Properties of Glassy Selenium and Selenium Based Chalcogenides and Low Limit of the Liquid

PROPERTIES OF GLASSY SELENIUM AND SELENIUM BASED CHALCOGENIDES AND LOW LIMIT OF THE LIQUID STATE

Edward Bormashenko a, Roman Pogreb a, Semion Sutovskya, Victor Lusternikb and Alexander Voronelb

aThe College of Judea and Samaria, The Research Institute, 44837, Ariel, Israel

bTel-Aviv University, Ramat Aviv, 66978 Tel-Aviv, Israel

Abstract

Complex Young’s moduli and specific heats of glassy selenium and selenium based chalcogenides Se55As45, Se67.5As20Ge12.5 and Se57I20As18Te3Sb2 have been measured in the range of their glass transformation. The temperature of a specific heat anomaly is situated well below the maximum of a loss tangent for every material under study. The mean square amplitude of atomic vibration in glassy Se at a point of its transformation into liquid happens to be equal to that value in a crystalline Se at its melting point. Both valuescorrespond to the Lindemann’ criterion of melting. It is plausible to suggest that the glass transition microscopically corresponds to a fusion of small clusters constituting the glass.

PACS number(s): 64.70.Pf, 64.70.Dv, 65.60.+a, 62.10.+s

I. INTRODUCTION

The problem of glass transition in amorphous media has been the subject of extensive theoretical and experimental investigation for a few decades1. Yet exhausting understanding of the phenomenon (and even a rigorous definition of the very point of glassification Tg) still has not been achieved.

U. Buchenau and R. Zorn2 carried out the neutron scattering measurements of a mean square amplitude of atomic vibration of liquid and glassy selenium (Fig. 1). It was demonstrated that the mean square amplitude of atomic vibration in Se glass at a point of its transformation into liquid happens to be equal to that value in a crystalline Se at its melting point. Both valuescorrespond to the Lindemann’ criterion of melting3. Investigations performed by U. Buchenau and R. Zorn allowed to single out a point Tgof a change in microscopic behavior of glassy Se. This point happened to be slightly below of a point Tc of a maximum of an anomaly in specific heat Cp.

Selenium is a generally amenable object for glass transition process study: on one hand both kinetic and thermodynamic characteristics of Se were investigated thoroughly4,5, on the other hand Se gives rise to a large variety of Se-based, relatively low melting, chalcogenide glasses suitable for experiment6-8.

The novelty of our experimental techniques lies in application of both dynamical mechanical analysis (DMA) and scanning calorimeter to the amorphous Se and Se-based chalcogenide glasses. DMA method was developed for a study of mechanical properties and phase transformations of polymer materials9, and hadn’t been applied for the study of chalcogenide glasses previously because of its instrumental limitations: usual glasses demonstrate their softening at the temperatures much higher than those of polymers. Low softening points of the Se-based chalcogenide glassy materials under investigation allow the DMA method to be effectively applied hear.

II. EXPERIMENTAL

Pure Se (99.99+%) in pellets (d<4 mm) was supplied by Sigma-Aldrich Co. Se-based chalcogenide glasses were supplied by St. Petersburg Research Institute of Optical Materials. These glasses were initially developed for IR optics applications because of their exclusive transparency in wide middle and far IR-range7. Properties of pure selenium and Se-based chalcogenide glasses have been studied by both dynamic mechanical analysis (DMA) (Ref. 9) and scanning calorimetry (SC) (Ref. 10).

Material studied by DMA method (Perkin-Elmer DMA-7 device) is subjected to a forced mechanical vibration at a fixed frequency (1 Hz in our case) with amplitude of oscillatory stress. Chalcogenide glass samples (dimensions 1.50x15.0x4.1 mm) have been prepared by a die-casting process and put into the device. For polymers, the most common experiment was a temperature sweep under the fixed parameters of vibration. For chalcogenides we have used this well developed experimental procedure in higher temperature range from 273 K to 550 K at the rate 3 K/min.

