ELECTRON SPIN RESONANCE (ESR) SPECTROSCOPY

ELECTRON SPIN RESONANCE (ESR) SPECTROSCOPY (Lecturer : Dr. Dwi Siswanta)

By

Indarto 11/321947/PPA/03523

POSTGRADUATE POSTGRADUATE OF CHEMISTRY FACULTY OF MATHEMATIC AND NATURAL SCIENCE UNIVERSITY OF GADJAH MADA YOGYAKARTA

2012

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Indarto(3523) ESR Spectrometry 2012

I. INTRODUCTION

A. What is ESR?

The phenomenon of electron spin resonance spectroscopy can be explained by considering the behavior of a free electron. According to quantum theory the electron has a spin which can be understood as an angular momentum leading to a magnetic moment. Consequently, the negative charge that the electron carries is also spinning and constitutes a circulating electric current. The circulating current induces a magnetic moment µ S which, if the electron is subjected to a steady magnetic field H 0 ‖ z, causes the electron to experience a torque tending to align the magnetic moment with the field. The relation between the magnetic moment and the spin vector is

where µB µ B is the Bohr magneton and g is the Landé factor. The energy of the system depends upon the projection of the spin vector along H 0. Quantum theory stipulates that only two values are permitted for an electron S z = ±ħ /2, which means that the electron magnetic moment can only assume two projections onto the applied field as shown on Fig.1.1 Consequently,

and the ensemble of energy levels therefore reduce to the two values










Figure 1.1: (a) Schematic representation of a single electron spin in a steady magnetic field H0 (b) Corresponding energy-level scheme.

If electromagnetic radiation is applied at a frequency that corresponds to the separation between the permitted energies energies equal to ∆ E = E + - E - = gµ B H 0 = ħω, energy is absorbed from the electromagnetic field. This is the phenomenon of ESR. For electrons bound into an atom or a molecule, the phenomenon of ESR may not be observed at all, because electron spins pair off in atomic or molecular orbitals so that virtually no net spin magnetism is exhibited and the material is said to be diamagnetic. When an atom or a molecule has an odd number of electrons, however, complete pairing is clearly not possible and the material is said to be paramagnetic. In that case ESR can be observed. So far we have considered a single electron interacting with an external magnetic field. In the present experiment, however, we deal with a macroscopic sample which means a statistical ensemble of magnetic moments. Therefore, we need to consider consider the t he relative populations of the energy energ y levels N + and N -, which are given by the Boltzmann distribution:










that is observed, this difference between the two populations should therefore be made as large as possible. At room temperature N + ≤ N - for a Zeeman splitting corresponding to a frequency of 10 GHz.

Figure 1.2: Spliting of ESR line Mn

2+

owing to hyperfine interaction .

B. The hyperfine interaction

Hyperfine interaction is the interaction between the magnetic moment of an electron with the magnetic moment of the nucleus in its vicinity. Nuclei individually associated with the electron spin system often have a magnetic moment I which also has different allowed orientations (2 I + 1) in H0. The magnetic field associated with the nuclear moment then can add to or subtract from the applied field experienced by the electron spin system associated with it. In the bulk sample some electrons will therefore be subject to an increased field and some to a reduce field. Consequently, the original electron resonance line is split into (2 I +1) components. For example, when the electronic spin of a transition metal or a free radical interacts with its own nuclear spin the hyperfine interaction is described by the Hamiltonian term










with A the coupling constant. The hyperfine coupling constant varies with the nuclear species, and it is a measure of the strength of the interaction between the nuclear and electronic spins. Fig.1.2 illustrates well the phenomenon: the hyperfine interaction between the electronic spins and the nuclear spin I=5/2 in the Mn2+ ion splits the resonance line of the 3d electrons into six sub-levels.

Figure 1.3: DPPH-Molecule (C6H5)2N-NC6H2(NO2)3

In molecules, the unpaired electron circulates between several atoms and the resulting hyperfine structure is the result of a Hamiltonian term of t he form

where the projection mi of the ith nuclear spin on the magnetic field direction may take on the following 2 Ii +1 values: I ,i I i-1 , I i-2 ,....,1-I ,-I i i. For example, the hyperfine interaction with the two equally coupled nitrogen nuclei (I=1) in DPPH molecule (see Fig.1.3) leads to a splitting of the resonance into five components of respective intensity 1:2:3:2:1.

