Low-temperature nucleation anomaly in silicate glasses shown to be artifact in a 5BaO·8SiO2 glass

For over 40 years, measurements of the nucleation rates in a large number of silicate glasses have indicated a breakdown in the Classical Nucleation Theory at temperatures below that of the peak nucleation rate. The data show that instead of steadily decreasing with decreasing temperature, the work of critical cluster formation enters a plateau and even starts to increase. Many explanations have been offered to explain this anomaly, but none have provided a satisfactory answer. We present an experimental approach to demonstrate explicitly for the example of a 5BaO ∙ 8SiO2 glass that the anomaly is not a real phenomenon, but instead an artifact arising from an insufficient heating time at low temperatures. Heating times much longer than previously used at a temperature 50 K below the peak nucleation rate temperature give results that are consistent with the predictions of the Classical Nucleation Theory. These results raise the question of whether the claimed anomaly is also an artifact in other glasses.

108 which is only valid only under certain conditions, for some substances. I am not 109 sure whether it is valid for this bariumsilicate material. Perhaps the authors should 110 also test their results with other approximations for Dg. 111 112 The reviewer is correct; the Turnbull approximation assumes that the heat capacities of 113 the liquid and glass are the same. If the heat capacity difference between glass and 114 crystal as a function of temperature were known, a more accurate thermodynamic 115 driving free energy could be obtained. Unfortunately, these heat capacities are not 116 known. However, even if they were known, the magnitude of the thermodynamic 117 driving free energy would still increase approximately linearly with decreasing 118 temperature over the range of nucleation temperatures studied and would not change 119 the direction of the trend in the interfacial free energy or the work of critical cluster 120 formation. So, the key conclusion in our manuscript would remain the same.
SECOND ROUND: OK, thank you 121 5. They show error bars in all figures and Figure 4 shows the 95% confidence limits. 122 However, I should stress that the smooth curve through the red points (previous 123 data above the maximum) and black point (new data point at 50K below the 124 maximum) do not match. 125 In the text describing Figure 4 we state, "The data point at 1048 K falls outside of the 126 higher limit of the confidence bounds. This likely is an artifact of the fit, however. 127 The induction time was not measurable at this temperature; instead, it was estimated 128 from the data at 998 K, 1011 K and 1023 K." Further, the solid curve doesn't go exactly 129 through the data points because we used the linear fit to the interfacial free energy to 130 obtain a continuous curve, which will not go through the data exactly.
SECOND ROUND: OK 131 6. They could also include the confidence limits of the fit in Fig.3 (not mandatory) 132 133 We do not feel that it is necessary to add confidence bands for any type of fitting in Fig.  134 3 because it will not provide any additional useful information for the final conclusion. 135 Confidence bands are a statistical tool used to examine the fit for an assumed fitting 136 function. By fitting to different fitting functions, the confidence bands can be used as 137 a tool to allow a determination of the best function. They do not provide information 138 about the original data. Since in each subplot of Fig. 3 there is only one assumed 139 function, no information can be gained about the best function that matches the data. 140 With or without confidence bands the final conclusions are clear and the same. SECOND ROUND: OK if one accepts that a single datapoint, without a rigorous statistical analysis is sufficient to reach such important conclusion. Although, given the results of Cassar for 4 other systems, this indeed seems to be the case. This reviewer is convinced that this break does not exist, as demonstrated by Cassar et al and Xia et al 141 7. it resulted from only ONE new data point (at 50K below the maximum), so at least a 142 test in another low T should be relevant. 143 144 While it would be useful to obtain other low temperature measurements, due to the 145 COVID-19 pandemic this was not possible. These are extremely long experiments, 146 with each new measurement at a given low temperature nucleation temperature 147 requiring many months. The new nucleation measurement at the lowest temperature 148 reported in this glass clearly demonstrates that the low temperature anomaly previously 149 reported by us for this glass is incorrect. It is also likely incorrect in the other silicate 150 glasses where the anomaly has been reported.
SECOND ROUND: This reviewer is fully aware of the COVID-19 problem. However, another data point at a somewhat higher temperature, which would not take that long to collect, would be essential to confirm their conclusions, which is based on a single nucleation rate datapoint. 97 8. this study with one particular glass corroborates the results of a much stronger 98 article (arxiv 2019) that analysed 6 glasses, and has reached exactly the same 99 conclusion. 100 101 We have discussed this in an earlier response. The initial conclusion proposed by as 102 Cassar et al. from the San Carlos group in their original arxiv paper has changed in the 103 current arxiv entry and in their published Journal of Non-Crystalline Solids article. In 104 those later articles, they conclude that they were not able to reach a definitive 105 conclusion regarding the low-temperature anomaly in the nucleation rate. So, their 106 article was not stronger as stated by the referee. Their analysis suggested that the 107 anomaly was an artifact. Our data are the first to definitively demonstrate that it is an 108 artifact for the glass we studied, and raises the serious question of whether it is an 109 artifact in other glasses that show the same low-temperature anomaly. Since we have 110 not yet been able to confirm this in other glasses due to the COVID-19 pandemic, 111 impacting our laboratory studies and our colleagues at Corning Glass Inc., who were 112 going to furnish the samples but were abruptly required to work remotely before the 113 glasses could be prepared and characterized, we have changed the title, abstract and 114 conclusion in our submitted paper to focus on the 5BaO·8SiO2 glass. Our future 115 studies will investigate whether it is also an anomaly in other silicate glasses.
