53Cr, 17O and 14N nuclear quadrupole resonance in ammonium ... Hyperfine... · 53Cr, 17O and 14N...

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Hyperfine Interact (2016) 237:118 DOI 10.1007/s10751-016-1332-3 53 Cr, 17 O and 14 N nuclear quadrupole resonance in ammonium dichromate David Stephenson 1 · Nadia Singh 1 © Springer International Publishing Switzerland 2016 Abstract The 53 Cr resonance frequency in ammonium dichromate has been detected at 4202 kHz giving a Qcc of 8404 kHz (assuming η = 0). Calculations suggest that the value of the 53 Cr quadrupole moment is about 84 mB lower that the currently accepted value. The resonance frequencies of two 17 O nuclei have also been detected giving Qcc = 2800, 2890 kHz and η = 0.726, 0.780 respectively. The value for coupling and asymmetry parameter for 14 N has been refined using zero field NQR giving a value Qcc = 78.8 kHz and η = 0.645 the asymmetry value being considerably lower than the value previous reported. Keywords NQR · 14 N · 17 O · 53 Cr · Ammonium dichromate 1 Introduction The nuclear quadrupole spectrum of ammonium dichromate has been published on two previous occasions [1, 2]. Both using cross relaxation as the detection mode [3]. This form of detection relies on matching the splitting of the proton levels to that of the quadrupole levels by magnetic field adjustments, so line(s) in the spectrum are subject to Zeeman broadening. The cross relaxation spectrum is dominated by a broad peak at around 690 kHz which has been previously attributed to 53 Cr [1, 2]. The problem with this assignment is that the This article is part of the Topical Collection on Proceedings of the International Conference on Hyperfine Interactions and their Applications (HYPERFINE 2016), Leuven, Belgium, 3-8 July 2016 David Stephenson [email protected] 1 Chemistry Department, University of the West Indies, St. Augustine, Trinidad and Tobago

Transcript of 53Cr, 17O and 14N nuclear quadrupole resonance in ammonium ... Hyperfine... · 53Cr, 17O and 14N...

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Hyperfine Interact (2016) 237:118 DOI 10.1007/s10751-016-1332-3

53Cr, 17O and 14N nuclear quadrupole resonancein ammonium dichromate

David Stephenson1 ·Nadia Singh1

© Springer International Publishing Switzerland 2016

Abstract The 53Cr resonance frequency in ammonium dichromate has been detected at4202 kHz giving a Qcc of 8404 kHz (assuming η = 0). Calculations suggest that the valueof the 53Cr quadrupole moment is about 84 mB lower that the currently accepted value. Theresonance frequencies of two 17O nuclei have also been detected giving Qcc = 2800, 2890kHz and η = 0.726, 0.780 respectively. The value for coupling and asymmetry parameterfor 14N has been refined using zero field NQR giving a value Qcc = 78.8 kHz and η =0.645 the asymmetry value being considerably lower than the value previous reported.

Keywords NQR · 14N · 17O · 53Cr · Ammonium dichromate

1 Introduction

The nuclear quadrupole spectrum of ammonium dichromate has been published on twoprevious occasions [1, 2]. Both using cross relaxation as the detection mode [3]. This formof detection relies on matching the splitting of the proton levels to that of the quadrupolelevels by magnetic field adjustments, so line(s) in the spectrum are subject to Zeemanbroadening.

The cross relaxation spectrum is dominated by a broad peak at around 690 kHz whichhas been previously attributed to 53Cr [1, 2]. The problem with this assignment is that the

This article is part of the Topical Collection on Proceedings of the International Conference onHyperfine Interactions and their Applications (HYPERFINE 2016), Leuven, Belgium, 3-8 July 2016

� David [email protected]

1 Chemistry Department, University of the West Indies, St. Augustine, Trinidad and Tobago

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applied field required to produce the cross relaxation condition would not be expected toproduce much broadening of the 53Cr resonance due to the low magnetogyric ratio of 53Cr.Calculation suggests that a 53Cr line at this frequency should have a maximum width of 150kHz whereas the width of the recorded line is approximately 400 kHz. It was suggested [1]that there was some crystal disorder causing the excess broadening. There is no evidencefor this in the crystal structure [4], neither is there any broadening of the 14N resonances(which are seen below 100 kHz [5]). In this paper it is demonstrated that the peak at 690kHz is due to the other quadrupolar nucleus present in the sample namely 17O and that the53Cr resonance is at a much higher frequency of 4202 kHz.

