Increasing dynamics in solids featuring nuclei subjected to second-order quadrupolar interactions lead to central-transition spectra that undergo two consecutive line-shaped transitions. Conventional motional narrowing occurs when the molecular exchange rate is on the order of the strength of the dominant interaction. In a second step, the resulting intermediately narrowed spectra change further when the motion becomes faster than the Larmor precession rate, leading to terminally narrowed spectra that can display a residual quadrupolar shift. We derive analytic expressions for this shift and analyze the quadrupolar central-transition spectra in terms of CN symmetrical cone models. Increasing the number of sites to N ≥ 3, the terminally narrowed spectra remain unaltered, while the intermediately narrowed spectra remain unaltered only for N ≥ 5. This finding relates to the different (cubic vs. icosahedral) symmetries that are required to average out the spatial second- and fourth-rank terms in the second-order quadrupolar interaction. Following recent work (Hung et al., Solid State Nucl Magn Reson 84:14–19, 2017), 17O NMR is applied to examine the three-site rotation of the nitrate group in NaNO3. Line shapes are measured and analyzed, and in addition to prior work, satellite-transition and stimulated-echo experiments are carried out. The final-state amplitudes extracted from the latter are reproduced using model calculations. It is shown how two-dimensional exchange spectra relating to N-site cone motions can be decomposed in terms of effective two-site-jump spectra. This latter approach is successfully tested for NaNO3.

中文翻译：

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从超慢到极快的硝酸钠动力学：17O NMR 研究

以核受二阶四极相互作用为特征的固体中不断增加的动力学导致中心跃迁光谱经历两个连续的线形跃迁。当分子交换率处于主要相互作用的强度数量级时，会发生传统的运动变窄。在第二步中，当运动变得比拉莫尔进动速率更快时，产生的中间变窄的光谱会进一步变化，导致最终变窄的光谱可以显示残留的四极位移。我们推导出这种位移的解析表达式，并根据 CN 对称锥模型分析四极中心跃迁光谱。将站点数量增加到 N ≥ 3，最终变窄的光谱保持不变，而中间变窄的光谱仅在 N ≥ 5 时保持不变。这一发现与平均二阶四极相互作用中的空间二阶和四阶项所需的不同（立方与二十面体）对称性有关。根据最近的工作（Hung 等人，Solid State Nucl Magn Reson 84:14–19, 2017），应用 17O NMR 来检查 NaNO3 中硝酸根基团的三中心旋转。测量和分析线形，除了先前的工作外，还进行了卫星过渡和受激回波实验。使用模型计算再现从后者提取的最终状态幅度。显示了如何根据有效的双位点跳跃光谱来分解与 N 位点锥体运动相关的二维交换光谱。后一种方法成功地测试了 NaNO3。二十面体）对称性，这是在二阶四极相互作用中平均空间二阶和四阶项所需的对称性。根据最近的工作（Hung 等人，Solid State Nucl Magn Reson 84:14–19, 2017），应用 17O NMR 来检查 NaNO3 中硝酸根基团的三中心旋转。测量和分析线形，除了先前的工作外，还进行了卫星过渡和受激回波实验。使用模型计算再现从后者提取的最终状态幅度。显示了如何根据有效的双位点跳跃光谱来分解与 N 位点锥体运动相关的二维交换光谱。后一种方法成功地测试了 NaNO3。二十面体）对称性，这是在二阶四极相互作用中平均空间二阶和四阶项所需的对称性。根据最近的工作（Hung 等人，Solid State Nucl Magn Reson 84:14–19, 2017），应用 17O NMR 来检查 NaNO3 中硝酸根基团的三中心旋转。测量和分析线形，除了先前的工作外，还进行了卫星过渡和受激回波实验。使用模型计算再现从后者提取的最终状态幅度。显示了如何根据有效的双位点跳跃光谱分解与 N 位点锥体运动相关的二维交换光谱。后一种方法成功地测试了 NaNO3。