SECOND ROUND: Based on published experimental data from different authors, Cassar demonstrated that the break does not appear in 4 systems (out of 6 analysed), Figures 6 and 7. Hence, the present results confirm Cassar´s findings. 116 9. Finally, I do not understand the several black squares in Figs. 3 and 4 labelled "this 117 work". I mean, only the point at the lowest T was obtained and should to referred as 118 to "this work". 119 120 In this work, although only one point reflects the new measurements of the number of 121 nuclei as a function of time at the nucleation temperature, all four black data points in 122 Figs. 3 and 4 were recalculated and updated in this work's analysis section (details 123 can be seen in the supplementary methods section in the Supplementary Information 124 file). So, in this work, for the outcome after measurement and analysis, there are four 125 points instead of one point. SECOND ROUND: OK 126 10. I believe the use of a linear fitting using only the last data points influence both the 127 value of the resulting steady-state nucleation rate and the theta? I believe the fitting 128 procedure should be made with the Kashchiev model using ALL points of the Nv(t) 129 curve. Apparently, the red points in the beginning were completely neglected? 130 131 The linear fitting method we used is a widely accepted method to obtain the 132 steady-state nucleation rates and the induction times. That there are other ways to 133 obtain the result doesn't invalidate this approach. Further, while the Kashchiev 134 expression is indeed the best analytical expression (see "Transient Nucleation in 135 Condensed Systems," K. F. Kelton, A. L. Greer and C. V. Thompson, Journal of 136 Chemical Physics, 79, 6261 (1983)), it is still based on assumptions. We feel that the 137 standard method of analyzing the nucleation data is the best approach. SECOND ROUND: The problem in using only the final data points -which seem to be in a straight line -rather than the whole N vs. time curve, is that you are implicitly assuming that steady-state conditions have already been reached.
138 11. Also, Schneidman has shown long ago that there is an interdependence between the 139 true nucleation induction times, theta, and t_(ind_d), hence a time shift, ts, should 140 be considered in the model for properly fitting these curves. And these true thetas 141 should be used in the CNT plots. Please comment. 142 143 There are several ways to obtain the correct induction time (at n* for the nucleation 144 temperature) from the measured data. We have chosen to use the Shneidman-Weinberg 145 expression, the validity of which has been confirmed (Nucleation in Condensed Matter 146 -Applications in Materials and Biology, K. F. Kelton and A. L. Greer, Pergamon 147 Materials Series, Elsevier, Amsterdam (2010)). That is why we corrected the 148 measured induction times, which were for n* at the growth temperature, to obtain the 149 induction time for n* for the nucleation temperature. As discussed on page 81, figure 11 150 of chapter 3 in "Nucleation in Condensed Matter -Applications in Materials and 151 Biology," K. F. Kelton and A. L. Greer, Elsevier (2010), this approach gives a valid 152 correction to the data so that the standard Kashchiev treatment can then be used. SECOND ROUND: Ok, let´s leave it this way. However, please keep in mind that nucleation in a glass (below Tg) is further complicated due to the glass relaxation's interference on the nucleation pathways and kinetics. Nucleation above Tg takes place in a SCL, whereas below Tg it takes place in a glass. This is likely the reason why you cannot describe your N vs. time curve with the Kash equation 220 221 12. The test of the proposed hypothesis (no break in the theory) was done using only 222 one temperature below the maximum (50 K). It would be good practice to double or 223 triple check this result by using at least another low enough temperature. In other 224 words, this study would be much stronger if it were extended to, at least, another 225 temperature (say, 973 K or 985 K), for times long enough to reach the steady-state. 226 227 Unfortunately, due to the COVID-19 pandemic, we are not in a position to supply 228 another low T measurement, which is a very long experiment. But, we maintain that the 229 data we have obtained in the manuscript clearly demonstrate that in this glass the low 230 temperature anomaly in the steady-state nucleation rate previously reported is 231 incorrect. 232 SECOND ROUND: OK, we have already discussed this issue 233 13. The points in Figure 3 (d) are not well aligned; it would be educational to include 234 the confidence interval of the adjustments, as you did in Figure 4. 235 236 The linear fit doesn't have to go through the data points exactly. Currently, Figure 3d is 237 good and clear in presenting the trend observed in this work. So, we don't think it is 238 necessary to add confidence bands for the linear fit. The detailed reasons are the same 239 as our response to the 6th comment. (One minor note: the reason we do include 240 confidence bands in Fig. 4 is as a guide to the eye; it can better differentiate the trends 241 of the data in this work from that of the previous work. But in Fig. 3d, confidence bands 242 are not necessary for this differentiation. 274 Specifically, when we input the nucleation data at 948 K into equation S-1, we also 275 input S-1 the related growth temperature, 1073 K. When we input the nucleation data 276 at 998 K, 1011 K, and 1023 K into equation S-1, the related growth temperature, 1119 277 K is also input. The details about the iterative calculation steps can be found in the 278 analysis steps part of the Supplementary Methods in the Supplementary Information 279 file. 280 SECOND ROUND: OK, thank you.

