University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Gerard Harbison Publications Published Research - Department of Chemistry February 1994 The nuclear hexadecapole interaction of iodine-127 in cadmium iodide measured using zero-field two dimensional nuclear magnetic resonance Ming-Yuan Liao University of Nebraska - Lincoln Gerard S. Harbison University of Nebraska - Lincoln, [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/chemistryharbison Part of the Chemistry Commons Liao, Ming-Yuan and Harbison, Gerard S., "The nuclear hexadecapole interaction of iodine-127 in cadmium iodide measured using zero-field two dimensional nuclear magnetic esonancer " (1994). Gerard Harbison Publications. 3. https://digitalcommons.unl.edu/chemistryharbison/3 This Article is brought to you for free and open access by the Published Research - Department of Chemistry at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Gerard Harbison Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. The nuclear hexadecapole interaction of iodine-127 in cadmium iodide measured using zero-field two dimensional nuclear magnetic resonance Ming-Yuan Liao and Gerard S. Harbison Department of Chemistry, University of Nebraska at Lincoln, Lincoln, Nebraska 68588-0304 (Received 25 June 1993; accepted.18October 1993) Two dimensional nuclear quadrupole correlation spectroscopy has been used to measure simultaneously the two nuclear spin transition frequenciesfor the iodine resonanceof cadmium iodide at zero magnetic field. Becauseof the layer structure and resultant polymorphism in this substance, conventional zero-field NMR spectra are inhomogeneously broadened by several hundred kHz. However, the 2D spectra obtained by our method are subject only to homogeneous linewidth, which for this compound is of the order of 5 kHz. This greatly increased precision allows more accurate evaluation of the nuclear hexadecapolecoupling- in cadmium iodide; which we measure as 0.216*0.5 14 kHz (i.e., indistinguishable from zero). This gives a maximum value of the nuclear hexadecapolemoment severaltimes lower than that recently reported for the same nucleus in potassium iodide. INTRODUCTION spuriously interpreted as due to a-hexadecapole.The high- field NMR method is limited by the fact that the electric Of all the fundamental electrostatic interactions of or- field gradient at the nuclear site is never identically zero in dinary matter, the nuclear hexadecapolecoupling is per- any real crystal, regardlessof symmetry; even in the most haps the most ephemeral.Since it was reported in 1955,’ it perfect crystal, strain and residual imperfections causethe has gone through cycles of measurement2-4and refuta- NMR linewidth to be inhomogeneouslybroadened, just as tion;5’6 almost 40 years after its initial appearancein the it is in the quadrupolar case.In addition, if the quadrupo- literature, its very existence as a nonzero quantity is still lar interactions are large enough, they may enter the somewhat in doubt. Perhapsthe most rigorous recent work second-orderregime; a second rank perturbation on a first on the subject, by Doering and Waugh in 1986,5showed rank tensor has fourth rank components in the second or- that most of the measurementsup to that point in time der of approximation; these fourth rank components have were within experimental uncertainty of zero; they them- the same symmetry properties as the first order part of the selves were unable to determine a nonzero hexadecapole hexadecapoleperturbation and so may mimic them closely. interaction in a tantalate salt due to residual line broaden- Since one of the goals ,of the high field method-to ing. choose the point symmetry of the lattice site to eliminate Since hexadecapolar interactions themselves, if they the quadrupolar interaction-can only be achieved,even in are measurableat all, are certainly very small, they have ideal circumstances,for a limited number of materials, and until now been measured as perturbations on some much is almost never attainable in practice, the zero-field large interaction which provides the Boltzmann distribu- method, where only two terms needbe considered,appears tion and increased resonancefrequency necessaryfor et& to hold the most promise. The two major drawbacks of the cient detection. The two main approaches have been to zero-field method, inhomogeneous linewidth and nonsi- measure the spectrum at zero field, in the presenceof a multaneity of measurements-may both be circumvented quadrupolar interaction (conventionally but not com- by using two-dimensional correlation spectroscopy,which pletely accurately called NQR spectroscopy); this requires has recently been applied by us to quadrupolar nuclei at measurementof three independent transition frequencies, zero field.7 We report here the utilization of these methods or of two frequenciesin systemswhere the lattice site sym- to measurewith unprecedentedprecision the hexadecapo- metry is no lower than axial-or at high field in a site of lar interaction of lz71in cadmium iodide; setting