Free Access

This article has an erratum: []

Eur. Phys. J. Appl. Phys.
Volume 94, Number 3, June 2021
Article Number 31101
Number of page(s) 4
Section Physics and Mechanics of Fluids, Microfluidics
Published online 14 June 2021

© EDP Sciences, 2021

1 Introduction

Hardness is a complex property of solids that involves plastic deformation, elastic deformation, and rupture. Such quantities as the elastic boundary, yield point, tensile and compressive strength, fragility, and cohesive force are all related to hardness: although these quantities are known for very few minerals, hardness measurements of different types have long been used in mineral identification. The first scale was proposed by Mohs in 1824 [1] and is still used in the hand-specimen examination. It is based on the relative hardness of one mineral to another on a scale of 1–10 from talc to diamond. At the microscopic level [1] proposed a relative scale based on the resistance of ore minerals to polish. The resulting ‘relief’ between adjacent minerals can be used to determine their relative hardness since a line of light moves from the hard to the soft mineral when a grain boundary is observed whilst raising the microscopic tube. Absolute methods of determining micro-hardness began in 1890 when Martens [1] placed a loaded indenter on the mineral surface mounted on a microscope stage and moved the stage in a direction parallel to the cutting edge of the indenter. A modified version of this apparatus was used by Talmage to produce a scale. In this scale, the hardness was designated by a series of letters from A (soft) to G (hard). In the quantitative determination of the micro-hardness of ore minerals such as sulfides, these techniques have been suppressed by micro-hardness determination by indentation technique, particularly using the Vickers indenter [1].

The survey of scientific literature shows that the mechanical characterization of only a few multi-component systems of ChGs has been done by different research groups [24]. Elshafie [2] reported the Micro-hardness studies in some glassy Se-Te-As alloys. Boycheva et al [3] investigated Vickers hardness in some Se-based chalcogenide glasses. Pattanaik et al. studied the compositional dependence of Vickers hardness by changing the Te concentration in some multi-component chalcogenide glasses [4]. Thermo-mechanical Characteristics of Arsenic-Sulphide Glasses Doped with Bismuth were investigated by Siljegovic et al. [5]. Freitas et al [6] proposed the empirical relation of glass transition temperature with the micro-hardness. Dergal et al. reported the impact of the laser exposure on some significant mechanical parameters of Ge-Se ChGs [7].

In a recent report, we have investigated the impact of some metallic impurities on thermo-mechanical parameters of Selenium elemental glass [8]. However, the explanations for the change in micro-hardness of chalcogenide glasses given by various groups are manifold. This necessitates more research studies (both theoretical and experimental) to reveal more information about this scientific issue.

In the light of the aforesaid discourse, it is evident that composition variation of the hardness and related parameters is still not fully comprehensible and so further investigations in this field may shed light on the critical issues that are practically important for cutting-edge applications and provide a novel explanation behind the fractural behavior of ChGs. Hence, we have decided to start work on this parameter that is a significant property. In the present work, we have determined the hardness of a parent glassy alloy (i.e., Se90In10 binary glass) as well as ternary glassy Se90In6M4 alloys to see the impact of chemical modifier M (M = Sn, Ag, Sb, and Ge). An attempt has been made to explain the impact of Sn, Ag, Sb, and Ge on the hardness of binary Se90In10 alloy. The role of the third element for forming ternary alloys has been decided on basis of a literature survey. Literature shows that the role of a specific third element on thermo-mechanical properties by varying composition has been discussed frequently but no painstaking endeavors have been done to realize the consequence of varying the third element itself for a fixed composition.

2 Theoretical basis

Among the various noteworthy mechanical properties of materials, the micro-hardness has unique importance from the application point of view. In general, it represents the resistance of a material against the eternal deformation occurring due to the application of external pressure on it. In glass science research, the prediction of micro-hardness of various kinds of glasses is an essential demand [9,10]. In practice, the micro-hardness and related thermo-mechanical parameters form a basis for the characterization of glasses for application in electronics and optoelectronics devices (like development of scratch-resistant glass coating, highly durable optical fibers, micro-lenses, etc).

