Vij D.R. Handbook of Applied Solid State Spectroscopy

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Figure 4.3 EPR,

H, and

N ENDOR spectra for free-base porphycene radical anion with the

nuclear frequencies (Q

) for

H and

4.2 EXPERIMENTAL CONDITIONS FOR ENDOR

The classical double resonance experiment is performed by applying

microwave (mw) and radio frequency (RF) fields in a continuous fashion; this

technique is called continuous wave, CW-ENDOR spectroscopy.

The fundamentals of the ENDOR experiment can be illustrated for a

simple electron-proton system (Figure 4.1). First, the EPR spectrum is

recorded. Then: (1) the magnetic field B is set at the resonance of one of the

observed EPR transitions; (2) this transition is partially saturated by the

appropriate microwave power (partial saturation allows maximum

sensitivity). The saturation condition for EPR can be obtained from the

condition satisfied by equation (4.16).

B

 1 (4.16)

where J

= gE

and T

are electron spin-lattice and relaxation

times, and E

is the time-dependent magnetic field of the microwave

radiation; (3) a second oscillating RF field B

is applied perpendicular

to the applied microwave B

and to the externally applied field B to

induce and saturate the NMR transition. The NMR condition for

saturation has to be satisfied:

 1 (4.17)

where J

is the gyromagnetic ratio for the nucleus, T

and T

are the nuclear

spin-lattice and spin-spin relaxation times, and B

is the time-dependent

4. ENDOR Spectroscopy

156

N indicated. From [2].

magnetic field at the radio frequency. The frequency of the RF field is swept

and the EPR absorption is recorded as a function of NMR frequency.

When hQ

= h (Q

± »a»/2), the resonance condition for nuclear transition

is fulfilled: saturated EPR transition can become desaturated by NMR

transitions provided both transitions have energy levels in common. This

desaturation of EPR transition is detected as a change (typically enhancement)

in the EPR signal intensity vs. the NMR frequency.

4.2.1 Sensitivity, Magnetic Field Homogeneity, and Stability

Since the ENDOR signal-to-noise ratio is always some fraction of the ESR

signal-to-noise ratio (for liquids, typically 1% of the ESR height), it is

necessary to have a well-tuned ENDOR spectrometer. This requires that the

ESR spectrometer be in perfect working order and ideally be capable of

producing a signal-to-noise ratio of at least 100:1 or better from a standard

weak pitch sample. The weak pitch (0.00033% pitch in KCl) sample contains

1 10

spins cm

–1

providing the ESR signal is recorded with a 1.7-G

linewidth. Most good commercial instruments can achieve such a signal-to-

noise ratio for 10

spins (the effective length of a rectangular cavity is 1 cm).

The magnetic field homogeneity of most commercial magnets used in ESR

experiments is ±10 milligauss (mG), which is quite adequate. A homogeneity

of this magnitude is usually necessary in order to properly investigate organic

free radicals in solution where frequently EPR linewidths of 60 mG or smaller

are encountered. Deuterium ENDOR may require slightly better homogeneity.

The most serious problem is one of magnetic field and microwave

frequency stability. After setting the field to coincide with a selected position

of the ESR line, the magnetic field and the microwave frequency should be

invariant for the duration of the experiment. Since the experiments may take

several hours, special attachments are added to the standard ESR

spectrometers to provide adequate magnetic field and microwave oscillator

stability required for ENDOR investigations. Small drifts in magnetic field

can occur because of temperature changes in the immediate surroundings.

The field and frequency can be prevented from drifting by using a field

frequency lock system. An alternative method appears to work adequately

whenever the cavity can be immersed in a refrigerant. In this case the cavity

can be kept at constant temperature, and thus the microwave frequency

remains reasonably constant for the duration of each ENDOR experiment.

However, the magnetic field stability still remains a problem. ESR experi-

ments at 35 GHz require ESR fields around 12.5 kG. Assuming 0.5 G for

linewidth requires a magnetic field stability of 1 part in 10

or better over the

duration of each ENDOR experiment. This type of stability can be obtained

by locking the field to the nuclear magnetic resonance signal of deuterium

(obtained by an NMR gaussmeter). Any change in the deuterium NMR signal

157

4.2 Experimental Conditions for ENDOR

is amplified and applied to a pair of coils on the magnet that compensate for

any changes in the main magnetic field.

