High Sensitivity Nuclear Quadrupole Resonance Approach for Detection of Modulation Wave Motion in Incommensurate Systems

Abstract

In contrast to conventional NMR techniques that use magnetic field gradients (MFG's) to detect the diffusion of moving atoms, we have developed a highly sensitive approach for detecting electric field gradient (EFG) Iluctuations seen by stationary atoms. These EFG Iluctuations were observed in the quadrupole perturbed NMR behavior of a stationary nucleus ( 'Nb) in the incommensurate insulator barium sodium niobate and are attributed to motion of the modulation wave. We observed effective diffusion constants of order 10 " cm2/s, which are 4 orders of magnitude smaller than those currently detectable with MFG NMR.

Magnetic resonance investigations of phase transitions and modulation wave motions in incommensurate solids

“…Normally, a Hahn echo decay which is more rapid than a Carr-PurcellMeiboom-Gill (CPMG) decay indicates slow diffusion of the observed spin in an inhomogeneous magnetic field, particularly if the Hahn echo decay is characterized by an exponential dependence on the cube of the echo time T. However, such behavior has recently been observed in quadrupolar systems in which the magnetic field is homogeneous [2][3][4] and in which the observed spin may be stationary [2]. These observations were attributed to a spatially inhomogeneous electric field gradient (EFG) which fluctuates in time due to the diffusionlike motions of the incommensurate modulation wave between the pinning centers.…”

“…For singly-modulated (lq) systems the transverse magnetization in a spin-echo experiment has been shown to decay as [2][3][4] (1) z where T is the pulse separation, Du, depends on the NMR angular frequency ríß within the inhomogeneously broadened I lineshape and equals the diffusion coefficient D at the center of the line, q is the modulation wave wavevector, and WINC is the I frequency splitting between the edge singularities. Since w NC and q are, in principle, known, this equation can be used together with the measured Hahn decay to obtain values for the effective diffusion coefficient D of the modulation wave.…”

What Are the Conditions for Exponential Time-Cubed Echo Decays?

“…[7] In this equation ᐂ ϭ 0, removing the cross-term. The first term is the random walk result and is linear in time, because the correlation time of the white noise ᐂ is infinitesimal and consequently short compared to t, yielding…”

“…[In detail, in terms of the autocorrelation U of the input noise voltage ᐂ, the first term F of [7] may be written as a double integral. The end result is F ϭ t ͐ U () d, where the infinitesimally short correlation time allows the integral limits on to be taken to Ϯϱ.…”

“…Indeed, in the limit that the pulse spacing approaches 0, the diffusive damping is zero, allowing the "true T 2 " (neglected here) to be determined; this was an original purpose of the Carr-Purcell pulse sequence (5,6). Recently, spin echoes have been used to measure the diffusion coefficient of the modulation wave of incommensurately distorted solids (7)(8)(9)(10). Here the distortion wave couples through the quadrupole interaction to the frequency of a given spin transition.…”