Techniques and applications of electron spin resonance

70 Pages·2007·5.11 MB·English

Bull. Mater. Sci., Vol. 21, No. ,1 February 1998, pp. 1-70. © Printed in India.
Techniques and applications of electron spin resonance*
C S SUNANDANA
School of Physics, University of Hyderabad, Hyderabad 046, 500 India
MS received 27 January 1996
Abstract. A broad-spectrum review of the applications of electron spin resonance to advanced materials is
presented. Starting with basic concepts the reader is taken through a quick tour of techniques including
continuous-wave and pulse ESR, microscopy and imaging, as well as a few emerging techniques. Applications
of spin identification, spin counting, spin mapping and spin imaging of a variety of advanced solid state
materials including metals and alloys, semiconductors, inorganics, electroceramics, catalysts, intercalates,
polymers, glasses, and organic charge-transfer complexes besides superionic conductors and high-temperature
superconductors are included. It is thus demonstrated that the technique is at once specific, sensitive to
composition, phase and texture yet accurate enough to be a quantitative but non-invasive tool that promises
to be useful in the study of newer and newer materials including multilayers, ferrofluids and nanomaterials.
Keywords. Electron spin resonance; advanced materials; ESR microscopy and imaging; semiconductors;
polymers; glasses; superionic; superconductors.
1. Preamble 2. A brief historical perspective
The use of magnetic moment of an unpaired electron- Electron spin resonance (ESR) or more generally speaking
a fundamental particle with an intrinsic property of 'spin' electron paramagnetic resonance (EPR), discovered by
(table 1) that is naturally found (or artificially created) Zavoiskii (1944) in MnSO 4 employing a 47-6Gdc
in materials as an essential part of their unique crystal magnetic field and a 133 MHz rf magnetic field, is an
structures, and dictating their electrical, optical and mag- extension of the original Stern-Gerlach experiment (Stern
netic behaviour -- as a microscopic, resonance spectroscopic 1921; Gerlach and Stern 1924), on atomic beams which
probe of characterization is the basis of electron spin demonstrated the space quantization of atomic magnetic
resonance (ESR) or more generally speaking electron para- moments. In between, Rabi (1939a, b) had performed
magnetic resonance (EPR). It is the hierarchy of interactions the 'nuclear Zeeman effect' experiment by using a radio
of this magnetic moment with its neighbouring and the frequency electromagnetic field perpendicular to a
more distant material environment that is exploited in this homogeneous dc magnetic field. Theoretically, the
technique to learn more about either the materials processing possibility of quantum transitions between magnetic
per se or the induced process(es) that take place within sublevels of atoms under the influence of an external
the material. It could be said that the EPR technique and magnetic field was suggested by Einstein and Ehrenfest
advanced materials are 'made for each other'.
(1922).
Starting with a brief historical perspective, this article The earliest applications of microwave resonance
goes on to provide a brief account of the methods and spectroscopic technique were on 0(i)2 H5-4OSuC crystals
applications of this technique. The spectrum of the in which 'exchange narrowing' was discovered (Bagguley
advanced materials covered include semiconducting and Griffiths 1950), (ii) F-centres in alkali halides from
materials, polymer materials, ceramics and glasses, and which structural information was obtained (Kip et al
optoelectronics and superionic materials. ESR imaging 1953), and (iii) donor atoms (P, As and Sb) in silicon
and microscopy as well as certain emerging techniques in which motional 'narrowing' and delocalization of
such as millimeter ESR are briefly discussed. The donor electron wave functions were observed (Fletcher
examples chosen are meant to be representative, and the et al 1954), which paved the way for the discovery of
seemingly inexhaustible information is available in electron-nuclear double resonance-ENDOR in phos-
standard books, review articles and papers referenced in phorus doped silicon (Feher 1959), which has been very
this article. profitably applied to the elucidation of defects in amor-
phous semiconductors. The EPR studies of surfaces also
*Dedicated to my teacher, the Late Prof. C Ramasastry (1923- began with silicon (Fletcher et al 1954; Feher 1959;
)9891 Brodsky and Title 1961; Roitsin and Maevskii 1989).
2 C S Sunandana
Table 1. Properties of fundamental particles relevant for magnetic resonance spectroscopy.
