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Critical analysis of the different glass stability criteria in chalcogenide glasses
Análisis crítico de los diferentes criterios de estabilidad del vidrio en vidrios de calcogenuro
S. Fouada, H.E. Atyiaa, Neeraj Mehtab,
Corresponding author
dr_neeraj_mehta@yahoo.co.in

Corresponding author.
a Departamento de Física, Facultad de Educación, Universidad Ain Shams, El Cairo, Egypt
b Departamento de Física, Instituto de Ciencias, Universidad Hindú Banaras, Varanasi, India
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    "textoCompleto" => "<span class="elsevierStyleSections"><span id="sec0005" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0020">Introduction</span><p id="par0005" class="elsevierStylePara elsevierViewall">Glass stability &#40;GS&#41; or thermal stability &#40;TS&#41; represents the resistance of the glass to the devitrification of glassy alloys through the nucleation and growth processes <a class="elsevierStyleCrossRefs" href="#bib0205">&#91;1&#8211;3&#93;</a>&#46; To determine thermal stability for glasses&#44; several parameters must be determined which are known as the glass stability criteria&#46; Glass stability criteria can be estimated based on the determination of the characteristic temperature values&#44; which determined using standard Differential Thermal Analysis &#40;DTA&#41; or Differential Scanning Calorimetry &#40;DSC&#41; methods&#46; In the present work&#44; the DTA technique was used to determine the characteristic temperatures at different heating rates&#46;</p><p id="par0010" class="elsevierStylePara elsevierViewall">The first endothermic peak in the DTA thermogram represented the peak glass transition temperature <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">g</span></span>&#44; Another peak is an exothermic peak that manifests the crystallization process and it appears due to an abrupt increase in the specific heat of the sample&#46; This exothermic peak has three characteristic points&#59; the first point is the onset temperature of crystallization <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">c</span></span>&#46; The second is the peak temperature of crystallization <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">p</span></span>&#44; The third is the finish temperature of crystallization <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">f</span></span>&#46; At higher temperatures in DTA pattern an endothermic peak appeared corresponds to the melting temperature <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">m</span></span>&#46;</p><p id="par0015" class="elsevierStylePara elsevierViewall">The advantages of the glass stability criteria are that they are an easy and fast estimation based upon the above mentioned characteristic temperatures&#46; Moreover&#44; the thermal stability of glass &#40;which is the indicator of resistance against crystallization&#41; and its tendency of glass formation &#40;i&#46;e&#46;&#44; glass-forming ability&#41; play an important role to determine the utility of chalcogenide alloys as the recording materials because that the phase-change optical recording and erasing technique based on laser-induced crystallization of chalcogenide glasses <a class="elsevierStyleCrossRef" href="#bib0220">&#91;4&#93;</a>&#46; Therefore&#44; the study of glass stability can be considered a great interest subject <a class="elsevierStyleCrossRef" href="#bib0225">&#91;5&#93;</a>&#46; On the other hand&#44; the study of the composition dependence on the thermal stability for recording materials is very important because the recording materials must remain stable in the amorphous state so that the life-time of the memory devices is large&#46; Further&#44; if we consider the rewritable memory devices&#44; then the crystallization rate of recording materials must be fast for erasing of the recorded spots so that a laser pulse of short duration can complete the erasing of data in a very short duration &#40;&#8764; nano-second to the pico-seconds range&#41;&#46;</p><p id="par0020" class="elsevierStylePara elsevierViewall">In chalcogenide glasses&#44; it is important to be aware of the knowledge of thermal stability because this parameter is very useful for the specific technological applications <a class="elsevierStyleCrossRefs" href="#bib0230">&#91;6&#8211;9&#93;</a>&#46; Thermal stability is the direct measurement of stability against crystallization and so the aging effects are found less dominant in the glasses having high thermal stability <a class="elsevierStyleCrossRefs" href="#bib0250">&#91;10&#44;11&#93;</a>&#46; Consequently&#44; it helps us in determining the optimized conditions for the durability of the optical devices made from chalcogenide glasses <a class="elsevierStyleCrossRefs" href="#bib0260">&#91;12&#44;13&#93;</a>&#46;</p><p id="par0025" class="elsevierStylePara elsevierViewall">In the present paper&#44; we determined and reported the glass stability of glassy SeTePb system&#44; by determining their glass stability criteria&#46; We can say that the main target of this work is related to the delimiting of the more stable alloy and both of the more suitable and sensitive GS criteria for the studied compositions and the less one&#46; Such investigations are very important for determining the utility of the chalcogenide glasses and these studies are found closely related to the durability of the devices fabricated from these materials <a class="elsevierStyleCrossRefs" href="#bib0270">&#91;14&#8211;19&#93;</a>&#46;</p></span><span id="sec0010" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0025">Experimental details</span><p id="par0030" class="elsevierStylePara elsevierViewall">For the thermal investigation of aforesaid glass stability criteria&#44; the samples were prepared by using a cost-effective and conventional melt-quench technique <a class="elsevierStyleCrossRefs" href="#bib0300">&#91;20&#8211;22&#93;</a>&#46; Appropriate amounts of 99&#46;999&#37; purity Se&#44; Te&#44; and Pb elements were weighted according to their atomic percentage and loaded in two silica tubes &#40;length 15<span class="elsevierStyleHsp" style=""></span>cm&#44; internal diameter 12<span class="elsevierStyleHsp" style=""></span>mm&#41; for two compositions &#40;Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">8</span>Pb<span class="elsevierStyleInf">2</span> and Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">4</span>Pb<span class="elsevierStyleInf">6</span>&#41; which then sealed under the vacuum of 10<span class="elsevierStyleSup">&#8722;5</span><span class="elsevierStyleHsp" style=""></span>Torr&#46; The contents of the tubes were heated gradually in an oscillatory furnace with rising temperature up to a suitably high value&#46; The tubes were kept at these temperatures for 10&#8211;12<span class="elsevierStyleHsp" style=""></span>h with frequent rocking to ensure the homogeneity of the melt&#46;</p><p id="par0035" class="elsevierStylePara elsevierViewall">The elements &#40;Se&#44; Te&#44; and Pb&#41; present in the sealed tube tend to have significant effects on the melting point of the collective system during the process of alloying&#46; Thus&#44; the