Manifestation of dipole-dipole reservoir in systems with non-equidistant spectrum at saturation of quadrupolar transitions

JoumaIofMolecularStnrcture, 83 (1982) 233-237 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

SHAKIRsYitirov

liLlYI.

Kazan

Yhysico-TechnLcal

of the

The

USSR,

Kazan

influence

voir (DDR) seturation the

iiC0uSti.C

of

due

upon

1-3)

the role

tions

(DDRj

processes

at saturation

line wing of acoustic resonance i)DR temperature shift. consider

magnetic

symmetrical

nuclear

ssin-

energy

However,

byoharacter1eSela

inreferences

of dipole-dipole

considered,

thou+1

interacix Ls xell

to take into account the DDR in ratura(ref.4,5J.Therefore of interest is the xtvzstigation

of the *RN? signals

US

is Studied.

dkfferent

dil'ferent

(ref.l-3). is not

In

acoustic

betxeen

it is necessary

effects

Let

rescmmce

produces

between

reser-

di;Jole-dipole

transitions

enerL;eti.c reservoir

in these

of

unrigurously

spectrum

inversion)

of the

to

quadrupolar

HLiR si&nels

decrease,

chan(l;e

transitions on the BLFt sign&s of a non-equidistant spectrum

z non-equidistszt

effects

Lxl0v.m that

temperature

eigenatates

of Sciences

CUSSR)

spins

aaturatior!_

(increase,

tion

t;he

of quadrupolar

with

istic

of

of the Academy

Ins%itute

420023

of nuclear

different

system

t&nt

233

the

field gl-adient

system

H, which of tne

of quadrupolar (kR)

i.e.

of spins

at the

1=3/2

is Farallelto crystal

transitions

electric

condi-ciom3

being the

on a

in strong

w~xis of the

field

of the

(the

consaxial12

exis

2).

that the running lon&i~udinal acoustic waves with the wave vector zlitlb and frequency w give rice to resonance transitions with (Ad =2 between the levels m,=-3/2 and nz=1/2. imd let the IW& signals be well resolvedime- W,%&M4&where w, =&Ho, k&, w,J are the Zee%an, quadrupolar and dipolar frequencies, respectively, think the width of resonance lines ~d~~~P~~JS~(~~)2~ j/2- tiire ie homogeneous end is due to the part (g&i of the dipole-dipole interactions (%a,), which is secular relative to the spectrum. Assume

0022-2860/82/000~000/$02_75~ 1982 Else~erScient~icPub~h~~Company

;I spin-system of nuclear Na'%n .&NO3 can serve as an example of such 2 systen. To describe the spin-system behaviour we shall make use of equatlcns of the Provo-corov type (ref. 4,s) obtained by the Zubarev t> T2 is characterized BSO nlethod. The spin-system at the times quadruby four quasiilrtegrcls of motion - the Zeeman -&o.(FIt>, polarhOa ( i/2; S:> and ciipolar
In the equat:ens d: are the inverse temperatures of the _PP Zeeman, quadrupolar and dipolar subsystems, 8 is the thermodynamic parameter kelng appropriate to the average value of the operator k,W' is the probability oi the acoustic resonance transition witl the line ShaLJe f,(S)' Sii are the cons-cants of the spin->honon interaction (ref.21, cl0 is the &mplitude of deformations, T is the 0 equilibrium temperature, E is the arbitrary frequency, T (r = PL are the times of the spin-lattice relaxation of the =plS,GLO1 subsystenia. On cond;.tion that the probabilities of the relaxation transitions between different states are equal one may obtain for relaxation times the relations (ref.7): Jy2 = ~~/+C 4/3 j%= T,,/$= '/3, &=r,,jr,,= f/6, i%o_z the equations obtained by analogy with (1) and describing the spin-system behaviour in the r.f.field (H,II 21, which gives rise to resonance transitions with \at?7!=1,it is easy to derive an expression for the r.f..power absorbed in the spin-system (ref.81. And, using the solutions of equations at strong stationary (11,

235

acoustic saturatson (W T >>I )$for three cases of the r.f.excitaA P6 tion, the absorbed power, taking into account the values J!i =9!3 ' may be written as follows:

(trsnsftioa

-3/Z?+---l/2)

Fix)= ~~~~~~~~

II j!=a, k’,c (2) * Q where Pe(n]~s the gower absorbed in the abeen.& of ths zcoustic pumping, when %*jl)) W,Wis -c& probabj.lity of the ,d.*g,, _P$ transition excit4 by the r,f,field of ths ~rcquency urn . Here we consider that the weak r,f.field does r,ot influence upon tha i;d.ues I For c-L:a~t:r;~i: (re1,5,6,9i.

