Nuclear spin relaxation by translational diffusion in liquids and solids: high- and low-frequency limits
Nuclear spin relaxation by translational diffusion in liquids and solids: high- and low-frequency limits
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DOI：
10.1088/0022-3719/14/4/018
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发表时间：
1981-02
期刊：
影响因子：
--
通讯作者：
C. A. Sholl
中科院分区：
文献类型：
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作者：
C. A. Sholl
由于经历相对扩散的单个物质的自旋之间的磁偶极耦合引起的核自旋弛豫速率依赖于双自旋相关函数J（p）（ω）。讨论了液体、立方晶体以及二维和一维系统的J（p）（Ω）的高频和低频极限。本文证明了J（p）（ω）的低频形式在液体和晶体中为J（p）（0）-A3 ω 1/2，在二维系统中为A2 ln ω-1，在一维系统中为A1 ω-1/2，并导出了系数A1，A2和A3的表达式，这些表达式适用于任何扩散模型，长时间行为可以通过扩散方程来描述。对于一维、二维和三维晶格上自旋的简单跳跃模型，导出了J（p）（ω）的高频形式，并且在每种情况下J（p）（ω）都具有B ω-2的形式。表达式推导出的系数B，为每个维度，其中正确地包括自旋的跳跃之间的相关性的影响。
Nuclear spin relaxation rates due to magnetic dipole coupling between spins of a single species undergoing relative diffusion depend on two-spin correlation functions J(p)( omega ). The high- and low-frequency limits of J(p)( omega ) are discussed for liquids, cubic crystals and two- and one-dimensional systems. It is shown that the low-frequency form of J(p) ( omega ) is J(p)(0)-A3 omega 1/2 in liquids and crystals, A2ln omega -1 in two-dimensional systems and A1 omega -1/2 in one-dimensional systems and expressions for the coefficients A1, A2 and A3 are derived which are valid for any diffusive model whose long-range, long-time behaviour may be described by the diffusion equation. The high-frequency form of J(p)( omega ) is derived for a simple-hopping model of spins on one-, two- and three-dimensional lattices and in each case J(p)( omega ) is of the form B omega -2. Expressions are derived for the coefficient B, for each dimension, which correctly include the effect of correlations between the hops of the spins.