman) field, B, over a large number of orientations (θ, ϕ) on the unit sphere weighted in proportion of sinθ dθ dϕ, which takes into consideration the distribution of various crystallites, whose principal symmetry axes are oriented about (θ, ϕ) in the interval dθ, dϕ. The simulated polycrystalline spectrum is then expressed as:

From eq. (14) it is seen the resonant field values for the various transitions must be known, along with their transition probabilities, to compute polycrystalline spectrum. The integrals in Eq. (14) are evaluated by summing over single-crystal spectra for magnetic-field orientations (θj, φj) over a grid of points covering the entire unit sphere with appropriate weight factors. See Ref [8] for more details.

Calculation of First-derivative EPR Spectrum

The experimental EPR spectrum is most often obtained as the first derivative with respect to the external magnetic field intensity of the absorbed mw power. This first-derivative spectrum is simulated by calculating the derivative with respect to B of S(B,νc), as given by eq. (14), as well as that of the lineshape. In particular, for the Gaussian and Lorentzian lineshapes, given by eqs. (12) and (13), respectively, the first-derivatives are:

The expression for the simulated first-derivative absorption spectrum, as obtained from eq. (14), is

From eq. (17), one has for the two lineshapes, using eqs. (12) and (13):

Gaussian lineshape:

Lorentzian lineshape:

In eqs. (18) and (19), the normalization constant, N, may be arbitrarily chosen. For example, |Fc(Bk,νc)|max= 1, obtained by dividing all values by |Fc(Bk,νc)|max, which is the largest magnitude of all the calculated values.

The details given above can be used to write a source code for simulation of a powder (polycrystalline) spectrum. On the other hand, the software Easyspin [9], downloadable from the Internet, is useful for simulations, provided that one has MATLAB available.

PULSE EPR

In this technique, mw pulses are applied over selected finite intervals of time to the sample, so that the orientation of the precessing magnetic moment can be turned by chosen angles about the x, y, or z axes around the external magnetic field (Larmor precession). (Conventionally, the z-axis is chosen to be parallel to the external magnetic field). These angles are usually multiples of 30˚ or 45˚. To this end, one can use a single pulse or more pulses with chosen intervals of time in between, recording a signal referred to as echo signal that is proportional to the magnetization of the sample at appropriate intervals after the application of the last pulse. Consequently, several varieties of pulsed EPR techniques have been developed, e.g. electron spin echo (ESE), ESE envelope modulation (ESEEM), electron-electron double resonance (ELDOR), double quantum coherence (DQC), double electron-electron resonance (DEER), also referred to as pulse ELDOR (PELDOR) and ELDOR in ESE, two-dimensional Fourier transform EPR (2D-FTEPR), spin-echo correlated spectroscopy (SECSY), correlation spectroscopy (COSY), hyperfine spin-correlation spectroscopy (HYSCORE). Pulse EPR provides information that is not possible to obtain with CW EPR. For pulse EPR the instrumentation required is much more costly; as well, the analysis of the data is also much more complicated in comparison to that for CW EPR.

Nuclear Modulation Effects Leading to ENDOR and ESEEM

The energy levels of a paramagnetic system with an interacting electron spin (S = 1/2) and a magnetic nucleus of spin I = 1/2 are given in Fig. (4) [10, 11]. Two of the energy levels in which the z-component of the electron spin angular momentum component with mS = |+1/2> is the α-manifold, whereas that with mS = |–1/2> is the β-manifold, and there are two sublevels in this manifold with the nuclear spin angular momentum components ±|1/2>, and likewise there are two sub levels in the β-manifold, leading to four levels labeled as |αα>, |αβ>, |βα> and |ββ>, the two letters denote the electron and nuclear spins, respectively.

