1 Introduction

The blue color of the mineral lapus lazuli and of ultramarine blue (UMB) is due to the radical S3−. The history of lapis lazuli (LL) and synthetic ultramarine pigments was surveyed by Seel [1]. The utility of S3− and S2− trapped in various zeolites as long-lasting pigments stimulates extensive studies of physical properties of synthetic ultramarines of various colors (see Fig. 22 in Ref. [2]). The EPR signal in UMB was identified as S3− by Gardner and Fraenkel [3]. Because of the stability of S3− in UMB, the strong continuous wave (CW) EPR signal at room temperature, and the separation of the g value of S3− (~ 2.028, Table S1) from the free-electron value, UMB has been suggested as a CW EPR standard [4]. Consequently, it is valuable to document the EPR spectra and relaxation times for well-defined samples, compare with prior results on UMB and LL samples, and extend interpretations of relaxation mechanisms. Our prior EPR study of UMB focused on the frequency dependence of CW linewidths [5]. Spin relaxation of S3− has been studied in synthetic UMB and its analogs [6,7,8,9,10]. Although there has been extensive study of synthetic UMB, the natural LL that are emulated by synthetic UMB have not been studied by pulsed EPR. In this study we report EPR spectra and electron-spin relaxation for three samples of synthetic UMB, four samples of natural LL, and a solution of S3− in DMSO:dioxane.

2 Experimental

UMB from Pfaltz & Bauer (product U00031) is designated as UMB-PB. A sample of UMB purchased by Dr. Ralph Weber, Bruker Biospin, from Spectrum Chemical Manufacturing Corporation is designated as UMB-Spec. Both suppliers reported that they have no record of the chemical composition. A third sample, found in a storage room at University of Denver, had been repackaged in a glass jar with a style and label that an on-line search indicates was produced about 100 years ago. We refer to this sample as UMB-old. The UMB samples were used as received.

The natural products we acquired were all provided as LL. The sample identified as from Afghanistan was sold by a local Denver store and is designated as LL-Afghan. The sample from a deposit in Colorado, USA, was purchased from Zacchariah Zypp (https://zypp.net/) in Crested Butte, Colorado and designated as LL-Colo. A sample from a deposit in Chile was provided by Prof. Filipe Herrera, Department of Physics, Universidad de Santiago de Chile and designated as LL-Chile. A sample from a deposit in Pakistan was provided by Prof. Velavan Kathirvelu, National Institute of Technology, Goa and designated as LL-Pakis. Although lazurite is a soft mineral, in LL it occurs with other minerals that make the rock hard. The rock samples were broken into fragments small enough to fit in quartz EPR tubes by hitting with a hammer and crushing with hand pliers. Fragments were selected that were intensely blue, but still have substantial admixtures of light-colored minerals mixed with the blue stone.

For comparison with the Mn2+ lines in the mineral samples, measurements were also made on the Mn2+ impurity in reagent grade CaO powder (Sigma-Aldrich 248568 lot 17201BJV).

A solution of S3− was prepared by the method of Li et al. [11]. A 1:1 mixture of 1,4-dioxane and DMSO (2 mL each, Sigma Aldrich) was prepared in a graduated cylinder and bubbled with nitrogen gas, using Teflon tubing. Potassium polysulfide (2.5 mg, K2Sx Sigma Aldrich) was ground into smaller pieces with a mortar and pestle and added to the degassed solvent mixture. Nitrogen bubbling through the mixture was continued for ~ 15 min until the polysulfide had completely dissolved and the solution turned blue.

The presence of the S3− was confirmed through both UV–Vis and CW-EPR spectroscopy. The blue color and the λ max = 617 nm indicate the presence of the S3•− radical [11]. The slight greenish cast to the blue and a band in the visible spectrum with λmax = 415 nm indicate the presence of S42− [11]. While collecting the CW-EPR on the EMX-nano, the sample (in ~ 1 mm ID Teflon tubing supported within a 4-mm quartz tube) was continually degassed with nitrogen. CW EPR confirmed the sulfur radical (g = 2.025) and using an internal standard, the concentration of sulfur radical was ~ 0.4 mM.