4.2.2 Sample Size

Sample shape and size are not really critical parameters. However, it is

usually advantageous to have as large a sample size as possible to take

advantage of the cavity-filling factor. The ESR signal intensity depends on

the total number of spins in the active part of the cavity and not on the

concentration per unit volume. Therefore signal intensity can be gained if the

largest sample tube is used. However if the sample is at all polar,

the microwave electric field will be absorbed by the electric dipole of the

sample, and this may prevent detection of the magnetic dipoles by

the microwave magnetic field. Physically this phenomenon is observed to be a

loss of cavity Q. However, excellent solvents with low dielectric constants,

such as ethyl benzene and toluene, do exist and are highly recommended for

carrying out ENDOR investigations in solution. When a polar sample

constant drops to nonpolar values and ENDOR can easily be done.

Polycrystalline or glassy samples generally have broad ESR lines and thus

both ESR and ENDOR sensitivity is decreased. With a large sample access

cavity, it is possible to carry out successful ENDOR experiments on frozen

glasses [1] or power samples. Most crystals can also be used. Thus the sample

size or shape does not limit one from observing ESR and/or ENDOR spectra.

However, a severe problem can arise in collecting ENDOR data from a

crystal. In order to determine accurately the principal hyperfine splittings,

ENDOR data must be collected from three orthogonal crystal planes. In many

cases the crystal needs to be aligned to 2 minutes of an arc so very precise

alignment is required.

4.2.3 Introduction of RF Power into Cavity

The method by which RF power is introduced into the cavity depends largely

on the type of ENDOR experiment. For instance, ENDOR experiments on

samples (transition metal complexes or semiconductors) that are carried out at

4 K normally require RF power levels on the order of 0.1 W or less because

the paramagnetic relaxation times are long. As the temperature is raised above

4 K, relaxation times shorten and larger RF powers are required. Near room

temperature, RF powers of 10 to 20 G are typically needed to observe free

radicals in solution. When RF powers of 0.1 W or less are used, the RF coil

can be wrapped around the sample and the entire sample and RF coil

immersed in the liquid helium refrigerant or in cooled gas without any

4. ENDOR Spectroscopy

(i.e., ice) is frozen to a sufficiently low temperature (i.e., T < 100 K) the diel-

ectric

158

difficulties from RF power dissipation. At high RF power levels (1 to 20 G), it

would be impossible to carry out an ENDOR experiment using this RF coil

configuration as the liquid helium would boil away as the RF power is

dissipated.

However this problem can be eliminated by placing the RF coil on the

inside of the cavity walls, outside of a dewar insert extending through the

cavity. This removes the load on the cryogenic system and a successful

experiment can be carried out. The large RF coil also allows a large access

area in the cavity, permitting the investigation of large amounts of liquids,

frozen glasses, or large single crystals [1].

4.2.4 RF Power Level: CW versus Pulsed Schemes

Successful experiments have been carried out using a high power wideband

amplifier in which no pulsed RF is used. Instead, 100 to 500 W of continuous

RF power is used to irradiate the sample. Whether the 1 kW pulsed ENDOR

delivering 100 W of radio frequency will be better than a CW spectrometer

delivering 100 W of continuous RF power turns out to be dependent [1, 3] on

how easily the nuclear signal can be saturated. If the nuclear signal is easily

saturated, using continuous RF irradiation is better than a pulsed RF by a

factor of 10

1/2

. On the other hand, if the nuclear signal saturates with

difficulty, the pulsed RF will give signals that are 10

1/2

times more intense

than those with continuous RF.

4.2.5 Mode of Detection and Modulation Scheme

The results of several experiments show that the ENDOR lineshape and

intensity depend critically on the detection and modulation scheme used

[1, 3]. However, before the optimum field, RF modulation, and detection

schemes can be established, it will be necessary to predetermine the ENDOR

mechanism for each given free radical sample. This is unfortunately still not

possible. Thus several different schemes are used, and a great deal of

discussion is carried out on the merits of each.