melting point of the alloy is significantly lower as compared to the melting points of constituent elements&#46; Though the melting points of Se &#40;220<span class="elsevierStyleHsp" style=""></span>&#176;C&#41;&#44; Te &#40;449&#46;5<span class="elsevierStyleHsp" style=""></span>&#176;C&#41;&#44; and Pb &#40;327&#46;5<span class="elsevierStyleHsp" style=""></span>&#176;C&#41; are different&#44; but when they are mixed for alloying then the resulting alloy have a lower melting point&#46; Therefore&#44; we have chosen the maximum temperature &#8764;470<span class="elsevierStyleHsp" style=""></span>&#176;C in the melt-quench technique&#46; After sufficient heating and rocking of the tube at this appropriate temperature&#44; the molten materials were quenched in ice-cooled water to have glassy forms&#46; The bulk samples were taken out by breaking the silica ampoules&#46; These ingots were then ground into a fine powder using a pestle and mortar&#46; The grain size of the powdered samples was &#8764;5&#8211;10<span class="elsevierStyleHsp" style=""></span>&#956;m&#46; The thermal behavior was investigated using a differential thermal analyzer &#40;Shimadzu DTA-50&#41;&#46; Typically&#44; almost the same amount &#40;&#8764;5<span class="elsevierStyleHsp" style=""></span>mg&#41; of both samples in fine powder form were crimped in standard aluminum sample pans then&#44; heated at different heating rates&#46; The DTA analyses were carried out under non-isothermal conditions&#46; The temperature range covered in DTA was raised from room temperature 303 to 773<span class="elsevierStyleHsp" style=""></span>K&#46; DTA traces have been studied at five different heating rates &#40;from 10 to 50<span class="elsevierStyleHsp" style=""></span>K&#47;min&#41;&#46; The accuracy of the heat flow is &#177;0&#46;01<span class="elsevierStyleHsp" style=""></span>mW&#46; <a class="elsevierStyleCrossRef" href="#fig0005">Fig&#46; 1</a> shows the DTA scans of the samples at a particular heating rate &#40;50<span class="elsevierStyleHsp" style=""></span>K<span class="elsevierStyleHsp" style=""></span>min<span class="elsevierStyleSup">&#8722;1</span>&#41;&#46; Each DTA trace shows an endothermic peak and an exothermic corresponding to well-defined glass transition and crystallization&#46; The on-set temperature <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">x</span></span> of the glass transition peak is followed by glass transition temperature <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">g</span></span>&#46; Similarly&#44; the crystallization peak starts with the onset of crystallization temperature <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">c</span></span> and reaches to maximize value at peak crystallization temperature <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">p</span></span>&#46; At a higher temperature in the obtained DTA thermograms&#44; another endothermic peak represented the melting temperature <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">m</span></span>&#46; The temperature precision of this equipment is &#177;1<span class="elsevierStyleHsp" style=""></span>K with an average standard error of about &#177;0&#46;03 in the measured values of characteristic temperatures <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">g</span></span>&#44; <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">x</span></span><span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">c</span></span>&#44; <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">p</span></span>&#44; and <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">m</span></span>&#41;&#46; Similar results were obtained at other heating rates&#46; The homogeneity of our samples was checked by Energy dispersive X-ray &#40;EDX&#41; composition analysis&#46; From DTA scans&#44; it is evident that well-defined single endothermic and exothermic peaks appear during the glass transition and crystallization phenomenon in the samples&#46; Thus&#44; there is no sign of phase separation which also ensures the homogeneity of your samples&#46;</p><elsevierMultimedia ident="fig0005"></elsevierMultimedia></span><span id="sec0015" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0030">Results and discussion</span><span id="sec0020" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0035">Differential Thermal Analysis measurements &#40;DTA&#41;</span><p id="par0040" class="elsevierStylePara elsevierViewall">Differential thermal analysis DTA measurements have been carried out under non-isothermal conditions for glassy Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">8</span>Pb<span class="elsevierStyleInf">2</span> and Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">4</span>Pb<span class="elsevierStyleInf">6</span> compositions at different heating rates of 10&#44; 20&#44; 30&#44; 40&#44; and 50<span class="elsevierStyleHsp" style=""></span>K<span class="elsevierStyleHsp" style=""></span>min<span class="elsevierStyleSup">&#8722;1</span>&#46; The characteristic temperatures&#44; the glass transition <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">g</span></span>&#44; the onset crystallization <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">c</span></span>&#44; the peak crystallization <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">c</span></span>&#44; and melting <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">m</span></span> temperatures were extracted from the DTA thermograms for the studied compositions at different heating rates in the studied range&#46; These values and their interrelationship between them will be used to determine the glass stability criteria values according to different theories&#44; models&#44; and authors&#46; The change of these characteristic temperatures with the heating rate helps us to study and analyze the heating rate dependence of the glass stability criteria which play an important role to examine and evaluate them&#46;</p></span><span id="sec0025" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0040">Estimation of the glass stability criteria for the investigated compositions</span><p id="par0045" class="elsevierStylePara elsevierViewall">Various glass stability criteria related to the characteristic temperatures have been investigated&#44; in recent years&#44; according to several workers depending on a different theory&#46;</p><p id="par0050" class="elsevierStylePara elsevierViewall">Based on the thermal analysis of the crystallization process during cooling and reheating of the super-cooled liquid&#44; Lu and Liu <a class="elsevierStyleCrossRef" href="#bib0315">&#91;23&#93;</a> proposed a new criterion that is defined as Lu-Li criterion C<span class="elsevierStyleInf">LL</span>&#46; This criterion can be expressed according to the following equation&#58;<elsevierMultimedia ident="eq0005"></elsevierMultimedia></p><p id="par0055" class="elsevierStylePara elsevierViewall">It is necessary to mention that glass-forming ability and glass thermal stability are independent properties but they are empirically related to each other&#46; Therefore&#44; we have examined <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">LL</span></span> parameter