Each of the solid samples was placed in a standard ca. 3.9 mm o.d. (2.9 mm i.d.) fused quartz tube purchased from Wilmad Glass. The tubes were evacuated, back-filled with He gas at ca. 200 mTorr, and flame-sealed. The solution in DMSO:dioxane was deoxygenated by freeze–pump–thaw prior to back-filling with He gas and flame sealing. CW spectra at 295 K were acquired on a Bruker EMXnano with operating frequency about 9.65 GHz, 100 kHz modulation frequency and microwave power in the linear response regime. The spin concentrations for weighted aliquots of solids were measured using the spin-count software of the Bruker EMXnano spectrometer. CW spectra at cryogenic temperatures were acquired with a Bruker E580, 100 kHz modulation frequency, and microwave power in the linear response regime.

Pulsed EPR spectra and relaxation time data were acquired using a Bruker E580 spectrometer with an ER4118X-DM5 dielectric resonator at X-band. The spin echoes of the UMB and LL samples are intense, fully consistent with the measured spins per gram. A few 1 to 2 mm fragments in a standard EPR tube yielded echoes that did not require detection amplifier gain or signal averaging. Tm was measured with 2-pulse echo decays using a π/2 – τ – π – τ – echo pulse sequence and 2-step phase cycling. T1 was measured by 3-pulse inversion recovery with a π – Tpulse – π/2 – τ – π – τ – echo pulse sequence in which Tpulse was stepped to monitor signal recovery. ESEEM data were collected at two magnetic field positions in the spectrum via a three-pulse sequence (π/2 – τ – π/2 – T – π/2 – τ – echo). In this resonator the maximum echo for S = ½ is observed at 15 to 17 dB. The S = 5/2 Mn2+ signal required 9 dB less power.

The length of the π/2 pulse was 40 ns for most experiments, although π/2 pulse lengths up to 160 ns were used to check for instantaneous diffusion in the echo decays, and pulse lengths of 16 ns were used to decrease the impact of spectral diffusion on T1 and to perform 3-pulse ESEEM. At 78 K the temperature was controlled by cold N2 flow in a Bruker/Oxford CF935 cryostat. Temperatures between 4.2 and 60 K were achieved using the same cryostat and a Bruker/ColdEdge Stinger closed cycle He refrigeration system. Temperature at the sample was measured with a Cernox sensor. By monitoring changes in echo amplitude it was evident that temperature equilibration was almost immediate.

Although distributions were observed for Tm, the short time constants and impact of instrumental deadtime caused us to use a single exponential fit, Eq. (1). Because of the substantial distributions in T1, the inversion-recovery curves were fit with stretched exponentials Eq. (2).

$$Y\left(\tau \right)=Y\left(0\right)\text{exp}\left(\frac{-2\tau }{{T}_{m}}\right)$$
(1)
$$Y\left(T\right)=Y\left(0\right)\left(-1+\text{exp}{\left(\frac{-T}{{T}_{1}}\right)}^{\beta }\right)$$
(2)

where Y(0) is signal intensity at time = 0 and β is the stretch factor. The time constants calculated using either biexponential or stretched exponential fits depended strongly on the time window of the recorded data. Deletion of one or a few early time data points dramatically altered the derived values, which is symptomatic of contributions from components with short time constants that may be due to spectral diffusion. Approximations using two exponentials to fit the inversion-recovery data usually yielded two time constants differing by about an order of magnitude.