Property Electron Proton Neutron Muon
Charge (C) -1-602192 × 10 -19 0
Mass (kg) 9.109534(47) x 10- 3t )68(5846276.1 x 01 72- 1.6749543(86) × -01 72 1.883566(11) x 10 -28
Magnetic moment 9-284832(36) x 10 -24 )15(176104-1 x 01 72-
(Joule/Tesla) 2.7923456( 11 ~tk) -1-91304 nik)88(481 4-490474(18) × 10 -26
~ltk X = 5.0505 -01 72 J/l"
g-factor (Zeeman) 92913200-2 )13.0(61661100.1
g-factor (spin-orbi0 2.00463858
Sources;
.1 Weast R C (ed.) 1988 CRC Handbook of Physics and Chemistry ts1 Student edn.
.2 Krane K S 1988 Introduction to Nuclear Physics (New York: Wiley).
An investigation of permeability of ferromagnetic metals motion of these moments and an angular momentum
Fe, Co and Ni, by Griffiths (1946) led to the discovery thereof; (iii) quantization of these angular momenta S
of ferromagnetic resonance. An examination of free radi- and I for electron and nuclei, respectively; (iv) distinct
cals in leaves, seeds and tissue preparation saw the first magnetic energy levels created by an externally applied
biological application (Commoner et al 1954). McConnell static magnetic field and a separation between these
pioneered the use of 'spin labels' or free radical sub- levels; (v) a substantial number of 'spins' in their lowest
stituents in biological systems (Stone et al 1965), while energy states at ambient temperatures according to
Sands (1955) pioneered a continuing structural investi- Boltzmann distribution law, according to which the popu-
gation on transition metal ion-doped glasses. Weeks lation difference between two energy levels at temperature
(1956) applied the technique for studying radiation- T is proportional to the negative exponential of ratio of
induced centres in crystalline quartz, and, Yasaitis and the difference between concerned energies and the thermal
Smaller (1953) investigated the paramagnetic centres in energy kBT, where B k is the Boltzmann constant, and
irradiated borate glasses. The studies on mechanically finally, (vi) the natural precession frequency called the
produced free radicals in polymers were pioneered by Larmor frequency for the spin system (which for the
Zakrevskii et al (1968). electronic moment depends on the external magnetic
The observation of electron spin echoes (Gordon and field and for the nuclear moment on the internal electronic
Bowers 1958; Mims et al 1961) ushered in the era of field) which may be approached either by scanning the
pulsed electron spin resonance, coming in the wake of frequency of the alternating field at a fixed static magnetic
Hahn's discovery of nuclear spin echoes (Hahn 1950). field or by scanning the static magnetic field at a fixed
The last decade has seen the emergence of EPR imaging frequency.
and microscopy (Ikeya 1991), again following the dis-
covery of NMR imaging (Lauterbur 1973).
3.1 Classical picture
The bludgeoning activity in this field is evidenced by
the very recent appearance of a number of comprehensive
A planetary model of an atom with a magnetic nucleus
monographs and workshop proceedings (Piibrow 1990;
~t/( :~ 0) and an unpaired electron (/t c :* 0) illustrates their
Yordanov 1991; Mabbs and Collison 1992; Ikeya 1993),
intrinsic property of 'spin' in a classical way (figure !).
besides the existing classics (Wertz and Bolton 1972;
An electron of spin S with a magnetic moment /t
Atherton 1973; Abragam and Bleaney 1989).
