## 4 Results and Discussion  
Figure 5 shows the calculated temporal waveforms for the SCQ (a) and UQG (c) samples. Time t is normalized to the heat diffusion time \(\tau_{\mathrm{diff}}\). Figure 5b demonstrates a  
typical waveform after the end of the heating pulse upon cooling of the UQG sample due to heat diffusion. The calculation of the correction factor for theoretically obtained oscillograms was similar to the above calculation for oscillograms obtained in the experiment. First, waveforms of the time-varying component were constructed for the Suprasil 311 UQG calibration sample and the SCQ sample for two cases, namely, under conditions of developed heat diffusion and in its absence. In the second case, the amplitude of the time-varying component increases linearly with time. Its diagram coincides with the tangent to the functional dependence, describing the shape of the time-varying component at the moment the heating pulse starts. Further, the ratios of the maxima of the calculated signals, namely, 2.36 and 1.25 for SCQ and Suprasil 311, respectively, were obtained. The resulting correction factor for SCQ was calculated as \(\mathrm{k}_{\mathrm{diff}}=2.36/1.25=1.73\). Note that, despite the difference in the slopes of the theoretical and experimental tangents (Figure 5a) due to the notable difference between the leading edge of the heating pulse and the rectangular one, the calculated and measured coefficients almost coincide. Such an exact coincidence is accidental due to the ambiguity in constructing tangents to the experimental curves, mentioned in Section 2. In addition to calculating the correction factor, to check the validity of the theory, the amplitude decay time of the time-varying component due to cooling of the heated area after the end of the heating pulse was also calculated. It should be noted that the cooling rate nontrivially depends on the transverse size of the temperature profile deformed during heating due to heat diffusion. For all three samples, the cooling conditions were markedly different, and the decay times normalized by \(\tau_{\mathrm{diff}}\) were also expected to be markedly different. Table 2 shows the results of calculations of the amplitude decay time of the time-varying component for Suprasil 311 UQG, SCQ samples, and ambient air. When calculating \(\tau_{\mathrm{diff}}\) for SCQ, the heat conductivity value was taken as the average of heat conductivities along the crystallographic axes C and \(\mathrm{a}_{\mathrm{i}}\). The \(\tau_{1/2,\mathrm{exp}}\) column shows the measured decay times at a half-maximum signal amplitude of the time-varying component after the end of the heating pulse. The signal amplitude decay time was measured using digital oscillograms obtained by averaging over \(10^{4}\) pulses, and the level of the noise component did not exceed \(1/100\). The uncertainty of the obtained values did not exceed \(\pm 1\%\). For the SCQ sample, measurements were taken in high-absorption regions of the crystal, for which the  
Figure 5: Calculated forms of temporal dependences of signals U(t) of the time-varying component of the probe radiation power (red line) in the interval of exposure to a heating pulse of 1 ms duration in the TPCI scheme (time t is normalized to the characteristic time of heat diffusion \(\tau_{\mathrm{diff}}\)) for (**a**) SCQ and (**c**) UQG samples; (**b**) typical waveform after the end of the heating pulse upon cooling of the UQG sample due to heat diffusion (the start of the decay is reckoned from 0; the transverse line corresponds to the half-maximum level), “tan” are the tangents at the point where the pulses start, and “tan\({}_{\mathrm{exp}}\)” is the corresponding experimental tangent [22]. ambient air effect is masked by the high absorption of the material. In the SCQ sample, laser radiation propagated along one of the second-order crystallographic axes, and the polarization of the heating radiation was parallel to the third-order axis.