Temperature Effects in Nuclear Quadrupole Resonance...

Temperature Effects in Nuclear Quadrupole Resonance

Spectroscopy

Allen MajewskiDepartment of Physics

University of FloridaFall 2016

Allen Majewski (University of Florida) Temperature Effects in NQR September 2016

Overview

• What is nuclear quadrupoleresonance (NQR)?– NMR vs NQR– Electric field gradients (EFGs) and

quadrupole coupling constants (QCCs)

– Applications of NQR

• Advantages and disadvantages of NQR

• Theory of temperature dependence of NQR

• DFT calculations of NQR parameters

What is NQR?

• Nuclear quadrupole resonance (NQR) is a radio frequency (RF) spectroscopy technique for solid materials

• The instrumentation is like NMR but NQR doesn’t require an applied B0 field because the physical mechanism is different

• There are benefits and drawbacks to NQR as compared with NMR


• In NMR spectroscopy, the nuclear magnetic moment interacts with an applied static magnetic field B0

• Energy gap is probed with a radio frequency (RF) pulse of the corresponding “Larmor frequency”

γ: gyromagnetic ratio of

nucleus1H has γ of 42 MHz/tesla

NMR overview



NMR overview: spectrometer

B0

B1

RF pulse in

NMR signal out

chemical shifts

NQR overview: spectrometer


• NQR does not require a big magnet great news

• Reduced cost, complexity

NQR signal out

B1

RF pulse in

NQR


Simple but good NQR instrument

• NQR is valued for simplicity of instrumentation


Simple but good NQR instrument

• NQR is valued for simplicity of instrumentation

Spectrometer Block Diagram

Bridge Circuit


• In NQR, the nuclear electric quadrupolemoment Q interacts with the natural electric field gradient (EFG) of the solid. No static field is applied.

NQR and the Electric Field gradient


Electric field gradients (EFGs) and quadrupole coupling constants (Cq)

• NMR: B0 and γ determine operating frequency

• NQR: natural EFG and Qdetermine operating frequency

• Cq: coupling constantη: asymmetry parameter

• NQR frequencies go like Cq × f(η)

NQR transition frequencies

Spin 3/2 case e.g. 35Cl:

Spin 1 case e.g. 14N:


coupling constant &asymmetry parameter

local electric field gradient

nuclear electric quadrupole moment

• NQR is a sensitive probe to changes in the electronic structure.– any physics which affects the

local electronic structure– NQR freq. is discontinuous

over phase change

Applications of NQR: basic science


Applications of NQR: basic science


• NQR is sensitive to chemical and crystallographic inequivalence of nuclear sites

TNT molecule

chemically inequivalentnitrogen sites

crystallographicallyinequivalent nitrogen sites


Applications of NQR: industrial

• NQR can identify arbitrary materials from absolute frequencies observed

– Frequencies are material specific

– Explosives detection• NQR for landmine sensing• NQR for passenger bag

screening• NQR can even determine

who manufactured an explosive sample

NQR advantages

• Simplicity of instrumentation (do not need a big magnet) <- huge deal

• High sensitivity – can probe electronic structure directly– Sensitive to small changes in local EFG

• Gives material specific fingerprint from the absolute frequencies



NQR disadvantages

• Only works for quadrupolar nuclei (spin ≥ 1) in solids – no solutions, or fluids

• Low signal to noise ratio (SNR) compared to NMR (in NMR a high operating frequency can be chosen)

• No ability to control NQR frequency– νNMR determined by B0 and γ– νNQR determined by natural crystal E field gradient, Q– If you don’t know NQR frequency, good luck finding it …

– NQR at very low frequency if there is high crystal symmetry poor SNR– Maybe so low, you’ll never detect it even if you tried due to noise floor– Frequency can be really zero if EFG is: e.g. cubic symmetry

no humans


NQR disadvantages

• What is needed: a reliable method of theoretical prediction or computation of EFGs in order to find out unknown NQR frequencies

• Once thought impossible, EFGs can be computed for the static lattice case (as if T=0)

• Calculation is good if you can also predict T-dependence …


T-dependence of NQR frequencies

• NQR frequencies in a given structure almost always decrease with rising temperature

• The most dominant temperature affect comes from internal motions of the quadrupolar nucleus


T-dependence of NQR frequencies

• Horst Bayer considered the effect of small rotations of the EFG axes (1956)

• He related the EFG in the primed system φ’ to that of the unprimed system φ through the displacements <θ>, and <θ2>

• He concluded that the time averaged EFG experienced by the quadrupole is less than the static lattice value

EFG is always reduced by oscillatory motions

• Theory was extended by Kushida, et al Bayer&Kushida BK-model

θ

35Cl


T-dependence of NQR: BK model

• Replace the <θ2> with harmonic oscillators, sum over all modes of system to get the EFG component as a function of temperature

q0: q(V, T=0) q is static lattice EFG EFG at zero temperature (constant volume)ωi: frequency of ith mode of oscillationAi: corresponding moment of inertia

• case of axial symmetry (η = 0)• counting only the lowest N vibrational modes • expand where … after pages and pages and pages …


T-dependence of NQR: BK model

static lattice EFG when the cell volume is that of the non-zero temperature!

highest mode counted is Nth

Ai: moment of inertia for ithmode

ωi: frequency ith of mode


The problem with using the BK model

• Clearly the EFG depends on volume V(T)• a = ν0 “static lattice EFG” (T=0), in system of

volume V(T) may be unphysical, or require extreme pressures

• a = ν0 has implicit T-dependence through V(T)• Need volume dependence of the static-lattice

EFG … NQR is normally measured at constant pressure

… but a = ν0 is itself a function of temperature through volume


Volume dependence of NQR through ν0

Monoclinic TNT Molecule of TNT

Thermal expansion

6 inequivalent sites6 frequencies

2 inequivalent sites2 frequencies

• The effects of changing volume on the static lattice EFG value (fitting parameter a) can be dramatic, or small

• In general depend on the system• Is the thermal expansion negligible or huge? Is the expansion isotropic? • Rule of thumb:

– in molecular crystal: EFG as V (EFG goes like V 1+x where 0 < x < 1)– In ionic crystal: EFG as V (EFG goes like 1/V1/3)


The solution for using the BK model

• Plane wave DFT codes allow direct calculation of ν0 at various volumes

… but a = ν0 is itself a function of temperature through volume


Recipe for DFT enhanced NQR study

• Use either ESPRESSO or CASTEP to compute missing ν0 directly

• Obtain relevant motional spectrum (either by calculation, or experiment, or both)

• Apply BK to calculated EFGs • Perform statistics, fits, analysis, publish ...

• Alternatively, calculations enhance existing NQR data can lead to structural information, bonding, molecular dynamics interpretations

If you don’t do this part, the calculations are rubbish


Value of DFT for NQR

y = x

points nearest to this line are closest to experimental results


Summary

• NQR has many scientific and commerical applications• The major advantage: no huge magnets are required, the

design is basic• A major disadvantage: you can’t find the signal• EFGs of the (fictitious) static lattice can be calculated with

DFT codes• Then you can “turn on” temperature, install T-dependence

using the BK model• DFT calculation of static lattice EFGs + BK model may give

more complete NQR predictions from theory• Calculations can also assist interpretation of NQR data


Acknowledgements

This work was supported by the National Science Foundation’s Division of Materials Research, award DMR-1303599

Temperature Effects in Nuclear Quadrupole Resonance...

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