1 Introduction

Shock compression of heterogenous materials is known to produce hot spots through mechanisms such as pore collapse [1], binder/crystal interface friction, crystal/crystal friction, microfractures, and plastic deformation [2,3,4]. These hot spots are believed to be the initiating mechanism of detonation in plastic-bonded explosives [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. While hot-spot formation has been studied extensively, it is currently unknown how important each mechanism is to thermally initiated decomposition given specific loading conditions and material compositions [3].

To better understand hot-spot formation in heterogenous materials, it is necessary to perform simultaneous imaging thermometry and microstructural imaging on the ns–\(\upmu\)s time scale. Currently, the ability to perform microstructural imaging under dynamic shock (using synchrotron X-ray phase contrast imaging [15,16,17,18,19]) exists at the Dynamic Compression Sector of the Advanced Photon Source [20, 21]. Therefore, the next technique to develop is imaging thermometry with the required spatiotemporal resolution. To address this need, we have proposed using two-color thermometric imaging (TCTI), which has previously been applied to slower heating events (e.g., furnaces and turbine engines) [22,23,24,25,26,27,28].

TCTI determines temperature by measuring the temperature-dependent photoluminescence (PL) from a phosphor that has two closely spaced excited state energy levels. When this phosphor is excited using an appropriate wavelength, the two energy levels become populated, with their ratio being given by a Boltzmann distribution:

$$\begin{aligned} \frac{n_2}{n_1}={\text {e}}^{-\Delta E/kT}, \end{aligned}$$
(1)

where \(n_i\) is the population of the \(i{\text {th}}\) level, T is the temperature, k is Boltzmann’s constant, and \(\Delta E\) is the energy spacing between the excited states. When these two states relax they emit PL with the intensity ratio of their emissions being proportional to their population ratio:

$$\begin{aligned} \frac{I_2}{I_1}&\propto \frac{n_2}{n_1}, \end{aligned}$$
(2)
$$\begin{aligned}&=A{\text {e}}^{-\Delta E/kT}, \end{aligned}$$
(3)

where A is a proportionality factor that depends on the material and spectroscopy system. Therefore we can determine the temperature of the phosphor by measuring this spectral ratio.

While there are many different phosphors that are used for two-color thermometry (TCT) [23, 24, 29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49], one of the most common classes is Dy\(^{3+}\)-doped materials [22, 24,25,26,27,28,29, 33, 34, 37, 49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71]. These materials are attractive TCT phosphors as the Dy\(^{3+}\) ion has two closely spaced excited energy levels (\({}^4F_{9/2}\) and \({}^4F_{15/2}\), \(\Delta E \approx 0.115\) eV) with a large energy difference (\(\approx 0.97\) eV) between the lowest excited state (\({}^4F_{9/2}\)) and highest ground state (\({}^6H_{15/2}\)) [72]. This large energy difference between ground and excited states ensures that the majority of energy will be emitted through radiative transitions.

Given the advantageous features of Dy\(^{3+}\)-doped materials for TCT, we recently developed a series of Dy\(^{3+}\)-doped organic crystals for use as energetic crystal analogues that are also temperature sensors [40, 41]. Of these different phosphors, we found that Dy:Y(acac)\(_3\)(DPEPO) provides the best optical properties, with the brightest PL, longest lifetime, and highest quenching temperature [41]. Note that this previous study focused on the spectral properties of the phosphors and did not evaluate their performance for TCTI.

Therefore, in this study, we investigate Dy:Y(acac)\(_3\)(DPEPO)’s potential as a TCTI phosphor by embedding it in a polymer and performing TCTI during pulsed laser heating. For comparison, we also perform the same testing using samples prepared with the well-known TCT phosphor Dy:YAG. The use of Dy:YAG allows us to characterize our TCTI system and get accurate heating profiles as its TCTI potential has been well established [22,23,24,25,26,27,28]. Note that the need to produce reproducible heating and PL from our samples to demonstrate functionality precludes using fast heating and high excitation fluences as they irreversibly damage our samples. Therefore, this demonstration is not a direct evaluation of the phosphor for the proposed application—TCTI during shock compression—but instead provides indirect validation of the technique.

2 Method

2.1 Two-color thermometric imaging setup

Our two-color thermometric imaging setup (shown schematically in Fig. 1) consists of a frequency tripled Nd:YAG laser (Continuum Powerlite II, 355 nm, 10 Hz, 1 mJ), a delay generator (SRS DG645), a PI-Max 4 ICCD (1024i, SB Phosphor), a Cairn Optosplit II image splitter containing two Semrock bandpass filters (Semrock BrightLine® FF01-460/14-25 and FF02-485/20-25), and various mirrors and lenses. For heating, we use a Synrad Firestar f100 CO\(_2\) laser which is directed onto the sample near the center of the 355 nm beam. Note that the CO\(_2\) laser beam is elliptical with a Gaussian profile with dimensions of 3.5 mm \(\times\) 2 mm, while the 355 nm beam is a round top-hat with a beam diameter of 10 mm.

