⇦Chinese Physics Letters, 2016, Vol. 33, No. 2, Article code 026301⇨ Pressure and Time Dependences of the Supercooled Liquid-to-Liquid Transition in Sulfur * Dou-Dou Zhang(张豆豆), Xiu-Ru Liu(刘秀茹), Zhu He(何竹), Shi-Ming Hong(洪时明)** Affiliations School of Physical Science and Technology, Key Laboratory of Advanced Technologies of Materials (Ministry of Education), Southwest Jiaotong University, Chengdu 610031 Received 12 September 2015 ^*Supported by the National Natural Science Foundation of China under Grant No 11004163, and the Fundamental Research Funds for the Central Universities under Grant No 2682014ZT31.
^**Corresponding author. Email: smhong@home.swjtu.edu.cn Citation Text: Zhang D D, Liu X R, He Z and Hong S M 2016 Chin. Phys. Lett. 33 026301 Abstract Thermal behavior of bulk amorphous sulfur is investigated by in situ temperature measurements at high pressures of 0.9, 1.4 and 2.1 GPa, and under different heating rates of 8, 10 and 12 K/min at 0.9 GPa. The results show that the onset temperature of the transition from the supercooled liquid to the liquid state for sulfur increases with the pressure and the heating rate. It is deduced that the transition does not follow the Clapeyron equation, indicating considerable coupling of the molecular structure change in the transition. Along with the data at ambient pressure and high pressure, we present a dynamic diagram to demonstrate the relationship between the amorphous solid, supercooled liquid, liquid, and crystal phases of sulfur, and suggest an experimental approach to establish pressure–temperature–time transition diagrams for supercooled liquid and liquid. DOI:10.1088/0256-307X/33/2/026301 PACS:63.50.Lm, 61.43.Dq, 64.70.Ja © 2016 Chinese Physics Society Article Text Following the successes of metallic glass preparation through melt quenching,[1] the solidification behavior of melts in the rapid cooling process has been investigated for many substances, the process includes transitions from the liquid to supercooled liquid phase and then from the supercooled liquid to an amorphous solid (glass).[2] Differential scanning calorimetry (DSC) is a very useful tool for the study of thermal properties of amorphous materials. In DSC measurement, the heating curve usually displays a transition from amorphous solid to supercooled liquid (glass transition or melting of glass) and then a transition from supercooled liquid to crystalline solid (crystallization).[3] However, our understanding of the direct transition from supercooled liquid to liquid is quite limited. Such a process needs sufficiently rapid heating rates to avoid crystallization, while the essential heating rate is very fast and difficult to actualize for most amorphous materials.[4] To date, knowledge of the supercooled-liquid-to-liquid transition has been obtained almost wholly from conventional glass, such as oxides and organic glass,[5] and these materials have very slow critical cooling rates to form glass and also slow critical heating rates to melt avoiding crystallization. While it seems reasonable that the rate of specific volume and entropy is continuous between the supercooled liquid and liquid, such that there is neither volume break nor latent heat in the transition,[6] experimental evidence of the supercooled-liquid-to-liquid transition is still lacking for many substances. Recently we reported that bulk amorphous sulfur (a-S) prepared via rapid compression has exceptional thermodynamic stability.[7,8] During heating of the a-S, crystallization was easily avoided and a direct transition from the supercooled-liquid-to-liquid was clearly observed. The transition is a distinct exothermic process with a volume expansion.[9] This novel melting phenomenon is different from the glass transition or crystal melting behavior, and also varies from the direct transition to liquid of known oxides and organic glass.[5] Through Raman spectral analysis we have attributed the exothermic energy to a possible chain–ring transition of molecules in a-S when it was heated to the melting point.[10] This is undoubtedly an interesting topic in the metastable phase transition, and should be significant and helpful to understand the essence of amorphous matter. Therefore, it is necessary to investigate further the abnormal event, and to confirm the mechanism of the transition from supercooled-liquid-to-liquid sulfur. In this Letter, the thermal behavior of the bulk a-S is measured under different high pressures and also for separate heating rates. Based on the relationship among the temperature of the transition from supercooling liquid to liquid, pressure, and time, we estimate that a molecular structure change is coupled with the transition, and then suggest an experimental method to establish the dynamic phase diagram under high pressure for the supercooled-liquid-to-liquid transition of sulfur. Bulk a-S was prepared by a rapid compression process, in which sulfur with a high purity of 99.999% was melted at a temperature of 435 K and then compressed to 1.8 GPa within 20 ms. Details of the preparation method and apparatus can be found in our previous reports.[7,8] Structural characterization of the recovered sample under ambient pressure was confirmed by using x-ray diffraction (XRD) with Cu $K_{\alpha}$ radiation from a Philips x-ray generator (X'Pert Pro MPD. Philips). The thermal behavior analysis of the obtained a-S at separate heating rates was carried out with a DSC instrument (TA-2920). Nitrogen was used as the purging gas with a flow rate of 50 ml/min. A prepared a-S sample with diameter of 12 mm and height of 8 mm was fitted into a cylindrical hexagonal boron nitride container, and was placed into a cubic pyrophyllite block. Graphite pipe was used as the heater, and a NiCr–NiSi thermocouple was placed in the center of the sample to measure in situ temperature. A Midi LOGGER GL900-8 device was used to record the temperature change with time. The sample configuration is shown in Fig. 1. High-pressure experiments of the bulk a-S were conducted on a slide-type multi-anvil apparatus.[11] Pressure was calibrated at room temperature according to the known phase transitions of Bi and Ba.