Minor comments
The title is considerably long but more appropriate than the previous one since the test was performed only on one glass. Data for this particular Ba-silicate glass are available just in publications of the Kelton group.
Introduction: "A barium-silicate glass was chosen since they have higher nucleation rates than other glasses, such as lithium disilicate or soda-lime silicate so that it takes less time to obtain a significant number of nuclei.": Some soda-lime silicate glasses may have higher nucleation rates (e.g., the 2-1-3 glass) than barium silicates.
Results, line 5: It would need to clarify that it refers to the induction time at the growth temperature (as written in line 7, page 6), since this is the first time this variable is mentioned, and this is not a specific glass science journal.
Conclusion: "For the new measurements reported here the glasses were given a much longer nucleation treatment than was used in all previous measurements. These new data do not show a low-temperature anomaly": This paragraph is somewhat confusing; it implies that various nucleation rates at different temperatures were determined.
The used heating rates of the double stage heat treatment and their possible effects on IST were not reported.
Measurement of possible athermic nuclei were not reported.
Overall this is a very good paper, with a few problems.
Reviewer #3 (Remarks to the Author): Glasses have accompanied and facilitated human civilization in the last 2000 years and are indispensable to modern communication and computation apparati. The amazing optical, thermodynamic, mechanical, and electronic properties of glasses are extensively researched, however, the prime issue of the origin of glasses, i.e., why some melts fail to crystallize upon cooling, is still elusive. A classical explanation form the 1950 relied on crystal nucleation theory and posited that at lower temperatures the viscosity of melts of complex molecules increased so much that it suppressed crystal nucleation. An important open question was whether the lower temperatures also enforced a higher nucleation barrier. Numerous determinations of nucleation rates in glass forming melts, aptly summarized in this manuscript, appear to furnish a positive answer to this question. This outcome implies that classical nucleation theory does not apply to glass forming melts and elaborate non-classical phenomena dominate the kinetic pathways. Xia et al. design a technique which allows them to maintain stable temperature for months on end and in an experimental tour de force monitor the time evolution of the crystal nucleation rate in a judiciously chosen glass. This approach convincingly demonstrates that the investigations that demonstrate increasing nucleation barriers at lower temperatures have ignored a second corollary of the high viscosity, the exceedingly slow egress of the nucleation process to a steady state, manifested as a nucleation delay time longer than expected by orders of magnitude. In consequence, the monitored crystal nucleation events were not in a steady regime and, accordingly, their rates were substantially slower than the predictions of classical theory. The slow measured nucleation rates were misinterpreted as an outcome of higher nucleation barriers. Xia et al. clearly demonstrate that classical nucleation theory applies to glass forming melts and potential alternative nucleation pathways are not in play. The study is well conceived and perfectly executed, the paper is carefully written, the results are placed in the context of classical theory and the basic assumptions that appeared violated by previously collected data are properly stated. Particularly appealing is Fig. 3, which displays three tests of the compliance of the measured nucleation behaviors to CNT. Owing to its huge fundamental and applied merit and the quality of the investigation, I certainly think that the manuscript by Xia et al. should be published in Nature Communications. I suggest a few mostly editorial revisions that will significantly enhance the impact of this paper. In the Introductions, please specify that previously measured nucleation rates below a certain temperature were significantly lower than the prediction of CNT based on assuming slower kinetics due to greater viscosity at the lower temperatures. This discrepancy enforced the assumption that the nucleation barrier shoots up. This explanation will tie the misinterpretation of the previous results with your powerful demonstration that the nucleation rates measured before steady state is reached are lower. Along the same line of thought, please use Ref. 28 or the more recent book by Kashchiev to explain why nucleation rates measured before steady state is reached are slower and not faster than the steady state values; this transition imposes a superlinear correlation N(t), so nicely demonstrated in Fig. 2. p. 4: please denote the increase of the number of crystals that nucleate per unit volume per unit time as superlinear instead of the more generic nonlinear. Do not use parentheses to bracket the values of Ist and theta. Please report the values of Ist and theta with fewer significant digits as demanded by the standard deviations of the respective measurements. Consult a book on statistics of experiment if needed. Please use same units of volume and time throughout. Volume is now reported in cubic microns and cubic millimeters, whereas time is measured seconds, minutes and even days. This makes verifying the stated parameter values with the presented data confusing. In Fig. 3b, the legends that state growth T 1093K and growth T 1119K in both black and red are confusing. It is not clear if the points belong to the figure legend or to the linear correlation starting at lower temperatures.
We thank the referees for a second round review of our manuscript. To better acknowledge that the analysis by Cassar et. al. motivated us to carry out the experiment outlined in our manuscript, we have changed our discussion in the introduction section. We received second round reviews only from Reviewers #1 and #3; our responses follow. The paragraph starting with SECOND ROUND COMMENT in italics font are the reviewers' comments in the second round, and the paragraph beginning with SECOND ROUND RESPONSE in normal font are our related responses. For completeness, we also include the first round comments and our first round responses when they are related to second round comments. FIRST ROUND RESPONSE: Thank you for this comment. We agree that the possibility "without a break" has been suggested by other researchers (ref. 17), but this has not been proven in any glass studied. Our results presented are the first to definitively show that the break is an artifact in the glass that we have studied. The reference to the arxiv article of the previous study (ref. 17 in our initial manuscript) has now been updated by the authors on the arxiv and published in the Journal of Non-Crystalline Solids (547 (2020) 120297). The conclusion in their published paper is different than that in the initial arxiv version. The authors conclude that the statistical analysis that they applied to the existing data in the literature could not establish whether the low-temperature behavior was real or an artifact. In the discussion section they state "In the end, having discussed the procedures and the current results in this communication, we are not able to draw a definitive conclusion regarding the existence or not of the nucleation "break." Our results, however, cast reasonable doubt about whether the "break" is a phenomenon that happens for all oxide glasses. A recent report by Xia et al. [59], with new measurements of the nuclei density in a Ba5Si8O21 glass at 50 K below Tmax, supports our conclusion that the nucleation "break" is an artifact." The conclusion of their JNCS ends with the statement, "With this setup, our results cast reasonable doubt on whether the nucleation "break" is a universal phenomenon that happens for all oxide glasses." Their study only casts doubt on whether the low-temperature anomaly was an artifact or not. Our work that was submitted to