The temperature dependence of 1/T1 was modeled using Eq. (3), [12]

$$\frac{1}{{T}_{1}}=AT+{A}_{\text{Ram}}{\left(\frac{T}{{\uptheta }_{D}}\right)}^{9}{J}_{8}\left(\frac{{\theta }_{D}}{T}\right)+{A}_{\text{loc}} \left[\frac{{e}^{{\Delta }_{\text{loc}/T}}}{{\left({e}^{{\Delta }_{\text{loc}/T} }-1\right)}^{2}}\right]$$
(3)

where A is an experimentally-determined adjustable parameter, T is temperature, ARam is an experimentally-determined adjustable parameter that scales the contribution from the 2-photon Raman process [13, 14], θD is the Debye temperature, J8 is the transport integral Eq. (4), that was developed to model heat capacity, Aloc is an experimentally determined adjustable parameter that scales the contribution from the local mode, and Δloc is the energy of the local mode [15].

$$J_{8} \left( {\frac{{\theta_{{\text{D}}} }}{T}} \right) = \int\limits_{0}^{{\theta_{{\text{D}}} /T}} {x^{8} \frac{{e^{x} }}{{(e^{x} - 1)^{2} }}dx}$$
(4)

An approximately linear dependence of 1/T1 on temperature can occur in high-concentration samples, and is attributed to cross relaxation. In some publications this linear dependence is incorrectly labeled a direct process, from which it cannot be distinguished based solely on temperature dependence. The coefficient A in Eq. (3) includes the effects of both cross relaxation and the direct process.

3 Results and Discussion

3.1 CW and Echo-Detected Spectra of S3 − in UMB

Room temperature X-band CW EPR spectra of the three synthetic UMB samples (Figs. 1 and S1) and for S3− in DMSO can be approximated with Lorentzian line widths, as previously reported for UMB-PB [5]. However, the lineshape is more complicated than a single Lorentzian. The simulations shown in Figs. 1 and S1 were obtained with anisotropic g values and anisotropic peak-to-peak line width ranging from about 10 to 100 G (Table S1). Since the g anisotropy is not resolved at room temperature, the three components of the g tensor are not defined, but averages are in the range reported for S3− in many sodalite and zeolite samples. The spin concentrations in the three UMB samples (Table 1) are between 3.2 × 1020 and 5.1 × 1020 spin/g. Wieckowski [16] reported that in the range 1018 to 1019 spins/g the CW EPR line width increased with concentration, and then between 1019 and 1020 spins/g the line width decreased due to exchange interactions. Gobeltz-Hautecoeur et al. [17] used copper sulfate and ruby crystal standards to estimate the S3− concentration in three UMB pigments. They found 1.0, 4.4, and 5.4 ± 0.2 × 1020 spins/g, corresponding to 0.08 to 0.43 spins per sodalite cage. Wieckowski [16] reported a 10 G linewidth for a synthetic UMB sample with 2 × 1020 spins/g and 5.9 × 1020 zeolite cells per gram, which corresponds to 0.34 ± 0.05 spins per cell. Comparison of the 5.1 × 1020 spins/g in our deeply blue UMB-PB sample with these literature reports indicates that the S3− in our sample occupy about half of the cages [17]. Our two other UMB samples have slightly lower spin concentration, but S3− radicals still occupy about a third of the cages, which is high enough to cause exchange narrowed lines at 295 K. Raulin et al. [18] reported 5 × 1019 S2− spins/g for an industrial green ultramarine, and 1 and 3 × 1019 spins/g for other pigments prepared from zeolites. Hoffmann et al. [10] reported 4 × 1016 spins/g in zeolite L, 3.3 × 1018 spins/g in zeolite A, and 3 × 1016 spins/g in cancrinite. The variations in spin concentration reflect the strong dependence on sample preparation.

Fig. 1
figure 1

Spectra of UMB-PB. A CW spectrum at 295 K (black line), with simulation (red dashed line). B Field-swept echo-detected spectrum at 9.8 K

Full size image
Table 1 Spin concentrations in UMB and lapis lazuli samples
Full size table

CW and field-swept echo-detected spectra of the UMB samples were recorded at cryogenic temperatures. The echo-detected spectrum of UMB-PB at 9.8 K exhibits g anisotropy that is not detectable at 295 K (Fig. 1B). Temperature dependence of spectra of UMB have previously been reported between 77 and 376 K [6]. The loss of resolution in the room temperature spectra reveals dynamic averaging and exchange in the solid. A UMB based on zeolite A with 3.2 × 1017 spins per gram described in ref. [6] exhibited partial resolution of g anisotropy at 295 K, so in that case there was not full dynamic averaging or spin exchange at 295 K. Hoffman [8] observed broadening of the S3− spectra when warmed above 70 K. Hoffman et al. reported five spectral components with varying g values that were attributed to difference is local environments [9]. Field-swept echo-detected spectra of UMB-Spec at 9.4 K revealed underlying broad signals (Fig. S2A) that were not present in UMB-PB (Fig. 1B) or UMB-old (Fig. S2B).