4.2.6 ENDOR Mechanism

The diagram for a simple systems with S = ½ and I = ½ in Figure 4.4 shows

the four levels involved in the relaxation [1]. All relaxation processes, both

electronic and nuclear, must be considered, i.e., T

and T

are the electronic

and nuclear relaxation times, respectively; T

–1

describes the relaxation rates;

and T

describe cross-relaxation processes in which electron and nuclear

4.2 Experimental Conditions for ENDOR

159

spin flips occur simultaneously (so-called flip-flop and flop-flop processes of

electron coupled to nuclear spins). First, sufficient microwave power is

applied to one of the two EPR transitions, e.g., (1) ļ (3), to overpower the

relaxation mechanism connecting the two states, so that their populations

become almost equal.

Figure 4.4 Schematic representation of the four energy levels for an S = ½, I = ½ system. The

possible relaxation processes are characterized by the respective relaxation times. (The energy

levels are separated horizontally to distinguish between the two electron traditions).

Second, a radio frequency field, B

, at the NMR frequency is applied

simultaneously. The ENDOR experiment can be described as the creation of

an alternative relaxation path for electron spins which are irradiated with

microwaves. The role of the RF field is to couple the nuclear and electron

levels and open this alternative relaxation path. If the system is irradiated at

the nuclear frequency corresponding to (3) ļ (4) transition, e.g., then the

relaxation can go via:

i.e., (4) ļ (1) (4.18)

, i.e., (4) ļ (2) and T

, i.e., (2) ļ (1). (4.19)

The extent to which the alternative relaxation paths can compete with the

direct T

relaxation (3) ļ (1) determines the degree of desaturation of the

EPR, and consequently determines the ENDOR signal intensity.

After the Q



transition is saturated, i.e., (3) ļ (4) in Figure 4.4, the relaxa-

tion can go via T

or T

and T

, while for the Q

transition, i.e., (1) ļ (2),

the relaxation can occur only via T

and T

if T

~ 0. In general, T

 T

effective in some cases.

If T

dominates relaxation, the intensity inequality of both Q

and Q



ENDOR transitions is predicted because T

relaxation is effective only

between the (1) and (4) levels. Their relative intensities depend on the amount

by which cross-relaxation is faster than the nuclear spin-lattice relaxation

4. ENDOR Spectroscopy

160

process. If cross-relaxation is very slow and can be neglected, both ENDOR

transitions can have equal intensity. The ENDOR effect is therefore described

as the relaxation time T

effectively shortened by the application of an RF

field at the NMR transition frequency.

4.2.6.1 Enhancement of Radio Frequency Field at the Nucleus

The RF enhancement effect is very important because it often allows

detection of those nuclear transitions which would otherwise be difficult or

even impossible to saturate with the RF fields B

available in conventional

ENDOR spectrometers, i.e., to meet the J



B

 1 condition given by

equation (4.17).

The effect occurs because the electric magnetic moment creates an

additional magnetic field component (hyperfine field) at the nucleus. This can

be described by an enhancement factor k, changing the magnetic field seen by

a nucleus:

eff

= kB

, (4.20)

where

|1 |

k 

»(4.21)

The RF enhancement is particularly significant for nuclei other than

protons with small magnetic moments (small J

), and large hyperfine

constants a, e.g.,

N. No enhancement exists for m

= 0. Equation (4.21)

holds only for the isotropic case, i.e., the liquid phase. In single crystals, the

hyperfine interaction is anisotropic. Consequently, k is governed by different

hyperfine components.

4.2.6.2 Signal Intensity

The absolute intensity of an ENDOR signal is not related to the fractional

change in T

(desaturation) caused by the RF field, but also depends on the

intensity of the EPR signal itself. The signals observed depend very critically

on the balance between the various relaxation times and the magnitude of the

microwave and the RF field.

In ENDOR spectra, the intensities of individual lines are not, in general,

proportional to the number of nuclei contributing to the ENDOR effect, in

contrast to EPR and NMR. The important criterion for assigning the hyperfine

coupling constants to particular nuclei is lost, partially due to different nuclear

relaxation mechanisms for different sets of nuclei. Additionally the effect of

incomplete hyperfine separation of the EPR lines reduces the ENDOR signal.

When microwave irradiation saturates one EPR transition, other EPR

4.2 Experimental Conditions for ENDOR

161

transitions may also be partially saturated, because of overlap. This effect

depends on the hyperfine coupling, as well as a T

2e,

which defines the

homogeneous EPR linewidth. When the experimental variables are optimized,

the signal intensity in ENDOR spectroscopy is usually only a few percent of

the EPR signal intensity.