an upper cubic point symmetry, in which the thermal nuclear polar- limit on the Sternheimer-weighted nuclear hexadecapole ization results from the Zeeman interaction, and the qua- moment of this nucleus several times lower than previous drupolar interaction is theoretically zero. measurements.6 The two methods have had significant drawbacks: The hexadecapolarinteraction at zero field is manifest as a per- THEORY turbation of the ratios of two (in the caseof axial symme- try) or three (in the general case) quadrupolar-induced Hexadecapolar perturbation of the zero-field NMR spin transition frequencies.Both transitions are often sub- spectrum -~ ject to significant inhomogeneousline width, often tens or For a nucleus at the zero field, the quadrupole Hamil- hundreds of kHz. In addition, if the two or three frequen- tonian is given by cies are measured sequentially, changes in experimental conditions between the time of the measurementsmay in- e2Qa (31,~14) +; (IZ,+I:) . (1) ducea changein the ratio of frequencieswhich may be Hp=41(w- 1) 1 0021-9606/94/100(3)/1695/7/$6.00~ @ 1994 American institute of Physics 1895 J. Chem.Downloaded Phys. 100 20 Apr(3), 12007 February to 129.93.16.206. 1994 Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp 1896 M.-Y. Liao and G. S. Harbison: Nuclear hexadecapole of iodine-127 ConventionallyI representsthe spin of a nucleus,eQ is the where q is the monopole moment due to the point charge, quadrupolemoment for the nucleus, eq is the secondde- P is the induced dipole moment due to the electric field at rivative of the electric potential at the nuclear site. v is the r, and Q is the induced quadrupole moment due to the asymmetry parameter, and e2Qq is the quadrupole cou- electric field gradient at that point, By using standard vec- pling constant (QCC). Similarly, the Hamiltonian for the tor calculus methods we can derive theeformula diagonal (T& part of the hexadecapoleinteraction can be i” -1 written as V-p’J”+’ [ (m+n)i”+‘-n3”-‘] . e2Hh Hh=12*1’(1-1)(2~-1)(21--3) [351f-30m1) In an ionic crystal, the total electric field gradient would be the summation of the electric field gradient due to the +3(I*I)2+25f;-6(I~I)], (2) monopole, induced dipole and induced quadrupole eH where is the hexadecapolemoment of the nucleus and -q 3iP-1 P lSiFP-9i eh is the fourth derivative of the electric potential at the VE(r)=-- - 4~-ec7 + 4~~s r4 nucleussite. We definee2Hh as the hexadecapolecoupling constant (HCC). LQ 3532?P--25fl+2 + . For a spin 5/2 system with axial symmetry, the mea- + 871.~~ r4 (11) sured NQR frequenciesperturbed by HDI can be written as Similarly, the first three terms of the expansionof the sec- ond derivative of the electric field gradient are I&-;) =$QCC+$ HCC, (3) 1 4 V3E,(r) = -G ;5 (105ilPi-9O?f+9) +&; &-f) =& QCC-j$ HCC . (4) 0 Therefore, the quadrupolecoupling constant QCC and x (945i’i?i?i- 1050iiP+225f) -&; hexadecapolecoupling constant HCC can be calculatedby 0 QCC-g (5Y1+4v2), (5) x (3465?ifiX+4410fPf3-t 136519-60) . (12) HCC=F (~i-2~~) . (6) EXPERMENT From the experimental quadrupole and hexadecapole coupling constants, using the Sternheimerrelationship, the Cadmium iodide (99.5%) was obtained from Johnson electric field gradient and the secondderivative of the elec- Mathey Electronics. Samplesfor NMR were obtained by tric field gradient around. the ion site can be calculated cooling a saturated solution of the compound at 40 “C using down to 4 “C over a 24 h period in the absenceof light; the QCC i soft, platelike crystals were separatedfrom the mother li- (7) quor by careful filtration and air dried. They were inserted eq=(l-y&Qy into a glass sample tube without crushing or applying any HCC avoidablestress, and were packedby carefully agitating the eh=(l-~,)eH’ (8) tube and allowing them to settle gravitationally. The _- double-resonanceprobe, and detailed experimental proto- wherey, and 7, are the Sternheimerfactors for the quad- cols for the .two dimensional experiments, are described rupole and hexadecapolemoment. previously.7The experimentwas carried out using a home- built pulsed solid-state NMR spectrometer at zero field. The temperaturewas kept at 23 * 0.5 “C by air cooling. For Calculation of the electric field gradient and its one dimensionalspectra, a simple (r/2--7-~-~) Hahn- second derivative echo sequencewas used. A series of two dimensional ex- periments were carried out over the range where Cd12 If there exists an electric field E at the site of a closed- shell ion, the induced electric dipole moment is given by shows significant signal intensity: i.e., for yl( 5/2-3/2) P=adE, where ad is the dipolar polarizability of the ion. =29.60&29.420 MHz and ~,(3/2-l/2) = 14.8OG14.710 Similarly, the electric field gradient VE will produce an MHz. The 90” pulse lengths, basedon the maximum nuta- induced electric quadrupole moment which is given by tion frequency observedfor a powder sample,were 3.5 ,us Q=aqVE, where a4 is the quadrupolarpolarizability of the for the (5/2-3/2) transition and 3.0 ,USfor the (3/2-l/2) ion.