The field-swept, echo-detected spectra in the UMB samples are about 100 G wide, which includes the wings of the derivative CW spectra. The amount of sample that could be used for spin echo measurements overwhelmed the spectrometer detection system when used for CW measurements, especially at low temperatures. It appears that different subsets of the distributions of spins are observed in pulse and CW measurements, with fewer spins detected after the instrumental dead-time of the pulse spectrometer.

A striking observation is that the shape of the anisotropic central 100 G of the echo-detected spectrum of S3− in UMB at 4.2 K depends strongly on the position in the spectrum at which the pulse phase is adjusted (Fig. 2). The phenomenon occurs at low temperature where the T1 values are very long. Similar phase dependence was observed for the two other synthetic UMB samples, but not for the mineral samples. We attribute this sample dependence to lower S3− concentration in the mineral samples (Table 1). Consequently, the appearance of the spectra at about 4 K, including relative intensities, depend on pulse-repetition time relative to T1 and on phasing. We speculate that this phase effect is analogous to the absorption/emission spectra observed in photoexcited triplets [19, 20]. Some subset of the S3− radicals are close to another S3− radical and at low temperatures have very long relaxation times—possibly many seconds. Excitation of one radical in a pair polarizes the other in the pair. One could anticipate similar observations for other radicals included in porous solids such as metal–organic-frameworks.

Fig. 2
figure 2

UMB-PB A Phase adjusted at 3395G, in-phase channel (black), quadrature phase channel (red). B Phase adjusted at 3460 G in-phase channel (black), quadrature phase channel (red)

Full size image

3.2 CW and Echo-Detected Spectra of Lapis Lazuli

Strong Mn2+ lines are superimposed on the S3− signals in CW spectra of the mineral samples. For LL-Pakis (Fig. 3) and LL-Afghan the S3− signal at 298 K is strong relative to the Mn2+ signal. However, for LL-Chile (Fig. 4) the overlap with the Mn2+ signals makes it difficult to quantitate the S3− and for LL-Colo (Fig. S3) the S3− signal 293 K is so weak relative to the Mn2+ lines that quantitation was not attempted. The concentration of S3− in the LL samples (Table S1) is one to two orders of magnitude smaller than for UMB. The lower average values are due in part to presence of other minerals in the samples, but may also reflect differences in the conditions under which the minerals were formed.

Fig. 3
figure 3

The S3− radical signal was strong relative to the Mn2+ spectra in LL-Pakis at A 293 K and B 82 K. The decreased anisotropy at 293 K relative to 82 K is attributed to partial motional averaging

Full size image
Fig. 4
figure 4

Room temperature CW spectrum of LL-Chile illustrating the Mn2+ spectra overlapping the S3− spectrum

Full size image

At 80 K the Mn2+ signals in the LL samples saturate more readily than the S3− signals so the S3− signal can be more readily distinguished in the CW spectrum of LL-Colo at 80 K than at 293 K (Fig. S3). Field-swept echo-detected spectra of LL-Afghan are shown in Fig. 5. When B1 is optimized for S = 5/2 the Mn2+ lines are emphasized (Fig. 5A), but when B1 is optimized for S = ½ the S3− signal and the Mn2+ forbidden transitions are emphasized (Fig. 5B). Similar data for LL-Colo are shown in Fig. S4. The field-swept echo-detected spectrum of Mn2+ in CaO powder recorded at 81 K (Fig. S5) with B1 optimized for S = 5/2 is in good agreement with the experimental spectrum of Mn2+ doped into zinc formate [21]. When B1 is optimized for S = 1/2 the allowed Mn2+ transitions are nearly nulled and the forbidden transitions dominate the spectrum (Fig. S5B). The similarity between spectra in Fig. S5 and S6 confirms the assignment of the Mn2+ lines in the LL samples. Field-swept echo-detected spectra of LL-Chile (Fig. S6A) and LL-Pakis (Fig. S6B) acquired with B1 optimized for S = ½ also distinguish the signal for S3− from the underlying Mn2+ lines.