Response to
Nature Materials provides the proof (note, this review was for our original submission of this article to Nature Materials; it was transferred to Nature Communications). It is the first study to definitively show that the anomaly in the steady-state nucleation rate is in fact an artifact in the glass we studied, and raises serious questions of whether it is an artifact in other glasses that show the same low-temperature anomaly.  Fig. 6a, for the first Li2Si2O5 dataset, 5 out of the 7 data points below the peak nucleation temperature Tmax were not considered in their analysis because they did not pass their data quality test standards. And the 2 data points at low temperature that did pass their standards showed no nucleation anomaly below Tmax for this glass. In Fig. 6b, for the second Li2Si2O5 dataset, one low-temperature point below Tmax failed to meet their standards and two low-temperature points below Tmax showed no nucleation anomaly. In Fig 6c, for the third Li2SiO5 dataset, there is one data point below Tmax; the value of that point is slightly below or approximately equal to the Tmax point in Fig. 6c and its interfacial free energy is larger than the value at Tmax, as shown in Fig. 7c. Figures 6c and 7c suggest that there is a nucleation anomaly below Tmax in Li2Si2O5. However, it might be argued for Fig. 6c that the low temperature point is still within the confidence band for linear fitting. It should be emphasized that the 95% confidence band for linear regression is a statistical evaluation tool, used when a linear relationship is assumed. The band will differ for other functional forms (i.e. nonlinear). If the change of trend from the Tmax point to the low-temperature point in Fig. 6c is correct an assumed linear relationship would be incorrect for calculating the confidence band.

