Microscopic structure and quantitative characterization of the colour centre producing the 8373.3 Å (N1) zero-phonon line in irradiated sodium chloride

This record concerns the open question of A. E. Hughes, 'The symmetry of an N centre in sodium chloride' (1966). Hughes showed that the sharp zero-phonon absorption line at 8373.3 Å in irradiated NaCl at 4 K (the N1 line) belongs to a colour centre of monoclinic I symmetry with its twofold axis along [110], measured its four linear stress/strain-coupling coefficients, and analysed its phonon sideband against the calculated vibrational density of states of NaCl, but left the atomic structure of the centre undetermined. The problem is the microscopic identification of this centre: a unique structural model — the number, arrangement and electron occupancy of the aggregated anion vacancies, and the resulting spin state — discriminating Pick's proposal from the F3- and F4-based alternatives discussed in later work, and quantitatively consistent with the established symmetry, the measured coupling coefficients, the observed phonon sideband and the observed diamagnetism. The follow-up literature has not closed the question: the last substantive engagement (Evarestov and Slonim, 1971) favours but does not settle the four-vacancy F4 model and leaves F3-based alternatives explicitly unreconciled, and the subfield is dormant.

Background

When an alkali-halide crystal such as NaCl is irradiated (X-rays, gamma rays, electrons) or additively coloured, point defects called colour centres appear and absorb light in the visible and near infrared. The elementary colour centre is the F centre: a halide-ion vacancy that traps electrons. Under irradiation or thermal annealing, F centres migrate and aggregate — two adjacent anion vacancies with trapped electrons form the M (or F2) centre, three form the R (or F3) centres, and still larger aggregates are held responsible for the N absorption bands (N1, N2, ...). At liquid-helium temperature the broad bands of many centres are accompanied by very narrow zero-phonon lines — optical transitions in which the lattice remains in its vibrational ground state, the optical analogue of a Mössbauer line — together with a phonon sideband of phonon-assisted transitions. The ratio of the integrated sideband absorption to the zero-phonon absorption defines the Huang–Rhys factor $S$, a dimensionless measure of how strongly the electronic transition couples to lattice vibrations.

A standard method for identifying the site symmetry of an unknown centre is uniaxial-stress spectroscopy of its zero-phonon line: stress applied along [100], [110] and [111] directions of the cubic crystal splits and shifts the line in patterns determined by the centre's point group, its polarization selection rules, and the number of crystallographically equivalent orientations. In this classification a 'monoclinic I' centre is one whose point group is $C_{2h}$ (or $C_2$ or $C_{1h}$), with its monoclinic axis (the twofold axis, or, for the mirror-plane member $C_{1h}$, the reflection-plane normal) along a [110] direction of the lattice; such a centre has 12 equivalent orientations in the cubic crystal if it is centrosymmetric ($C_{2h}$) and 24 if it is not ($C_2$ or $C_{1h}$). The measured first-order shifts are fitted by linear stress-coupling coefficients $A_i$ (energy shift per unit stress component) or, after conversion through the host's elastic stiffness constants, strain-coupling coefficients $B_i$ (shift per unit strain).

For the NaCl line studied here, Crozier (1964) had searched for a Zeeman effect and observed none, and Pierce (1964) had catalogued the discrete phonon and zero-phonon absorption spectra of irradiated alkali halides, including phonon satellites of the 8373 Å line. Hughes and Runciman (1965) had used stress spectroscopy to assign the analogous 5234 Å line in lithium fluoride to a monoclinic I centre and to determine its strain-coupling coefficients, and Johannson, Lanzl, von der Osten and Waidelich (1965) had reported stress splitting of the corresponding zero-phonon line in NaF at 5803 Å. Hughes (1966) then determined the symmetry of the NaCl centre: the 8373.3 Å zero-phonon absorption is an electric-dipole transition between A and B states of a monoclinic I centre with its axis along [110] and its transition dipole in the (110) plane; the stress-splitting patterns (2, 4 and 3 components for stress along [100], [110] and [111]) exclude a trigonal assignment. The four stress-coupling coefficients were measured as $A_1=1.85\pm0.15$, $A_2=0.41\pm0.10$, $A_3=-0.07\pm0.10$ and $A_4=1.25\pm0.15$ in units of $\mathrm{cm^{-1}\,kg^{-1}\,mm^{2}}$, corresponding, via the 4 K elastic constants, to $B_1=(12.01\pm1.10)\times10^{3}$, $B_2=(5.13\pm0.85)\times10^{3}$, $B_3=(-0.10\pm0.10)\times10^{3}$ and $B_4=(1.71\pm0.20)\times10^{3}$ in $\mathrm{cm^{-1}}$ per unit strain, qualitatively similar to the LiF values. The phonon sideband resolves into twelve peaks, predominantly one-phonon processes matching features of the calculated vibrational density of states of NaCl, with the satellite nearest the line attributed to a quasi-localized vibrational mode of the defect; the coupling strength is $S\simeq3$–$4$. An Ivey-type power law $\lambda\propto d^{n}$ ($d$ the lattice parameter) fitted to the LiF and NaCl lines gives $\lambda=724.4\,d^{1.41}$ but fails for NaF.

What such an analysis cannot deliver is the atomic structure: several distinct arrangements of anion vacancies and trapped electrons are compatible with monoclinic symmetry, and the stress data fix only the point group and the coupling constants. The structural model for the N1 centre proposed by Pick (in his reviews of alkali-halide defect structure) was consistent with the observations but not uniquely identified by them, and alternative proposals (for example those discussed by Johannson et al. 1965) remained viable. The unresolved question is therefore the microscopic identification of this one centre: the number, arrangement and electron occupancy of the aggregated anion vacancies, and the resulting spin state.