The allowed EPR transitions are two in number indicated by vertical arrows (a) with ΔmS = ±1, and ΔmI = 0, 1↔3 and 2↔5. There are two forbidden EPR transitions (f) with ΔmS = ±1, and ΔmI = ±1, 1↔4 and 2↔3, the so-called zero-quantum and double-quantum transitions involving the simultaneous flip of the electron and nuclear spins. There are also two transitions involving exclusively nuclear spin flips (ΔmS = 0), and ΔmI = ±1) denoted as ωα(1↔2) and ωβ(3↔4).

If one denotes the isotropic part of the hyperfine coupling by aiso:

where Ai are the principal components of the observed anisotropic hyperfine tensor such that the principal components of the dipolar hyperfine tensor is given by

The allowed (ω24 and ω13) and the forbidden (ω14 and ω23) EPR transitions are noted in Fig. (4), and the extreme transitions are seldom seen except in weak-coupling cases where the magnitude of hyperfine coupling at any orientation |Aθ| « 2ωI, where ωI is the NMR transition energy of the nucleus. By setting up the 4 x 4 matrix representation of the spin Hamiltonians HZee, HHF and HNZee within the product spin space |αα>, |αβ>, |βα> and |ββ>, and diagonalizing the matrices one can arrive at the energies of the nuclear(ENDOR) and the electronic (EPR) transitions and their transition probabilities. They are given below:

Fig. (4))

The schematic EPR spectrum (right) and the corresponding energy level diagram (left) for S = 1/2, I = 1/2 model system with |As| < |2ωI| (weak coupling case). Here a: Allowed EPR transitions (1↔3) & (2↔ 4). f: forbidden EPR transitions (1↔4) & (2↔ 3). Nuclear transitions are (1↔2) & (3↔ 4). As for notation, As is the hyperfine coupling at an arbitrary orientation. Reprinted from [10] with Permission from John Wiley and Sons.

And, for an axially symmetric hyperfine tensor (A1 = A2 ≠ A3), A and B above are given by

where θ is the angle between the electron-nuclear vector and the Zeeman field axis. The probabilities of the EPR transitions for the allowed (a) and forbidden (f) transitions are given by

Here, 2η is the angle between the nuclear quantization axes in the two electron manifolds (α & β), ωI is the nuclear Larmor frequency and ω+ = ωα + ωβ and ω- = ωα – ωβ. It is clear from the schematics in Fig. (4) that the nuclear transitions gain intensity when the forbidden transitions (f) have finite probability. In ESEEM where the mw pulses excite both the allowed and the forbidden EPR transition one can see (indirectly) the nuclear transition frequencies manifest themselves as modulation of the electron spin echo. In ENDOR, on the other hand, the nuclear transition frequencies are excited directly with rf irradiation at the appropriate frequencies; since nuclear transitions are excited between levels whose polarizations are governed by electron spin polarization, one gets an enhancement in transition on the order of the ratio of the respective gyromagnetic factors γelectron/γnucleus.

CW ENDOR: Theory

The following description is basically adapted from Kulik and Lubitz [12], who have discussed this very competently. ENDOR (Electron-nuclear double resonance) was introduced in solid state physics first by Feher [13]; Hyde and Maki [14] later extended it to radicals in solution. One combines the techniques of EPR and NMR spectroscopies in ENDOR, but the two techniques play different roles here. The EPR signal is observed here at a fixed magnetic field, whereas its intensity is varied by the applied scanning rf NMR radiation. ENDOR monitors only the paramagnetic species, e.g. those in SiCN ceramics. The addition of NMR enhances the resolution of ENDOR as compared to that obtained by EPR alone. In ENDOR, one studies HFI, (hyperfine interactions), which represent the magnetic interactions of the unpaired electron spin with the spins of magnetic nuclei, which can belong either to (i) the molecule on which the unpaired electron is localized, or (ii) to the surrounding molecules. One detects the electron spin echo (ESE) signal in pulse ENDOR, which limits its application to systems with a sufficiently large transverse electron spin relaxation time (T2 > 100 ns). This makes it unsuitable to study liquid samples, requiring measurements at low temperatures. CW ENDOR, on the other hand, is free from this limitation. It allows the experiments to be done at ambient temperatures. On the other hand, it requires, for an optimum signal intensity, fine tuning of the longitudinal relaxation times of the electron and nuclear spins. Pulse ENDOR is better than CW ENDOR at low temperatures due to the strong temperature dependence of these relaxation rates. The simplest system that can be investigated by ENDOR is a radical with the electron spin S = 1/2 associated with a nucleus of spin I = 1/2. When the hyperfine coupling between them is isotropic, then if the g-matrix is also isotropic, the spin-Hamiltonian H of this system is (in frequency units):