SECOND ROUND COMMENT:
Also, in their paper Cassar et al. themselves point to the third dataset for the composition Li2Si2O5 as the supporting evidence existence of nucleation break. They state -"Subplot 6c, however, is the first result for which we cannot completely reject the presence of the nucleation "break"." In another paragraph they state -"In the subplots of Fig. 7, we seek evidence for the nucleation "break" in the form of a change in the monotonic growth of σ regarding the temperature. If we consider only the data points that passed the steady-state test, we observe that only subplot 7c may have a non-monotonic growth of σ." In summary, in the analysis of previously published nucleation data, different researchers have reached opposite conclusions. This is the reason that although we certainly respect the work by Cassar et al., which is based on a more strict assessment of the data quality, it does not present a firm conclusion, nor a proof regarding the nucleation anomaly question for any of the glasses that they have studied.
We gratefully acknowledge, however, that the analysis by Cassar et. al. partially motivated us to carry out the experiment outlined in our manuscript. We have modified the discussion in the introduction to emphasize as follows.
"Already in some previous studies (Zanotto et al. 18 and Greer et al. 19 ) the possibility was raised that the nucleation anomaly might be an artifact, but without providing conclusive evidence. A series of previously published nucleation data sets were recently re-analyzed by Cassar et al. 20 , focusing on data near the peak nucleation temperature. They concluded that not all data points could be taken with equal confidence, finding variations even across data sets for the same type of glass. From this, they cast doubt on the widely studied nucleation anomaly. Partially motivated by the conclusions of Cassar et al. 20 and by those from other data analyses (such as Gupta et al. 17 ) we concluded that the anomaly might be an artifact resulting from insufficient heating time at the low nucleation temperatures.
Here we show that the anomaly previously reported in a 5BaO·8SiO2 glass 10 was indeed an experimental artifact. This was demonstrated by using a suitably designed experimental procedure and tracking the nucleation process over extensively long periods of time ..."  1902/1902.03193.pdf In that arxiv paper, the authors selected and analysed nucleation rates for 6 glasses in temperature ranges where they (claimed) have reached the steady-state regime.

Their conclusion was: "With this strategy, we proved that the alleged nucleation break is indeed an experimental artifact! This result ends a four decade-old dilemma and corroborates the use of CNT for analyses of crystal nucleation rates."
And, indeed, their figures 5a-f and 6a-f seem to support their conclusion. So, the conclusion of this manuscript is exactly the same of the arxiv paper? (https://arxiv.org/ftp/arxiv/papers/1902/1902.03193.pdf) The only difference is that another glass was used. But Casar already demonstrated this same fact for 6 glasses.
FIRST ROUND RESPONSE: As we mentioned in our reply to the first comment from the reviewer, the initial arxiv of Cassar et al. from the San Carlos group has been updated in the arxiv and has now been published as (Journal of Non-Crystalline Solids 547 (2020) 120297). A close examination of the published paper (not the initial arxiv version) shows a different conclusion than in the initial arxiv version. The authors conclude that the statistical analysis that they applied to the existing data in the literature could not establish whether the low-temperature behavior was real or an artifact. Our study is the first one to definitively show that it is an artifact for the glass we studied. Since the same anomaly has been reported in other silicate glasses, our work indicates that these are also likely artifacts and should be reinvestigated.
In our revised manuscript, we have updated the reference to the Cassar paper from that of the initial arxiv to the published paper (Journal of Non-Crystalline Solids 547 (2020) 120297), which contains a different discussion and conclusion from the initial arxiv version. We have also updated our manuscript to their work: "Recently, without being able to draw a definitive conclusion, Cassar et al. 20 also cast reasonable doubt about whether the low-temperature anomaly is a real phenomenon. Their conclusion was based on a statistical analysis of existing published data on several silicate glasses, but contained no firm demonstration in any glass. No new direct measurements were made to demonstrate that the steady-state nucleation had indeed been obtained below the peak nucleation temperature."