The determination of Vickers hardness by micro-indentation experiments is an effective and reliable method that provides a novel and useful knowledge regarding the mechanical characterization of fragile solids [11,12]. Furthermore, the approach of using the micro-indentation marks for calculating the micro-hardness is a universally adopted method for acquiring significant information regarding the mechanisms involved directly in the distortion of solids like the creation of the holes or appearance of the fractures [13,14]. Investigation on the fractures created by indentation marks in the fragile substances reveals that indentation testing is a straightforward and convenient approach for depicting the fractural origin and growth behavior of solids [15].

A sharp indenter either in the shape of a cone or pyramid is employed for the indentation. Thus, the residual impressions have geometrical similarity and consequently, mathematical formulation becomes more accurate and simpler. Another advantage of such geometry is that the contact pressure does not depend on the indent size that makes this technique cost-effective and less time-consuming due to the convenient art of measurement [11]. In most of the Vickers hardness testers for indenting purposes, a diamond indenter is used. The geometry of the indenter is a right pyramid with a square base and an angle of 136 degrees between opposite faces subjected to a load (≤100 kgf). Figure 1 represents the geometrical diagram of the indenter having pyramidical geometry of a square-shaped base.

thumbnail Fig. 1

Diagram showing the geometrical overview of the indentation mark in micro-indentation experiment.

3 Synthesis and experimental techniques

Glassy Se90In10 and Se90In6M6 (M = Sn, Ag, Sb, and Ge) alloys were synthesized using highly pure (99.999%) Se, Te, and M (M = Sn, Ag, Sb, and Ge) elements. The chosen compositions of elements were sealed in silica tubes by using a seating unit equipped with the facility of creating a vacuum (∼ 10−6 Torr). After sealing, all the tubes were heated inside a furnace at a suitable high temperature for a sufficient period (∼10 h). Each tube containing the glass melt was cooled at a very fast rate to obtain the glasses in bulk form. This glass character is confirmed by X-ray diffraction (XRD) and Differential Scanning Calorimetry (DSC) techniques (see Fig. 2). The absence of sharp peaks in the XRD pattern and the presence of a well-known glass transition peak in the DSC scan confirm the glassy nature of the present alloy. Similar results were obtained for other glasses.

For the hardness measurements, we employed robotic digital equipment (Vaiseshika Electron Devices, Model: DHV-1000). The values of Hv for each sample were measured at a load of 50 g load. We repeated the indentation experiment ten times to ensure the consistency of the results. The photographs showing the impressions of the indenter are shown in Figure 3 for glassy Se98In6Sb4 alloy at 50 g load. Similar impressions were got for other samples.

thumbnail Fig. 2

XRD pattern and DSC scan of glassy Se90In6Ag4 alloy.

thumbnail Fig. 3

Micrograph of the imprint on the surface of a sample (ternary Se98In6Sb4 alloy).

4 Results and discussion

Table 1 tabulated the Hv values for the present samples. This table reveals that Hv is decreased when we incorporate Sn, Ag, Sb, and Ge in binary Se90In10 alloy. This can be explained to some extent based on the volume of micro-voids formed in the alloys.

The minimum volume of micro-voids (Vh) in glassy alloys can be determined using the relation [1,16]:(1)

Here the letter k represents the Boltzmann's constant. Bartenev and co-authors derived the above relation based on the free-volume theory by using some assumptions that were reported in [16]. The value of Tg was determined using calorimetric experiments reported by us in our previous work [17]. These values are shown in Table 1.

Once measuring the Tg and Hv values that are determined in the present work, the volume of micro-voids was calculated for each alloy. The values of Vh are tabulated in Table 1. One can see the rise in the value of Vh after the replacement of In atoms by foreign atoms of Sn, Ag, Sb, and Ge. Thus, one can expect a decrease in the density of the ternary alloys due to an increase in the Vh values. Consequently, the micro-hardness decreases with an increase in the volume of micro-voids. The variation of Hv with Vh is shown in Figure 4. It is interesting to note that Hv decreases linearly with Vh following an empirical relation Hv = –1.257 Vh + 100.