Fig. 1
figure 1

Schematic of pulsed laser heating setup using a Cairn Optosplit II and a PI-Max 4 ICCD for two color imaging

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2.2 Materials

To synthesize Dy:YAG, we use a co-precipitation technique previously reported in the literature [73]. This procedures begins by first making an aqueous ammonium hydrogen carbonate solution. This is done by adding an aqueous salt solution (0.4 M) containing dysprosium nitrate (GFS Chemicals, 99.999% purity), yttrium nitrate (Alfa Aesar, 99.99% purity), and aluminum nitrate (Alfa Aesar, >99.0% purity) to an aqueous ammonium hydrogen carbonate (Alfa Aesar, 98% purity) precipitant solution (1.5 M). The resulting Dy/Y/Al mole ratio is 0.06/2.94/5, which gives a Dy/Y ratio of 2/98. The precipitate is aged for 1 h, followed by multiple washings using deionized water and alcohol. The washed product is dried in a vacuum oven at 353 K for 12 h and then crushed with a mortar and pestle and run through a 100-mesh sieve. The resulting powder is heat treated at 1873 K for 6 h to yield the crystalline YAG phase. This phase is confirmed by XRD measurements of the material, with Fig. 2 showing the XRD spectra of the material, which is found to be consistent with the literature on crystalline YAG [56].

Synthesis of Dy:Y(acac)\(_3\)(DPEPO) begins by first synthesizing Dy:Y(acac)\(_3\). To start, we prepare a 10 mL aqueous solution of Dy(NO\(_3\))\(_3\).5H\(_2\)O/Y(NO\(_3\))\(_3\).6H\(_2\)O (0.625 M) that is mixed with a solution of acetylacetone, acac (7.5 M), in 2.5 mL methanol. To this solution, we add a 2.5 mL aqueous solution of NaOH (1.5 M) leading to precipitation of the product. The resulting suspension is aged for 2–3 h and the product is washed with deionized water and dried in vacuum oven at 80 \(^\circ\)C for \(\approx 12\) h. After preparing Dy(acac)\(_3\), we prepare Dy:Y(acac)\(_3\)(DPEPO) by mixing Dy(acac)\(_3\) and DPEPO at an equimolar ratio. This mixture is then dissolved in a methanol/DMF solution (0.06 M) and refluxed overnight. The supernatant is decanted to give the solid product, followed by drying in a vacuum oven at 80 \(^\circ\)C for \(\approx 12\) h.

To characterize the resulting molecular crystal, we measure its XRD pattern, which is shown in Fig. 2. This X-ray diffraction pattern can be fit to a single-phase monoclinic crystal structure with a space group P1, with lattice parameters of: \(a=21.20\) Å, \(b=21.20\) Å, \(c=18.78\) Å, \(\alpha =106.62^{\circ }\), \(\beta =113.39^\circ\), and \(\gamma =60.49^\circ\). The unit cell volume is 6679.69 Å\(^3\).

For our heterogeneous samples, we blend Dy:YAG or Dy:Y(acac)\(_3\)(DPEPO) crystals with hydroxyl-terminated polybutadiene/isophoronediisocyanate polyurethane (HTBP/IPDI)—containing Bis(2-ethylhexyl)adipate (DEHA) plasticizer—at a 75/25 and 50/50 crystal/polyurethane weight ratio, respectively. The crystal/polyurethane mixture is then poured onto a glass slide and cured overnight at ambient temperature.

Fig. 2
figure 2

X-ray diffraction patterns for Dy:YAG and Dy:Y(acac)\(_3\)(DPEPO)

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2.3 Timing

After preparing the samples and setting up the TCTI system, the next step is to correctly determine the timing of the various components. To begin, we consider two key timing details: (1) that the ideal Q-switch delay is 295 \(\upmu\)s meaning that once the lamp fires (at a rate of 10 Hz), the sample will be excited 295 \(\upmu\)s later (as there is minimal delay between the Q-switch firing and the laser pulse exciting the sample), and (2) our temperature sensors have relatively short lifetimes compared to the heating pulse duration (10-100 ms). Given these two factors, we set up our experimental timing, such that the CO\(_2\) laser fires at \(t_0\), followed by the flashlamp at \(t_0+w-305\) \(\upmu\)s, the Q-switch at \(t_0+w-10\) \(\upmu\)s, and the ICCD gate starting at \(t_0+w\) (with an ICCD gate width of 750 \(\upmu\)s). Figure 3 shows a schematic of the timing with \(t_0\) marking the start of the CO\(_2\) laser pulse and w being the gate width of the laser pulse. Note that this timing scheme measures the PL immediately following the laser heating pulse.