SECOND ROUND RESPONSE:
We have already addressed this comment in our Second Round response to the comment No. 1.

FIRST ROUND COMMENT: Data & methodology: validity of approach, quality of data, quality of presentation-A standard approach was used: two-step crystallization, followed by optical analyses of the microstructures. Then, they used the Kaischiev expression to analyse the number density vs. time curves. This is also a well-known, accepted procedure in this field.
FIRST ROUND RESPONSE: Since there is no question raised by the reviewer in this comment, there is no change in the revised manuscript on this point. The aim of our work was not to develop a new methodology, but to use a tested method to examine the anomalous behavior that has been reported in silicate glasses at low temperature.

FIRST ROUND COMMENT: The use of the Turnbull equation for the Dg(T) calculation is an approximation, which is only valid only under certain conditions, for some substances. I am not sure whether it is valid for this barium silicate material. Perhaps the authors should also test their results with other approximations for Dg.
FIRST ROUND RESPONSE: The reviewer is correct; the Turnbull approximation assumes that the heat capacities of the liquid and glass are the same. If the heat capacity difference between glass and crystal as a function of temperature were known, a more accurate thermodynamic driving free energy could be obtained. Unfortunately, these heat capacities are not known. However, even if they were known, the magnitude of the thermodynamic driving free energy would still increase approximately linearly with decreasing temperature over the range of nucleation temperatures studied and would not change the direction of the trend in the interfacial free energy or the work of critical cluster formation. So, the key conclusion in our manuscript would remain the same. Figure 4 shows the 95% confidence limits. However, I should stress that the smooth curve through the red points (previous data above the maximum) and black point (new data point at 50K below the maximum) does not match.

FIRST ROUND COMMENT: They show error bars in all figures and
FIRST ROUND RESPONSE: In the text describing Figure 4 we state, "The data point at 1048 K falls outside of the higher limit of the confidence bounds. This likely is an artifact of the fit, however. The induction time was not measurable at this temperature; instead, it was estimated from the data at 998 K, 1011 K and 1023 K." Further, the solid curve doesn't go exactly through the data points because we used the linear fit to the interfacial free energy to obtain a continuous curve, which will not go through the data exactly.

SECOND ROUND RESPONSE: Thanks
6. FIRST ROUND COMMENT: They could also include the confidence limits of the fit in Fig.3 (not mandatory) FIRST ROUND RESPONSE: We do not feel that it is necessary to add confidence bands for any type of fitting in Fig. 3 because it will not provide any additional useful information for the final conclusion. Confidence bands are a statistical tool used to examine the fit for an assumed fitting function. By fitting to different fitting functions, the confidence bands can be used as a tool to allow a determination of the best function. They do not provide information about the original data. Since in each subplot of Fig. 3 there is only one assumed function, no information can be gained about the best function that matches the data. With or without confidence bands the final conclusions are clear and the same.

SECOND ROUND RESPONSE:
Thank you for these comments. Although an additional temperature point could be useful, one temperature point as one counter example is sufficient to prove that the previous general statement of low-temperature nucleation anomaly is wrong in this glass. Concerning the statistical analysis, we have already included the necessary error analysis and we have already replied to the confidence band comment in our First Round response. Regarding Cassar et al., we have addressed this comment in our Second Round response to the comment No. 1.

FIRST ROUND COMMENT: it resulted from only ONE new data point (at 50K below the maximum), so at least a test in another low T should be relevant.
FIRST ROUND RESPONSE: While it would be useful to obtain other low temperature measurements, due to the COVID-19 pandemic this was not possible. These are extremely long experiments, with each new measurement at a given low temperature nucleation temperature requiring many months. The new nucleation measurement at the lowest temperature reported in this glass clearly demonstrates that the low temperature anomaly previously reported by us for this glass is incorrect. It is also likely incorrect in the other silicate glasses where the anomaly has been reported.