Fig. 1. Sample assembly for high pressure experiments. (1) Pyrophyllite block; (2) steel plug; (3) steel plate; (4) graphite heater; (5) amorphous sulfur sample; (6) NiCr–NiSi thermocouple; (7) hBN pressure medium; and (8) alumina insulating tube.

In each run of high-pressure experiments, the sample was first pressurized to the target pressure at room temperature. Then, the sample was isobarically heated with a selected rate up to a high temperature above 673 K. The generated pressure was held constant and the temperature of the sample was recorded during the heating process. Finally, the sample was cooled naturally to room temperature and was released slowly to the ambient pressure. The XRD results from the prepared sample of sulfur indicate a fully amorphous structure, which is consistent with our earlier reports.[9] The DSC results at ambient pressure obtained at 10 K/min are also very similar to those reported in Refs. [7,9], which include broad exothermic and endothermic peaks.[7,9] It has been made clear that the former peak corresponds to a direct transition from supercooled liquid to liquid,[9] and the latter is the known liquid–liquid transition of sulfur ($\lambda$ transition).[12,13] It is also confirmed that the supercooled-liquid-to-liquid transition of a-S is exothermic and expands the liquid volume.[9] Effects of pressure on the two transitions were investigated with a heating rate of about 10 K/min at high pressures of 0.9, 1.4, and 2.1 GPa. A temperature curve of the sample at 0.9 GPa is shown in Fig. 2. A clear temperature rise peak with an onset temperature of 470.3 K and then a valley starting at about 560.2 K are observed in this curve. Similar fluctuations were also recorded in every sample at higher pressures of 1.4–2.1 GPa. It is reasonable and credible that the two fluctuations correspond to exothermic and endothermic peaks in the DSC curve at ambient pressure, and that they are induced by the supercooled-liquid-to-liquid transition and the liquid-to-liquid transition ($\lambda$ transition), respectively. In this work, we refer to these two events as transitions I and II. Combined with data at ambient pressure, the onset temperatures of the two peaks under different pressures are shown in Fig. 3, indicating that both of the transition temperatures increase with the pressure.

Fig. 2. Temperature curve of the sample at 0.9 GPa with heating rate of 10 K/min.

Fig. 3. Onset temperatures of transitions under different pressures with heating rate of 10 K/min.

We now focus on how pressure affects transition I. The uptrend of onset temperature of transition I with pressure is remarkable and it can be interpreted as $dp/dT>0$. By contrast, as shown in our last report, an observable volume expansion and energy exothermic occurred within transition I,[9] suggesting $v_{2}-v_{1}>0$ and $h_{2}-h_{1 } < 0$, where $v_{1}$ and $v_{2}$ are molar volumes and $h_{1}$ and $h_{2}$ are molar enthalpies of the a-S before and after transition I, respectively. If transition I is a first-order phase transition, according to the Clapeyron equation $dp/dT=(h_{2}-h_{1})/[T(v_{2}-v_{1})]$, we should observe $dp/dT < 0$, while this result disagrees with the experimental behavior of the pressure effect on the temperature of transition I, $dp/dT>0$. Such inconsistency indicates that the Clapeyron equation does not hold for transition I. A possible reason is that the internal energy changes, such that the Gibbs function would not remain constant during the transition, thus an essential condition of the Clapeyron equation is lost. This viewpoint supports our explanation regarding the Raman spectral analysis: a chain–ring transition of the a-S happened during the supercooled-liquid-to-liquid transition,[10] due to the fact that the internal energy of the system should be changed if chain–ring transition occurs. In fact, the WAXS results before and after the transition also indicate the existence of structure change.[9] Although there is not direct evidence of the chain–ring transition, it is also necessary to clarify how pressure inhibits the transition of a-S, at least the inconsistency in $dp/dT$ indicates that transition I of a-S is not a simple first-order phase transition. This fact further reminds us that Clapeyron's equation does not always fit to all transitions between two phases, especially when they have different structures.