Fig. 3
figure 3

Timing scheme used to capture PL images of the heated phosphors immediately after pulsed laser heating. The ICCD gate is set with a 10 \(\upmu\)s delay and a 750 \(\upmu\)s width

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3 Results

3.1 Phosphor comparison

We have previously reported on the performance of both Dy:YAG [74] and Dy:Y(acac)\(_3\)(DPEPO) [41] as TCT phosphors. Table 1 tabulates relevant TCT parameters for both materials, which include: the amplitude parameter A (Eq. 5), energy level splitting \(\Delta E\), PL lifetime, and max sensitivity defined as:

$$\begin{aligned} S&=\frac{100}{r}\frac{\partial r}{\partial T}, \nonumber \\&= 100\times \frac{\Delta E}{kT^2}, \end{aligned}$$
(4)

where r is the intensity ratio and the max value occurs at the minimum temperature used (i.e., 298 K). From Table 1, we find that both materials have the same calibration parameters (A and \(\Delta E\)) within uncertainty, as well as the same sensitivity. Note that these materials have similar sensitivities to other Lanthanide-doped thermometry phosphors (\(\sim\) 1–2 %/K), but are less sensitive than some organic phosphors [46], which have sensitivities reported as high as 19.6 %/K [75].

Table 1 Thermometric performance and calibration parameters for both phosphors used in this study
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The primary difference between the two materials is the PL lifetime, with Dy:YAG having a lifetime \(\approx 40 \times\) as large. This difference in lifetime also translates into a difference in absolute intensity [72]. To demonstrate this effect, we plot the PL emission spectra of both materials using two different ICCD gate widths (500 ns and 10 ms) in Fig. 4. From Fig. 4, we find that for the 10 ms gate width, the Dy:YAG is significantly brighter, but when using the 500 ns gate width, the two materials have similar intensities. This means that while Dy:YAG is the brighter phosphor for slow heating events (e.g., furnaces and engines), the two phosphors intensities are similar for fast heating events, such as the proposed application of shock compression.

Fig. 4
figure 4

Comparison of PL spectra for Dy:YAG and Dy:Y(acac)\(_3\)(DPEPO) for gate widths of 10 ms and 500 ns. While Dy:YAG is significantly brighter at long gate widths (due to its significantly longer lifetime), the two materials intensities are within a factor of two for short gate widths

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To use Dy:Y(acac)\(_3\)(DPEPO) as a TCT phosphor in shock compression, experiments will require increasing the pump laser fluence to obtain sufficient signal. However, care must be taken not to damage the sample using a single pulse. In lab, we have been able to obtain sufficient signal for imaging Dy:Y(acac)\(_3\)(DPEPO) using a 100 ns gate width, with a 15 mJ laser pulse focused into a 4 mm diameter spot. This fluence (119 mJ/cm\(^2\)) is found to take about 10 to 15 pulses before the sample shows obvious signs of damage. Additionally, we can also bin the ICCD pixels to increase the number of counts/pixel, albeit at the cost of spatial resolution.

3.2 Dy:YAG in HTPB

For the baseline test of the TCTI system, we used the well-known TCT phosphor Dy:YAG, which was dispersed into HTPB. For these trials, we limited our heating pulse widths to < 100 ms as longer durations are found to burn holes in the polymer. Figure 5 shows example two-color images for heating durations of 0 ms, 50 ms, and 100 ms. The PL emission dominates in band 1 (470–520 nm) for the ambient measurement, with the PL intensity transferring into band 2 (440–470 nm) as the sample is heated. Note that the total emission from both bands is diminished at 100 ms due to thermal quenching of the PL emission.

Having measured the two-color images for different gate widths, we next computed the spatially resolved intensity ratio for each gate width. This ratio is found to have a baseline spatial profile due to spatial inhomogeneity in the sample, excitation profile, and the optical path. Therefore, to obtain the changes in the PL band ratio due to heating, we subtract the ambient temperature ratio from each gate width’s ratio profiles. These background subtracted ratios are shown in Fig. 6.

