Temperature Effects in Nuclear Quadrupole Resonance Spectroscopy Allen Majewski Department of Physics University of Florida Fall 2016
Overview What is nuclear quadrupole resonance (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 B 0 field because the physical mechanism is different There are benefits and drawbacks to NQR as compared with NMR
NMR overview In NMR spectroscopy, the nuclear magnetic moment interacts with an applied static magnetic field B 0 Energy gap is probed with a radio frequency (RF) pulse of the corresponding Larmor frequency γ: gyromagnetic ratio of nucleus 1 H has γ of 42 MHz/tesla
NMR overview: spectrometer B 1 chemical shifts B 0 NMR signal out RF pulse in
NQR overview: spectrometer B 1 NQR NQR does not require a big magnet great news NQR signal out RF pulse in Reduced cost, complexity
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
NQR and the Electric Field gradient In NQR, the nuclear electric quadrupole moment Q interacts with the natural electric field gradient (EFG) of the solid. No static field is applied.
Electric field gradients (EFGs) and quadrupole coupling constants (C q ) NMR: B 0 and γ determine operating frequency NQR: natural EFG and Q determine operating frequency C q : coupling constant η: asymmetry parameter NQR frequencies go like C q f(η)
NQR transition frequencies Spin 3/2 case e.g. 35 Cl: Spin 1 case e.g. 14 N: coupling constant & asymmetry parameter local electric field gradient nuclear electric quadrupole moment
Applications of NQR: basic science 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 NQR is sensitive to chemical and crystallographic inequivalence of nuclear sites crystallographically inequivalent nitrogen sites chemically inequivalent nitrogen sites TNT molecule
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 no humans Low signal to noise ratio (SNR) compared to NMR (in NMR a high operating frequency can be chosen) No ability to control NQR frequency ν NMR determined by B 0 and γ ν NQR 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
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) 35 Cl He related the EFG in the primed system φ to that of the unprimed system φ through the displacements <θ>, and <θ 2 > θ 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
T-dependence of NQR: BK model Replace the <θ 2 > with harmonic oscillators, sum over all modes of system to get the EFG component as a function of temperature q 0 : q(v, T=0) q is static lattice EFG EFG at zero temperature (constant volume) ω i : frequency of i th mode of oscillation A i : 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 ith mode ωi: frequency ith of mode
The problem with using the BK model but a = ν 0 is itself a function of temperature through volume Clearly the EFG depends on volume V(T) a = ν 0 static lattice EFG (T=0), in system of volume V(T) may be unphysical, or require extreme pressures a = ν 0 has implicit T-dependence through V(T) Need volume dependence of the static-lattice EFG NQR is normally measured at constant pressure
Volume dependence of NQR through ν 0 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/V 1/3 ) Monoclinic TNT Molecule of TNT Thermal expansion 6 inequivalent sites 6 frequencies 2 inequivalent sites 2 frequencies
The solution for using the BK model but a = ν 0 is itself a function of temperature through volume Plane wave DFT codes allow direct calculation of ν 0 at various volumes
Recipe for DFT enhanced NQR study Use either ESPRESSO or CASTEP to compute missing ν 0 directly Obtain relevant motional spectrum (either by calculation, or experiment, or both) Apply BK to calculated EFGs Perform statistics, fits, analysis, publish... If you don t do this part, the calculations are rubbish Alternatively, calculations enhance existing NQR data can lead to structural information, bonding, molecular dynamics interpretations
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