At room temperature, the number of network constraints governs the Hardness. Consequently, a crucial number of constraints is mandatory for a substance to demonstrate mechanical resistivity. Therefore, another possible explanation comes from the determination of fragility index F for the present glasses. The fragility index of a glassy alloy tells us whether the given material is mechanically fragile glass or a strong glass.

On basis of this approximation that the high frequencies shear modulus of glass-forming liquid is independent of temperature, the following relation was proposed for the determination of the fragility index [1822]:(2)

Here ΔEg is the activation energy involved in thermal relaxation in the vicinity of Tg of the alloy and k is Boltzmann's constant. The values of Tg were noted by running DSC scans of present samples in a standard DSC in non-isothermal mode at four heating rates and the ΔEg values were determined by well-known Moynihan theory.

Moynihan et al. interpreted the heating/cooling rate dependence of the Tg in chalcogenide glasses [2325] by considering the thermal relaxation phenomenon. They derived the following relation by assuming that the difference between the equilibrium liquid and glass heat capacities, (CpeCpg) is constant over the experimental range of Tg:(3)

Equation (3) shows that ln β vs 1/Tg plot should be straight line and the activation energy involved in the molecular motions and rearrangements around Tg can be calculated from the slope of this plot.

Table 1 shows the values of F too. Broadly speaking, the value of F is limited at a lower value (F ≈ 16) in the case of the kinetically strong-glass-forming (KS) liquids. However, such a limiting value is sufficiently high (F ≈ 200) in the case of the kinetically fragile-glass-forming (KF) liquids [1822]. The values of the fragility index for all samples are tabulated in Table 1. It is worthy to mention here that the fragility index has values for ternary Se90In6M4 (M = Sn, Ag, Sb, and Ge) alloys that are close to the KF limiting value, whereas the values of the fragility index are close to KS limiting value for the parent glass. This reveals that the glass network of binary Se90In10 alloy undergoes a structural transformation from KS to KF glass-forming criteria when Sn, Ag, Sb, and Ge are incorporated. Consequently, the micro-hardness of the ternary alloys is less as compared to parent Se90In10 glass.

Table 1

Values of Tg, Hv, Vh, and F for glassy Se90In10 and Se90In6M4 (M = Sn, Ag, Sb, and Ge) alloys.

thumbnail Fig. 4

Variation of micro-hardness Hv with the volume of micro-voids Vh.

5 Conclusions

The major conclusions drawn from the present work are listed below:

  • the value of Hv is reduced significantly after the addition of Sn, Ag, Sb, and Ge additives in binary Se90In10 alloy.

  • the volume of micro-voids in ternary Se90In6M4 (M = Sn, Ag, Sb, and Ge) alloys is more than that in Se90In10 parent glass.

  • an opposite relationship is obtained between the Hv and Vh volume of micro-voids for binary Se90In10 alloy and ternary Se90In6M4 (M = Sn, Ag, Sb, and Ge) alloys.

  • the incorporation of Sn, Ag, Sb, and Ge additives causes a transition of the glass network from kinetically strong-glass-forming kind behavior to kinetically fragile-glass-forming behavior.


The author (A. Dahshan) extends his appreciation to the Deanship of Scientific Research at King Khalid University for the financial support through research groups program under grant number (RGP.2/89/42).

Author contribution statement

Neeraj Mehta carried out the calorimetric experiment. H. Kumar carried out the hardness experiment. A. Dahshan wrote the manuscript with support from Neeraj Mehta.