2 Experimental

The nuclear quadrupole spectra were recorded indirectly by monitoring the size of a recov-ered proton NMR signal in high field following a low field phase. During the low fieldphase transfer of energy from the quadrupole system to the proton system using various dou-ble resonance methods (described below) was attempted. The switch between high and lowfield was achieved by mechanic transport of the sample tube using compressed air. In highfield the proton magnetization was measured (at a resonance frequency of 20 MHz) using aBruker NMS 120Minispec. The ammonium dichromate sample was obtained from Hopkinsand Williams (Analar grade) and was ground to a fine powder before use. The proton T1 inthis sample is 10 s and is little changed by magnetic field strength. This allowed relativelylong contact time (4 s) in low field and a relative short polarization time in high field (20 s).Because of the short cycle time the signal to noise ratio could be further improved by addingseveral spectra together. All spectra were recorded at ambient temperature estimated to be295 K.

3 Cross relaxation detection

Using the double resonance method of cross relaxation the proton and quadrupole systemare brought into contact by applying a small magnetic field. The method is based on the factthat the 1H magnetogyric ratio is usually much larger than that of the quadrupole spins sothat increasing the field will sequentially bring the protons into contact with the quadrupoleenergy levels allowing the two systems to exchange energy. The low magnetic field wasswept in 4.58 kHz steps using a solenoid connected to a digital current supply. A 10 bit sig-nal from the control computer’s parallel port allowed currents up to 10.23 A to be deliveredin 10 mA steps.

3.1 RF excitation

The spectra were scanned in 1 kHz steps using a PTS 250 signal generator which wasconnected to the control computer via a parallel port. During the high field sequence theRF was gated off by selecting zero frequency on the signal generator. This gating preventedinterference with the proton NMR detector and it also reduced the duty cycle of the RFamplifier (Amplifier Research KAW 1050). The excitation coil was part of a series tunedLC circuit. The tuning was optimized using feedback from a pickup coil fed into amicroprocessor which controlled a stepper motor driving an air-spaced capacitor.

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3.2 Zero field NQR

The zero field NQR spectrum was recorded using the two pulse sequence described by Zaxet al [6]. The pulse timing was derived from microprocessor (PIC12F675) using a 20 MHzclock rate. The pulse lengths and gaps between the two pulses were derived from a softwaredelay loop which was incremented after each double resonance cycle. The pulses were fedto a transistor switch (B817) connected to the sample coil. The design of the sample coilwas not critical; anywhere between 5 and 30 turns was effective. The power to the coil wasfrom a standard DC power supply charging a low esr 1000 µF capacitor to 50 V.

4 Results and discussion

4.1 Cross relaxation spectrum and simulation

The cross relaxation spectrum of ammonium dichromate is shown in Fig. 1 (lower trace)along with the simulated spectrum, calculated as described below, in Fig. 1 (upper trace)

Cross relaxation spectra are recorded by varying the applied magnetic field. There istherefore a significant change in the relative contributions of the quadrupole and Zeemaninteractions when scanning through a broad resonance which is particularly significant forhalf-integer spin nuclei such as 17O (spin 5/2). Previous attempts to computer simulate crossrelaxation spectra have used the method of iteratively finding the cross relaxation conditionfor each transition over a large number of crystal orientations [7]. The advantage of thismethod is its computational speed however serious problems can arise in cases where fre-quencies cross and for crystal orientations for which the cross relaxation condition cannotbe achieved. The method used in this paper is to simulate the spectrum in the same way itis recorded experimentally.

The magnetic field is incremented in 10 kHz steps of the proton resonance frequency.At each magnetic field strength the energy of the quadrupole levels are calculated for 400crystal orientations (more may be needed when η is large). Transition frequencies and tran-sition probabilities are then calculated for these 400 crystal orientations. These values arethen stored if the transition frequency matches the proton Zeeman splitting (±70 kHz). Inthe example shown in Fig. 1 some 200 magnetic field steps were used (from 0 - 2000 kHz)generating around 200,000 cross relaxation contacts. This stored data file can then be com-piled (in 10 kHz steps) into a cross relaxation spectrum. Each stored data point contributesto the final spectrum based on transition probability and offset from exact frequency match-ing. The transition probabilities are calculated on the basis that cross relaxation can onlychange the quadrupole quantum number by ±1 or zero, as is expected for transitions onlyallowed on the basis of dipole-dipole interactions. Unlike RF induced transition where thereis a fixed orientation for the excitation field, cross relaxation is an energy exchange betweenquadrupole levels and protons. So, if the dipolar interactions are many and varied, it canbe assumed to have no angular dependence. The relative efficiency of cross relaxation isassumed to fall according to a Lorentzian function as the frequency mis-match increases.As expected for a spin 5/2 nucleus there are two dominant transitions ±1/2 to ±3/2 and ±3/2to ±5/2 . These show up as two distinct bands when η is small, but merge at higher (>0.5) η

values. So as only one band was seen in this case it indicated that η was quite large.The quadrupole coupling and asymmetry parameter are adjusted to give the best fit to

the experimental spectrum based on overall line width and the position of any features in