The complex mechanical modulus G* of the material can be resolved into elastic (or storage) modulus G' and the viscous (or loss) modulus G'':

G* = G' +i G'' (1)

Until the sample subjected to the forced vibration in the DMA device remains solid the main part of the pumped in vibration energy returns elastically and only a small fraction is absorbed. Then a loss tangent – tanδ - can be constructed:

tanδ = G''/ G' (2)

In parallel the temperature dependence of heat capacity Cphave been studied over the same temperature range with heating rates varied from 0.6 K/min up to 3 K/min. Our precise scanning calorimeter has been described previously10.

III. RESULTS AND DISCUSSION

The results of the DMA measurements for pure glassy selenium are presented in Fig. 2-3. While the magnitude of the storage modulus (G’ in Eq. (1)) remains rather stable through the range of the glass state and drops down in a softening region, the loss modulus – G” – undergoes a maximum corresponding to the softening point. This behavior is typical for all the series of Se-based chalcogenide glasses under investigation. A storage modulus of a typical glass is equal to a few GPa and its loss modulus is much smaller, reaching the same order of magnitude at its maximum only. In order to remove possible extrinsic factors and make easier a comparison of the results Figures 4-6 present both the loss tangent (tanδ in Eq. (2)) and the heat capacity Cp in dimensionless units. The experimentally measured values have been normalized to their values at the points of their maxima. The experimental results are summarized in Table I (Tc- temperature of the heat capacity maximum, Tf – temperature of the loss tangent maximum).

Table I. Properties of glassy Se and Se-based chalcogenide glasses

Material under study /

Density

(g/cm3)

Storage Modulus (GPa)

Tc (K)

/ Tf (K)
Se / 4.8 / 2.3 / 314 / 338
Se55As45 / 4.48 / 2.2 / 450 / 513
Se67.5As20Ge12.5 / 4.48 / 1.9 / 483 / 538
Se57I20As18Te3Sb2 / 4.40 / 5.0 / 313 / 326

Glass transition in all the investigated materials has common features. As for the most of glasses11 the heat capacity anomaly looks like a second order phase transition with a more symmetric phase situated at lower temperature12. Such an unusual configuration means that an upper phase has a higher number of degrees of freedom. This latter statement sounds quite reasonable for a metastable liquid phase in comparison with a glass (see Ref. 1). The second order phase transition image is highly pronounced in pure Se exhibiting also a significant singular part of heat capacity (Fig. 3). The same image repeats itself, though less pronounced, in all other materials (Fig. 4-6). Since the heat capacityCp = < ∆ S >2by definition (Ref. 12), the singularity in the Fig. 3 signifies a growth of structural fluctuations in the vicinity of the transition. From the Fig. 6 one can also see a negligible dependence of the specific heat anomaly on a heating rate between 0.6 and 3K/min. For a further discussion of the matter we have to consider here more in detail the paper of U.Buchenau and R.Zorn (Ref. 2) on neutron scattering in Se. In Fig. 1 one may see mean square displacements of Se atoms in all the three crystalline, liquid and glassy phases measured from their vibration motion with frequencies above 1011 Hz. These vibrational degrees of freedom play a mayor role in the frozen material. However, in the liquid state a diffusional motion takes its growing part in full energy. Until the thermal energy includes the vibration only the mean square displacement (or an average square amplitude of vibration) is proportional to a full thermal energy of the system. Thus the break in an upper curve (for a glassy and liquid states) in the Fig. 1 means the real change in degrees of freedom leading to a jump in a second derivative of the corresponding thermodynamic potential, in other words, a second order transition in the system. Similar breaks for mean square displacements have been observed in other glasses as well11.

In fact, the cut off the frequency at 1011 Hz has left some portion of energy out of the account. Consequently the mean square displacement is not exactly proportional to the full thermal energy of the frozen system. Therefore the break in the curve looks not exactly sharp (leave for a moment other reasons). In accordance, both the step of Cp in Fig. 3 and the singularity are also not too sharp.