Fig. 5
figure 5

Echo-detected spectrum of LL-Afghan at 41 K. The Mn2+  ± 1/2 transitions can be seen near the maximum in this spectrum. A The pulse-turning angle was chosen to emphasize the S = 5/2 Mn2+ spin state. B The Mn2+  ± 1/2 transitions are less visible in this spectrum. The pulse-turning angle was chosen to emphasize the S = 1/2 spin state. The “spike” near the maximum is not at the g value for S3− and might be an unknown defect or other radical in the mineral lattice. The S3− radical is not obvious in this spectrum

Full size image

Similar to the behavior in UMB the CW spectrum of S3− in LL-Afghan (Fig. S7A) and LL-Chile (Fig. S7B) at 82 K also exhibit g anisotropy that was not observed at 295 K. A CW spectrum similar to that in Fig. S7A was previously attributed to Fe3+ [22], but analogy with spectra for S3− suggest this alternate assignment.

3.3 Distributions of Relaxation Times

A striking feature of the relaxation measurements for the S3− radical in the UMB, LL, and DMSO samples is the very wide distribution of relaxation times. Exponential curves and in most cases biexponential curves did not fit the experimental data well. For the S3− signal in the solid samples the stretch exponent, β, for Tm (Eq. 1) varied from about 0.6 at 4 K to 1.0 at 75 K and for T1 (Eq. 2) varied from about 0.3 at 4 K to 0.7 at 75 K. The values of β much less than 1.0 are indicative of a wide distribution of relaxation times. A similar trend was observed by Goslar et al. [6]. The distribution of spins in the lattice is unlikely to be uniform, and differences in inter-spin distances contribute to the range in relaxation times for both UMB and LL samples. For the solution in DMSO:dioxane β for fits to the inversion-recovery data varied from 0.64 at 4 K to 0.79 at 50 K. In the LL samples there are overlapping signals from S3− and Mn2+ (and possibly other species from the minerals) which contribute to the phase memory decay times and inversion-recovery times that are challenging to distinguish. Since the S3− spectrum is narrow relative to the width of the Mn2+ spectra we could measure the metal relaxation independent of the S3−, but not the S3− independent of the underlying Mn2+. The width of the S3− radical spectrum made it feasible to measure relaxation times, and spin echo phases, at two well-separated field positions within the spectrum. By selection of temperatures, pulse-repetition rates, and pulse-turning angles the S3− or Mn2+ contributions could be emphasized. For Mn2+ the allowed or forbidden transitions could be selected. ESEEM was observed in 2-pulse echo decays of S3− but not of Mn2+, which helped to identify contributions to overlapped spectra.

At 78 K T1 increased and Tm decreased slightly when the π/2 pulse length was increased from 16 to 80 ns. This trend is not consistent with instantaneous diffusion or spectral diffusion, and may illustrate the changes in sampling of the range of relaxation times due to changes in the time window during which data can be acquired. Since the room temperature spectrum is approximately Lorentzian, it is assumed that spin exchange decreases Tm and that spectral diffusion is so fast within the line that the tests applied did not measure its rate. As motion slows at lower temperature, a wide range of relaxation times result from a range of motional effects on both dipole and exchange interactions. In addition, due to the superposition of Mn2+ and S3− spectra, changes in temperature and acquisition parameters can change the relative contributions to the relaxation measurements. This makes the usual plot of relaxation rate vs. temperature less meaningful for the mineral samples so only the data for LL-Chile are reported.