experiences- much like a tiny bar magnet- a torque
tt, o × H in an external magnetic field. This angular motion
constantly and continuously changes direction so that
3. ESR concepts
)~S(d
d--7- =~ =l~ x no, (1)
The phenomenon of resonance absorption of the magnetic
component of external electromagnetic radiation by a
paramagnetic or spin system such as a hydrogen atom being always normal to the #-H o plane, changes only
in silicon, or an irradiated polymer or cobalt in barium the direction of t I as the latter precess around o H with
titanate is based on the existence or postulation of: (i) a frequency
intrinsic magnetic moments due to 'spins' of electrons
~,) and certain nuclei u,( 0 (table 2); (ii) gyroscopic )o = y ° ,oH (2)
Techniques and applications of electron spin resonance 3
where y, = electron magnetogyric ratio =- gel2mc, with when the total magnetic field acting on the spin system
g being the spectroscopic splitting factor, e the electron is the vector sum
charge, m the electron mass (see table 2) and c the
velocity of light. For the electron, the dipole moment H = Ht(i cos tot +j sin too + Hok,
opposes the angular momentum so that
and ge is assumed to be 2. The resonance condition can
# =-y~S. (3) be arrived by considering the allowed energies of the
electron magnetic dipole
The magnetic component of the electromagnetic field
(which lies in microwave region for ESR and radio- it[ lit I =y i~ S(S + 1)'/2],
frequency region for nuclear magnetic resonance or
NMR), (<<Ho) IH, I also rotates with microwave frequency in the field H ,0 using the energy operator
to and exerts a torque itxH, on it. As long as to ctoo
this torque is zero on the average but when to = to o, it H =-It 'H o=y?iS'H o. (6)
precesses around n H with a frequency to, =yHt besides
its usual precession around 0 H with frequency Taking o H along + z axis (figure 2) the allowed energies
to0(>>w0. Consequently, it slowly changes its direction are
flipping down and eventually reaching a position opposite
to the original orientation (figure 2). In the flipping )7(
M E = 7 ;IHoM ,
process work is done on the dipole moment by the
microwave magnetic field. In other words, the system where the quantum number s M specifies the allowed
absorbs energy from the microwave field L H during values of the z-components of S viz. -S, -S+ 1
resonance. At resonance the oscillatory magnetic moment, ... S-l, .S For S=1/2, M=+1/2 and the allowed
normal to H, produced by Larmor precession interacts energies are
with the small oscillatory magnetic field H, cos tot, also
normal to H, and changes the direction of component e 1 + + = y~no. (8)
of it along H by 180 °, and thus changes the energy of
the electronic dipole, causing ESR absorption. Thus at Transitions between these levels (figure 3) caused by
resonance, magnetic dipole radiation require that AM.,=+ 1. The
resonance condition that the energy quantum ~to of ~H
v o v g(e/2m) H (2zt) must satisfy is
= =
= 139.96(gH) (v in Hz, H in T). (4) ~.o=E+ I-E-~ 1 = 7eP/no, (9)
H is also expressed in Oersted and gauss, with 10,000 which coincides with the classical picture to =TH0 = to .0
such units to a Tesla. The basic gyromagnetic ratio for the free electron is
3.2 Quantum picture ~7 = 2.rr(28.0246 GHz/T). (lO)
Quantum mechanically, the phenomenon of electron
3.3 Spin relaxation
paramagnetic resonance is described as the magnetic
dipole transitions brought about by the interaction of the The above pictures are valid for the hypothetical case
magnetic field of the microwave radiation with a magnetic of a single isolated spin or a paramagnet. In the real
moment in the absorbing system. Quantum mechanics helps world materials contain a large number of spins, so that
in arriving at the probability of these transitions and shows the concept of a 'reservoir' or a 'bath' or the concept
that this probability has a sharp maximum when of a 'thermal equilibrium' comes into the picture. The
oc = 2it 8 H/If or hv = 2it B ,oH where BtI is the Bohr mag- reservoir (a crystal lattice or a glassy/polymer matrix)
neton. In other words, to is too, the Larmor frequency, so can take energy from the spin system when the latter
that the probability for the absorption of microwave power makes the transition to the upper of the two states
by the system is maximum when H, is rotating at the ~=_+ 1/2.