The intensities of the low and high frequency lines in ENDOR have, in

general, different magnitudes. One reason is the effectiveness of the cross-

relaxation mentioned above. The relative intensity of the low- and high-

frequency lines depends on which EPR line is monitored [Figure 4.4, (2) ļ

(4) or (1) ļ (3)].

Another cause of different intensities is the RF enhancement effect.

Frequently, the RF power available in ENDOR spectrometers is not constant

over the whole frequency range; thus, line intensities are affected. Even when

RF power is constant, two effects are observed as a consequence of RF

enhancement: (1) for small hyperfine couplings, i.e., when the ENDOR

signals are close to the free nuclear frequency, they are often very weak; (2)

the high frequency line of an ENDOR line pair (Q

pair) is usually more

intense than the low frequency as the difference between the two components

and Q



) increases. In spectra of single crystals, however, the RF

enhancement factor is governed by different hyperfine tensor components.

This often leads to unexpected intensity patterns of the Q

and Q



lines.

4.2.7 Extension of ENDOR: TRIPLE Resonance

The ENDOR technique has been expanded to include a second NMR exciting

field, thus giving so-called electron-nuclear-nuclear (TRIPLE) resonance.

The advantages of TRIPLE are: (1) enhanced sensitivity and resolution and

(2) the possibility to directly determine relative signs of hyperfine coupling

constants.

4.2.7.1 Special TRIPLE (ST)

The special TRIPLE (ST) technique is used for hyperfine couplings »a»/2 <

. Referring again to Figure 4.4, if two RF fields are tuned to simultaneously

saturate both NMR transitions (Q

and Q

–

) of the same nucleus, the efficiency

of the alternative relaxation path is enhanced.

Further, when both RF fields are sufficiently strong to completely saturate

nuclear transitions, the EPR desaturation becomes independent of T

. Thus

the line intensities are not determined by the relaxation of the various nuclei.

As a consequence, an ST spectrum may reflect the number of nuclei involved

in the transition [2].

4. ENDOR Spectroscopy

162

4.2.7.2 General TRIPLE (GT)

In general TRIPLE (GT) resonance, NMR transitions of different sets of

nuclei of the same kind (homonuclear TRIPLE) or of different kinds (hetero-

nuclear TRIPLE) are saturated simultaneously. In this experiment, one EPR

and one NMR transition is saturated, the NMR transition being saturated with

the first RF while the second RF field is scanned over the whole range of

NMR resonances. The characteristic intensity changes of the high and low

frequency signals, compared with those of the ENDOR signals, give the

relative signs of the hyperfine coupling constants. GT always gives larger

TRIPLE line amplitudes for opposite signs of a than it does for equal signs,

provided the g

-factors of both nuclei have the same sign [4]. In general,

ENDOR measurements are used to significantly improve the resolution of the

EPR spectrum; directly identify the nuclei being measured; to determine the

relative sign of the hyperfine coupling; to differentiate the species of

overlapping spectra; and to give information obscured by inhomogeneous

broadening. Steady state ENDOR requires the presence of a minimum of 10

radicals in the sample, thus this technique is restricted to stable radicals or to

relatively long-lived species with lifetimes of at least 10

–3

s. ENDOR studies

in liquids are confined to organic radicals including their ion pair complexes

formed with alkali cations. For paramagnetic transition metal complexes in

fluid solution the required microwave and RF fields cannot be achieved, so

solution ENDOR spectra are almost never observed for transition metal

nuclei, or any other nuclei present in a complex.

The hyperfine constants obtained from ENDOR spectra are useful in

deducing the electronic structures of the radicals. Further, the temperature

dependence of the spectra permits a study of the conformations and rates of

intermolecular motions in radicals.

A major problem in EPR/ENDOR spectroscopy is the assignment of the

observed hyperfine coupling constants to specific molecular positions in the

radical. In solving this problem it is very helpful to obtain (1) intensity ratios

of the signals from ST; (2) relative signs of the hyperfine constants form GT;

(3) temperature dependence of the hyperfine constants; and the individual

ENDOR linewidth; (4) computer simulation of the EPR spectra with

ENDOR-derived coupling constants; and (5) ENDOR spectra of compounds

containing specific isotropic labeling such as

N, and

4.3 ENDOR IN THE SOLID STATE

A variety of chemical systems and nuclei have been studied in the solid state

by the ENDOR method, made possible by the wide temperature range

available for solids. Since the relaxation processes affecting ENDOR signal

163

4.3 ENDOR in the Solid State

intensity are temperature-dependent, changing the temperature can make the

relaxation of the system favorable of the ENDOR experiment.