A UPEN [23, 24] analysis confirms that broad distributions in T1 values occur at all temperatures measured. In some cases, there is more than one peak in the distributions, showing that double exponential fits at least roughly approximate the distributions. For example, at 5.2 K the double exponential fit yielded 3 and 22 μs at the center of the S3− spectrum. UPEN yielded 2 and 20 μs. The stretched exponential fit yielded 8.1 with a stretch factor of 0.59, and the geometric mean in UPEN was 5.2 μs. In almost all cases there was a very fast component of T1 and Tm. The relaxation time values obtained depended very strongly on the starting time of the data. Excluding the first point or the first couple of points in the decay or recovery changed the weighting of the contribution of the shortest relaxation time. With Tm values of the order of 200 ns, about half of the signal was missed within the dead-time of the instrument. Similarly, when T1 is long, requiring several microsecond step sizes in the inversion-recovery data collection, fast recoveries are missed entirely. Tm measurements tended to become simple exponentials at high temperatures with values of about 160–220 ns. Shorter values would have been missed. At lower temperatures there was also a component slower by a factor of three or so. Another indication of incomplete sampling of the real full range of relaxation times is that in some cases the derived T1 appeared to become longer when the sample temperature increased from 4.2 to 10 K. Physical models of the relaxation mechanisms are needed to account for this wide distribution of relaxation times.

3.4 Nuclear Modulation

The S3− signal in LL-Pakis exhibited long enough Tm to define nuclear modulation. Coupling to nuclei in the lattice was observed as modulation in 2-pulse echo decays when π/2 pulses were 80 ns or shorter. To record the modulation frequencies accurately, 3-pulse ESEEM was employed. The Fourier transform of our 3-pulse ESEEM data yielded a single frequency of 3.8 MHz at 3460 G, as expected for coupling to 23Na and/or 27Al. X-band HYSCORE showed coupling to 23Na and/or 27Al. Our results agree with those of Hoffmann et al. [6, 8,9,10] who measured modulation of the S3− echo decays at the ca. 3.8 MHz Larmor frequencies of 23Na and 27Al, which cannot be distinguished at X-band.

3.5 Temperature Dependence of Relaxation

The temperature dependence of Tm and T1 for S3− in UMB-PB at high-field (g = 2.007) and low-field (g = 2.046) positions in the spectrum are presented in Fig. 6. Relaxation rates for the three UMB samples and for LL-Chile are compared in Fig. S8 and S9. The values plotted in the Figures are single exponential fits for Tm and stretched exponential fits for T1. With the cautions about distributions of times in mind, we note that in general Tm values were similar, a few hundred ns, and nearly independent of temperature for the three UMB samples. Tm for the Mn2+ components in the mineral samples was short also, except that Tm at 4.2 K was 2.6 μs in LL-Colo, and 935 ns in LL-Chile. Goslar et al. [6] measured relaxation for S3− up to 50 K in UMB with spin concentrations of about 1017 spin/cm3. Up to 12 K Tm was constant at 1.9 μs, which is longer than the ~ 400 ns in UMB-PB. When the concentration is about 1017 spins/cm3 T2 would be ~ 20 μs if the electron–electron dipole interaction dominated [25]. The ca. 2 μs Tm measured by Goslar et al. [6] show that another mechanism dominates, which could be reorientation of the anisotropic radical, taking excited spins off resonance [26]. Although the rigid-limit EPR spectra observed at low temperature was interpreted by Goslar et al. [6] as indicating that the S3− radical motion was largely stopped (other than the vibration) below ca. 77 K, low-amplitude librations can still impact Tm. Our Tm values in UMB were an order of magnitude shorter than observed by Goslar et al. [6]. If the 5 × 1020 spins per gram in our sample were uniformly distributed, the dipole–dipole contribution would cause a T2 of ca. 60 ns. We assume a non-uniform distribution. This is consistent with the very short Tm values in the distributions observed, and with the suggestion that some of the spins are not observed in the pulse experiments because Tm is so short. The non-observation of some spins due to short Tm also means that some T1 values are not observed. For S3− in DMSO:dioxane Tm between 4 and 30 K was between 0.87 and 1 μs, which is longer than in the higher concentration UMB samples. At the low concentrations echo dephasing is attributed to low-amplitude librations.

