1
MultinukleMultinukleáárnrníí NMR spektroskopieNMR spektroskopie
C6800C6800
MateriMateriáályly vv ISuISu
ŘŘeeššenenéé úúlohy ze spektroskopie nuklelohy ze spektroskopie nukleáárnrníí
magnetickmagnetickéé resonanceresonance
http://http://nmrnmr..scisci..munimuni..czcz
ÚÚlohylohy –– vyvyřřeeššit a odevzdatit a odevzdat
Prezentace (na konci semestru) 10Prezentace (na konci semestru) 10--15 min na15 min na
vybranvybranéé ttééma NMRma NMR
ZZáávvěěrereččnnáá ppíísemnsemnáá zkouzkoušškaka
2
NMRNMR –– Historical PerspectiveHistorical Perspective
1922 Electron spin observed1922 Electron spin observed (Stern(Stern--GerlachGerlach))
19261926 NNuclearuclear spinspin -- David Dennison (HDavid Dennison (H22))
19381938 NMRNMR waswas firstfirst observedobserved in a molecularin a molecular beambeam
19391939 I. I.I. I. Rabi observes absorption of radioRabi observes absorption of radio
frequency (RF) energy by nuclei of Hfrequency (RF) energy by nuclei of H22 gasgas
IsidorIsidor II.. RabiRabi Nobel prize in physics in 1944Nobel prize in physics in 1944
"for his resonance method for"for his resonance method for
recording the magneticrecording the magnetic
properties of atomic nuclei"properties of atomic nuclei"
((18981898 –– 19881988))
3
NMRNMR –– Historical PerspectiveHistorical Perspective
1945 Purcell, Torrey, Pound @ Harvard1945 Purcell, Torrey, Pound @ Harvard solidsolid paraffinparaffin
1945 Bloch, Hansen, Packard @ Stanford1945 Bloch, Hansen, Packard @ Stanford liquidliquid HH22OO
Varian Bros. & RussellVarian Bros. & Russell klystron for radars (WWII)klystron for radars (WWII)
19481948 PakePake, van, van VleckVleck solid state NMRsolid state NMR
1950 W. G. Proctor, F. C. Yu @ Stanford1950 W. G. Proctor, F. C. Yu @ Stanford
δδ -- chemical shift inchemical shift in 1414NHNH44
1414NONO33
1950 W. C. Dickinson @ MIT1950 W. C. Dickinson @ MIT
δδ -- chemical shift inchemical shift in 1919FF
19521952 CCommercialommercial NMR instrumentsNMR instruments usedused atat DuPont, Shell, Humble OilDuPont, Shell, Humble Oil
4
NMRNMR –– Historical PerspectiveHistorical Perspective
Edward M. Purcell (Edward M. Purcell (19121912--1997)1997) & Felix Bloch (1905& Felix Bloch (1905--1983)1983)
NP in physics 1952NP in physics 1952
"for their development of new methods for nuclear"for their development of new methods for nuclear
magnetic precision measurements and discoveries inmagnetic precision measurements and discoveries in
connection therewith"connection therewith"
5
NMRNMR –– Historical PerspectiveHistorical Perspective
1952 Hahn, Maxwell @ Berkeley - J scalar coupling
1953 Gutowsky, McCall, Slichter @ U. of IL - J
1955 Bloom, Shoolery spin decoupling
1960 Shoolery integration
1966 Ernst, Anderson FT NMR at Varian
1968 Waugh @ MIT HR, multipulse NMR in
solids
6
NMRNMR –– Historical PerspectiveHistorical Perspective
1971 Jeener 2D NMR
1971 Damadian different NMR relaxation times of
tissues and tumors
1972 CP, HP decoupling
1972 The first routine 13C NMR spectrometer
((beforebefore mainlymainly 1H, 19F, and 31P NMR)
1973 Lauterbur MRI
7
MRIMRI--Magnetic ResonanceMagnetic Resonance
ImagingImaging
Paul C.Paul C. LauterburLauterbur
(1929(1929--))
Sir Peter MansfieldSir Peter Mansfield
(1933(1933--))
NP in physiology and medicine 2003
8
NMRNMR –– Historical PerspectiveHistorical Perspective