as a glass stability criterion though&#44; originally&#44; this parameter was proposed by Lu and Liu as a new glass-forming ability criterion&#46;</p><p id="par0060" class="elsevierStylePara elsevierViewall">They <a class="elsevierStyleCrossRef" href="#bib0315">&#91;23&#93;</a> also suggested that the interrelationship between this new criterion and the critical cooling rate of critical section thickness is elaborated and discussed in comparison with two other parameters such as the reduced glass transition temperature <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">rg</span></span> which is given as &#40;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">rg</span></span><span class="elsevierStyleHsp" style=""></span>&#61;<span class="elsevierStyleHsp" style=""></span><span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">g</span></span>&#47;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">m</span></span>&#41; <a class="elsevierStyleCrossRef" href="#bib0320">&#91;24&#93;</a>&#46; In general&#44; <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">rg</span></span> values are almost constant which reflects the &#40;two-third rule&#41; for almost glassy alloys&#46; Turnbull <a class="elsevierStyleCrossRef" href="#bib0325">&#91;25&#93;</a> gave more details about the case of larger values above 2&#47;3 of <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf">rg</span>&#44; the homogeneous crystal nucleation will be essentially suppressed due to the sluggishness of crystallization kinetics&#46; Furthermore&#44; <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">rg</span></span> parameter has been considered an earlier parameter to evaluate the glass stability and glass formation ability&#46; Lu and Liu criterion <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">LL</span></span> can be recalculated using the maximum &#40;peak&#41; crystallization temperature <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">p</span></span> instead of the onset crystallization temperature <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">c</span></span> in the last equation <a class="elsevierStyleCrossRef" href="#bib0330">&#91;26&#93;</a>&#46; The heating rate dependence of <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">LL</span></span> criterion is shown in <a class="elsevierStyleCrossRef" href="#fig0010">Fig&#46; 2</a> for glassy Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">8</span>Pb<span class="elsevierStyleInf">2</span> and Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">4</span>Pb<span class="elsevierStyleInf">6</span> alloys respectively&#46;</p><elsevierMultimedia ident="fig0010"></elsevierMultimedia><p id="par0065" class="elsevierStylePara elsevierViewall">In &#40;2004&#41;&#44; Xioa et al&#46; <a class="elsevierStyleCrossRef" href="#bib0335">&#91;27&#93;</a> give an expression for a new criterion for the glass stability and glass formation ability as follows&#58;<elsevierMultimedia ident="eq0010"></elsevierMultimedia></p><p id="par0070" class="elsevierStylePara elsevierViewall">Mondal and Murty <a class="elsevierStyleCrossRef" href="#bib0340">&#91;28&#93;</a> proposed a new criterion to evaluate the glass stability for glasses using the following equation&#58;<elsevierMultimedia ident="eq0015"></elsevierMultimedia></p><p id="par0075" class="elsevierStylePara elsevierViewall">The values of C<span class="elsevierStyleInf">XF</span> and C<span class="elsevierStyleInf">MM</span> were calculated according to equations &#40;2 and 3&#41; with <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">c</span></span> as well as <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">p</span></span> and have been plotted versus the heating rate as shown in <a class="elsevierStyleCrossRefs" href="#fig0015">Figs&#46; 3 and 4</a> respectively for the studied compositions&#46;</p><elsevierMultimedia ident="fig0015"></elsevierMultimedia><elsevierMultimedia ident="fig0020"></elsevierMultimedia><p id="par0080" class="elsevierStylePara elsevierViewall">Chen et al&#46; <a class="elsevierStyleCrossRef" href="#bib0345">&#91;29&#93;</a> shown that both <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">rg</span></span> and <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">LL</span></span> criteria cannot in many cases reflect the glass stability&#46; So they developed a new criterion <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">CS</span></span>&#44; given by equation <a class="elsevierStyleCrossRef" href="#eq0020">&#40;4&#41;</a>&#44; based on the classical nucleation&#44; growth theory&#44; and respective of phase transformation kinetics&#46; Moreover&#44; Chen <a class="elsevierStyleCrossRef" href="#bib0345">&#91;29&#93;</a> used this new criterion to evaluate the glass stability and glass formation ability of bulk glasses in a wide range&#58;<elsevierMultimedia ident="eq0020"></elsevierMultimedia></p><p id="par0085" class="elsevierStylePara elsevierViewall">Considering that the glass stability related to crystallization resistance not only the liquid phase stability a modified <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">DH</span></span> criterion was reported by Du et al&#46; <a class="elsevierStyleCrossRef" href="#bib0350">&#91;30&#93;</a> as follows&#58;<elsevierMultimedia ident="eq0025"></elsevierMultimedia></p><p id="par0090" class="elsevierStylePara elsevierViewall">Moreover&#44; the above criterion shows a good correlation with the glass stability of different bulk glasses with the statistical correlation factor&#46;</p><p id="par0095" class="elsevierStylePara elsevierViewall">Du et al&#46; modified the <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">DH</span></span> criterion <a class="elsevierStyleCrossRef" href="#bib0355">&#91;31&#93;</a> and derived another new criterion as follows&#58;<elsevierMultimedia ident="eq0030"></elsevierMultimedia></p><p id="par0100" class="elsevierStylePara elsevierViewall">Here &#916;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">xg</span></span><span class="elsevierStyleHsp" style=""></span>&#61;<span class="elsevierStyleHsp" style=""></span><span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">x</span></span><span class="elsevierStyleHsp" style=""></span>&#8722;<span class="elsevierStyleHsp" style=""></span><span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">g</span></span>&#44; which is considered as a good indicator of thermal stability&#44; because the higher value of &#916;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">xg</span></span> causes the delay in nucleation&#46; <a class="elsevierStyleCrossRefs" href="#fig0025">Figs&#46; 5&#8211;7</a> show the calculated values of <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">CS</span></span>&#44; <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">DH</span></span>&#44; and <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">DH2</span></span> criteria respectively calculated according to <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">c</span></span> and <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">p</span></span> as well for the investigated