Fig. 6
figure 6

Relaxation rates of the S3− radical in UMB-PB from 5.2 to 78 K at high-field (gx = 2.007, red symbols and lines) and low-field (gy = 2.046, black symbols and lines) positions in the spectrum (Fig. 1B). The values plotted for Tm (open symbols) are single exponential fits and for T1 (closed symbols) are stretched exponential fits. The contributions from cross relaxation (dashed lines) and a Raman process (dash-dot lines) combine to give the fits (solid lines) to the experimental data as discussed in the text

Full size image

Our Tm values are in reasonable agreement with prior reports on other types of ultramarines, given the wide distributions measured and their dependence on exactly where in the spectrum they were measured. S2− and S3− radicals were measured in several green ultramarine pigments with various concentrations of radicals [18]. Tm for S2− in ultramarine green is less than about half a microsecond over the full temperature range studied. The short Tm limits the pulsed EPR measurements to temperatures below about 78 K [18]. At 4 K Tm was about 200 ns and T1 ranged from 55 to 297 μs for S3−. T1 of S2− ranged from 7 to 137 μs. Arieli et al. [27] reported three different environments for S3− radicals in UMB, with temperature dependent anisotropy, interpreted as indicating that motion of the radical occurs. Extensive pulsed EPR measurements were made in the liquid helium range, but relaxation times per se were not reported for direct comparison with our results. Spectral diffusion and very short Tm were observed in samples with higher spin concentrations.

As shown in Fig. 6 and also by Goslar et al. [6], T1 for S3− in UMB is much shorter on the low-field side of the spectrum (g = 2.0503 which they label as gy) than at the high-field side (g = 2.0016 which they label gx). At 10 K Hoffmann et al. [8] found 0.33 ms along x and 0.13 ms along y and z. Using the labeling from Fig. 1 in Ref. [6], the z axis of the S3− radical is the principal axis of the C2v symmetry point group. The y axis is in-plane and the x axis is perpendicular to the plane of the molecule. T1 was longest for S3− in the UMB-Spec sample and shortest for the UMB-old sample, and only weakly temperature dependent (Figs. S8 and S9). The metals in the LL samples complicate the measurements because of the overlap of the spectra, but are not expected to have much effect on the actual relaxation times of the S3− radicals because the metals are in a different mineral component. Temperature dependence of T1 for S3− in the mineral samples was small, as in the UMB samples. Using the fits to the stretched exponential, T1 for two aliquots of the LL-Afghan mineral averaged 3.4 μs almost independent of temperature within scatter of data from 4.2 to 60 K. The extremes for the LL-Pakis were 9.6 μs at 10 K and 2.4 μs at 60 K. T1 for the LL-Chile sample was 16 μs at 4.9 K and 4.1 μs at 60 K. The longest T1 measured was for the LL-Colo sample at 4.9 K, 45 μs, which decreased to 9.8 μs at 20 K. The S3− signal was too weak relative to the Mn2+ background to measure the LL-Colo sample at higher temperatures. In 1:1 DMSO:dioxane the temperature dependence of T1 for S3− (Fig. 7) is more strongly temperature dependent than in the highly concentrated UMB samples, which is expected for magnetically dilute samples.

Fig. 7
figure 7

Comparison of relaxation rates for 0.4 mM S3− in 1:1 DMSO:dioxane with literature values [6] in UMB sample with ~ 1017 spins/g; 1:1 DMSO:dioxane (red lines and symbols), along gx = 2.0016 in UMB (blue lines and symbols), and along gy = 2.0503 in UMB (green lines and symbols). The contributions from cross relaxation (dashed lines) and a Raman process (dash-dot lines) combine to give the fits (solid lines) to the experimental data