1974/19791974/1979 R. R. ErnstR. R. Ernst 2D COSY2D COSY, NOESY, NOESY
19771977 MASMAS
19811981 BaxBax, Freeman, Freeman INADEQUATEINADEQUATE
19821982 APTAPT
1983 Freeman1983 Freeman BB decoupling, MLEV, WALTZBB decoupling, MLEV, WALTZ
1990 3D and1990 3D and 11H/H/1515N/N/1313C Triple resonanceC Triple resonance
19911991 R. R.R. R. ErnstErnst NP in chemistryNP in chemistry
20012001 TheThe firstfirst commercialcommercial 900 MHz instrument900 MHz instrument
20022002 K.K. WWüüthrichthrich NP in chemistryNP in chemistry
9
NMRNMR –– Historical PerspectiveHistorical Perspective
RichradRichrad R. ErnstR. Ernst
(1933(1933--))
NP in chemistry 1991NP in chemistry 1991
"for his contributions to the"for his contributions to the
development of the methodology ofdevelopment of the methodology of
high resolution nuclear magnetichigh resolution nuclear magnetic
resonance (NMR) spectroscopy"resonance (NMR) spectroscopy"
KurtKurt WWüüthrichthrich
(1938(1938--))
NP in chemistry 2002NP in chemistry 2002
"for his development of nuclear magnetic"for his development of nuclear magnetic
resonance spectroscopy for determining theresonance spectroscopy for determining the
threethree--dimensional structure of biologicaldimensional structure of biological
macromolecules in solution"macromolecules in solution"
10
NMRNMR –– Historical PerspectiveHistorical Perspective
11
Nuclear Magnetic ResonanceNuclear Magnetic Resonance
High resolution liquid state NMRHigh resolution liquid state NMR
spectroscopyspectroscopy
Solid state NMR spectroscopySolid state NMR spectroscopy
HighHigh--pressurepressure NMRNMR
NMR inNMR in thethe gasgas phasephase
NMR spectroscopy in liquid crystallineNMR spectroscopy in liquid crystalline
mediamedia
MagneticMagnetic resonanceresonance imagingimaging (MRI)(MRI)
12
HyperfineHyperfine InteractionsInteractions
••IInteractionnteractionss ofof nuclenucleii with the electric andwith the electric and
magnetic fieldsmagnetic fields
••InteractionsInteractions betweenbetween aa nucleusnucleus andand electronselectrons
••TransferTransfer ofof chemicalchemical ((electronicelectronic)) informationinformation
fromfrom bondsbonds andand lonelone pairpairss to ato a nucleusnucleus
•• IndirectIndirect
•• DirectDirect
13
HyperfineHyperfine InteractionsInteractions
IndirectIndirect
••ElectricElectric fieldfield gradientgradient ((EFGEFG)) withwith nuclearnuclear
electricelectric quadrupolequadrupole
••InducedInduced magneticmagnetic fieldfield withwith nuclearnuclear
magneticmagnetic momentsmoments ((shieldingshielding))
DirectDirect
••ss--electronselectrons withinwithin nucleinuclei,, polarizationpolarization ofof
bondingbonding spinsspins (J(J--couplingcoupling))
14
DirectDirect InteractionsInteractions
ONLY sONLY s--electronselectrons cancan interactinteract withwith nucleinuclei
ONLY sONLY s--electronselectrons havehave nonnon--zerozero electronelectron densitydensity atat aa nucleusnucleus
p, d - nodal planes
15
Relationship Between Wavelength,Relationship Between Wavelength,
Frequency and EnergyFrequency and Energy
Speed of light (Speed of light (cc) is the same for all wavelengths) is the same for all wavelengths
cc == 2.99792.9979 101088 m sm s−−11
Frequency (Frequency (νν), the number of wavelengths per second, is), the number of wavelengths per second, is