Larmor frequency. For a spin system with two energy The populations of spins ÷ N and N-, present in the
levels, this probability is given by (Atherton 1973): two energy states ~M =+ 1/2 and s M =-1/2 respectively,
, 4it.H { when the spin system is in thermal equilibrium with the
reservoir are governed by the Boltzmann distribution
sin ~ 1/2(2/tBHo/'ti - to)~it l
Pt2 - ~2 )5(
21tBHo/~ _ to2 J ' N÷ / - N = exp(- 71~H,/kBT). (11)
¢3 ;a
2t t) 0.2 1 II 29 76 151 270 11 20 75 149 229 382 586
(cm-
stable (S) ° o
H- Li Na
form
Most paramagnetic
-2)
moment cm
Electric 0.002875 - 0.000644 0.040 - 0.053 0-08608 0.040 0-01932 0-026 - 0-108 0.22 0.150 - 0-064 0.08249 -
e I x 10 -24
quadrupole (I
gN
studies. 5-586912 0-8574376 -4.255248 0-8220514 2A170961 -0.7850 0A600216 1.792424 2.0382 0.4037607 -0.757516 5.257934 1.478391 - 0.34218 1.456601 -1.1106 2.26320 0.42911 2.7639
(B0)
1.084
resonance t8 66 34 48 104 42 62 206 56 100
Anisotropic coupling
spin
(G)
78 39
electron Isotropic coupling Ais o 508 (1430)0 (- 6357) 105 (364.9) 130 (-451.6) 242 725 (2547) 1130 (3777) 552 (1811) 775 1660 (-5263) 17200 (52870) 317 (927-1) (-485-9) 985 (3911) 1220 (-4594) 3640 (13306) 975 (3463) 1680 (5723)
from s
3 )
(r- (a.u.) (0-9293) 1-692 (2.002) 3-101 (3.599) 4-974 (5.820) 7"546 (1-493) (2-691) 3.319 (4-242) 4.8140 (6.131) 6-709 (8-389)
constants
0-775 1.055 2.041
12 (8-766)
I Wn~(o) (a.u.) 0.314 (0-318)* (1.867) 0.1673 (0-2101) 0-5704 (0.7188) 1-408 (1.775) 2.767 (3-358) 4.770 (5.599) 7.638 (8-669) 11"966 (12"53) (0-7797) (1-763) 2-358 (3.327) 3-807 (5.115) 5-625 (7-252) 7.9187 (9-930) 10.643 (12.81)
hyperfine coupling
dipole (/.tN)
and
nuclei Nuclear magnetic moment 2.79284 + 0-85743 2.12762 + 0.822056 + 3-25644 - 1.1776 + 2.6886 + 0-70241 0.40376 0.28319 - 1-89379 + 2"62887 + 2-21752 - 0-85545 + 3.64150 0-5553 + 0.64382 + 0-82187
+ - + 1.13160
+ 1.8007
magnetic Spin 1/2 1 1/2 1 3/2 3/2 3/2 112 + - 1 3/2 5/2 5/2 - 1/2 3/2 312
of 3 1/2 1/2
1 5/2
Properties Natural abundance (%) 99.985 0.015 0.00014 7.5 92.5 19.8 80.2 1.10 99.63 0-37 0.038 100 100 10.00 100 4-67 100 0.75 75-77
2. 100
Table Isotope ~H 2H 3He 6Li 7Li 9Be "~B liB J3C 14N 15N 170 19F 23Na 2SMg 27A1 29Si 31p 33S 35C1
¢L 2
l)
38 154 104 55 57 87 85 100 180 335 852 386 551 940
(cm- - - - -
3+
stable (S) 4+, V 2+ 2+ 3÷ 2+ 3+ 3+ 2÷ 2+ 2+ 3+ 2+
Most paramagnetic form Ti3÷ V V Cr Cr Mn Mn Fe Fe Co Ni Ni Cu
-2)
moment cm
-24
Electric 10 0-06493 - 0-054 - 0.067 0-060 < 0.23 - 0.22 0.29 0-24 0.209 - 0-0515 0.0285/ - + 0.022 0.33 0-42 0-162 - 0-222 0-195 - 0.150 0-168 0-168 -0-19
e I x
quadrupole (I
gN
2.3006 0.2609909 0.1432542 - 0-376414 1-35906 - 0-31539 - 0.315477 0.556593 1.46836 - 0.3147 1-3819 0-1816 1.318 -0.50001 1.484 1-588 0.350312 1.34439 1-70818 -0.1954371
(Bo)
84
Anisotropic coupling
(G)
Isotropic coupling Aiso 1395 83 (228.5) 45 (-640-7) (2823) (-7820) (4165) (- 748-2) (5036) (747.20) (5947) (-2499) (5995) 376 (2087) 2675 (12210) 3400 535 (-2363)
-3)
(r (a.u.) (1.851) (2-444) (3-114) (3-414) (4.721) (5-659) (6-710) (7-864) (8-455) (lO-52) 2-8665 (3-973) 4-7848 (6.439)
~'.a(O)12 (a.u.) (1-066) (2-063) (2.506) (2.975) (3.378) (2-811) (4-300) (4-832) (5.233) (5.755) (4-617) 4-5222 (6.379) 6-9493 (10-18) 9.5721 (13.40)
I
(/.tN)
Nuclear dipole magnetic moment + 0.68412 + 0-39146 -1-298 + 0-21487 - 1-3173 + 4.756 - 0-7885 -0.10417 + 3.34745 + 5-1514 - 0.47454 + 3.4687 + 0.09044 + 4.627 - 0.75002 + 2.2233 + 2.3817 + 0.8755 + 2.01659 + 2.56227 - 0.87946
Spin 3/2 3/2 4 3/2 7/2 7/2 5/2 7/2 6 7/2 3/2 5/2 1/2 7/2 3/2 3/2 3/2 5/2 3/2 3/2 9/2
Natural abundance (%) 24.23 93.2581 0.0117 6-7302 0-135 100 7.3 5-5 0-25 99-75 9-50 100 2.2 100 1.13 69-17 30.83 60.1 39.9 7.8
(contd)
4-1
2.