compositions&#46;</p><elsevierMultimedia ident="fig0025"></elsevierMultimedia><elsevierMultimedia ident="fig0030"></elsevierMultimedia><elsevierMultimedia ident="fig0035"></elsevierMultimedia><p id="par0105" class="elsevierStylePara elsevierViewall">Fan et al&#46; <a class="elsevierStyleCrossRef" href="#bib0360">&#91;32&#93;</a> proposed a new dimensionless glass stability criterion based on a theoretical calculation using the fragility concept and nucleation theory for a model of glass formation system which indicates an excellent correlation with the critical cooling rate&#46; This criterion can be expressed according to the following equation&#46;<elsevierMultimedia ident="eq0035"></elsevierMultimedia></p><p id="par0110" class="elsevierStylePara elsevierViewall">Here <span class="elsevierStyleItalic">m</span> is an exponent equal to 0&#46;143 obtained by application of K<span class="elsevierStyleInf">F</span> criterion to different glasses <a class="elsevierStyleCrossRef" href="#bib0360">&#91;32&#93;</a>&#46; As shown in equation <a class="elsevierStyleCrossRef" href="#eq0035">&#40;7&#41;</a>&#44; the stability of glass can be quantified by the width of the super-cooled liquid region &#916;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">xg</span></span> because of the rapid decrease in the viscosity above T<span class="elsevierStyleInf">g</span>&#46; Therefore&#44; the overestimation of GFA using <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">rg</span></span> can be corrected by introducing &#916;T<span class="elsevierStyleInf">xg</span> in this criterion&#46;</p><p id="par0115" class="elsevierStylePara elsevierViewall">On the other hand&#44; a new criterion C<span class="elsevierStyleInf">YL</span> was proposed by Yuan et al&#46; <a class="elsevierStyleCrossRef" href="#bib0365">&#91;33&#93;</a> as follows&#58;<elsevierMultimedia ident="eq0040"></elsevierMultimedia></p><p id="par0120" class="elsevierStylePara elsevierViewall">Yuan et al&#46; reported that the C<span class="elsevierStyleInf">YL</span> criterion is statistically better than currently used criteria such as <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">CS</span></span> and <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">rg</span></span> and also was considered more sensitive than C<span class="elsevierStyleInf">FC</span> and C<span class="elsevierStyleInf">LL</span> criteria&#46;</p><p id="par0125" class="elsevierStylePara elsevierViewall"><a class="elsevierStyleCrossRefs" href="#fig0040">Figs&#46; 8 and 9</a> represented the plots of C<span class="elsevierStyleInf">FC</span> and C<span class="elsevierStyleInf">YL</span> criteria versus ln <span class="elsevierStyleItalic">&#946;</span> for amorphous Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">8</span>Pb<span class="elsevierStyleInf">2</span> and Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">4</span>Pb<span class="elsevierStyleInf">6</span> compositions respectively&#46;</p><elsevierMultimedia ident="fig0040"></elsevierMultimedia><elsevierMultimedia ident="fig0045"></elsevierMultimedia><p id="par0130" class="elsevierStylePara elsevierViewall">Based on the analysis of time-temperature transformation diagrams of glass formation using the fragility concept&#44; a dimensionless glass stability criterion <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">LX</span></span> can be written as&#58;<elsevierMultimedia ident="eq0045"></elsevierMultimedia></p><p id="par0135" class="elsevierStylePara elsevierViewall">This <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">LX</span></span> criterion was proposed by Long et al&#46; <a class="elsevierStyleCrossRef" href="#bib0370">&#91;34&#93;</a>&#46; They reported that this criterion exhibits the strongest correlation with the critical cooling rate for glass formation among all currently available glass stability criteria&#46;</p><p id="par0140" class="elsevierStylePara elsevierViewall">Another new criterion <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">ZW</span></span> has been proposed by Zhang et al&#46; <a class="elsevierStyleCrossRef" href="#bib0375">&#91;35&#93;</a> to evaluate the glass stability for bulk glasses&#46; This criterion can be expressed as follows&#58;<elsevierMultimedia ident="eq0050"></elsevierMultimedia></p><p id="par0145" class="elsevierStylePara elsevierViewall">Whereas&#44; the glass stability of glasses could be in proportion to the &#40;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">g</span></span>&#47;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">m</span></span>&#41; and &#40;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">c</span></span><span class="elsevierStyleHsp" style=""></span>&#43;<span class="elsevierStyleHsp" style=""></span>&#916;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">xg</span></span>&#41;&#47;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">g</span></span>&#41; values which can be used to characterize the liquid phase stability and crystallization resistance respectively&#46;</p><p id="par0150" class="elsevierStylePara elsevierViewall">Since the glass stability is defined from the cooling of the glass-forming liquid&#44; Guo and Liu et al&#46; <a class="elsevierStyleCrossRef" href="#bib0380">&#91;36&#93;</a> derived a new glass stability criterion <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">GL</span></span> as follows&#58;<elsevierMultimedia ident="eq0055"></elsevierMultimedia></p><p id="par0155" class="elsevierStylePara elsevierViewall">Considering the relationship between the cooling and heating process&#44; this criterion correlates well to the critical cooling rate and agrees exceptionally with the physically acceptable boundary condition <a class="elsevierStyleCrossRef" href="#bib0380">&#91;36&#93;</a>&#46;</p><p id="par0160" class="elsevierStylePara elsevierViewall">The heating rate dependence of the above criteria <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">LX</span></span>&#44; <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">ZW</span></span>&#44; and <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">GL</span></span> values according to equations 9&#44; 10&#44; and 11 &#40;with T<span class="elsevierStyleInf">c</span> as well as T<span class="elsevierStyleInf">p</span>&#41; is shown in <a class="elsevierStyleCrossRefs" href="#fig0050">Figs&#46; 10&#8211;12</a> respectively&#46;</p><elsevierMultimedia ident="fig0050"></elsevierMultimedia><elsevierMultimedia ident="fig0055"></elsevierMultimedia><elsevierMultimedia ident="fig0060"></elsevierMultimedia></span><span id="sec0030" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0045">Features of thermal stability parameters</span><p id="par0165" class="elsevierStylePara elsevierViewall">Different comments can be concluded to describe the thermal stability aspects for the two studied compositions&#46; Both of the two calculated glass stability criteria groups&#44; based on the data of the corresponding maximum &#40;peak&#41; crystallization temperature <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">p</span></span> instead of the onset crystallization temperature <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">c</span></span>&#44; have similar behavior as a function of composition as seen in <a class="elsevierStyleCrossRefs" href="#tbl0005">Tables 1 and 2</a>&#44; whereas both of them have incompatible values for amorphous Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">8</span>Pb<span class="elsevierStyleInf">2</span> and Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">4</span>Pb<span class="elsevierStyleInf">6</span> compositions respectively&#46; Furthermore&#44; all of the glass stability criteria which calculated according to the peak crystallization temperature <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">p</span></span> have larger values than that calculated with the onset crystallization temperature <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">c</span></span> except two new criteria <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">LX</span></span> and <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">ZW</span></span> which have opposite behavior for the two studied compositions as shown in <a class="elsevierStyleCrossRefs" href="#fig0050">Figs&#46; 10 and 11</a>&#46;</p><elsevierMultimedia ident="tbl0005"></elsevierMultimedia><elsevierMultimedia ident="tbl0010"></elsevierMultimedia><p id="par0170" class="elsevierStylePara elsevierViewall">As seen&#44; in general&#44; all the glass stability criteria &#40;with <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">p</span></span> and <span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">c</span></span>&#41; have the same behavior against the heating rate for Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">8</span>Pb<span class="elsevierStyleInf">2</span> amorphous compositions&#46; Since they were found to increase with increasing heating rate except for <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">LX</span></span> and <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">ZW</span></span> criteria where their values were found to decrease with increasing heating rate in the Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">8</span>Pb<span class="elsevierStyleInf">2</span> and Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">4</span>Pb<span class="elsevierStyleInf">6</span> compositions&#46;</p><p id="par0175" class="elsevierStylePara elsevierViewall">According to the above results&#44; one can conclude that the two new criteria <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">LX</span></span> and <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">ZW</span></span> have been considered not suitable to evaluate and examine the glass stability for the two studied compositions&#46;</p><p id="par0180" class="elsevierStylePara elsevierViewall">The larger values of all glass stability criteria have been observed in the studied compositions with the lowest Lead content &#40;Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">8</span>Pb<span class="elsevierStyleInf">2</span> composition&#41; than that of &#40;Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">4</span>Pb<span class="elsevierStyleInf">6</span> composition&#41;&#46; This result concluded that the decrease of the glass stability of the SeTePb system with increasing Pb content may be attributed to the decrease of the bond energy with increasing Pb content&#46; The addition of Pb atoms in Se&#8211;Te system reduces the effective bond energies of Se&#8211;Se bonds &#40;79&#46;5<span class="elsevierStyleHsp" style=""></span>kcal<span class="elsevierStyleHsp" style=""></span>mol<span class="elsevierStyleSup">&#8722;1</span>&#41; and Se&#8211;Te bonds &#40;64<span class="elsevierStyleHsp" style=""></span>kcal<span class="elsevierStyleHsp" style=""></span>mol<span class="elsevierStyleSup">&#8722;1</span>&#41; by forming the lower bond energies as Se&#8211;Pb bonds &#40;72&#46;4<span class="elsevierStyleHsp" style=""></span>kcal<span class="elsevierStyleHsp" style=""></span>mol<span class="elsevierStyleSup">&#8722;1</span>&#41; and Te&#8211;Pb bonds &#40;60<span class="elsevierStyleHsp" style=""></span>kcal<span class="elsevierStyleHsp" style=""></span>mol<span class="elsevierStyleSup">&#8722;1</span>&#41; <a class="elsevierStyleCrossRef" href="#bib0385">&#91;37&#93;</a>&#46; This reveals that the studied Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">8</span>Pb<span class="elsevierStyleInf">2</span> is more stable glass&#46;</p></span><span id="sec0035" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0050">Estimation of the most suitable and sensitive glass stability criterion and the less one for the studied compositions</span><p id="par0185" class="elsevierStylePara elsevierViewall">All the criteria have been displayed and discussed for the investigation compositions&#46; But their values have been considered not enough to evaluate glass stability for the studied compositions&#46;</p><p id="par0190" class="elsevierStylePara elsevierViewall">Another more important parameter called a relative change parameter <span class="elsevierStyleItalic">P</span> must be determined&#46; This parameter requires estimating the largest relative changes of the glass stability criterion concerning the relative change parameters of the other glass stability criteria&#46; The parameter <span class="elsevierStyleItalic">P</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">RC</span></span> which determined for different criteria can be expressed as follows <a class="elsevierStyleCrossRef" href="#bib0390">&#91;38&#93;</a>&#58;<elsevierMultimedia ident="eq0060"></elsevierMultimedia></p><p id="par0195" class="elsevierStylePara elsevierViewall">Here both <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">max</span></span> and <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">nim</span></span> are the certain criterion values estimated at maximum and minimum heating rate values respectively&#46; The values of the <span class="elsevierStyleItalic">P</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">RC</span></span> parameter for the different proposed glass stability criteria have been given in <a class="elsevierStyleCrossRefs" href="#tbl0015">Tables 3 and 4</a> for glassy Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">8</span>Pb<span class="elsevierStyleInf">2</span> and Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">4</span>Pb<span class="elsevierStyleInf">6</span> compositions respectively&#46; The different <span class="elsevierStyleItalic">P</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">RC</span></span> values corresponding to different glass stability criteria can be explained according to the change in the different values of &#40;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">g</span></span><span class="elsevierStyleHsp" style=""></span>&#8764;<span class="elsevierStyleHsp" style=""></span><span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">c</span></span>&#41; and &#40;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">m</span></span><span class="elsevierStyleHsp" style=""></span>&#8764;<span class="elsevierStyleHsp" style=""></span><span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">g</span></span>&#41; or between &#40;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">g</span></span><span class="elsevierStyleHsp" style=""></span>&#8764;<span class="elsevierStyleHsp" style=""></span><span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">p</span></span>&#41; and &#40;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">g</span></span><span class="elsevierStyleHsp" style=""></span>&#8764;<span class="elsevierStyleHsp" style=""></span><span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">m</span></span>&#41; at different heating rates&#46; The composition dependence of <span class="elsevierStyleItalic">P</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">RC</span></span> parameter values for different studied glass stability criteria shows that&#46; The <span class="elsevierStyleItalic">P</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">RC</span></span> parameter values for Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">8</span>Pb<span class="elsevierStyleInf">2</span> composition are higher than their values for Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">4</span>Pb<span class="elsevierStyleInf">6</span> composition&#46;</p><elsevierMultimedia ident="tbl0015"></elsevierMultimedia><elsevierMultimedia ident="tbl0020"></elsevierMultimedia><p id="par0200" class="elsevierStylePara elsevierViewall">The data was extracted from <a class="elsevierStyleCrossRefs" href="#tbl0015">Tables 3 and 4</a> can be plotted in <a class="elsevierStyleCrossRef" href="#fig0065">Fig&#46; 13</a> to show the values of relative change parameter P for different studied criteria&#46; As seen from <a class="elsevierStyleCrossRefs" href="#tbl0015">Tables 3 and 4</a> and <a class="elsevierStyleCrossRef" href="#fig0065">Fig&#46; 13</a> as well&#44; the most sensitive and suitable criterion is Yuan et al&#46; <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">YL</span></span>&#44; which have the greatest relative change parameter value for two studied compositions than other criteria&#46; Also&#44; the criteria itself have the greatest value as comparing with anther studied criteria&#46; The variation of the more suitable and more sensitive criterion <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">YL</span></span> with the heating rate is shown in <a class="elsevierStyleCrossRef" href="#fig0070">Fig&#46; 14</a> for both samples&#46; Meanwhile&#44; the less sensitive criterion is the Mondal and Murty criterion <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">MM</span></span> for glassy Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">8</span>Pb<span class="elsevierStyleInf">2</span> and Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">4</span>Pb<span class="elsevierStyleInf">6</span> compositions&#46;</p><elsevierMultimedia ident="fig0065"></elsevierMultimedia><elsevierMultimedia ident="fig0070"></elsevierMultimedia></span><span id="sec0040" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0055">Glass stability criterions based on the rate of crystallization and their correlation with other stability criterions</span><p id="par0205" class="elsevierStylePara elsevierViewall">To evaluate the stability in glasses&#44; some stability criterions based on the rate of crystallization were also developed&#46; Hu et al&#46; <a class="elsevierStyleCrossRef" href="#bib0395">&#91;39&#93;</a> and Vazquez et al&#46; <a class="elsevierStyleCrossRef" href="#bib0400">&#91;40&#93;</a> proposed the following <span class="elsevierStyleItalic">K</span>&#40;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">p</span></span>&#41; and <span class="elsevierStyleItalic">K</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">R</span></span>&#40;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">p</span></span>&#41; criteria respectively&#58;<elsevierMultimedia ident="eq0065"></elsevierMultimedia><elsevierMultimedia ident="eq0070"></elsevierMultimedia></p><p id="par0210" class="elsevierStylePara elsevierViewall">Here <span class="elsevierStyleItalic">H</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">R</span></span> is Hruby glass-forming ability parameter which is itself a stability factor and can be expressed as&#58;<elsevierMultimedia ident="eq0075"></elsevierMultimedia></p><p id="par0215" class="elsevierStylePara elsevierViewall">The values of <span class="elsevierStyleItalic">K</span>&#40;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">p</span></span>&#41; and <span class="elsevierStyleItalic">K</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">R</span></span>&#40;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">p</span></span>&#41; criteria are tabulated in <a class="elsevierStyleCrossRefs" href="#tbl0025">Tables 5 and 6</a> for the present samples at all heating rates&#46; From these tables&#44; it is clear that the rate of crystallization is fast for Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">4</span>Pb<span class="elsevierStyleInf">6</span> alloy as compared to Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">8</span>Pb<span class="elsevierStyleInf">2</span> because of the value of <span class="elsevierStyleItalic">K</span>&#40;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">p</span></span>&#41; and <span class="elsevierStyleItalic">K</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">R</span></span>&#40;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">p</span></span>&#41; are higher for Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">4</span>Pb<span class="elsevierStyleInf">6</span> alloy as compared to Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">8</span>Pb<span class="elsevierStyleInf">2</span> alloy&#46; Thus&#44; the results of <span class="elsevierStyleItalic">K</span>&#40;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">p</span></span>&#41; and <span class="elsevierStyleItalic">K</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">R</span></span>&#40;<span class="elsevierStyleItalic">T</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">p</span></span>&#41; criteria are consistent with all stability criteria except C<span class="elsevierStyleInf">LX</span> and C<span class="elsevierStyleInf">ZW</span> criteria&#46;</p><elsevierMultimedia ident="tbl0025"></elsevierMultimedia><elsevierMultimedia ident="tbl0030"></elsevierMultimedia></span></span><span id="sec0045" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0060">Conclusions</span><p id="par0220" class="elsevierStylePara elsevierViewall">Different characteristic temperatures &#40;the glass transition peak T<span class="elsevierStyleInf">g</span>&#44; the onset temperature of crystallization T<span class="elsevierStyleInf">c</span>&#44; the peak temperature of crystallization T<span class="elsevierStyleInf">p</span>&#44; the melting temperature T<span class="elsevierStyleInf">m</span>&#41; have been determined from Differential Thermal Analysis &#40;DTA&#41; measurements under the non-isothermal conditions at different heating rates &#40;10&#44; 20&#44; 30&#44; 40&#44; and 50<span class="elsevierStyleHsp" style=""></span>K<span class="elsevierStyleHsp" style=""></span>min<span class="elsevierStyleSup">&#8722;1</span>&#41;&#46; Based