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Fig. 1 The cross relaxation spectrum of ammonium dichromate. The lower trace is the experimental spec-trum, the upper is a calculated spectrum using combining two simulations with Qcc = 2800 kHz, η = 0.726and Qcc = 2890 kHz, η =0.780. The y-axis is recovered magnetization. The experimental spectrum is thesum of 11 sequential scans which took 5 days to record

the line shape. The fit can be further tweaked by adjusting the effective T2 (used in theLorentzian function) and the degree of saturation (ST). The relaxation of multilevel systemsis complex [8], but can be reasonably approximated to a single exponential. So the finalsignal at a particular frequency can be expressed:

Signal= 1 - exp(-TP*LZ*ST)

where TP is the transition probability based on the amount of 0, ±1 character in thequadrupole transition. LZ is the value of the Lorentzian function based on frequency offset.And ST is the saturation factor related to the time spent at the cross relaxation condition.Because of the low abundance of 17O the spectrum depends on the TP value which is ameasure of how efficiently energy is transferred between proton and quadrupole system.For nuclei with higher abundance the signal strength is more dependent on how fast thequadrupole nuclei are relaxing and TP can be given a value of one for all transitions. Thefinal simulated spectrum is shown in Fig. 1 (upper trace) with the combination of two lineshapes using Qcc = 2800 kHz, η = 0.726 and Qcc = 2890 kHz, η =0.780. Comparison ofthe experimental and simulated spectra reveal a good (but not perfect) fit. The discrepanciesare probably due to variations in relaxation rates for different crystal orienations. Followingthe detection of the 53Cr line at 4202 kHz using RF scanning a careful re-scan of the highfrequency part of the cross relaxation spectrum revealed a weak and much broadened 53Crresonance. A line-shape analysis gives a tentative η value for 53Cr of 0.30 ±0.02. The crossrelaxation spectrum and the simulated spectrum are shown in Fig. 2. The two small peaks

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Fig. 2 The cross relaxation spectrum showing the 53Cr resonance the lower trace is simulated, the uppertrace is experimental (the extreme high frequency edge was beyond the scan width of the spectrometer). Thetwo peaks arrowed are sensitive to η

near the line centre (arrowed) are very sensitive to the value of η and so have been primarilyused to determine the asymmetry parameter.

4.2 RF scanned spectrum

The 53Cr in ammonium dichromate was expected to fall in the range 3-5 MHz [9, 10] anda slow scan of this region indicated a peak at 4202 kHz (Fig. 3). The signal is detected viathermal mixing type polarization transfer with the lower frequency side of the line, whichnormally would show a signal enhancement, diminished in intensity compared with the highfrequency side.

Scanning the region 500 kHz to 1000 kHz revealed several 17O lines. The lower lines canbe assigned to 1/2 to 3/2 transition and the higher frequency lines to 3/2 to 5/2 transitions.The lines are detected by solid effect type cross polarization. Normally two peaks either sideof the line centre would be expected for this type of detection. This is not obvious as thelower frequency side of the line is very weak. Determination centre frequency of the lineswas assisted by applying a small magnetic field which separates the doublet according tothe proton magnetgyric ratio. Four transitions were detected at 613, 658, 775 and 793 kHz.Simulations of the expected Zeeman broadened cross relaxation line shapes showed that a(marginally) better fit was obtained by pairing the 613 and 775 kHz to give Qcc= 2800 kHz,η = 0.726 and the 658 and 793 kHz to give Qcc= 2891 kHz, η = 0.780. This pairing isalso more consistent with the ab intio calculations discussed below. Due to the poor signal

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Fig. 3 RF scanned spectrum showing the 53Cr resonance. Scan step 1 kHz experimental time 20 hours. They-axis is the recovered magnetization

to noise in the recorded spectra uncertainty in the measured frequencies propagates into alarge uncertainty in Qcc of ±30 kHz and in η of ±0.03.

4.3 Zero-field NQR

The 14N lines were recorded using zero field NQR [6]. The technique only works well forlow frequency resonances (<500 kHz) this being due to the difficulty of exciting the higherfrequencies with d.c. magnetic pulse. In a typical experiment the sample received two mag-netic field pulses of about 5 µs duration and the separation of the pulses was incremented in2 µs steps to build up a FID of the 14N region. Fourier transform of this gives the spectrumshown in Fig. 4. The spectrum was fairly insensitive to pulse length and strength. Noticethat the high and low frequency lines are much more intense than the middle line. This wasseen under all conditions. There is no obvious reason why this should be so.