SECOND ROUND COMMENT: This reviewer is fully aware of the COVID-19
problem. However, another data point at a somewhat higher temperature, which would not take that long to collect, would be essential to confirm their conclusions, which is based on a single nucleation rate datapoint.

SECOND ROUND RESPONSE:
Thank you for this point. As we said in our First Round response, the long-time nucleation measurement at the lowest temperature reported in this glass clearly demonstrates that the low-temperature anomaly previously reported for this glass is incorrect.

FIRST ROUND COMMENT: this study with one particular glass corroborates the results of a much stronger article (arxiv 2019) that analysed 6 glasses, and has reached exactly the same conclusion.
FIRST ROUND RESPONSE: We have discussed this in an earlier response. The initial conclusion proposed by as Cassar et al. from the San Carlos group in their original arxiv paper has changed in the current arxiv entry and in their published Journal of Non-Crystalline Solids article. In those later articles, they conclude that they were not able to reach a definitive conclusion regarding the low-temperature anomaly in the nucleation rate. So, their article was not stronger as stated by the referee. Their analysis suggested that the anomaly was an artifact. Our data are the first to definitively demonstrate that it is an artifact for the glass we studied, and raises the serious question of whether it is an artifact in other glasses that show the same low-temperature anomaly. Since we have not yet been able to confirm this in other glasses due to the COVID-19 pandemic, impacting our laboratory studies and our colleagues at Corning Glass Inc., who were going to furnish the samples but were abruptly required to work remotely before the glasses could be prepared and characterized, we have changed the title, abstract and conclusion in our submitted paper to focus on the 5BaO·8SiO 2 glass. Our future studies will investigate whether it is also an anomaly in other silicate glasses. FIRST ROUND RESPONSE: The linear fitting method we used is a widely accepted method to obtain the steady-state nucleation rates and the induction times. That there are other ways to obtain the result doesn't invalidate this approach. Further, while the Kashchiev expression is indeed the best analytical expression (see "Transient Nucleation in Condensed Systems," K. F. Kelton, A. L. Greer and C. V. Thompson, Journal of Chemical Physics, 79, 6261 (1983)), it is still based on assumptions. We feel that the standard method of analyzing the nucleation data is the best approach.

SECOND ROUND COMMENT:
The problem in using only the final data pointswhich seem to be in a straight line -rather than the whole N vs. time curve, is that you are implicitly assuming that steady-state conditions have already been reached.

SECOND ROUND RESPONSE:
As we indicated in our First Round response, that there are other ways to obtain the result doesn't invalidate this widely accepted linear fitting approach.
11. FIRST ROUND COMMENT: Also, Schneidman has shown long ago that there is an interdependence between the true nucleation induction times, theta, and t_(ind_d), hence a time shift, ts, should be considered in the model for properly fitting these curves. And these true thetas should be used in the CNT plots. Please comment.
FIRST ROUND RESPONSE: There are several ways to obtain the correct induction time (at n* for the nucleation temperature) from the measured data. We have chosen to use the Shneidman-Weinberg expression, the validity of which has been confirmed (Nucleation in Condensed Matter -Applications in Materials and Biology, K. F. Kelton and A. L. Greer, Pergamon Materials Series, Elsevier, Amsterdam (2010)). That is why we corrected the measured induction times, which were for n* at the growth temperature, to obtain the induction time for n* for the nucleation temperature.