In the solid state, the hyperfine interactions usually give rise to only

partially resolved EPR spectra. The unresolved couplings contribute to the

EPR linewidth, giving inhomogeneously broadened lines. Linewidths in solid

state EPR spectra are rarely less than a few megahertz (about 1 G), while in

ENDOR spectra the linewidths range from 3 kHz to 1 MHz.

4.3.1 Single Crystals

4.3.1.1 Hyperfine Interactions

All isotropic and anisotropic data are accessible from ENDOR single-crystal

studies. Since anisotropic interactions depend upon the orientation of the

crystal in the applied magnetic field, the tensor elements can be determined by

studying an oriented single crystal.

Let us assume, for simplicity, that g is isotropic so the spin Hamiltonian

can be written as

H = gEB

S – 6 g

+ h 6 S

(4.22)

where Ã

is the hyperfine coupling tensor for the ith nucleus. For the strong

field approximation (electron Zeeman interaction dominates, i.e., H

>> H

and H

), in the principal axis system the observed splitting is

1/2

22 22 22

obs

ËÛ



ÍÝ

AAAAA

xx x yy y zz z

(4.23)

where A

are the principal values of the hyperfine tensor, and the orientation

of an axis system xyz with respect to the B field direction is specified by the A

direction cosines. If the isotropic coupling in the resonance condition for the

ENDOR transition equation (4.13) is replaced by A

obs

, the ENDOR

frequencies ae given by

Q

= »v

± m

obs

or, for S =

, (4.24)

Q

= »Q

obs

»

From complete measurements of the dependence of the A values on the angle

of rotation around the three mutually perpendicular axes, all components of

the Ã tensor can be obtained.

The usual procedure in the EPR/ENDOR single-crystal study is to choose

a set of reference axes xyz related to the crystallographic axes of the crystal.

In general, the xyz-axis system will not coincide with the principal axes of any

tensor. In three separate experiments, the crystal is oriented in the magnetic

field with one of the reference axes perpendicular to B. The positions of the

4. ENDOR Spectroscopy

164

orientationally dependent ENDOR lines are recorded as the crystal is rotated

about each axis. Since such experiments give the square of the elements of

the hyperfine coupling tensor, the signs of the hyperfine coupling constants

are not deduced. The tensor is then diagonalized, and the principal values of

Ã are determined in its principal axis system. The orientation of this system

relative to the reference axes is defined by means of direction cosines. Since

the reference axes are related to the crystallographic axes, the location of the

paramagnetic center can be identified.

In general, the total coupling tensor Ã is composed of isotropic and

anisotropic (dipolar) components. The isotropic part is given by



a AAA (4.25)

The A

principal elements of the Ã tensor contain both isotropic and purely

dipolar components. The dipolar components of Ã are described by:

dip



xx xx

yy yy

zz zz

(4.26)

For small anisotropies, i.e., when »A

dip

»<<»a», the observed hyperfine

coupling A

obs

can be approximated by:













1/2

222

dip 2 dip 2 dip 2

obs

ËÛ

  

ÌÜ

ÍÝ

AAAAAAA

xx x yy y zz z

a (4.27)

In the common case of axial symmetry of Ã, if z is a symmetry axis, the

following notation is used:

dip dip

dip

dip dip

dip

xx yy



AAA

and

dip

obs

(3cos 1)

a T

 AA (4.28)

where T is the angle between B and the symmetry axis z of the tensor.

An example of the hyperfine coupling angular dependence can be found in

reference [1] pages 172–174 for a defect center (trapped) electron in a

bromide ion vacancy site of a KBr crystal. Although the broad EPR signal

(linewidth § 55 G) gave no information about the structure of the defect

center, the interaction of the electron with several shells of surrounding nuclei

was recognized by the ENDOR method. The shells are composed of

39,41

and

79,81

Br ions, each with spin I = 3/2. Identification of the shell number was

AA a.

165

4.3 ENDOR in the Solid State