C. The dipole-dipole interaction

For a large concentration of electronic spins, the electronic magnetic moments also interact appreciably with each other, and this can alter considerably the ESR spectra. The interaction is mediated by the dipolar field associated with the magnetic moment µ S










Combining equation 1.2 and 1.3, we see that the energy of dipole-dipole interaction between two adjacent electrons distant of r lays between E dd dd and -E dd dd with

The dipolar interaction induces therefore a broadening of the resonance line, which increases with the concentration of dipole moments.












II. ESR SPECTROMETER SPECTROMETER

We need four essential components to build an ESR spectrometer: 

A monochromatic microwave source



A waveguide for guiding the microwave power to the sample



A cavity designed to ensure a proper coupling between the sample and the incoming wave.



A detector for microwave power to detect the response of the sample to microwave irradiation.



A schematic drawing of the ESR spectrometer is shown in Fig.2.1










oscillator. The frequency can be read out with the frequency counter located next to the t he source. 2. A calibrated attenuator is use to control the level of microwave power from the source. The scale is logarithmic:

with P0 the output of t he microwave source. 3. “A T-hybrid" is the 4-ports device sketched in Fig.2.2. A wave entering from the source at input 3 splits equally into two waves travelling to 1 and 2. The port 4 being orthogonal, no transmission from port 3 to port 4 is allowed. Also, no reflection occurs at port 3 and 4 owing to the presence of the source and the detector. Waves are therefore reflected only from ports 1 and 2. Let ∆ϕ be the difference between these two reflected waves. If ∆ϕ = 0 then the two recombine in port 3. If ∆ϕ = π , the two recombine in port 4. In this experiment, the relative phase and amplitude of inputs 1 and 2 can be controlled with an attenuator and a moveable short located on the right arm of the hybrid.










4. The detector is a crystal rectifier (diode) which consists of a semiconducting material. The incident microwave power causes the current to flow. The current I increases with the microwave power P and the sensitivity of the detection strongly depends on the slope dI/dP which is specific to each diode. 5. The waveguide is a rectangular opened-ended metallic tube delimiting a dielectric media in which electromagnetic waves propagate according to Maxwell equations. Boundary conditions have to be fulfilled by the electrical and magnetic components of the wave on the metallic walls. Consequently the propagation is restricted to a set of modes occurring at well-defined frequencies which are the characteristic values of the wave equation. There is a cut-off wavelength above which no propagation is allowed and which corresponds for a rectangular waveguide of w idth a, to λc = a/ 2. 2.










6. The cavity is a closed metallic box with an iris to allow the microwave to couple in and out (see Fig.2.1) Any cavity possesses resonant frequencies at which the energy stored reaches large values. These frequencies are related to the dimensions of the cavity. The quality factor Q of a cavity measures the frequency width of the resonance or equivalently its selectivity. It is defined like

Q-values in general are of the order of magnitude of o f the volume-to-surface ratio of the resonator, divided by the skin depth in the conductor at the frequency of resonance. Figure 2.3 shows the detailed characteristics of the rectangular cavity used in the present experiment.

B. Electronic equipments

1. An oscilloscope with its X and Y channels. 2. A plotter also with its X and Y channels. 3. The pre-amplifier amplifies in two successive steps: a first dc amplification and an ac amplification through a 115 Hz-bandpass filter. Beware of not saturating the dc stage of amplification. 4. The GUN power supply delivers 15V. 5. A Hall-probe measures the static magnetic field. As indicated by its name, the principle of operation is based on the Hall-effect. The probe should therefore be positioned vertically relative to the magnetic field in order to get the maximum sensitivity. sensitivity. Be careful care ful when manipulating manipulating the probe. It is










current is extremely stable in order to avoid spurious noise that could interfere with the measurement. measurement. 9. The low frequency oscillator creates a sinusoidal current at the frequency of 115 Hz in the second pair of coil (II). This produces the field H m and provides the external reference signal for t he lock-in amplifier. 10. The ramp-generator produces a ramp of magnetic field by varying continuously the current in the pair of coils I. The voltage output of the ramp can be connected to the X-channel of the plotter if the variation of static fields are too small to be accurately read from the gaussmeter. For larger amplitude of change, the analogue output of the gaussmeter can be converted to a digital signal and sent to the X-channel X- channel of the plotter. 11. The lock-in amplifier amplifies signals at frequencies close to the frequency of a reference signal. More details concerning the principle of operation of a lock-in are given in the following section. Here we emphasize that the reference signal should come from the low frequency oscillator. Be careful to connect the t he 115Hz signal to the proper input of o f the lock-in amplifier.












