Documents

pnmrs159

Description
espectroscopia
Categories
Published
of 43
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
Share
Transcript
  Recent advances in experimental solid state NMR methodology forhalf-integer spin quadrupolar nuclei M.E. Smith a, *, E.R.H. van Eck  b a  Department of Physics, University of Warwick, Coventry CV4 7AL, UK  b School of Physical Sciences, University of Kent, Canterbury, Kent CT2 7NR, UK  Received 11 November 1998 Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1602. Nuclear interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1613. Background experimental principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1634. One-dimensional experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1694.1. Static broad line experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1694.2. Magic angle spinning observation of the central transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1714.3. Magic angle spinning and spinlocking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1794.4. Magic angle spinning observation of satellite transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1814.5. Variable angle spinning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1834.6. Double angle spinning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1835. Multiple resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1855.1. Cross-polarisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1855.2. SEDOR, REDOR and TEDOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1865.3. TRAPDOR and REAPDOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1886. Two-dimensional experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1906.1. Nutation NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1906.1.1. Off-resonance nutation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1916.2. Dynamic angle spinning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1916.3. 2D MQMAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1936.3.1. Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1956.4. 2D XY correlation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1977. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 Keywords:  Experimental NMR; Materials characterisation; Solid-state; Quadrupole nucleiProgress in Nuclear Magnetic Resonance Spectroscopy 34 (1999) 159–2010079-6565/99/$ - see front matter  1999 Elsevier Science B.V. All rights reserved.PII: S0079-6565(98)00028-4* Corresponding author. Tel.: +44 1203 522 380; fax: +44 1203 692 016.  E-mail address:  M.E.Smith.1@warwick.ac.uk (M.E. Smith)  1. Introduction NMR is applicable to any nucleus that possesses amagnetic moment and has made a significant impacton branches of science and technology as diverse asmeasuring spin gaps in magnetic materials at less than4 K to clinical diagnosis through imaging techniques.Although NMR has, in principle, widespread applica-tion to the Periodic Table, the vast majority of studieshave been limited to relatively few of the NMR-activenuclei. One of the main reasons for the limited rangeof nuclei studied has been low sensitivity, with  1 Hbeing the most studied nucleus because of its largegyromagnetic ratio, although with ever higher appliedmagnetic fields available the range of nuclei beingroutinely studied is expanding. Many of the othernuclei that are now commonly studied, such as  13 C, 15 N,  31 P and  29 Si, are spin-1/2 nuclei which have theattraction that their spectra are largely determined bychemical shift effects, especially if averaging techni-ques such as magic angle spinning (MAS) and decou-pling are applied, so that spectral interpretation isrelatively straightforward. However most NMR-active nuclei have a spin-quantum number  I     1/2and consequently have a non-spherically symmetricelectrical charge distribution within the nucleus thatgives rise to a nuclear electrical quadrupole moment.This quadrupole moment interacts with gradients inthe electric field producing splittings of the nuclearenergy levels. As outlined in the next section theseeffects can be very large such that first-order broad-ening can spread the intensity over a very significantfrequency range. Quadrupolar nuclei fall into twomajor categories depending on whether or not anucleus possesses integer spin. Non-integer spinnuclei experience no first-order broadening of thecentral (1/2,   1/2) transition (vide infra) and forNMR of powder samples containing such nuclei it isthe central transition that is usually observed. Thenon-central, or