Table Isotope 37CI 39K 4°K 41K 43Ca 455c 4~ri 49Ti 5°V StV 53Cr 55Mn 57Fe 59Co 6tNi 63Cu 65Cu 67Zn 69Ga 7 tGa 73Ge
o~
1)
X
(cm- 1550 1688 2460
(S)
stable
form
Most paramagnetic
-2)
moment cm
-24
Electric 0.29 0.293 0.27 0.26 0.273 0.130 0-15 O.28 - -0.019 0.2 0-076 0.44 0-66
e I x 10
quadrupole (I
gN
0.959647 1.0693 1.404266 1.513706 -0.215704 0.541253 1-83427 -0.24291 -0.274836 -0-521448 1-3712 -0-3656 -0.3734 -0-279 -0-279 -0-1768 -0.256 -0.227249 -0-261743 1-19043 -
(Bo)
Anisotropic coupling
(G)
o 853-6)
Isotropic coupling Ais 3430 (14660) 4840 (20120) 7810 (32070) 8400 (- 5937) (1037) (- (- 1250) (-2753) (6590) (-1984) (-1764) (-1229) (-1831) (- 13650)
-3)
(r (a.u.) 6-9871 (9.102) 9-2284 ( 12-05 ) I 1.8758 (15-25) (18.76) (2.373) (3-126) (3.494) (4-318) (6-145) (7-179) (7.666) (9-451) (11-37)
I ~.~(o)12 (a.u.) 12-5606 (16.75) 15.7791 (20.41) 19.4127 (24.47) (29.12) (2-OOO) (3.61.7) (4.616) (5-283) (4.736) (5.264) (6-085) (6.414) (7.170) (10.03)
(laN)
Nuclear dipole magnetic moment + 1.43947 0.53506 + 2.1064 2.2706 - 0-9767 + 1.35302 + 2.7512 -1.693 - 0-1373 1-3036 - + 6-1705 -0.9133 0.9335 - -0-6413 0.7188 - 0-0884 - - 0.642 - 0-1135 - 0"1305 - 0-5943
Spin 3/2 1/2 3/2 3/2 9/2 5/2 3/2 9/2 1/2 5/2 9/2 5/2 5/2 5/2 5/2 1/2 5/2 1/2 1/2 1/2
(contd) Natural abundance (%) 100 7.6 50.69 49"31 11.5 72.17 27.83 7-00 t 1-27 100 15.92 9.55 12.7 100 51.84 48.16
2. 100 17.0 22-33 12.8
Table Isotope 75As 77Se 79Br 81Br 83Kr 85Rb 87Rb 87Sr 89y 91Zr 93Nb 95Mo 97Mo 99Ru lmRu l°3Rh t°sPd l°7Ag 1°9Ag l~tCd
g: t~ ¢5 t~
i)
(cm- 800 900 1200
stable (S)
Most paramagnetic form
-2)
moment cm
-24
Electric 10 0.846 - 0-33 -0.68 -0.789 - 0-120 - 0-003 0-20 0.34 6-22 0.51 -0.041 -0-56 -0-29 -0-18 0.056
e I x
quadrupole (I
gN
+ 1-2454 1-22864 - 1.8377 - 2.00208 - 2-09456 1.3455 0-72876 - 1.4736 - 1.7766 1.12530 - 1-55595 0-461240 0-7378477 0-55884 0.62515 0-79520 0.74238 1-6 - 0-3076 -0.190 - 0-2322 0-1915
(Bo)
- 11.87375 + 64-60 -58-7543 (5)
Anisotropic coupling
(G)
o
Isotropic coupling mis (-43920) (351000) (-55590) (41600) (-67790) (2467) (3971) (6007) (12490) (-2399) (-2014)
(:3> (a.u.) (9.160) (12-25) (15.47) (18.92) (22-57) (3-127) (4.953) (5.565) (6.201) (7.546)
~I/na(O)12 I (a.u.) (17-46) (21-51) (25-29) (29.27) (33-79) (2-538) (4.722) (5-492) (4.950) (5-208) (5.309) (5.618)
(gN)
dipole
Nuclear magnetic moment - 0-6217 + 5.523 0.918 - 1-000 - - 1-046 + 3.359 + 2-547 -0-7359 - 0.8871 + 2-808 -0.7768 ? + 2.579 + 0-8365 + 0.9357 2-778 + 3-707 4.25 - 1.08 - 0-66 0-813 - -0-66
Spin 1/2 9/2 1/2 1/2 1/2 5/2 7/2 1/2 1/2 5/2 1/2 3/2 7/2 3/2 3/2 7/2 5 5/2 7/2 7/2 7/2 7/2
Natural abundance (%) 12.22 4-3 0.4 7-7 8-6 57.3 42-7 0-903 7-14 1 O0 26.4 21.2 100 6.592 11-23 99.91 0-09 100 12.18 8-30 15-0 13-8
(contd)
2.