inversely proportional to wavelength:inversely proportional to wavelength:
νν == cc/λ/λ
Energy of a photon is directly proportional to frequencyEnergy of a photon is directly proportional to frequency
and inversely proportional to wavelength:and inversely proportional to wavelength:
EE == hhνν == hhcc//λλ
h = Plankh = Plank’’s constants constant == 66..626176626176 1010−−3434 J sJ s
16
ElectromagneticElectromagnetic RadiationRadiation
NMR
17
Method Energy ScaleMethod Energy Scale
18
Energy Scale Conversion FactorsEnergy Scale Conversion Factors
111.036 101.036 10−−552.506 102.506 1099
J molJ mol−−11
9.649 109.649 1044112.418 102.418 101414
eVeV
3.990 103.990 10−−10104.136 104.136 10−−151511HzHz
J molJ mol−−11eVeVHzHz
19
IIssotopotopeses
IIssotopotopeses = a set of= a set of nunucclidlideses of an elementof an element,, samesame Z,Z, differentdifferent AA
there is aboutthere is about 2600 nu2600 nucclidlideses ((stabilstabilee andand radioaradioacctivtivee))
340 nu340 nucclidlideses found in naturefound in nature
272700 stabstabiillee aandnd 7070 radioaradioacctivtivee
MonoiMonoissotopicotopic elementselements::
99Be,Be, 1919F,F, 2323Na,Na, 2727Al,Al, 3131P,P, 5959Co,Co, 127127I,I, 197197AuAu
PolyiPolyissotopicotopic elementselements::
11H,H, 22H (D),H (D), 33H (T)H (T)
1010B,B, 1111BB
SnSn has the highest number ofhas the highest number of stabilstabilee iissotopotopeses –– 1010
112, 114, 115, 116, 117, 118, 119, 120, 122, 124112, 114, 115, 116, 117, 118, 119, 120, 122, 124SnSn
20
NaturalNatural AAbundancebundance,, %%
00
00
3/23/2
00
1/21/2
00
00
II
6.8506.850204204
29.8029.80202202
13.2213.22201201
23.1323.13200200
16.8416.84199199
10.0210.02198198
0.1460.146196196
NANA%%AAHgHg
Mass number, A
Isotopic Compositions of the ElementsIsotopic Compositions of the Elements
21
NaturalNatural AAbundancebundance,, %%
11HH 99.98599.985
22HH 0.0150.015
1212CC 98.8998.89
1313CC 1.111.11
1414NN 99.6399.63
1515NN 0.370.37
1616OO 99.75999.759
1177OO 0.0370.037
1818OO 0.2040.204
3232SS 95.0095.00
3333SS 0.760.76
3434SS 4.224.22
3636SS 0.0140.014
Isotopic Compositions of the ElementsIsotopic Compositions of the Elements
22
Variability inVariability in Isotopic CompositionsIsotopic Compositions
IsotopeIsotope RangeRange AverageAverage
1010BB 18.92718.927 -- 20.33720.337 19.9 (7)19.9 (7)
1111BB 81.07381.073 -- 79.66379.663 80.1 (7)80.1 (7)
1616OO 99.738499.7384 -- 99.775699.7756 99.757 (16)99.757 (16)
1717OO 0.03990.0399 -- 0.03670.0367 0.038 (1)0.038 (1)
1818OO 0.22170.2217 -- 0.18770.1877 0.205 (14)0.205 (14)
Natural Abundance, %
23
NuclearNuclear SSpinpin
electron spinelectron spin ss == ½½
proton and neutron Iproton and neutron I == ½½
nuclear spinnuclear spin II = z= z ½½ z = integer 0, 1, 2, 3, .....z = integer 0, 1, 2, 3, .....
multiples ofmultiples of ½½
integerinteger
00
II
evenevenoddodd
oddoddeveneven
oddoddoddodd
eveneveneveneven
Number of neutronsNumber of neutrons,, NNNumber of protonsNumber of protons,, ZZ
24
NuclearNuclear SSpinpin
protons and neutrons are Fermions, obey Pauli exclusion principlprotons and neutrons are Fermions, obey Pauli exclusion principlee
1212
CC 1313
CC
nn nnpp pp
II == ½½II = 0= 0
25
NuclearNuclear SSpinpin
eveneven –– eveneven:: II = 0= 0 44He,He, 1212C,C, 1616O,O, 2020Ne,Ne,