In normal double resonance detection the line width is dominated by proton dipole-dipoleinteraction and is therefore quite broad (typical half height width about 50 kHz), howeverfor ZFNQR the quadrupole nuclei (14N in this case) are evolving in the time domain inde-pendently of the protons so the peaks obtained are sharp (half-height width of about 1kHz) allowing the peak positions can be determined to ±200 Hz. This gives a considerablymore accurate value of Qcc = 78.8 ±0.4 kHz and η = 0.645±0.002. This is a considerablerefinement on the previously reported values of Qcc=76 kHz and η = 0.84 [5].

4.4 Ab initio calculations

Electric field gradient calculations were carried out using atomic positions from the crys-tal structure of ammonium dichromate [4]. The program used was PQS (Parallel Quantum

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Fig. 4 The zero field NQR spectrum of ammonium dichromate showing the 14N resonances. 1000 pointsfilled to 2048 with pulse separations increment of 2 µs (SW = 256 kHz)

Table 1 Calculated quadrupole parameters for quadrupole active nuclei in ammonium dichromate

Nuclei qzz a.u. qyy a.u. qxx a.u. η qzz kHz mB−1 Q mB Qcc kHz

Cr 53Cr −0.4138 0.2916 0.1222 0.41 −97.24 −150 [12] 14586

O1 17O −0.6106 0.5130 0.0977 0.68 −143.5 −25.58 [12] 3671

O2 17O 0.4228 −0.3820 −0.0469 0.78 88.8 −25.58 [12] −2578

O3 17O 0.4117 −0.3238 −0.0878 0.57 112.1 −25.58 [12] −2474

O4 17O 0.4973 −0.4303 −0.0670 0.73 116.9 −25.58 [12] −2990

ammonium 14N −0.2280 0.2082 0.0196 0.83 −53.6 20.44 [12] −1096

For atom labels see Fig. 5

Solutions) version 3.2 [11]. Although calculations using several different basis sets werecarried out the best correlation with experiment (based on the 17O resonances) wereobtained with the hybrid DFT calculation using the B3LYP/m6-31G(d,p) (the values areshown in Table 1). The quadrupole coupling constants and asymmetry parameters were cal-culated from the principal components of the electric field gradient for each qudrupolarnuclei in the molecule. Values of 20.44 mB and -25.58 mB were used for the quadrupolemoments of 14N and 17O respectively [12].

To get a double resonance signal from a low abundance nuclei such as 17O (abundance0.034 %) a single 17O needs to relax many 1H nuclei. For this to happen the 17O nuclei

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Fig. 5 Labeling of the atoms inammonium dichromate (seeTable 1)

has to relax quickly and the transfer of energy between the two systems needs to be effi-cient. Efficient energy transfer only takes place when the two nuclei are spatially close asenergy transfer is by dipole-dipole interactions which fall off rapidly with separation. Soit is unlikely that the bridging oxygen will be picked up in the double resonance experi-ment. The terminal oxygen atoms are all calculated to have Qcc and η values close to theexperimental values (though only two lines were resolved in the experiment)

Ammonium groups in many compounds in the solid state have a low barrier to rotation[13]. The activation energy in ammonium dichromate is particularly low at 4.6 kJ mol−1

[14]. Consequently, on the NQR timescale at room temperature, the ammonium group islikely undergoing almost free rotation. So it is not surprising that the calculated 14N Qcc,which is based on a static structure, is much higher than the experimental value. The Qcc of14N, though very low, is non-zero which indicates that the rotation of the ammonium groupis not isotropic. The rotation of the ammonium probably assists in relaxing the 17O as it willcause modulation of the dipole-dipole interaction between oxygen and the protons.

The Qcc value calculated for 53Cr differs considerably from that found experimentally,though the η values are similar. This is probably due to the large uncertainty in the 53Crquadrupole moment of -150 ±50 mB [12, 15]. Taking the 53Cr resonance frequency to be4202 ±2 kHz and η determined from the line shape analysis to be 0.30 ±0.02 this gives aQcc of 8280 ±20 kHz. If the quadrupole moment is now adjusted such that qzz × Q = 8280kHz this give a quadrupole moment of 84 mB almost within the uncertainty of the publishedvalue.

References

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P. O. Box 293, Fayetteville, Arkansas 72702–0293, U.S.A. www.pqs-chem.com12. Pyykko, P.: Mol. Phys. 99, 1617 (2001)13. Smith, D.: Chem. Rev. 1994(94), 1567 (1994)14. Koksal, F., Bahceli, S.: J. Chem. Soc. Faraday Trans. 2 74, 1844–1850 (1978)15. Ertmer, W., Johann, U., Mosmann, R.: Z. Phys. A 309, 1 (1982)