Fig. 5
figure 5

PL intensity in band 1 (470–520 nm) and band 2 (440–470 nm) during laser heating. As the temperature rises, the intensity transfers from band 1 to band 2

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Fig. 6
figure 6

Change in intensity ratio images for different laser heating pulse lengths

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From Fig. 6, we find several results: (1) the heating profile is elliptical, which corresponds to the CO\(_2\) laser’s known beam profile; (2) for durations < 20 ms, there is very little change in the ratio; and (3) the hottest areas (largest ratios) are not uniformly distributed. This last observation is best observed by considering the ratio profile for the 100 ms heating pulse, which displays splotchy hot spots. These hot spots could either be due to the CO\(_2\) laser beam’s quality or nonuniformity in the sample (e.g., the distribution of Dy:YAG particles in the polymer).

With the change in PL intensity ratio determined for each pulse durations, we next convert these ratio profiles into temperature profiles. To do so, we begin by writing the change in ratio \(\Delta r\) as a function of time:

$$\begin{aligned} \Delta r(t)&=r(t)-r(t_i), \nonumber \\&=r_0+A{\text {e}}^{-\frac{\Delta E}{kT}}-r_0-A{\text {e}}^{-\frac{\Delta E}{kT_i}}, \nonumber \\&=A{\text {e}}^{-\frac{\Delta E}{kT}}-A{\text {e}}^{-\frac{\Delta E}{kT_i}}, \nonumber \\&=A{\text {e}}^{-\frac{\Delta E}{kT}}-D_i, \end{aligned}$$
(5)

where \(T_i\) is the initial temperature at time \(t_i\), A and \(\Delta E\) are material parameters, \(r_0\) is an offset parameter due to the optical setup, and \(D_i\) is a parameter related to the room temperature ratio and is given by:

$$\begin{aligned} D_i=A{\text {e}}^{-\frac{\Delta E}{kT_i}}. \end{aligned}$$
(6)

For Dy:YAG, we measured the materials calibration parameters to be A = 1.71 and \(\Delta E\) = 121.2 meV, which results in \(D_i\) = 0.0141 [74].

Rearranging Eq. 5, we find the temperature as a function of ratio to be:

$$\begin{aligned} T=\frac{\Delta E}{k \ln \left[ \frac{\Delta r(t)+D_0}{A}\right] }. \end{aligned}$$
(7)

Taking the change in ratios from Fig. 6 and Eq. 7, we compute the temperature profiles at the different times, which are shown in Fig. 7.

From Fig. 7, we find that the heating profiles are elliptical (as expected) with the peak temperatures being near 1200 K. Comparing the different profiles at each time, we find that the heated region increases as the time increases, which is consistent with heat diffusion from the laser spot into the surrounding materials.

Fig. 7
figure 7

Temperature map at different times during pulsed laser heating of Dy:YAG dispersed in HTPB. Note that the profile is elliptical, which corresponds to the underlying CO\(_2\) laser beam profile

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3.3 Dy:Y(acac)\(_3\)(DPEPO) in HTPB

Having demonstrated the TCTI technique with Dy:YAG, we next consider the performance of Dy:Y(acac)\(_3\)(DPEPO) as a TCT phosphor with the heating limited to pulse widths of 50 ms as further heating results in complete quenching of the phosphors PL. For brevity, we suppress the PL and ratio images for Dy:Y(acac)\(_3\)(DPEPO) and instead turn directly to considering the measured temperature profiles, which are shown in Fig. 8. Note that in Fig. 8, we apply an elliptical mask to hide noise outside of the region of interest.

Fig. 8
figure 8

Temperature map at different times during pulsed laser heating of Dy:Y(acac)\(_3\)(DPEPO) dispersed in HTPB

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From Fig. 8, we find that once again little-to-no heating is observed for durations \(<20\) ms. We also observe that the heated region for Dy:Y(acac)\(_3\)(DPEPO) has significantly more temperature variations than were observed for Dy:YAG. These variations are due to the Dy:Y(acac)\(_3\)(DPEPO) sample displaying more concentration inhomogeneity and a rougher surface than the Dy:YAG samples. This nonuniformity is visible to the naked eye as a rough surface and visible clumps of phosphor. Most likely, this lower uniformity is due to the Dy:Y(acac)\(_3\)(DPEPO) particles being larger than the Dy:YAG particles.