The three terms on the right in this equation, respectively, describe the electron Zeeman interaction, the nuclear Zeeman interaction, and the HFI. Here h is Planck’s constant, B0 is the intensity of the external magnetic field, μB is the Bohr magneton, g is the electronic g-factor, μN is the nuclear magneton, gn is the nuclear g-value, a is the HFI constant, S and I electron and nuclear spin operators. The z-axis is parallel to the orientation of the constant magnetic field of the EPR spectrometer B0 (laboratory frame). The spin-Hamiltonian in eq. (25) applies to a radical in a liquid solution, wherein fast rotation averages out all anisotropic interactions. The first term is dominant in eq. (25) in the strong-field approximation, The energy levels of the system are characterized by the electronic and nuclear magnetic quantum numbers, mS = ± 1/2 and mI = ± 1/2, respectively. The first-order eigenvalues are:

In the above equation, νe = gμBB0/h is the electron frequency and νn = gnμnB0/h is the nuclear Larmor frequency. The energy level diagram, describing eq. (26) is shown in Fig. (5). In EPR, the selection rules are ΔmS = ± 1 and ΔmI = 0, which implies that there are possible two allowed EPR transitions in this system The rf field drives also the NMR transitions in an ENDOR experiment with the selection rules: ΔmS = 0 and ΔmI = ±1. The frequencies of these transitions are:

Fig. (5))

A plot of the energy levels for coupled electron spin (S = 1/2) and nuclear spin (I = 1/2) system. The spin functions are shown on the four energy levels of this system. The EPR and NMR transitions, together with the electron spin (We), nuclear spin (Wn) and cross-relaxation rates (Wx1, Wx2) are indicated. The NMR resonances, shown by black arrows, are detected by the change of an irradiated saturated EPR line (gray arrow) simultaneously in a CW ENDOR experiment; for further details, see text (adapted from [12] with Permission from Springer).

Continuous wave ENDOR can be considered as NMR-induced partial desaturation of a saturated EPR line for a stable radical in thermodynamic equilibrium. The spin relaxation processes affecting the S = 1/2, I = 1/2 system are shown as dashed lines in Fig. (5).

The rate of population relaxation that is the longitudinal spin relaxation, of the electron spin is denoted as We, that of the nuclear spin as Wn, and those of the electron-nuclear cross-relaxation are denoted as Wx1and Wx2. The ENDOR transition takes place when the two, mw and rf fields, are, respectively, in resonance with the EPR and NMR transitions and there is a common energy level shared by these transitions. One EPR transition is saturated by mw irradiation in CW ENDOR, as indicated by the thick vertical arrow in Fig. (5).

One NMR transition (NMRII or NMRI) is saturated by the rf field simultaneously, opening an alternative relaxation path for the pumped electron spin. When NMRII is pumped, it can relax via a two-step pathway We(|+ ->↔|- ->), Wn(|- ->↔|- +>)) or directly by Wx1(|+ ->↔|- +>). The intensity of the ENDOR signal is determined by the extent to which the EPR line is desaturated by the bypass of the additional relaxation. As a consequence, the number of contributing nuclei is usually not reflected in the intensity of the ENDOR line, in contrast to NMR or EPR. The intensity of the ENDOR signal, E, in the limit of the simplifying assumption Wx1 = Wx2 = 0 and in the presence of strong NMR saturation, is:

where E is the ‘ENDOR enhancement’ and b = Wn/We. It represents the relative change of the EPR signal. E depends strongly on the relaxation properties of the system (Plato et al. 1981). To achieve the matching condition: Wn = We, corresponding to the maximum ENDOR enhancement, which is Emax = 1/8, careful optimization of the respective rates, e.g., by variation of temperature, is required. This value might be increased by cross-relaxation. An asymmetry of the ENDOR spectrum is produced by the asymmetric relaxation network Usually Wx1= Wx2.