2424Mg,Mg, 2828Si,Si, 3232S,S, 3636Ar,Ar, 4040CaCa
oddodd –– oddodd:: II = integer= integer
ONLYONLY 22HH,, 66Li,Li, 1010B,B, 1414N,N, 4040K,K, 5050V,V, 138138La,La, 176176LuLu
eveneven –– odd and oddodd and odd –– eveneven::
II = multiples of= multiples of ½½
1133CC ½½,, 1177OO 5/2,5/2, 3333SS 3/23/2
26
NuclearNuclear SSpinpin
5050evenevenoddodd
5757oddoddeveneven
88
168168
Number of nuclidesNumber of nuclides
oddoddoddodd
eveneveneveneven
Number of neutronsNumber of neutrons
NN
Number of protonsNumber of protons
ZZ
27
28
NuclearNuclear SSpinpin
29
NuclearNuclear SSpinpin
NO stable nucleus hasNO stable nucleus has spin 2spin 2
the highest value of spin for a stable nucleus is 7the highest value of spin for a stable nucleus is 7
171766
LuLu
uunstablenstable nucleinuclei
highest integralhighest integral spin 16spin 16 -- isomerisomer 178178
HfHf
highest halfhighest half--integerinteger 37/237/2 -- isomerisomer 177177
Hf)Hf)
30
NuclearNuclear SSpinpin
• Nuclei with spin ½ - a spherical charge distribution
• Nuclei with I > ½ - nonspherical charge distributions
(prolate or oblate)
• All nuclei with non-zero spins – magnetic moments (μ)
• Nonspherical nuclei - an electric quadrupole moment (eQ)
31
NuclearNuclear SSpinpin
32
NuclearNuclear SSpinpin
33
NuclearNuclear SSpinpin
Nuclear spin =Nuclear spin = SpinSpin angularangular momentummomentum,, PP (vector)(vector)
Spin quantum numberSpin quantum number II
Magnetic quantum numberMagnetic quantum number mmII
Magnitude ofMagnitude of PP is quantized:is quantized:
Direction with respect to the magneticDirection with respect to the magnetic
fieldfield BB00 is quantized:is quantized:
PP
µµ
( )1
2
+= II
h
P
π
Iz m
h
P
π2
=
34
SpinSpin AngularAngular MomentumMomentum,, PP
5959CoCo,, II = 7/2= 7/2
mmII
II == NuclearNuclear spin quantum numberspin quantum number
II = 0,= 0, ½½, 1, 3/2, 5/2,, 1, 3/2, 5/2, 3,3, 7/27/2,,..........
mmII == Nuclear spinNuclear spin magnetic quantummagnetic quantum
numbernumber
Multiplicity,Multiplicity, MM 22II + 1+ 1 valuesvalues
mmII = I, I= I, I--1, I1, I--2, ...,2, ..., --I+2,I+2, --I+1,I+1, --II
-1/2
-3/2
-5/2
3/2
-7/2
1/2
5/2
7/2
BB00( )1
2
+= II
h
P
π Iz m
h
P
π2
=
( )1
cos
+
==
II
m
P
P Iz
θ
35
SpinSpin AngularAngular MomentumMomentum,, PP
1.9361.9363/23/2
2.9582.9585/25/2
3.4643.46433
3.9693.9697/27/2
4.4724.47244
4.9754.9759/29/2
1.4141.41411
0.8660.866½½
[[II ((II + 1)]+ 1)]½½II
( )1
2
+= II
h
P
π
36
Spin Magnetic Moment, µ
The electrons, nucleons (protonThe electrons, nucleons (protonss, neutron, neutronss) and some) and some
nuclei possess intrinsic magnetism, which is not due to anuclei possess intrinsic magnetism, which is not due to a
circulating current.circulating current.
PPermanent magneticermanent magnetic moment similarly as spin angularmoment similarly as spin angular
momentum.momentum.
Magnetic moment,Magnetic moment, µµ, is directly proportional to the spin, is directly proportional to the spin
angular momentangular momentumum,, PP ::
µµ == γγ PP
γγ is theis the gyromagneticgyromagnetic ((magnetogyricmagnetogyric) ratio) ratio
37
MagnetogyricMagnetogyric RatioRatio
γγ -- thethe magnetogyricmagnetogyric ratioratio isis thethe ratioratio ofof thethe
nuclearnuclear magneticmagnetic momentmoment µµ toto thethe nuclearnuclear
angularangular momentummomentum P.P.