However, one has a solid ground to identify the glass transition point Tg of selenium with this break in a curve for its glassy state in the Fig. 1 at about 305 K. One can see in the Fig. 3 that this temperature corresponds to the onset of Cp anomaly (about 10 K below the very maximum). This is a rather usual shift of the maximum of Cp anomaly of an imperfect sample (Ref. 13). As it had been shown earlier (Ref. 12, 14) maxima of critical anomalies in imperfect systems should be shifted in the direction of the less symmetric phase.

Actually the onset of a softening also starts as early as the heat capacity growth. One can observe this in the Fig. 6. However, the maximum of the loss tangent appears usually at a much higher temperature depending on brittleness of a material. The maximum of the loss tangent corresponds not to the glass transition itself but to the point where the glass becomes already soft enough to absorb a substantial portion of mechanical energy.

Data for the ordered, crystalline phase in the Fig. 1 lay noticeable below the curve for the disordered, glassy one. The mean square displacement in glass at the point of vitrification Tg corresponds rather accurately to the value of this magnitude for crystalline Se in its melting point Tm at much higher temperature of about 496 K. This cannot happen just by chance. Data on the relative mean square displacements for other glasses exhibit breaks at roughly the same values (Ref. 11). Thermal vibration with the relative mean square amplitude, which makes impossible a close packed structure, destroys small (medium range) clusters constituting a glass in the same way as it does the long range crystalline structure. Since the difference in density between the glass and the crystal here is not large enough one cannot notice also a difference in the mean square displacements at these two points.

Thus one sees that the same Lindemann’ criterion which predicts the melting of a crystal, remains also valid for a fusion of micro-clusters in the process of the glass softening. It seems convincing that the glass transition microscopically corresponds to a disintegration of small clusters constituting the glass. Both size and symmetry of these spontaneously created clusters fluctuate at low temperature and the structure of glass depends on a thermal history of the sample. That’s why the anomalies of different macroscopic properties in glass transition are smeared in different ways.

Conclusions

Selenium and Se-based chalcogenide glasses have been studied in parallel using both dynamical mechanical analysis (DMA) and calorimetric experimental techniques.
The drastic changes of mechanical properties for all the investigated glasses have been observed at higher temperature Tf than the heat capacity maxima Tc. Both temperatures are situated well above Tg - the temperature of glass transition.
The glass transition is defined here as a point of disintegration of micro (medium range) clusters constituting a glass. Thus the low limit of the liquid state may be defined by the same Lindemann’ criterion as the melting of crystals: the relative mean square deviation of atoms of a glass from their average positions should be roughly below the same value as that one in the melting point of a corresponding crystal.

Acknowledgements

The authors wish to thank Avigdor Sheshnev and Yelena Bormashenko for their help in treatment of experimental data.

References

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FIG.1. Mean-square displacements in glassy, liquid and crystalline selenium determined from neutron scattering data for motions above 1011 Hz according to U.Buchenau and R. Zorn2.

FIG. 2. Temperature dependencies of the storage and loss modulus of pure Se (heating rate 3 K/min, frequency 1 Hz).

FIG. 3. Temperature dependencies of the normalized to maximal values loss tangent (curve a) and thermal capacity (curve b) of pure selenium (Cp(T) – studied by Stephens4 ).

FIG. 4. Temperature dependence of the normalized to maximal values loss tangent (curve a) and thermal capacity (curve b) of Se55As45 chalcogenide glass.

FIG. 5. Temperature dependence of the normalized to maximal values loss tangent (curve a) and thermal capacity (curve b) of Se67.5As20Ge12.5 chalcogenide glass

FIG. 6. Temperature dependencies of the normalized to maximal values tanδ (curve a) and thermal capacity of the Se57I20As18Te3Sb2 glass (curve b - heating rate 0.6 K/min, curve c – heating rate 3 K/min, frequency 1 Hz).

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