on the interrelationship between these characteristic temperatures&#44; the more recently various glass stability criteria &#40;<span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">CS</span></span>&#44; <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">XF</span></span>&#44; <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">LL</span></span>&#44; <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">MM</span></span>&#44; <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">DH</span></span>&#44; etc&#46;&#41; have been estimated and studied as a function of heating rate and composition as well&#46; They have been found to increase with increasing heating rate except for <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">LX</span></span> and <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">ZW</span></span> criteria where their values were found decrease with increasing heating rate in the Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">8</span>Pb<span class="elsevierStyleInf">2</span> and Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">4</span>Pb<span class="elsevierStyleInf">6</span> alloys&#46; The two new criteria <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">LX</span></span> and <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">ZW</span></span> have been considered not suitable to evaluate and examine the glass stability for the two studied compositions&#46; The stability criteria of Hu et al and Vazquez et al based on Arrhenius dependence of rate constant K are also analyzed and they have shown excellent agreement with all other stability criteria except <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">LX</span></span> and <span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">ZW</span></span> criteria&#46;</p><p id="par0225" class="elsevierStylePara elsevierViewall">The comparative analysis shows that the larger values of all glass stability criteria have been observed for the sample having the lowest Lead content of atomic weight percentage 2&#46; The most sensitive and suitable criterion is Yuan et al&#46; C<span class="elsevierStyleInf">YL</span>&#44; which have the greatest relative change parameter value for two studied compositions than other criteria and the less one is the Mondal and Murty criterion C<span class="elsevierStyleInf">MM</span> for glassy Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">8</span>Pb<span class="elsevierStyleInf">2</span> and Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">4</span>Pb<span class="elsevierStyleInf">6</span> alloys&#46; No direct link has been observed between the structure of the two glasses with the process of glass-formation and criteria applicability at the present stage&#46; We are hopeful that the future experiments in this direction could provide the qualitative information to reveal some connection between the structural properties&#44; the process of glass-formation&#44; and criteria applicability&#46;</p></span></span>"
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          "identificador" => "sec0005"
          "titulo" => "Introduction"
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        4 => array:2 [
          "identificador" => "sec0010"
          "titulo" => "Experimental details"
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          "titulo" => "Results and discussion"
          "secciones" => array:5 [
            0 => array:2 [
              "identificador" => "sec0020"
              "titulo" => "Differential Thermal Analysis measurements &#40;DTA&#41;"
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            1 => array:2 [
              "identificador" => "sec0025"
              "titulo" => "Estimation of the glass stability criteria for the investigated compositions"
            ]
            2 => array:2 [
              "identificador" => "sec0030"
              "titulo" => "Features of thermal stability parameters"
            ]
            3 => array:2 [
              "identificador" => "sec0035"
              "titulo" => "Estimation of the most suitable and sensitive glass stability criterion and the less one for the studied compositions"
            ]
            4 => array:2 [
              "identificador" => "sec0040"
              "titulo" => "Glass stability criterions based on the rate of crystallization and their correlation with other stability criterions"
            ]
          ]
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        6 => array:2 [
          "identificador" => "sec0045"
          "titulo" => "Conclusions"
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        7 => array:2 [
          "identificador" => "xack569283"
          "titulo" => "Acknowledgments"
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        8 => array:1 [
          "titulo" => "References"
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    "fechaRecibido" => "2020-03-10"
    "fechaAceptado" => "2020-05-25"
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          "clase" => "keyword"
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          "palabras" => array:2 [
            0 => "Vidrios de calcogenuro"
            1 => "Estabilidad del vidrio"
          ]
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      ]
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    "resumen" => array:2 [
      "en" => array:2 [
        "titulo" => "Abstract"
        "resumen" => "<span id="abst0005" class="elsevierStyleSection elsevierViewall"><p id="spar0005" class="elsevierStyleSimplePara elsevierViewall">In this endeavor&#44; various glass stability criteria have been discussed by using two ternary alloys of SeTePb glassy system&#46; These criteria can be obtained based on the interrelationship between the characteristic temperatures&#46; Differential Thermal Analysis measurements under the non-isothermal conditions can be used for this purpose&#46; Two groups of these criteria according to the onset and peak crystallization temperaturas have been studied as a function of composition&#46; The heating rate and composition dependences of all criteria concluded that the C ZW and C LX criteria are not suitable to discuss the glass stability &#40;GS&#41; for the studied compositions&#46; The extracted data from various GS criteria and their relative change parameters reveal that the criterion C YL of Yuan et al is best and it exhibits the best ability for apprising the GS&#46;</p></span>"
      ]
      "es" => array:2 [
        "titulo" => "Resumen"
        "resumen" => "<span id="abst0010" class="elsevierStyleSection elsevierViewall"><p id="spar0010" class="elsevierStyleSimplePara elsevierViewall">En este esfuerzo se han discutido varios criterios de estabilidad del vidrio utilizando dos aleaciones ternarias del sistema v&#237;treo SeTePb&#46; Estos criterios pueden obtenerse en funci&#243;n de la interrelaci&#243;n entre las temperaturas caracter&#237;sticas&#46; Las mediciones de an&#225;lisis t&#233;rmico diferencial en condiciones no isot&#233;rmicas se pueden utilizar para este prop&#243;sito&#46; Se han estudiado dos grupos de estos criterios seg&#250;n las temperaturas de inicio y pico de cristalizaci&#243;n en funci&#243;n de la composici&#243;n&#46; La tasa de calentamiento y las dependencias de composici&#243;n de todos los criterios concluyeron que el criterio Zhang-Wei CZW y el criterio Long-Xie CLX no son adecuados para discutir la estabilidad del vidrio &#40;GS&#41; para las composiciones estudiadas&#46; Los datos extra&#237;dos de varios criterios de estabilidad del vidrio y sus par&#225;metros de cambio relativo revelan que el criterio CYL de Yuan-Lu es el mejor y exhibe la mejor capacidad para conocer el GS&#46;</p></span>"