Problem Statement

Determine the microscopic structure of the colour centre responsible for the zero-phonon absorption line at 8373.3 Å (the N1 line, in the N-band region) in irradiated NaCl at 4 K — the centre whose point symmetry Hughes (1966) established to be monoclinic I with its [110] monoclinic axis and whose linear stress/strain-coupling coefficients are already measured. The required answer is a single, definite structural model of this one centre: the number, arrangement and electron occupancy of the aggregated anion vacancies, and the resulting spin state, discriminating between the structural model proposed by Pick and the F3- and F4-based alternatives discussed by Johannson et al. (1965), Evarestov and Slonim (1971). The model must be quantitatively consistent, within the stated uncertainties, with the established data for the centre: its monoclinic I symmetry with the [110] monoclinic axis and the corresponding polarization selection rules; the measured stress-coupling coefficients $A_i$ and the strain-coupling coefficients $B_i$ derived from them; the observed phonon sideband, including the quasi-localized-mode satellite nearest the zero-phonon line and the Huang–Rhys factor $S\simeq3$–$4$; and its observed diamagnetism (the null Zeeman effect searched for by Crozier 1964, and the absence of an electron-spin-resonance signal). The formation and aggregation behaviour of the centre in NaCl, and the cross-host comparison with the analogous zero-phonon lines in LiF and NaF, are relevant context for the structure question rather than required deliverables of it.

References

1. A. E. Hughes (1966), 'The symmetry of an N centre in sodium chloride', Proceedings of the Physical Society 87, 535–542. DOI: 10.1088/0370-1328/87/2/322, https://doi.org/10.1088/0370-1328/87/2/322
2. A. E. Hughes and W. A. Runciman (1965), 'Stress spectra of colour centres in lithium fluoride', Proceedings of the Physical Society 86, 615–627. DOI: 10.1088/0370-1328/86/3/321, https://doi.org/10.1088/0370-1328/86/3/321
3. G. Johannson, F. Lanzl, W. von der Osten and W. Waidelich (1965), 'Splitting of zero-phonon lines in alkali halides by uniaxial stress', Physics Letters 15, 110–111. DOI: 10.1016/0031-9163(65)91293-X, https://doi.org/10.1016/0031-9163(65)91293-X
4. M. H. Crozier (1964), 'Search for the Zeeman Effect of a Color Center in Sodium Chloride', The Journal of Chemical Physics 41, 1510. DOI: 10.1063/1.1726102, https://doi.org/10.1063/1.1726102
5. C. B. Pierce (1964), 'Discrete Phonon and Zero-Phonon Optical Absorption Spectra in Alkali Halides', Physical Review 135, A83–A86. DOI: 10.1103/PhysRev.135.A83, https://doi.org/10.1103/PhysRev.135.A83
6. A. E. Hughes (1968), 'Strain broadening of the N1 zero-phonon line in sodium chloride', Journal of Physics and Chemistry of Solids 29, 1461–1477. DOI: 10.1016/0022-3697(68)90197-2, https://doi.org/10.1016/0022-3697(68)90197-2
7. Moo Jin Jun and Theodore J. Neubert (1971), 'F-Aggregate Centers in Sodium Chloride. I', The Journal of Chemical Physics 55, 1583–1587. DOI: 10.1063/1.1676283, https://doi.org/10.1063/1.1676283
8. R. A. Evarestov and V. Z. Slonim (1971), 'The electronic structure of the N1- and N2-colour centres in alkali halides', physica status solidi (b) 47, issue 1. DOI: 10.1002/pssb.2220470160, https://doi.org/10.1002/pssb.2220470160
9. W. von der Osten and K. Riemenschneider (1969), 'Formation kinetic study of aggregate color centers with zero-phonon lines in NaF', Solid State Communications 7, 1551–1553. DOI: 10.1016/0038-1098(69)90095-7, https://doi.org/10.1016/0038-1098(69)90095-7
10. G. Baumann, F. Lanzl, W. von der Osten and W. Waidelich (1967), 'Recent results on zero-phonon lines in NaF', Journal de Physique Colloques 28, C4-72–C4-74. DOI: 10.1051/jphyscol:1967410, https://doi.org/10.1051/jphyscol:1967410
11. W. von der Osten (1976), 'Vacancy Aggregate Centers in Ionic Crystals', in Defects and Their Structure in Nonmetallic Solids (Plenum Press, New York), 237–259. DOI: 10.1007/978-1-4684-2802-5_9, https://doi.org/10.1007/978-1-4684-2802-5_9
12. Karl Konrad and Theodore J. Neubert (1967), 'F-Aggregate Centers in Sodium Fluoride. I', The Journal of Chemical Physics 47, 4946–4950. DOI: 10.1063/1.1701744, https://doi.org/10.1063/1.1701744
13. R. G. Bessent (1969), 'Paramagnetic resonance of an N centre in calcium oxide', Journal of Physics C: Solid State Physics 2, 1101–1104. DOI: 10.1088/0022-3719/2/6/122, https://doi.org/10.1088/0022-3719/2/6/122
14. Heinz Pick (1965), 'Struktur von Störstellen in Alkalihalogenidkristallen', Springer Tracts in Modern Physics 38, 1–83. DOI: 10.1007/BFB0045737, https://doi.org/10.1007/bfb0045737
15. Wei Chen, Christoph Tegenkamp, Herbert Pfnür and Thomas Bredow (2010), 'Color centers in NaCl by hybrid functionals', Physical Review B 82, 104106. DOI: 10.1103/PhysRevB.82.104106, https://doi.org/10.1103/PhysRevB.82.104106