  1. S.V. Boycheva, V.S. Vassilev, P. Petkova, J. Optoelectron. Adv. Mater. 3, 503 (2001) [Google Scholar]
  2. A. Elshafie, J. Phys. D: Appl. Phys. 29, 991 (1996) [Google Scholar]
  3. S.V. Boycheva, V.S. Vassilev, Z.G. Ivanova, J. Phys. D: Appl. Phys. 32, 529 (1999) [Google Scholar]
  4. A.K. Pattanaik, P.S. Robi, A. Srinivasan, J. Optoelectron. Adv. Mater. 5, 35 (2003) [Google Scholar]
  5. M.V. Siljegovic, S.R. Lukic Petrovic, F. Skuban, M. Avramov, L.S. Danin, Mater. Manuf. Processes 28, 96 (2012) [Google Scholar]
  6. R.J. Freitas, K. Shimakawa, S. Kugler, Chal. Lett. 10, 39 (2013) [Google Scholar]
  7. A. Dergal, K. Rahmoun, Y. Gueguin, J.C. Sangleboeuf, V. Keryvin, Phys. Proc. 55, 227 (2014) [Google Scholar]
  8. H. Kumar, A. Sharma, N. Mehta, Mater. Lett. 121, 194 (2014) [Google Scholar]
  9. A. Simunek, J. Vackar, Phys. Rev. Lett. 96, 085501 (2006) [Google Scholar]
  10. K. Li et al, Phys. Rev. Lett. 100, 235504 (2008) [Google Scholar]
  11. S.K. Arora, G.S. Trivikrama, N.M. Batra, J. Mater. Sci. 19, 297 (1984) [Google Scholar]
  12. M.M. Smedskjaer, J.C. Mauro, Y.Z. Yue, Phys. Rev. Lett. 105, 115503 (2010) [Google Scholar]
  13. N.A. Ghoneim, H.A. El Batal, A.M.A. Nassar, J. Non-Cryst. Solids 55, 343 (1983) [Google Scholar]
  14. M. Hammam, J.J. Santiago, J. Mater. Sci. 21, 4019 (1986) [Google Scholar]
  15. N. Miyata, H. Jinno, J. Mater. Sci. Lett. 1, 156 (1982) [Google Scholar]
  16. G.M. Bartenev, I.V. Razumovskaya, D. S. Sanditov, I.A. Lukyanov, J. Polym. Sci., Part A: Polym. Chem. 7, 2147 (1969) [Google Scholar]
  17. H. Kumar, N. Mehta, A. Kumar, J. Therm. Anal. Calorim. 103, 903 (2011) [Google Scholar]
  18. R. Bohmer, K.L. Nagi, C.A. Angell, D.J. Plazek, J. Chem. Phys. 99, 4201 (1993) [Google Scholar]
  19. T.A. Viglis, Phys. Rev. B 47, 2882 (1993) [Google Scholar]
  20. C.A. Solunov, Eur. Polym. J. 35, 1543 (1999) [Google Scholar]
  21. A. Saiter, M. Saiter, J. Grenet, Eur. Polym. J. 42, 213 (2006) [Google Scholar]
  22. A. Saiter, E. Dargent, J.M. Saiter, J. Grenet, J. Non-Cryst. Solids 354, 345 (2008) [Google Scholar]
  23. S.O. Kasap, C. Juhaz, J. Mater. Sci. 21, 1329 (1986) [Google Scholar]
  24. S.O. Kasap, in Handbook of imaging materials, edited by DiamondAS (Marcel Dekker, New York, 1991), p. 355 [Google Scholar]
  25. C.T. Moynihan, A.J. Easteal, J. Wilder, J. Tucker, J. Phys. Chem. 78, 2673 (1974) [Google Scholar]

Cite this article as: Alaa Dahshan, Horesh Kumar, Neeraj Mehta, Role of some modifiers on the thermo-mechanical properties of Se90In10 chalcogenide glass (ChGs), Eur. Phys. J. Appl. Phys. 94, 31101 (2021)

All Tables

Table 1

Values of Tg, Hv, Vh, and F for glassy Se90In10 and Se90In6M4 (M = Sn, Ag, Sb, and Ge) alloys.

All Figures

thumbnail Fig. 1

Diagram showing the geometrical overview of the indentation mark in micro-indentation experiment.

In the text
thumbnail Fig. 2

XRD pattern and DSC scan of glassy Se90In6Ag4 alloy.

In the text
thumbnail Fig. 3

Micrograph of the imprint on the surface of a sample (ternary Se98In6Sb4 alloy).

In the text
thumbnail Fig. 4

Variation of micro-hardness Hv with the volume of micro-voids Vh.

In the text

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.