Fig. 4. Schematic diagram of temperature–time transition of sulfur under ambient pressure. $T_{1}$ is the onset temperature of the transition from supercooled liquid to liquid;[9] $T_{\lambda}$ is the onset temperature of transition II ($\lambda$-transition);[9] $T_{\rm g}$ is the glass transition temperature; $T_{\rm m}(\alpha)$ and $T_{\rm m}(\beta)$ are the melting points of $\alpha$ and $\beta$ crystal phases, respectively; $R_{1}\ldots R_{6}$ correspond to different heating rates, such as 2, 5, 7, 10, 15, and 20 K/min;[9] and $T_{\rm r}$ is the room temperature (starting condition in DSC tests).

The DSC curves of the a-S sample at heating rates 2, 5, 7, 10, 15, and 20 K/min were presented in our recent report.[9] Every DSC curve includes a broad exothermic and an endothermic peak, although the 2 K/min curve is complex, due to the fact that partial crystallization processes happen. When the heating rate is increased, the overall profile becomes the same two peaks while the locations of the peaks shift toward higher temperatures, and the difference between the two temperatures decreases. To show clearly dynamic behavior of the transitions of sulfur, based on the DSC data, we present a temperature-time-transition diagram (TTT diagram) of sulfur in Fig. 4. The diagram displays a conceptual relationship among the amorphous solid, supercooled liquid, liquid and crystalline phases of sulfur under ambient pressure, especially between supercooled liquid and liquid. Similar dynamic investigations are also carried out under high pressure in this work. Figure 5 displays the temperature measurement results of transition I at a high pressure of 0.9 GPa by using different heating rates of 8, 10, and 12 K/min, indicating that the onset temperature of transition I increases observably with the heating rate. Transition II shows similar trends, while it is comparatively insensitive to the heating rate. The reason could be considered such that transition I is a coupling process including chain–ring transitions and liquefaction, in which both molecular structure and total density change remarkably,[9] and this complex process may be related strongly to the heating rate. In comparison with it, transition II is the liquid-to-liquid transition without observable density change,[9,12,13] some possible structural changes should be dependent mainly on the temperature.

Fig. 5. Relationship between the onset temperature of transition I and the heating rate under a high pressure of 0.9 GPa.

Experimental routes with different heating rates under separate pressures are depicted conceptually in Fig. 6, in which boundaries between supercooled liquid and liquid of sulfur can be simulated by the temperature data of transition I for the different heating rates at ambient pressure and high pressure of 0.9 GPa. Figure 6 does not include data at 1.4 and 2.1 GPa, due to the fact that the boundary of the phases could not be fixed by one point at the respective pressure. Such an image is actually a pressure–temperature–time transition (PTTT) diagram,[14] although more experimental data at different pressures are needed. In principle, we can establish a three-dimensional diagram for transition I of a-S by different heating rates under a series of separate pressures. This experimental method is also propitious to establish PTTT diagrams for other materials. The PTTT diagram is very significant and helpful to study the dynamic behavior of metastable phases under high pressure and temperature.[14]

Fig. 6. Schematic diagram of pressure–temperature–time transition (PTTT) of supercooled liquid to liquid transition of sulfur. Here $T_{1}(P_{0})$ and $T_{1}(P_{1})$ are onset temperatures of transition from supercooled liquid to liquid at ambient pressure and a set high pressure, such as 0.9 GPa, respectively, $R_{1}$ to $R_{3}$ are routes with different heating rates, such as 8, 10, and 12 K/min, and $t_{1}$ is the time of pressurizing to $P_{1}$ at room temperature.

In summary, the thermal behavior of bulk amorphous sulfur (a-S) is investigated by in situ temperature measurements at high pressures of 0.9, 1.4 and 2.1 GPa, and under different heating rates of 8, 10 and 12 K/min at 0.9 GPa. The results show that the onset temperature of the transition from supercooled liquid to liquid of sulfur increases with the pressure and the heating rate, which does not follow the Clapeyron equation, indicating that a molecular structure change of the a-S could be coupled with the liquefaction transition. Combined with the data under ambient pressure and high pressure, we present a conceptual diagram of the relationship among the amorphous solid, supercooled liquid, liquid, and crystal phases of sulfur, and suggest an experimental method to establish dynamic phase diagrams under high pressure for the transition from supercooled liquid to liquid. We thank Xiao-Wei Lv and Ming-You Wang for their kind help in experiments. References Non-crystalline Structure in Solidified Gold–Silicon Alloys???Glass—liquid transition in hyperquenched metal alloysBeating Crystallization in Glass-Forming Metals by Millisecond Heating and ProcessingRapid compression induced solidification of bulk amorphous sulfurUnderstanding exceptional thermodynamic and kinetic stability of amorphous sulfur obtained by rapid compressionExothermic Supercooled Liquid—Liquid Transition in Amorphous SulfurChain-ring transition during exothermic "melting" in amorphous sulfurThe structural properties of liquid and quenched sulphur II Origin of the

λ

Transition in Liquid Sulfur Pressure-temperature-time-transition diagram in a strong metallic supercooled liquid

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