Interpretation of crystallization kinetics results provided by DSC

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Thermochimica Acta 526 (2011) 237– 251

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Interpretation of crystallization kinetics results provided by DSC

Roman Svoboda ∗, Jirí MálekDepartment of Physical Chemistry, Faculty of Chemical Technology, University of Pardubice, Studentská 573, 532 10 Pardubice, Czech Republic

a r t i c l e i n f o

Article history:Received 27 June 2011Received in revised form 1 October 2011Accepted 3 October 2011Available online 8 October 2011

PACS:64.70.ph81.10.Aj

Keywords:Crystallization kineticsDSCComplex processesSe70Te30

a b s t r a c t

Differential scanning calorimetry (DSC) measurements were used to study crystallization in the Se70Te30

glass under non-isothermal conditions. The crystallization kinetics was described in terms of thenucleation-growth Johnson–Mehl–Avrami and autocatalytic Sesták–Berggren models.

An extensive discussion of all aspects of a full-scale kinetic study for a complex crystallization processwas performed. Number of suggestions regarding the experimental part (sample and glass preparation,temperature programs, data acquisition, etc.) was introduced to maximize precision and reproducibil-ity of the experimental data. Complexity of the crystallization process was in this particularly describedcase represented by very closely overlapping consecutive competing surface and bulk nucleation-growthmechanisms. Mutual interactions of both mechanisms as well as all other observed effects were explainedin terms of thermal gradients, surface crystallization centres arising from the sample preparation treat-ments and changing amount of volume nuclei originating from the combination of pre-nucleation periodand the very glass preparation phase. Advanced error analysis was performed for each step of the kineticstudy.

Objective of the presented study was to demonstrate extensity of information the differential scanningcalorimetry is able to provide and, furthermore, to show how a thorough kinetic analysis may lead toreliable, valid and detailed description of complex processes as well as to interpretations of any observabletrend occurring in experimental data.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Crystallization process and its kinetics can be studied on variousphysical properties by numerous experimental techniques. Never-theless, generally one of the two main approaches is always beingapplied. Either a macroscopic property (enthalpy, volume, electricconductivity, etc.) is observed during the crystallization and thechange of the property is considered to be representing the over-all process kinetics, or during a so-called microscopic approach thenuclei/crystals and their growth are observed directly on the micro-or nanoscale. Various microscopic or probe techniques are usuallyused here.

Regarding the macroscopic approach, the differential thermalanalysis (DTA) and differential scanning calorimetry (DSC) belongto the most commonly used techniques. Both these methods allowregistering of basically every process during which enthalpy changeoccurs. Thorough description of these methods can be found in [1].Despite the high universality of these techniques (they can be usedfor studying various phase transformations and reaction kinetics,determination of heat capacities or heat conductivities, evaluation

∗ Corresponding author. Tel.: +420 466 037 346.E-mail address: [email protected] (R. Svoboda).

of impurities content, etc.), there are also several disadvantagesassociated with them. As in the case of almost all “macroscopic”thermal analysis methods, the two most important issues of TAinstruments are the detection limit and the time constant. Regard-ing the former, the sensitivity of modern DSC devices is usually veryhigh. Nevertheless, even in this case it is a common issue that forvery slow processes (slow evolution of heat) the signal is eitherbelow the detection limit (on the level of noise) or if it is reg-istered, the uncertainty of baseline subtraction causes extremelylarge errors and deforms the measured data. This issue could be,naturally, solved by increasing the measured amount of the mate-rial (for higher total mass the signal-to-noise would increase).However, this is where the instrument/experiment time constantcomes into question. Higher mass of the sample not only meanslarger thermal effects but also larger thermal gradients that canagain deform the measured signal. Concerning the thermal effectsstudied within the framework of this article, the process of nucle-ation obviously involves only a very small amount of material andits direct observation is impossible due to the signal being com-pletely dissipated or lost within the baseline noise. Nucleation canbe therefore by macroscopic TA methods studied only indirectly –in the form of an influence on the measurable crystallization effect.The crystallization (or more precisely the crystal growth), on theother hand, is usually a well pronounced event associated with a

0040-6031/$ – see front matter © 2011 Elsevier B.V. All rights reserved.doi:10.1016/j.tca.2011.10.005

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large amount of evolved heat. However, even for such process theabove mentioned techniques may fail. For example, when the evo-lution of crystallization heat is too fast, the quality of kinetic datamight be due to thermal inertia of the device adversely effected.Similarly limited may be the usage of DTA or DSC in the cases ofvery slow processes (as was already mentioned above) or for crys-tallization of diluted systems, where the thermal effect is close tothe limit of detection.

In addition, apart from the very question of ability to correctlyregister the heat changes associated with the studied thermaleffect, also the complexity of the studied crystallization processmay in some cases limit the researchers from performing or com-pleting full kinetic analysis. This in particular is quite a commonevent and issue of present-day publications dealing with crystal-lization in glasses [e.g. 2–4]. The complexity of the process maybe represented by, e.g. competing surface and bulk crystallizationmechanisms or by a change of the mechanism with experimen-tal conditions. In all these cases it is regular practice to pronouncethe crystallization process to be “complex” and “indescribable”.Although recently an excellent work by Vyazovkin et al. [5] review-ing the kinetic analysis methods and a work by Perejón et al.[6] suggesting a novel crystallization peak deconvolution proce-dure were published, authors feel that there is still somethingmissing on the field of evaluation of complex kinetic processes –namely emphasizing of the interpretation potential of establishedmethodology in combination with nowadays precise experimentaltechniques. Main purpose of this article is to show that it is notonly possible to perform complete kinetic analysis even for com-plex processes but also that the complexity of the process can giveus additional and valuable information about the kinetic behav-ior of the studied material. In addition, several new ideas relatedto the evaluation and consequent interpretation of complex crys-tallization data will be presented and an attempt to reveal andintroduce full potential of the DSC technique in regard to studyingcrystallization kinetics in glasses will be made.