in the

of

such

systems,

Then,Ilsing

t\*co-tesperature

proxir!:ated

values

freque12cY

the

iA&

as

a rule

Cd0 I the

Ws,

(ref.2,tj,

value & =s"eq#q$)*J

approsiniation,wh%.ch theorg

w,

is

(ref,tj),r"ormulGe

often (2)

utilised may

te

apu

bjf =xpreasions

shift at strong acoustic saturation on the kIi line wing (X-U&) the NMR signals between different stainfluences difrerently tes

of

the

spin-system,

r-t the

excitation

02

the

transitions

l/Z-

-3/2 (the case c)) tit;;sigzlal intensity is practically ~nvr~riable end at the indication a small asymmetry of the absorption line is to be observed (Fig,7,c)),(We assume the Gaussian shape of the lines). At the excrtation of the transitions -3/2~-112 and -l/2441/2 [expressions (3) aj and b),respectivelg) We 14i~Hsignals essentially depend upon the application point of the saLurating acoustic fieldThe variations 02 the magnitudes of IQ& sign&s, which are due to nonrigorously resonance saturation, ae some values of the magnetic f'i;eldH, may be considerable and com:)ared with the magnitude of the signals at the saturation in the center of the AEZ line (x=0). These values,are obt aFned frolu the condition that the value of the frex, I)which is detemined by quency untuning of the acoustic field P2?Olll JL x= the equality Ua o ~$iB~,silould be within the nEl line width. 0 is characterized a physical. goint of view, the equnlltyXaii!=~CD 2 a ad by the nor;--equilibri= DDR, by t&e fact that the r-f- power, absorbed

236

at the certain

values

of H, becomes

equal to the power,

absorbed

(or reradiated for an inverted hi signal) by a spin-system at strong acoustic saturation in a line centre- The value H,,necessary to fulfll this equality, for example, at x,cr~~for the nuclei Na 23 in NaNO 3 is withzin 4x103+ 104G (depending on the value ofJuz, taken in the interval O,l+O,OI) and is quite accessible in RI&R,

The absorption i&SIRlines at the stron acoustic saturation transition -3/2++l/2: la '5,lb),lc)-at the exact acoustic resonance (WA=2ti0 +Wa>; 2a)- at the saturation on the hR line wing (L&S %I+ x,) and at the exact magnetic resonance+ 3a), 3b),3c)- at the R&R line indication by the weak r.f, field, The frequency dependence of the I&JR line shaQe in this case,when is presented in Zc'ig.1.e) and I.b)* The RX& line shape 2-x: =&&, as in the case of the equidistant speckrum (ref.5,9), becomes asymmetrical in comparison with the line shape at the exact rosgnetic resonance (A =O), Depending upon the sign of d (x0> 0) there exist regions of increased and decreased absorption of the r.f,power for coincides the transitions -3/2--I/2. At a =x0 the signal magnitude with the value at the saturation in the line centre (x=0) and it is not -equal to zero as at the equidistant spectrum. iit A =0 and x=x0 the NIiLRsignal is two times increased in comparison with the signal at x=0- The investigatLon of the NMR signal between the states m, =-1/Z and mz=lf2 (the case b)) shows that the signal inverted disappears at the exact magdue to the non-equidistant =P=ctr~ And at&<0 (x,>O) one netic resonance ( A =0) if D Xi c3.t the radition of the r-f. may observe the absorption snd at power. Pig-l.

of the qusdrupolar

237

1 J.V.Vladimirtsev, V. A.Golenischev-Kutuzov, U.H Kopvillem and N.A.Shamukov, Acoustic Journal, 15 (19691, ~1.345. 2 V.BLSaraatskii, V.A.Shutilov, Piz.Tver.Tela, 14 (19721, p.761. 3 V.L.Komaehnja, V.A.Shutilov, Piz.Tver.Tela, 19 (13771, p.lW. 4 B.N.i?rovotorov, Zh.dksp.Teor.Fiz., 41 (19611, p.1582. E.V.Charnaja and V.A.Sautilov, 5 J.A.Antokolskii, L.N.Ferahtat, Zh.Eksp.Teor.Fiz., 63 (19721, p-1721. 6 ILGoldma, Spin temperature and W in solids, Dlir, Moscow,l972. 7 A.Abra&rn; Nuclear magnetism, FL, Moscow, 1963. 8 LLBuishvili, Zh.Eksp.Teor.Piz., 43 (13652, ~~1863. 9. A.E. Mefed, M-1. Rod&, zh.Eksp.Teor.Fiz., 59 (19701, p-404