Full size image

3.6 Relaxation Mechanisms

The temperature dependence of 1/T1 for S3− in UMB-PB was modeled using Eqs. (3) and (4). The fits shown in Fig. 6 were obtained with a combination of cross relaxation and a Raman process with a Debye temperature of 55 to 60 K (~ 40 cm−1). Equally good agreement with the data could be obtained by replacing the Raman process with a local mode with energy of 85 K (60 cm−1). Because of the much higher spin concentrations our T1 relaxation times in UMB (Fig. 6) are dominated by spectral diffusion via cross relaxation to a much greater extent than in the Goslar et al. study [6]. We digitized the Goslar et al. data from their Fig. 12 and fit the temperature dependence using Eqs. (3) and (4). We can fit their data with the same 40 cm−1 local mode energy as they reported. An equally good fit was obtained with a Raman process and Debye temperature of 40–45 K (~ 30 cm−1). The limited temperature range over which T1 could be measured in prior studies and in the present study introduce substantial uncertainty to the mechanistic interpretation. The fitting with Eqs. (3) and (4) is based on matching the temperature dependence, which can be poorly defined over a small range. Cross relaxation makes much smaller contributions for the samples with lower spin concentration than in the synthetic UMB samples. In 1:1 DMSO:dioxane the temperature dependence of 1/T1 was well fit with a Raman process with Debye temperature of 70 K and a very small contribution from cross relaxation. Alternatively, the data in solution could be fit with a local mode with energy of 55 K.

The similarity in quality of fits to the data for a Raman process or local mode raises the possibility that multiple motional modes contribute to T1. The wide distributions in relaxation rates also suggests that if a local mode dominates, there must be substantial uncertainty in the energy of that mode. In either case, the analyses indicate that relatively low-energy phonons dominate relaxation. One could speculate that these motions involve changes in the linear combinations of atomic orbitals on the central S, which would affect the in-plane y and z components more than the out-of-plane px orbitals. This is consistent with the faster T1 in the y and z directions than in the x direction. Hoffmann et al. [8] summarized calculations that the orbital energies are sensitive to the bond angle, and stated that gx is not sensitive to the angle, but gz and gy are sensitive to angle, thus explaining the anisotropy in T1.

3.7 Comparison with Relaxation of SO2 − and SO3 Radicals

Relaxation times have recently been reported for SO2− and SO3− in Na2S2O4, Na2S2O5, and K2S2O5 lattices [28]. The spin concentrations in those samples were between 4 × 1016 and 1.4 × 1017 spins/g, which is several orders of magnitude lower than for the commercial UMB samples. Even in these lower concentration samples wide distribution in relaxation times were observed which was attributed to non-uniform spin distributions [28]. The low spin concentrations contributed to much longer Tm at low temperatures than for S3− in UMB: 6 μs for SO3− and 14 μs for SO2−. Because of the lower spin concentrations cross relaxation had less impact on T1 below about 25 K for SO2− or SO3− than was observed for S3− in UMB. T1 for S3− in synthetic UMB is substantially shorter than for SO2− and SO3− [28]. Relaxation times are so long for SO2− and SO3− that spin echoes can be observed at 293 K, but for S3− echoes become difficult to detect above about 78 K. At 78 K T1 for S3− was ~ 1 μs, whereas T1 is ~ 125 μs for SO2− and ~ 900 μs for SO3−. Electron-spin relaxation has been observed to increase with increasing deviation of g from the free-electron value, which is attributed to increasing spin–orbit coupling [29, 30]. The spin lattice relaxation times at 78 K decrease in the order SO3− (gavg = 2.0035) < SO2− (gavg = 2.006) < S3− (gavg ~ 2.028). The faster relaxation for S3− is therefore attributed to increased spin–orbit coupling that also results in higher g value. The high mobility of S3− in the sodalite cages may also contribute to faster relaxation.

4 Conclusions

Commercial samples of UMB usually are not described by the vendor other than by color and a few other physical properties. The deep-blue pigments used in other studies are likely to be similar to the Pfaltz & Bauer pigment that we studied. As we demonstrated, the relaxation times for the S3− in the commercial samples can be very different from those of low-concentration samples because of cross relaxation. This is particularly evident at low temperatures where cross relaxation dominates relaxation at high spin concentrations. At ambient temperatures the rapid relaxation of the EPR signal for S3− has the advantage that the signal is difficult to power saturate. This property is convenient for an EPR standard. The faster relaxation for S3− than for SO2− or SO3− is attributed to larger spin–orbit coupling.