Cross Relaxation in Ruby

Mims, W. B.; McGee, J.D.

doi:10.1103/physrev.119.1233

Cited by 65 publications

(11 citation statements)

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“…Such an attempt (Sikri and Narchal 1978) has been made with regard to Grant's theory of two-spin CR for particles of spin 4. This temperaturedependent theory has been applied to Mims' (Mims and McGee 1960) experiment on ruby and produces better agreement with it in the negative frequency region, whereas Grant's theory (Grant 1964a, b, c, d, e) agrees with experiment in the positive frequency region. Since Mims' experiment has been done at a fixed temperature, this application does not test the temperature aspect of the theory.…”

Section: Introductionmentioning

confidence: 91%

“…Since the discovery of cross-relaxation (CR) in paramagnetic crystals by De Vrijer and Gorter (1952) a number of experimental papers (Mims and McGee 1960, Pershan 1960, Feng and Bloembergen 1963, Squire 1965, Weissfloch 1967, Minkowski 1968, Van Duyneveldt-et a1 1968 have appeared in which observation of two and three-spin cross-relaxation at fixed temperatures has been reported. Several theories (Bloembergen et al1959, Provotorov 1962, Grant 1964a, b, c, d, e, Kotzler 1972, Zobov and Provotorov 1975 have also come up in the wake of these experiments.…”

Section: Introductionmentioning

confidence: 99%

“…Several theories (Bloembergen et al1959, Provotorov 1962, Grant 1964a, b, c, d, e, Kotzler 1972, Zobov and Provotorov 1975 have also come up in the wake of these experiments. BSPA theory (Bloembergen et a1 1959) has been utilised to explain the experiments of Pershan (1960), Feng and Bloembergen (1963), Minkowski (1968) and others whereas the statistical theory of Grant (1964a, b, c, d, e) is successful in explaining the results of various workers such as Mims and McGee (1960), Pershan (1960) and Weissfloch (1967). But both these theories are valid in the high-temperature approximation.…”

Section: Introductionmentioning

confidence: 99%

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Spinodal Decomposition in Polymeric Systems

Lipatov¹,

Шилов²

1984

Russ. Chem. Rev.

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A temperature-dependent statistical theory of two-and three-spin cross relaxation processes is developed for S = 1 paramagnetic ions. It takes account of fluctuations of magnetic quantum numbers of the ions due to spin-spin and spin-lattice interactions in terms of the ensemble theory of statistical mechanics. Explicit two-and three-spin resonant cross relaxation rates are computed for Ni2+ ions in the diamagnetic host lattice of dioxane and compared with experimental results. Reasonably good agreement is obtained with experiment, both with regard to temperature dependence and the actual magnitudes of two-and three-spin cross relaxation rates.

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Section: Introductionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spinodal Decomposition in Polymeric Systems

Lipatov¹,

Шилов²

1984

Russ. Chem. Rev.

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“…The line is quite weak at this low concentration, resulting in appreciable scatter in the experimental points, but this could not be avoided in view of the concentration dependent relaxation times that have been observed in ruby at higher concentrations (Mims et al 1960).…”

mentioning

confidence: 98%

FIELD DEPENDENCE OF SPIN-LATTICE RELAXATION TIMES OF Cr³⁺

Rumin¹

1966

Can. J. Phys.

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ABSTRACT.The changes in spin-lattice relaxation time with the magnitude and orientation of the de magnetic field, frequency, and temperatut'e have been calculated from simplified expressions for the spin-phonon transition probabilities of an S c 3/2 ion.The relaxation times for INTRODUCTION.II. THEORY OF SPIN-LATTICE RELAXATION.III.1. 2.The Interaction Hamiltonian.Spin-Phonon Transition Probabilities for the Direct Process.THE MEASUREMENT OF SPIN-LATTICE RELAXATION TIMES.1. 2.3.Relaxation Times in a S=~ Spin System.Pulse Saturation Measurements on a S)~ System. PROCEDURE. 1.Experimental. 2.Calculations.VIII. RESULTS AND DISCUSSION. 1.Cr 3 + in K 3 Co(CN) 6 .IX.x. .Cr 3 + in A 1 2 0 3 • 3.Cr 3 + in RbAl(S0 4 ) 2 .12H 2 0. 4.The Slopes in the Logarithmic Plots of T 1 versus 1/Z. 5.Calculations for Steady-State Saturation Conditions. CONCLUSIONS.BIBLIOGRAPHY. INTRODUCTIONWhen the thermal-equilibrium energy distribution of a group of paramagnetic ions, whose paramagnetism is due to a net magnetic dipole moment associated with their spins, is in sorne way disturbed, the subsequent return to equilibrium is said to take place through spin-lattice relaxation if it occurs as the result of the exchange of energy-conserving quanta between the spins and the thermal spectrum of the host lattice. by Mattuck and Strandberg (1960), the spin-lattice interaction of paramagnetic ions in crystals is understood to occur through the thermal modulation of the crystalline electric field. The theory predicts that at very low temperatures, T, the spin-lattice transition probability, wij' between spin states i and j will be determined by a direct, one-phonon process with wij varying as T, while at higher temperatures a two-phonon, Raman mechanism will dominate with wij varying as T 7 or T 9 .In the case of a two-level system the return to equilibrium of the population of levels 1 and 2 is characterized by a spin-lattice relaxation time T 1 where T 1 = l/2w 12 • No such simple relationship exists in the case of multi-level systems but an effective spin-lattice relaxation time TR is still used to describe the return to equilibrium of the population of a pair of levels, even though this generally involves all the *Woonton (1961) furnishes an excellent bibliography related to theoretical and experimental work on spin-lattice relaxation.-2-other spin levels as well.Much of the early theoretica1 and experimental work was centred on the ions of the 3d iron group.The measured values of TR often did not agree well with the theory, and exp1anationsfor some of the inconsistencies were proposed by Bloembergen et al (1959), who considered the role played by cross-relaxation, and by , Van Vleck (1961), and , who extended the concept of crossrelaxation to excited states.Several effects predicted by the theory of spin-lattice relaxation have been verified experimentally. Thus Pace et al (1960) and Feng and Bloembergen (1963) have verified 3+ the inverse temperature dependence for the 8=3/2 Cr ion in Al 2 o 3 at low temperatures, while , Rannestad and...

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“…where r k~I are the radiative rate constants in field H for the spin level i to vib ronic band v. In the absence of CR , the N i are found by solving equation ( 1); if CR is occurring , the N 1 are obtained from equati on (2). In general , the populations will not be in steady state and the phosphorescence intensity will be a function of time .…”

Section: Theoretical Model For the Cr Dynamicsmentioning

confidence: 99%