At this point, we had planned on making a direct comparison of the full heating profiles of the two materials to demonstrate Dy:Y(acac)\(_3\)(DPEPO)’s performance as compared to Dy:YAG. Unfortunately, due to uniformity issues, this is not possible. While we cannot compare the full profiles, we can make some limited comparisons if we consider the regions in Fig. 8 that correspond to the highest temperatures. The motivation for this comparison is as follows: (1) the same laser profile and power was used for both samples, which means that, for equally uniform samples, the profiles should be identical. (2) the Dy:Y(acac)\(_3\)(DPEPO) crystals are larger and doped at a lower concentration, which means that the main impact of inhomogeneity will be voids and areas of lower concentration. Both of these will result in less heating and, therefore, lower temperatures. (3) The areas with the highest concentration of Dy:Y(acac)\(_3\)(DPEPO) crystals will, therefore, be heated the most similar to the Dy:YAG sample.

With these assumptions in mind, we compare the average temperature in a 10 px circle centered at (x = 110, y = 160) for both materials, with the resulting temperatures, as shown in Fig. 9. From Fig. 9, we find good agreement between the two sensor materials, which demonstrates Dy:Y(acac)\(_3\)(DPEPO)’s suitability as a phosphor for TCTI. We also observe that both materials display an exponential heating curve, which is expected in the case of constant-power heating with heat diffusion. At early times, the energy coming into the target area is far greater than the energy being transferred out, leading to the temperature increasing linearly. However, as the temperature rises the rate of heat loss to the surrounding material increases, resulting in a net decrease in the heating rate. This continues until the rate of energy input is balanced by the heat transfer out of the region of interest, leading to a steady-state temperature. Note that we do not reach the steady state temperature as we limit the pulse width to 50 ms.

Fig. 9
figure 9

Average temperature in 10 px circle centered at (x = 110, y = 160) for heating of both Dy:YAG and Dy:Y(acac)\(_3\)(DPEPO)

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3.4 Temperature resolution

Having demonstrated Dy:Y(acac)\(_3\)(DPEPO)’s usefulness as a TCTI phosphor, we now turn to characterizing the system’s temperature resolution \(\Delta T\), which is defined as [41]:

$$\begin{aligned} \Delta T(T)&=\sigma _r(T)\left( \frac{\partial r(T)}{\partial T}\right) ^{-1}, \end{aligned}$$
(8)
$$\begin{aligned}&=\frac{\sigma _R(T)}{r(T)}\frac{kT^2}{\Delta E}, \end{aligned}$$
(9)

where r(T) is the intensity ratio at temperature T (Eq. 5) and \(\sigma _r(T)\) is the systematic uncertainty in the ratio.

To characterize the systematic uncertainty in the ratio (as a function of temperature), we perform isothermal imaging measurements using Dy:YAG powder in a furnace. These measurements consist of taking ten images at each temperature, calculating the ratio mapping for each image, and then computing the variance in the ratio over the ten images. Figure 10 shows the calculated percent error as a function of temperature with a fit to a polynomial function. From Fig. 10, we find that the percent error in the ratio follows a U-shaped curve, with the uncertainty in the ratio being greatest at low and high temperatures, while the middle temperatures have the smallest errors. This is due to the higher energy band emission being dim at low temperatures (resulting in more intensity fluctuations), increasing in intensity, and then finally decreasing again as thermal quenching begins occurring.

Having measured the systematic uncertainty, we next computed the temperature resolution at each temperature, which is also shown in Fig. 10. From the temperature resolution curve in Fig. 10, we find that starting at room temperature, the resolution is \(\approx 1\) K and increases roughly as \(T^2\) up to around 1050 K. Above 1050 K, the temperature resolution begins increasing faster than \(T^2\) and reaches a peak value of \(\approx 83\) K at 1173 K. This change is the result of the systematic uncertainty increasing due to thermal quenching.

Fig. 10
figure 10

Percent error of ratio measurements (left axis) and temperature resolution (right axis) as a function of temperature

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4 Conclusion

In this study, we demonstrated both the TCTI technique and the usefulness of Dy:YAG and Dy:Y(acac)\(_3\)(DPEPO) as TCT phosphors for subsecond heating events using laser heating. For Dy:YAG, we observe a well-defined temperature profile corresponding to the CO\(_2\) laser beam’s intensity profile, while for Dy:Y(acac)\(_3\)(DPEPO), we find that the temperature profile is noisy and contains hot spots. This difference is attributed to the Dy:Y(acac)\(_3\)(DPEPO) sample being significantly more inhomogeneous than the Dy:YAG samples. However, while Dy:Y(acac)\(_3\)(DPEPO)’s profile is more variable, we find that the average temperature of the “hot spots” in Dy:Y(acac)\(_3\)(DPEPO)’s profile matches within experimental uncertainty the temperatures measured by Dy:YAG. This favorable comparison between materials suggests that Dy:Y(acac)\(_3\)(DPEPO) is a good material for TCTI in heterogeneous samples.