Table Isotope 113Cd 1~3In 115Sn l lTSn l l9Sn 12tSb 1235b t23Te 125Te 1271 129Xe 131Xe 133Cs t35Ba 137Ba 139La 138La t41pr 143Nd 145Nd 1475m 149Sm
oo
7.
(era- i) 1416 1540 - 1770 - 1860 -2000 - 2350 - 2940
stable (S)
2.47
Most paramagnetic form
-2)
moment
Electric lO-Ucm 1-53 1.30 1-34 1-34 -0.189 2.51 2.73 2-827 2.8 5-68 8.0 4-5 5.1 3-44 2.33
(lelx
quadrupole
gN
1.389 3.92 -0.1723 -0.2253 1.342 0.266 1.192 -0.1618 0.9885 -0.27185 0.63943 0.454 0.2267 -0.1424 0.67729 0.2355694 1.2748
(Bo)
0-6134
Anisotropic coupling
(6)
o ((3)
lsotropic coupling Ai~ (5722) (-2546) (-2546) (13630) (2963) (13560) (- 1934) (- 5835) (- 3670) (10630) (4410) (15020) (5777)
(:3) (a.u.)
(8.261) (3.993) (3.993) (9.783) (4.588) (5-756) (6.945) (8-174)
(10-59) (11-43) (12-31) (13.26) (13-26) (14-19)
12 I)
~na(O) I (a.u,) (5-952) (6-970) (6-97 (6.142) (-0.71415) (6-459) (6.624) (3.739) (6.919) (- 3.6302) (4) (7-245) (8.7oo) (9.942) (11.11) (11-97)
(1~)
Nuclear dipole magnetic moment + 3.464 + 1-530 - 0-27 - 0.36 + 1.95 - 0.48 + 0-673 + 4-173 - 0-5665 -0.2316 0.4919 - 0.6776 + 2-2327 +3-19 + 0-7935 - 0.6409 + 2.370 +0-11778
+
Spin 5/2 5/2 3/2 3/2 3/2 5/2 5/2 7/2 7/2 1/2 1/2 5/2 7/2 7 7/2 9/2 7/2 1/2 5/2
(%)
(contd) Natural abundance 47-8 52-2 14-80 15.65 100 18"9 24-9 100 22-95 100 14-4 97-40 2-59 18.6 13"74 99"998 14-3 37.40
2. 16.2
Gd
Table Isotope 151Eu 153Eu 155Gd 157 t59Tb 161Dy 163Dy 16SHo 167Er 169"rm tTtyb t73yb 175Lu 176Lu 177Hf 179Hf lSlTa lS3W 185Re
J)
(cm-
stable (5")
Dover)
form
Most paramagnetic
York:
(New
moment cm-2)
Electric 2-22 0-8 0-78 0.70 0.594 0.42 - 0.46 4.3
molecules
e I × 10-24
quadrupole and
(I
Elsevier)
gN
1.2878 0.1311 0-488 0-097 0.107 1-2190 0.097968 1.011770 0.373483 3-244514 3.2754 1.1748 0.938 0.10
- -
Magnetic atoms
(Bo) (Amsterdam:
1983
W
Anisotropic coupling edn Jr
(G) student Weltner
inorganic radicals
Isotropic coupling Aiso (35490) (13200) (3493) (34410) (2876) (41880) (183800) (81510) (77530) 1st of
3)
(r- chemistry, wavefunction.
