Correlated atomic diffusion and its effect on NMR spin-lattice relaxation rates

Bustard, L.D.

doi:10.1103/physrevb.22.1

Cited by 30 publications

(7 citation statements)

References 14 publications

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“…The procedure adopted by Bustard (1980) was to use a least-squares fit of a sum of exponentials to the Monte Carlo generated G*(t) and then to evaluate the Fourier transform analytically. Difficulties with this procedure are that the sum of exponentials does not properly describe the slow asymptotic t-312 behaviour of G*(t) and hence will underestimate g(0) and that the assumed exponential form prescribes an analytic form forg(y) which, in particular, does not give the correct low-frequency (g(y)g(0))ay''2 behaviour described by equation (2.15).…”

Section: Evaluation Of the Fourier Transformmentioning

confidence: 99%

“…Firstly, there have been exact results obtained in the limits of high and low frequency and spin concentration (see for example, Wolf 1974, Fedders and Sankey 1978, Sholl1981a, b, Fedders 1982, MacGillivray and Sholll983,1985a. Secondly, calculations have been performed for approximate analytic theories applicable for general values of frequency and spin concentration (see for example, Fedders and Sankey 1978, Barton and Sholll980) and thirdly there has been one (Bustard 1980) Monte Carlo calculation of the spectral density function for the simple cubic lattice. Each of these three approaches has its strengths and weaknesses.…”

Section: Introductionmentioning

confidence: 99%

“…The Monte Carlo method was first applied to the calculation of the NMR relaxation functions by Bustard (1980) and the present method is similar to this in some respects. However, an important aspect of the Monte Carlo method used here is that the numerical analysis makes use of some of the known exact limits of the correlation functions and this procedure results in a considerable improvement in accuracy.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Asymmetric Implantation Self-alignment Technique for GaAs MESFETs

Kimura¹,

Inokuchi²,

Akiyama³

et al. 1988

Jpn. J. Appl. Phys.

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The spectral density functionsJ(P'( w ) relevant to nuclear spin relaxation rates due to magnetic dipole coupling between diffusing spins in cubic crystals are calculated, for the simple hopping model, by a Monte Carlo method. The analysis makes use of known exact results in various limits. The statistical fluctuations in the Monte Carlo calculations become more significant at high frequencies but accurate analytic results are known in this regime. Numerical results are therefore obtained over the entire frequency range for all spin concentrations except the monovacancy limit.

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Section: Evaluation Of the Fourier Transformmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Asymmetric Implantation Self-alignment Technique for GaAs MESFETs

Kimura¹,

Inokuchi²,

Akiyama³

et al. 1988

Jpn. J. Appl. Phys.

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show abstract

“…Measurement of nuclear magnetic dipolar relaxation is an effective method for investigating hopping diffusion in crystalline solids and its success has been accompanied by the development of increasingly comprehensive theories of the relaxation rate applicable over a wide range of spin concentrations [l-31. This theoretical work has been reinforced by Monte Carlo simulation [4,5] and it is now possible to interpret in some detail experimental measurements of the relaxation rate for spins hopping on particular lattices. On the other hand, owing to the complexity of the problem and the wide diversity of types of disorder.…”

Section: Introductionmentioning

confidence: 99%

Nuclear magnetic relaxation in disordered solids: a Monte Carlo study of metal-hydrogen systems

Adnani

Havill

Titman

1994

J. Phys.: Condens. Matter

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The dipolar nuclear magnetic relaxation rate associated with the hopping diffusion of atoms in a disordered solid is calculated by Monte Carlo methods. The model is intended to simulate the diffusion of hydrogen atoms trapped at interstitial positions in the matrix of metal atoms in amorphous alloys. The principal features of the model system are that the atoms hop on a spatially disordered array of traps and the trapping energy varies from trap to trap so that the diffusion of the hydrogen is characterized by a distribution of jump rates. The effective jump rate from a trap is assumed to have an Arrhenius dependence on temperature. Calculated at constant temperature, the characteristic peak in the relaxation rate, which occurs in ordered solids when the product of the average jump rate and the Larmor frequency is approximately unity, is found to be broadened and shifted in frequency, particularly when the occupancy of the traps is high. The long-range diffusion constant is also calculated and used to evaluate the effect of atom-vacancy correlations. It is found that the shifts in the relaxation peak cannot be accounted for solely by these correlation effects and it is suggested that multiple hopping of the more rapidly diffusing spins is a contributory factor. The shifts have a profound effect on the temperature dependence of the relaxation rate when the distribution of jump rates is also dependent on temperature. The adjustments to the peak in the relaxation caused by the distribution are small when the temperature dependence is taken into account, showing that experiments involving only the temperature variation of the relaxation are unlikely to be a sensitive method for detecting the presence of a jump-rate distribution. This aspect of the results of the computer model is illustrated by comparison with experimental data.

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“…The first attempt at using a Monte Carlo (MC) method to evaluate the diffusion correlation functions necessary to determine relaxation rates was made by Bustard (1980), but his work was specifically geared towards the Ti/H system. The only other MC studies of the relaxation rate are those of Faux, Ross and Sholl (1986), hereafter referred to as FRS, and the follow-up study by Faux and Hall (1988).…”

Section: Introductionmentioning

confidence: 99%

Nuclear spin relaxation due to the translational diffusion of hydrogen in BCC metals

Faux¹,

Hall²

1989

J. Phys.: Condens. Matter

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The authors calculate the spectral density functions required for the theoretical determination of nuclear spin relaxation rates due to magnetic dipolar coupling between diffusing hydrogen spins in BCC metals. Both the like-spin (hydrogen-hydrogen) and unlike-spin (metal-hydrogen) contributions are determined using the Monte Carlo method of Faux, Ross and Sholl (1986). Results are obtained for hydrogen-to-metal ratios of 0.12, 0.3 and 0.6 for the simple hopping model (no multiple occupancy of sites) and for a multiple site-blocking model in which the hydrogen spins block all sites as far as the second or third neighbour. For the simple hopping model, the results are in very good agreement with the multiple-scattering theory of Sankey and Fedders (1980), in the high- and low-temperature limits. For the multiple site-blocking models, it is found that the BPP model (due to Bloembergen, Purcell and Pound, 1948) and Torrey model (1953), can differ significantly from the Monte Carlo result, particularly at higher concentrations. The results obtained for D/T1, where D is the tracer diffusion coefficient and T1 is the spin-lattice relaxation time, are compared to the experimental result on NbH0.6. The Monte Carlo method gives a value which is 2/3 of the experimental value if blocking to either the second or the third neighbour is assumed. Agreement with experiment may be obtained if it is assumed that the hydrogen diffuses by a combination of jumps to nearest-neighbour and second-nearest-neighbour sites.

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Correlated atomic diffusion and its effect on NMR spin-lattice relaxation rates

Cited by 30 publications

References 14 publications

Asymmetric Implantation Self-alignment Technique for GaAs MESFETs

Asymmetric Implantation Self-alignment Technique for GaAs MESFETs

Nuclear magnetic relaxation in disordered solids: a Monte Carlo study of metal-hydrogen systems

Nuclear spin relaxation due to the translational diffusion of hydrogen in BCC metals

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