SECOND ROUND COMMENT: Ok, let´s leave it this way. However, please keep in mind that nucleation in a glass (below Tg) is further complicated due to the glass relaxation's interference on the nucleation pathways and kinetics. Nucleation above Tg takes place in a SCL, whereas below Tg it takes place in a glass. This is likely the reason why you cannot describe your N vs. time curve with the Kash equation
SECOND ROUND RESPONSE: This is a valid point. Structural relaxation below T g could influence the kinetics and also, through the elastic strain energy, the thermodynamic work of cluster formation. Looking at the kinetics first; these are typically described in terms of the viscosity, which can be dramatically lower that the extrapolated value from the supercooled liquid and can change with structural relaxation. If the data were analyzed using the extrapolated value for the viscosity the results would be incorrect. The measured induction time, however, directly reflects the interfacial kinetics, which is the reason that we analyze our data using this. Structural relaxation could influence the induction time as well, but if that were the case over the measurement time we would not see a linear relation between the number of nuclei and time in the steady-state regime. This suggests that any change in the kinetics with structural relaxation occurs quickly at the nucleation temperature. This is consistent with numerical estimates that we have made based on the kinetic parameters.
Regarding the work of cluster formation, the role of the elastic strain energy is insufficient to explain the anomalous break observed by others (see Journal of Non-Crystalline Solids 432 (2016) 325-333). Finally, we have never suggested that the Kashchiev expression is incorrect. Indeed, we have used an expression obtained from this treatment in our analysis. As discussed in our First Round Response, the Kashchiev expression was used to obtain an expression that we use to correct the induction time from the induction time for n* at the growth temperature to the induction time for n* at the nucleation temperature (see Nucleation in Condensed Matter, K. F. Kelton and A. L. Greer, Elsevier (2010), pages 76-77). FIRST ROUND RESPONSE: Unfortunately, due to the COVID-19 pandemic, we are not in a position to supply another low T measurement, which is a very long experiment. But, we maintain that the data we have obtained in the manuscript clearly demonstrate that in this glass the low temperature anomaly in the steady-state nucleation rate previously reported is incorrect. Figure 3 (d) are not well aligned; it would be educational to include the confidence interval of the adjustments, as you did in Figure 4.

FIRST ROUND COMMENT: The points in
FIRST ROUND RESPONSE: The linear fit doesn't have to go through the data points exactly. Currently, Figure 3d is good and clear in presenting the trend observed in this work. So, we don't think it is necessary to add confidence bands for the linear fit. The detailed reasons are the same as our response to the 6th comment. (One minor note: the reason we do include confidence bands in Fig. 4 is as a guide to the eye; it can better differentiate the trends of the data in this work from that of the previous work. But in Fig. 3d, confidence bands are not necessary for this differentiation.

FIRST ROUND COMMENT:The use of the Kashchiev equation (Reference 27) for the calculation of the diffusion coefficient from the induction times is commented, but the equation is not shown.
FIRST ROUND RESPONSE: To address this comment, we have added the Kashchiev equation into the Supplementary Information file. See the section named as "Using the Kashchiev expression to calculate the diffusion coefficient from the induction time for the critical size at the nucleation temperature". FIRST ROUND RESPONSE: The Kashchiev treatment can only be used for the induction time for the critical cluster size at the nucleation temperature. That is why we corrected the measured induction times (which were for the critical cluster size at the growth temperature) using the expression developed by Shneidman and Weinberg.

SECOND ROUND COMMENT
As discussed on page 81, figure 11  The different growth temperatures have already been included in our calculations. Specifically, when we input the nucleation data at 948 K into equation S-1, we also input S-1 the related growth temperature, 1073 K. When we input the nucleation data at 998 K, 1011 K, and 1023 K into equation S-1, the related growth temperature, 1119 K is also input. The details about the iterative calculation steps can be found in the analysis steps part of the Supplementary Methods in the Supplementary Information file.

SECOND ROUND COMMENT:
OK, thank you.

New minor comment from SECOND ROUND:
The title is considerably long but more appropriate than the previous one since the test was performed only on one glass. Data for this particular Ba-silicate glass are available just in publications of the Kelton group.

SECOND ROUND RESPONSE:
In the new manuscript, we have updated the title to meet the 15 words limit from the Journal. The title has been changed from "The Low-Temperature Anomaly in the Steady-State Nucleation Rate in Silicate Glasses is Shown to be Artifact in a 5BaO·8SiO 2 Glass" to "Low-Temperature Nucleation Anomaly in Silicate Glasses Shown to be Artifact in a 5BaO·8SiO 2 Glass". It is true that currently we are the only group who have studied 5BaO·8SiO 2 glass and who have tested the low-temperature nucleation anomaly using 5BaO·8SiO 2 glass.
17. New minor comment from SECOND ROUND: Introduction: "A barium-silicate glass was chosen since they have higher nucleation rates than other glasses, such as lithium disilicate or soda-lime silicate so that it takes less time to obtain a significant number of nuclei.": Some soda-lime silicate glasses may have higher nucleation rates (e.g., the 2-1-3 glass) than barium silicates.

SECOND ROUND RESPONSE:
Thank you for this point. To address this point, in this sentence, we have changed "lithium disilicate or soda-lime silicate" into "Li 2 O 2SiO 2 or Na 2 O 2CaO 3SiO 2 ". Also, this sentence has been moved to the methods section.