so-called satellite transitions, can bespread over a frequency range of many MHz, andeven though this makes their observation by pulsetechniques difficult it has recently been realised theycan be measured, and provide useful information.The importance of non-integer spin quadrupolenuclei can be gauged by considering the 120 nucleiusually quoted in NMR Tables with 31 spin-1/2, 9with integer spin and 80 with non-integer spin   1/2(3/2 (32), 5/2 (22), 7/2 (18) and 9/2 (8)). Hence witharound two-thirds of NMR-active, stable nuclei beingnon-integer spin quadrupolar their study meritsserious attention. In solids the major difficulty forsuch nuclei is that for the more easily observed centraltransition the quadrupole interaction can be sufficientlystrongthatsecond-orderquadrupolareffects(videinfra)have to be considered, and these can cause broadeningof the central transition of tens of kHz that causes over-lapoftheresonancesintheNMRspectrafrompowders.The commonly applied approach of MAS, used sosuccessfully for averaging anisotropic dipolar andchemical shift effects can only partially reducesecond-order quadrupole effects. The residual aniso-tropy, and indeed the presence of isotropic second-order quadrupole effects has led to a great deal of theoretical and experimental endeavour, particularlyover the last decade, to produce alternative NMRapproaches for examining such nuclei in the solid stateto give better resolution. This has resulted in a wholerange of methods available for the study of such nuclei,some being very sophisticated. These methods includetwo-dimensional (2D) approaches, complex sample re-orientation during the experiment and excitation of multiple quantum transitions. The main categories are:1. Static, MAS and variable angle spinning for obser-ving the central transition.2. Static and MAS for observing the satellite transi-tions.3. Spatial reorientation; dynamic angle spinning(DAS) and double angle rotation (DOR).4. Multiple resonance including cross-polarisation(CP) and indirect detection (e.g. TRAPDOR).5. Nutation.6. Multiple quantum (MQ).There are some excellent review articles givingdetailed background information and applications of many of these techniques individually and these willbe extensively referenced here. This article seeks togive an overview of the physical background of theseapproaches, and in particular to compare their relativemerits. It is a goal that this article should be accessibleto the non-specialist who simply wants to use solidstate NMR of a non-integer spin quadrupole nucleusto better characterise samples. It will seek to answerpractical questions, such as how readily the differenttechniques can be implemented, what information  M.E. Smith, E.R.H. van Eck / Progress in Nuclear Magnetic Resonance Spectroscopy 34 (1999) 159–201 160  they provide, what are their limitations and how canthey be combined to give a complete NMR methodol-ogy for studying quadrupole nuclei in the solid state. 2. Nuclear interactions NMR interactions are represented by a spin Hamil-tonian that will have parts that correspond to theexperimental conditions, the so-called external part,and those parts that result from the sample itself, theinternal part, which provide information about thestructure of the sample. The total interaction energyof the nucleus may be expressed as a sum of indivi-dual Hamiltonians given in Eq. (1), which arediscussed in detail several excellent books [1–4].  H  tot      o  I   z      B 1    2   I   e  i   t    I   e  i   t     H   D   H  CS    H   1  q    H   2  q   …   1  The basis of the NMR experiment is the non-degen-erate nuclear energy levels created by the Zeemaninteraction (         o  I  z , Fig. 1(a)) of the nuclearmagnetic dipole moment    (        I , where     is thegyromagnetic ratio of the nucleus) with an appliedmagnetic field  B o . This field is taken to define the  z -axis in the laboratory frame and  I  z  is the  z -componentof   I  with eigenvalues  m z  (   I   m z   I  ), and   o  is theLarmor frequency. In this article we will onlyconsider the high field limit whereby the nuclearspin states are well described by the Zeeman energylevels and that all the other interactions can beregarded as perturbations of these spin states. Theactual NMR experiment involves measurement of the energy separation of these levels by applicationof a time-varying orthogonal magnetic field  B 1  (term 2in Eq. (1)).  