Breakdown of Carr-Purcell Meiboom-Gill spin echoes in inhomogeneous fields

TL;DR

This paper investigates how the CPMG spin echo sequence behaves differently in liquids and gases under inhomogeneous magnetic fields, revealing unexpected limitations in gases due to non-Fickian diffusion.

Contribution

It demonstrates that CPMG does not fully refocus inhomogeneous broadening in gases, contrasting with its effectiveness in liquids, and explains this difference through the nature of molecular motion.

Findings

CPMG fails to eliminate inhomogeneous broadening in gases.

In liquids, CPMG effectively measures intrinsic $T_2$ times.

Gases exhibit non-Fickian diffusion affecting spin echo behavior.

Abstract

The Carr-Purcell Meiboom-Gill (CPMG) experiment has been used for decades to measure nuclear-spin transverse ($T_2$) relaxation times. In the presence of magnetic-field inhomogeneities, the limit of short interpulse spacings yields the intrinsic $T_2$ time. Here we show that the signal decay in such experiments exhibits fundamentally different behaviors between liquids and gases. In gases, CPMG unexpectedly fails to eliminate the inhomogeneous broadening due to the non-Fickian nature of the motional averaging.