µµ == γγ PP
γγ -- Important characteristic of nucleiImportant characteristic of nuclei
[rad[rad TT--11 ss--11]]
38
Spin Magnetic Moment, µ
µµ == γγ PP == γγ (h/2(h/2π)π) [[II ((II + 1)]+ 1)]½½
µµzz == γγ PPzz == γγ (h/2(h/2π)π) mmII
NucleusNucleus 11HH 22HH 1313CC 1515NN 1919FF 2929SiSi 3131PP
γγ [10[10--77 radrad TT--11ss--11]] 26.7526.75 4.114.11 6.736.73 --2.712.71 25.1825.18 −−5.325.32 10.8410.84
electronelectron
γγee == 17 609 1017 609 1077 = 658= 658 γγ((HH))
39
Nuclear Spin in Magnetic Field
40
Nuclear Spin in Magnetic Field
ΔE = λ absorbed light
Applied
Magnetic
Field
Hext
ΔE = λ absorbed light
Applied
Magnetic
Field
Hext
RandomRandom orientationorientation
No Field Magnetic Field
AlignmentAlignment
41
Nuclear Spin in Magnetic Field
42
Nuclear Spin in Magnetic Field
• An angular momentum is associated with each
rotating object
• A nuclear spin possesses a
magnetic moment arising from
the angular momentum of the
nucleus
• The magnetic moment is a
vector perpendicular to the
current loop
• In a magnetic field (B) the magnetic moment
behaves as a magnetic dipole
μ = i A
43
Nuclear Spin in Magnetic Field
In B0, a magnetic moment
is directed at some angle w.rt.
B0 direction
the B0 field will exert a torque
on the magnetic moment. This
causes it to precess about
the magnetic field direction
Torque is the rate of change
of the nuclear spin angular
momentum
44
Nuclear Spin in Magnetic Field
Spin precession in the external magnetic field.Spin precession in the external magnetic field.
Quantum description of precession shows that theQuantum description of precession shows that the
frequency of the motion is:frequency of the motion is:
ωω00 == −− γγ BB00 [[radrad ss−−11
] or] or νν00 == −− γγ BB00/ 2/ 2ππ [Hz][Hz]
It is called theIt is called the LarmorLarmor frequency (iffrequency (if γγ > 0 then> 0 then νν00 < 0)< 0)
45
LarmorLarmor FFrequencyrequency
ωω00 == −− γγ BB00 [[radrad ss--11
]]
νν00 == −− γγ BB00/ 2/ 2ππ [Hz][Hz]
π
γ
ν
2
0
0
B
−=
46
LarmorLarmor FFrequencyrequency
Sir JosephSir Joseph LarmorLarmor
(1857(1857--1942)1942)
ωω00 == −− γγ BB00 [[radrad ss−−11
] or] or νν00 == −− γγ BB00/ 2/ 2ππ [Hz][Hz]
Ensemble of spins
Nuclei are charged andNuclei are charged and
if they have spin, theyif they have spin, they
are magneticare magnetic
No FieldNo Field
AppliedApplied
MagneticMagnetic
Field =Field = BB00
Energy of transition =Energy of transition =
energy ofenergy of radiowavesradiowaves
Higher energy state: magneticHigher energy state: magnetic
field opposes applied fieldfield opposes applied field
Lower energy state: magneticLower energy state: magnetic
field aligned with applied fieldfield aligned with applied field
NuclearNuclear ZeemanZeeman EffectEffect -- SplittingSplitting
mI -½
mI +½
48
Nuclear Spin in Magnetic Field
EEmagmag == −− µµ ⋅⋅ BB00 (scalar product)(scalar product)
EEmagmag == −− µµzz BB == −− γγ PPzz BB
EEmagmag == −− mmII ħħ γγ BB
The magnetic energy depends on the interaction between theThe magnetic energy depends on the interaction between the
magnetic moment and Bmagnetic moment and B00 field:field:
NMR selection ruleNMR selection rule ∆∆mmII == ±± 11
49
50
Spin in Magnetic Field
∆∆ EEmagmag == EEm=m=--1/21/2 −− EEm=1/2m=1/2 == ∆∆mmII ħħ γγ BB = h= h νν ⇒⇒ νν == γγ BB/2/2ππ
II == ½½
EEm=1/2m=1/2
EEm=m=--1/21/2
The frequency of the electromagnetic radiation thatThe frequency of the electromagnetic radiation that
corresponds to the energy difference between the twocorresponds to the energy difference between the two
energy levels is equal to theenergy levels is equal to the precessionalprecessional frequency offrequency of
the nuclei.the nuclei.