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                  """
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          "en" => "<p id="spar0090" class="elsevierStyleSimplePara elsevierViewall">Glass stability criteria values for glassy Se90Te4Pb6 alloy&#46;</p>"
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          "en" => "<p id="spar0095" class="elsevierStyleSimplePara elsevierViewall">Values of relative change parameters of different glass stability criteria &#40;calculating with the onset crystallization temperature T<span class="elsevierStyleInf">c</span>&#41; for glassy Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">8</span>Pb<span class="elsevierStyleInf">2</span> and Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">4</span>Pb<span class="elsevierStyleInf">6</span> alloys&#46;</p>"
        ]
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                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
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                  \t\t\t\t" scope="col">Composition&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t  " colspan="11" align="center" valign="\n
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                  \t\t\t\t" scope="col" style="border-bottom: 2px solid black">Relative change parameter</th></tr><tr title="table-row"><th class="td" title="\n
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                  \t\t\t\t  " align="" valign="\n
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                  \t\t\t\t" scope="col" style="border-bottom: 2px solid black">&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t" scope="col" style="border-bottom: 2px solid black">PYL&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t  " align="center" valign="\n
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                  \t\t\t\t\t\t</th><th class="td" title="\n
                  \t\t\t\t\ttable-head\n
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                  \t\t\t\t\ttable-head\n
                  \t\t\t\t  " align="center" valign="\n
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                  \t\t\t\t" scope="col" style="border-bottom: 2px solid black">PMM&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t\t\t</th></tr></thead><tbody title="tbody"><tr title="table-row"><td class="td-with-role" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
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                  \t\t\t\t">Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">8</span>Pb<span class="elsevierStyleInf">2</span>&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">0&#46;0890&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t">&#8722;0&#46;558&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t  " align="char" valign="\n
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                  \t\t\t\t">0&#46;470&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="char" valign="\n
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                  \t\t\t\t">0&#46;067&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="char" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">0&#46;238&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="char" valign="\n
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                  \t\t\t\t">0&#46;040&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="char" valign="\n
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                  \t\t\t\t">0&#46;041&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="char" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">0&#46;043&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="char" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">0&#46;025&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">4</span>Pb<span class="elsevierStyleInf">6</span>&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="char" valign="\n
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                  \t\t\t\t">0&#46;0002&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="char" valign="\n
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                  \t\t\t\t">0&#46;005&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="char" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">&#8722;0&#46;023&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="char" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">0&#46;013&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="char" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">0&#46;096&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="char" valign="\n
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                  \t\t\t\t">0&#46;047&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
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                  \t\t\t\t\ttop\n
                  \t\t\t\t">&#8722;0&#46;053&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="char" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">0&#46;004&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="char" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">0&#46;010&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="char" valign="\n
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                  \t\t\t\t">0&#46;007&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t">0&#46;002&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr></tbody></table>
                  """
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          "en" => "<p id="spar0100" class="elsevierStyleSimplePara elsevierViewall">Values of relative change parameters of different glass stability criteria &#40;calculating with the maximum &#40;peak&#41; crystallization temperature T<span class="elsevierStyleInf">p</span>&#41; for glassy Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">8</span>Pb<span class="elsevierStyleInf">2</span> and Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">4</span>Pb<span class="elsevierStyleInf">6</span> alloys&#46;</p>"
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          "en" => "<p id="spar0105" class="elsevierStyleSimplePara elsevierViewall">Values of stability criteria of Hu et al&#46; <a class="elsevierStyleCrossRef" href="#bib0395">&#91;39&#93;</a> and Vazquez et al&#46; <a class="elsevierStyleCrossRef" href="#bib0400">&#91;40&#93;</a> for glassy Se<span class="elsevierStyleInf">90</span>Te<span class="elsevierStyleInf">8</span>Pb<span class="elsevierStyleInf">2</span> alloy&#46;</p>"
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