(9-454)
(12.81) (10-13) (14-72) (19-15)
(a.u.) and The structure
12
(10-79) (12.19) (14-31) (16-78)
(a.u.) 3.09) physics
I W,~(o) (I (13.90) (14-87) (12.53) (12-86) (17-37) (22.97) (27.96) (33.09) of
1967
M C R Hermann-Skillman
(~N) from
dipole handbook
Symons
Nuclear magnetic moment + 3-2197 + 0-0646 0.6599 + 0.1461 + 0.1591 0.6095 + 0.1457 + 0-5059 - 0.5602 + 1.6222 + 1-6382 + 0.5926 + 4.110 - 0-35 CRC 1988 P W and (1993) parameters
Spin 5/2 1/2 3/2 3/2 3/2 + 3/2 1/2 3/2 1/2 1/2 1/2 9/2 7/2 (ed.) Atomic
Atkins
1/2 R C
(contd) Natural abundance (%) 62.6 1.6 16.1 37.3 62.7 33-8 100 16-8 13.2 29.52 70.476 22.1 100 0-720 1-3: Weast 4 to 7 & 11: Bruker Almanac 8-10: in parenthesis:
2.
Table Isotope ~87Re 187Cs lSgcs t91lr 193Ir 19Spt 197Au 199Hg 2°lHg 2°3T1 2°5T1 2°9pb 2°9Bi 235U Columns Columns Columns SNumbers
l0 C S Sunandana
Equation (l l) ensures that there is always an excess 4. ESR and allied phenomena
spin population in the ground state ready to undergo
transitions. More significantly, since the N-> ÷ N energy 4.1 Electron spin resonance
absorption would occur until N----N ,+ when the spin
When a material containing electron magnetic dipoles is
system would become saturated and no resonance would
placed in a static magnetic field and subjected to
be detectable. In fact, there are two mechanisms acting
electromagnetic radiation, absorption attributable to
within the material by which energy is effectively trans-
magnetic dipole transitions occurs at one or more
ferred by the spin system to the surroundings. The
characteristic frequencies in the microwave region of the
spin-lattice relaxation, characterized by time T, and
exponential in time, results from interactions of the electromagnetic spectrum.
For a system with electron spin S (ex: H atom in
electronic magnetic moments with each other and with
silicon (S=1/2)) there are 2S+1 energy levels in a
the other electrons of the host material, or the 'lattice'.
This 'longitudinal' relaxation causes changes in the static magnetic field H given by:
component of/t parallel to H .o A short T, affects the
e = (~,i I ~S A ),p~ = sM g ~.n, (12)
linewidth of the resonance through the energy-time
uncertainty relation AE Az >~, AE being the uncertainty
where iP~ is a characteristic wave function of the z-
of an energy level and Az being the lifetime of that
state, i.e. r T A very short 1 T would thus imply a large
AE and a broadened ESR line at ambient. ESR lines can
oHZ
be broadened by magnetic interaction among the spins
themselves, as a result of which the different spins would
(~o Y = "oH
experience slightly different local fields in the z-axis,
leading to a spread in the Larmor precession frequencies.
Eventually the spins would not precess in phase at all,
and there would be a gradual dephasing, exponential in
time, the process being characterized by a transverse or
a spin-spin relaxation time T .z Spin-spin relaxation pro-
cesses are adiabatic because there is no exchange of
energy between the spin system and the reservoir.
Thus the spin relaxation mechanisms are crucial to
the observation of electron spin resonance spectra. Aspects
of lineshape and iinewidth are considered in § 6.
.~y
t /
Mognetic field
Orbital angular x{h]
momentum
oHy-=ow
nipS
_L / angular
momentum
'-Z
I
Orbital
dipole spin
moment I dipole
moment
Ft Figure 2. Larmor precession of an electron spin (S=1/2)
magnetic moment (,u) ni an applied magnetic field 0 with H a
frequency too=TH o along z-axis. An oscillatory magnetic field
Figure .1 Planetary model for electron motion ni an applied l H <<( )oH at microwave frequency applied normal to 0 H 'tips',
magnetic field. 'Orbiting' and 'spinning' gives the electron the the moment and changes the sense of = precession o to yH o and
orbital and spin angular and momenta,/z= ,t/.etA = 0 for s-electrons causes electron spin/paramagnetic resonance absorption, depicted
and/z] ~ 0 for p, d f and "paramagnetic' electrons ni a material. as the 'cone inversion' through the origin.