B 1  excites transitions (through  I    and  I   ,the conventional spin raising and lowering operators)when its frequency (   ) is close to    o , typically in therf region 10 MHz–1 GHz.For spin-1/2 nuclei in diamagnetic insulatingsolids the important interactions experienced aredipolar (  H  D ) and chemical shielding (  H  CS ). Giventhe tensorial nature of these interactions, for apowder containing a random distribution of parti-cle orientations relative to the main magneticfield, these interactions give rise to broadeningof the NMR spectra. Fortunately, to first-order,all these interactions (  H  D ,  H  CS  and  H  q  (I)) have similarangular dependencies of (3cos 2      1      sin 2   cos 2   ) where     is the asymmetry parameter of theinteraction tensor in the molecular principal axes (     0 for axial symmetry).The interaction between the electric quadrupolemoment ( eQ ) of the nucleus and the electric fieldgradient at the nuclear site can have a profound effecton the NMR spectrum. The electric field gradient isagain a tensor interaction that in its principal axissystem (PAS) is described by the three components V   x   x  ,  V   y   y  and  V   z   z  , where   indicates that the axes arenot necessarily coincident with the laboratory axesdefined by the magnetic field. Although the tensor iscompletely defined by these components it is conven-tional to recast these into ‘‘the electric field gradient’’ eq    V   z   z   and the asymmetry parameter   q     V   y   y   V   x   x      V   z   z    The electric field gradient is set up by thecharge distribution outside the ion (e.g. Al 3  ) but theinitially spherical charge distribution of inner shells of electrons will become polarised to lower their energyin the electric field. This polarisation produces anelectric field gradient at the nucleus itself of   eq n   eq (1    ∞ ) where (1    ∞ ) is the Sternheimer anti-shielding factor which is a measure of the magnifica-tion of   eq  caused by distortion of the core electrons[5]. Full energy band structure calculations of electricfield gradients showhow important the contribution of the electrons on the ion itself are compared to thelattice [6]. Although the quadrupole interaction is anelectrical interaction it depends on the orientation of the nuclear spins and therefore affects the nuclearenergy level splittings [7]. The background of thequadrupole interaction is given in the classic articleby Cohen and Reif [7]. The quadrupole Hamiltonian(considering axial symmetry for simplicity) in thelaboratory frame with     being the angle between the  z  -axis of the quadrupole PAS and  B o  is  H  q    hC  q     8  I   2  I   1  3cos  2    1  3  I   z  a   3sin    cos      I  2   I     I       I     I     I   z   3sin 2      2   I  2    I  2    2  where  C  q    e 2 qQ    h  1    ∞   and  a    I   I  1  . Inthe limit  H   Z  q  H  q  a standard perturbation expansionusing the eigenstates of   H   Z   is applicable. The first-order term splits the spectrum into 2  I   components  M.E. Smith, E.R.H. van Eck / Progress in Nuclear Magnetic Resonance Spectroscopy 34 (1999) 159–201  161  (Fig. 1(a)) 1 of intensity   m  1   I   x  m  2   a  m  m  1   at frequency     1  m  away    1  m    3 C  q    4  I   2  I   1  3cos 2    1  m  z  1    2   3  This perturbation can cause the non-central transi-tions (i.e.  m  z    1/2) to be shifted (Fig. 1(b)) suffi-ciently far from the Larmor frequency that thesetransitions become difficult to observe with conven-tional pulse techniques. Fortunately for the central( m  z    1/2) transition,     1  m    0 and the dominantperturbation is to second-order only Eq. (4) whichgives a characteristic lineshape (Fig. 1(c) for axialsymmetry).    2  m     9 C  2q    64   o  I  2  2  I   1  2  a  3    4  1  cos 2     9cos 2    1   4   M.E. Smith, E.R.H. van Eck / Progress in Nuclear Magnetic Resonance Spectroscopy 34 (1999) 159–201 162Fig. 1. The effects of the quadrupolar interaction for an  I     5/2 nucleus showing (a) the energy level diagram and the corresponding (b)complete first-order spectrum and second-order (c) static and (d) MAS spectra for   q    0 for the central transition.    A     I    I   1   3    4    2q      0  . 1 The angular terms forthe second-order broadeningcorrect thosegiven in Fig. 2(a) of M.E. Smith, Appl. Magn. Reson., 4 (1993) 1.
Search
Similar documents
Tags
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks
SAVE OUR EARTH

We need your sign to support Project to invent "SMART AND CONTROLLABLE REFLECTIVE BALLOONS" to cover the Sun and Save Our Earth.

More details...

Sign Now!

We are very appreciated for your Prompt Action!

x