III. DETECTION SCHEME

A. ESR signal

In

a

resonance

experiment,

the

phenomenon

of

absorption

of

electromagnetic electromagnetic energy by the sample is generally t ranslated ranslated into a variation of the complex impedance Z = R+ jX of an oscillating circuit. When the sample experiences a time-varying feld, the absorptive component of the susceptibility to this field changes the resistivity R while the dispersive components changes the reactance X .1 .1 ◊ For a complex susceptibility χ sketch the variation through resonance of χ’ and χ” and also δR and δ X as a function function of frequency. frequency.

The sensitivity sensitivity of a given detection scheme to absorption or dispersion can thus be defined as the change of the measured quantity - a voltage, a current or a










and the ESR signal (S) is therefore defned as the scalar product

This means that the extent to which the absorption and dispersion components affect the modulus ǀГǀ depends on the phase of changes in δГ expressed relative to Г. This can be readily seen in Fig.3.1.

◊ Based on Fig.3.1 and what has been said above explain how to detect the dispersive component (ba') of the signal.

Figure 3.1: This contruction shows how the absorption and dispersion components of the signal are connected to the variations of the reflection










superimposed on the constant magnetic field H 0 + H δ. H δ is the local field induced by the surrounding of the considered electron. It is therefore H δ which determines the broadening of the ESR line. The "constant" magnetic field is normally swept over the range ∆ H 0 from ( H H 0 - ½∆ H 0) to ( H H 0 + ½∆ H 0) in a time t 0 where H 0 is the magnetic field strength at the center of the scan. At any time t during the scan, the instantaneous magnetic field strength H is given by

Consequently, the signal at the input of the detector is sinusoidal with the frequency !m and with an ampli a mplitude tude proportional pro portional to the derivative ∂s/∂ H . Note that in order to consider the field ( H 0+ H δ) as constant, the scan should be slow enough so that there are many cycles of the modulation frequency during the passage between the peak-to-peak (or half amplitude) points of the resonance line. ◊ Sketch the effect of field modulation on the ESR line.










where ϕs is another phase angle that may be close to ϕ. The multiplier produces an output that is the product esvr of the ESR signal and modulated voltages

The low pass filter removes the first term t erm to produce the dc output voltage V out out

and we see immediately that the sensitivity is maximal if ϕ is set equal to ϕs, which gives

When the electron spin resonance signal is measured by the lock-in amplifier it still contains a considerable amount of noise. A large part of t his noise may be removed by passing the signal through a low-pass filter. The filter has associated with it a time constant or response time τ , which is a measure of the










IV. EXPERIMENT

The following questions are of course suggestions and should not substitute the initiative of the experimentalist. experimentalist. The cabling of the spectrometer is described in Fig.4.1.












3. Measure the amplitude of the modulation of the field as a function of the modulating current. 4. Measure the ESR signal on a powder sample of DPPH in absorption and dispersion. Estimate Estimate the linewidth and the t he g-factor. 5. Measure the ESR signal of DPPH in solution for different concentration. Estimate the dipole-dipole coupling constant. From that estimate the range of concentration where the dipolar interaction becomes stronger than the hyperfine interaction and compare with experiments. 6. Repeat 6 and 7 for Mn

2+

in solution.

7. Observe and discuss the effect of varying the amplitude of the modulating field on different ESR lines. lines.










BIBLIOGRAPHY

Paramagnetic Resonance Resonance of of 1. Abragam and B. Bleaney, 1970, Electron Paramagnetic Transition Ions, Clarendon Press . Oxford. Introduction to microwav microwave e theory, McGraw-Hill. 2. H. A. Atwater, 1962, Introduction

3. J. E. Ingram, 1976, Radio and Microwave Microwave Spectroscopy Spectroscopy, Butterworth & Compagny. 4. P. Poole.Jr, 1967, Electron Spin Interscience Publishers. Spin Resonance Resonance, Interscience

ELECTRON SPIN RESONANCE (ESR) SPECTROSCOPY

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