51
Amplitude
Frequency (Hz)
Excitation of NMR SpinExcitation of NMR Spin
ΔE
α
β
ΔE
α
βIrradiate with
Frequency so as
to satisfy Planck's
Law
ΔE=hυ
Energy
52
53
EnergyEnergy LLevelsevels forfor II == ½½
∆∆E = (E = (66..626626 1010−−3434 J sJ s 26.75 1026.75 1077 rad Trad T--11ss--11 11.7411.7433 TT))/2/2ππ = 3.313= 3.313 1010−−2525 JJ
very small energy differencevery small energy difference
∆∆ EEmagmag == EEm=m=--1/21/2 −− EEm=1/2m=1/2 == ∆∆mmII ħħ γγ BB = h= h γγ BB/2/2ππ
54
EnergyEnergy LLevelsevels forfor II == ½½
α
β
α
β
55
Boltzmann Distribution
TheThe excessexcess ofof nucleinuclei onon thethe lowerlower energyenergy levellevel isis givengiven byby
BoltzmanBoltzmannn distributiondistribution::
NN↑↓↑↓//NN↑↑↑↑ = exp(= exp(−−∆∆EE//kkBBTT) = exp() = exp(−−ħħ γγ BB //kkBBTT))
= exp(= exp(−−3.33.31313 1010--2525/ 4.1/ 4.10101 1010--2121)) == exp(exp(−−8.078 108.078 10--55) =) =
0.999919220.99991922
IfIf NN↑↑↑↑ = 1 000= 1 000 000000 thenthen NN↑↓↑↓ == 999919999919
OnlyOnly 8811 outout ofof millionmillion 11HH nucleinuclei contributecontribute to NMRto NMR signalsignal atat 500 MHz!500 MHz!
ħħ = 1.055 10= 1.055 10--3434 J sJ s
γγHH = 26.75 10= 26.75 1077 rad Trad T--11ss--11
B = 11.7433 T (500 MHz)B = 11.7433 T (500 MHz)
kkBB = 1.38= 1.380707 1010--2323 J KJ K--11
T = 297 KT = 297 K
56
Boltzmann Distribution
NN↑↓↑↓//NN↑↑↑↑ = exp(= exp(−−∆∆EE//kkBBTT) = exp() = exp(−−ħħ γγ BB //kkBBTT))
the stronger the field andthe stronger the field and
the higher thethe higher the
magnetogyricmagnetogyric ratio, theratio, the
larger the populationlarger the population
differencedifference
the higher thethe higher the
temperature, the smallertemperature, the smaller
the population differencethe population difference
57
Boltzmann Distribution
The higher the field,The higher the field,
the larger the energy difference,the larger the energy difference,
the larger the population difference,the larger the population difference,
the larger the net magnetization,the larger the net magnetization,
and the bigger the NMR signaland the bigger the NMR signal
58
Nuclear Magnetic ResonanceNuclear Magnetic Resonance
(NMR)(NMR)
NuclearNuclear –– spinspin ½½ nuclei (e.g. protons) behave asnuclei (e.g. protons) behave as
tiny bar magnets.tiny bar magnets.
MagneticMagnetic –– a strong magnetic field causes a smalla strong magnetic field causes a small
energy difference between +energy difference between + ½½
andand –– ½½ spin states.spin states.
ResonanceResonance –– photons of radio waves can match thephotons of radio waves can match the
exact energy difference between the +exact energy difference between the + ½½ andand –– ½½
spin states resulting in absorption of photons asspin states resulting in absorption of photons as
the protons change spin states.the protons change spin states.
59
MagnetizationMagnetization
More nuclei point in parallel to theMore nuclei point in parallel to the
static magnetic field.static magnetic field.
The macroscopic magneticThe macroscopic magnetic
moment,moment, MM00
MM00 == ΣΣ μμii
In-Field
60
LongitudinalLongitudinal MMagnetizationagnetization
61
SpinSpin--LLatticeattice RRelaxationelaxation TTimeime
RR11 = 1/= 1/TT11 [Hz] longitudinal relaxation rate constant[Hz] longitudinal relaxation rate constant
TT11 [s] longitudinal relaxation time[s] longitudinal relaxation time
spinspin--lattice relaxation timelattice relaxation time
enthalpyenthalpy
62
TTransverseransverse MagnetisationMagnetisation
63
SpinSpin--SSpinpin RRelaxationelaxation TTimeime
RR22 = 1/= 1/TT22 [Hz] transverse relaxation rate constant[Hz] transverse relaxation rate constant
TT22 [s] transverse relaxation time constant[s] transverse relaxation time constant
spinspin--spin relaxation timespin relaxation time
entropyentropy
64
65
66
RelaxationRelaxation
67
68
FreeFree InductionInduction DecayDecay FIDFID
69
70
71