The situation is qualitatively similar for more complicated systems with k > 1 nuclei and with I = 1/2, for which Eq. (25) can be easily generalized to:

where the index i covers all nuclei. When these nuclei are non-equivalent, there are possible 2k EPR transitions, associated with only 2k ENDOR transitions with the frequencies:

ENDOR spectroscopy thus provides simplification of the spectra as compared to that in EPR. Its sensitivity is many orders of magnitude higher than those of the NMR experiments on paramagnetic systems, although ENDOR is less sensitive than EPR. This is due to the enormous increase in the linewidth as compared to that of NMR on diamagnetic molecules.

ENDOR Instrumentation

The instrumentation for ENDOR experiments is an extension of that for CW or pulse EPR, with the difference that for ENDOR, one requires an rf source and amplifier, whose rf output is introduced into the rf coils, which are placed at the EPR cavity. These coils are placed in such way that the magnetic component of the rf field B2 is perpendicular to both the static field (B0) and the excitation field (B1). See Kurreck et al. [15], Kevan and Kispert [16] and Poole [6] for more details on ENDOR instrumentation.

Mims and Davies Pulsed ENDOR Sequences

ENDOR can be performed both in CW and pulsed modes. (For a complete discussion refer to [10]). The CW experiment consists of saturating an EPR transition of the system with coupled nuclear spins. As the EPR transitions lose the intensity due to the reduction in population difference between the levels, a rf sweep is performed to excite the nuclear transitions, which releases the bottleneck in the population distribution and allows the EPR transition to regain the intensity and this is referred to as ENDOR induced EPR. The nuclear transitions are enhanced and occur at frequencies above and below the nuclear Larmor frequency depending on the hyperfine coupling and nuclear quadrupole coupling. Since nuclear resonances are quite narrow, hyperfine splitting which is on the order of EPR line width, and hence unresolved in the EPR spectrum can be evaluated with high precision in ENDOR. This is particularly true for low gamma nuclei such as ¹³C, ¹⁵N, ¹⁴N and ²H nuclei, when measured at high spectrometer frequencies. CW ENDOR consists of carefully locking the Zeeman field on a designated EPR transition and then sweeping a range of NMR frequencies keeping the resonator tuned to the changing rf all the time by servo-regulated automatic tuning and matching.

Instrumentation-wise CW ENDOR is quite challenging and requires a critical balance of rf power and relaxation times to achieve optimum sensitivity. Since rf and mw are present simultaneously, a lot of effort is required to reduce interference from low frequency and the associated artifacts. Pulsed ENDOR, on the other hand, is less susceptible to artifacts since the rf and mw power are applied only for short duration and seldom applied simultaneously. Pulsed ENDOR allows the study of the manifestations of electron T1, T2 and nuclear T1 and T2 as well as electron nuclear cross relaxation with good selectivity. Basically, the nuclear resonance frequencies which contain high-resolution hyperfine information are monitored by creating an enormous polarization between the nuclear sublevels by saturating the connected EPR transition. Upon exciting the nuclear transitions by selective rf pulses, the two-pulse or three-pulse echo gets enhanced when the nuclear resonance frequencies match with the rf frequency.

ENDOR techniques predominantly exploit the electron spin echo (ESE) effect, wherein the echo signal is created by proper mw pulse sequences. The rf pulse is applied during the mixing period of the pulse sequence. It induces transitions among nuclear spin levels, producing a change in the ESE intensity. The pulse ENDOR signal is represented by the amplitude of this change when the rf frequency is