Chalcogenide glass with composition Se70Te30 was chosen as amodel material due to the complex crystallization kinetics beingobserved in this system recently [7]. Chalcogenide glasses havebeen studied intensively during the past decades due to theirunique physical properties, namely low and often also close tem-peratures of glass transition and crystallization, large variety incrystallization tendency strongly depending on actual composi-tions, great distinction of amorphous and crystalline state bymeans of their reflectivity or electrical conductivity, numerous pho-toconductive effects or high transmittance in near, middle andfar infrared region. Utilization of these properties then leads tonumerous very important hi-tech applications in which often thecrystallization process plays a key role. This is another reason whywe should try to maximize our understanding to all aspects of thisimportant process.

2. Theory

Crystallization kinetics in glasses is very often studied by dif-ferential scanning calorimetry, DSC. The kinetic equation of DSCcrystallization peak can be described [8] as:

= �H · A · e−E/RT · f (˛) (1)

where is the measured heat flow, �H is the crystallizationenthalpy, A is the pre-exponential factor, E is the apparent acti-vation energy of the process, R is the universal gas constant, T istemperature and f(˛) stands for an expression of a kinetic modelwith being conversion.

In order to describe the crystallization process by means of fullkinetic analysis Eq. (1) has to be evaluated. As the question of

correct �H determination will be discussed in Section 3, first step ofthe kinetic analysis discussed within the framework of Theoreticalsection will be calculation of apparent activation energy of crystal-lization. There are numerous methods to calculate the activationenergy E, however, probably the three most commonly and oftenused are the Kissinger [9], Ozawa [10] and Friedman [11] methods.

The methods by Kissinger and Ozawa are both applicable onlyunder non-isothermal conditions and are based on the shift of themaximum of the crystallization peak Tp with heating rate q+ accord-ing to the following equations:

ln

(q+

T2p

)= − E

RTp+ const. (2)

ln(q+) = −1.0516E

RTp+ const. (3)

Both these methods are based on an assumption that the con-version degree corresponding to the maximum crystallizationrate is constant and independent of experimental conditions. Thisassumption is in fact the fundamental essence of the Friedman’sisoconversional method. In this method the apparent activationenergy is calculated for various degrees of conversion accordingto the following equation:

ln(˚˛) = − E

RT˛+ const. (4)

where Ф˛ and T˛ are the specific heat flow and temperature corre-sponding to certain chosen value of conversion ˛. The experimentaldata are here obtained again from crystallization curves measuredat different heating rates and are plotted for each value of sepa-rately. In this way eventually the dependence of activation energy Eon the degree of conversion is obtained. Due to the large influenceof experimental conditions on the data quality of the crystalliza-tion peak tails, it is a common practice to consider only values ofE obtained for the interval = 0.3–0.7 when calculating averagevalue. In an ideal case of a single and simple crystallization pro-cess, the apparent activation energy should be independent of thedegree of conversion ˛.

Second step of the kinetic analysis consist of choosing an appro-priate kinetic model for the description of crystallization peaks. Forthis procedure Málek [12,13] suggested an algorithm based on theshape of characteristic functions z(˛) and y(˛). These functions areobtained by a very simple transformation of experimental data, fornon-isothermal conditions the characteristic functions are definedas follows:

y(˛) = · eE/RT (5)

z(˛) = · T2 (6)

The introduced functions are in fact a universal way for determi-nation of an appropriate kinetic model applicable to any physicalprocess. Determination of the most suitable kinetic model thenutilizes both, values of corresponding to the maxima of the char-acteristic functions and the overall shape of the functions. Based onthis information, the optimal kinetic model can be chosen accord-ing to the algorithm [13] shown in Fig. 1 (where concrete values forseveral most common kinetic models are shown as well).

In our work the two probably most popular and widely usedkinetic models for description of the crystallization behavior will beused – the nucleation-growth Johnson–Mehl–Avrami (JMA) modeland the autocatalytic Sesták–Berggren (AC) model. JMA(m) model[14–16] is a one-parameter model and its fundamental derivationhas an actual physical basis. It can be expressed through the fol-lowing equation:

f (˛) = m(1 − ˛)[− ln(1 − ˛)]1−(1/m) (7)

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Fig. 1. Algorithm [13] for determination of appropriate kinetic model based on values of maxima of y(˛) and z(˛) functions.

where m is the parameter reflecting nucleation and crystal growthmechanisms, as well as the crystal morphology. Eq. (7) was derivedstrictly for isothermal conditions with additional assumptionsbeing: the growth rate of a newly formed phase is controlled onlyby temperature and is independent of time and previous thermalhistory; nucleation is either homogeneous or heterogeneous onrandomly distributed active centres; and growing crystals have lowanisotropy. Nevertheless, Henderson [17,18] showed that the valid-ity of this model can be extended also to non-isothermal conditions.This extension may be done under an assumption that the entirenucleation process takes place during early stages of the transfor-mation and becomes negligible afterwards during the very crystalgrowth.

Crystallization kinetics following the JMA equation can beassumed when the value of degree of conversion correspondingto the maximum of the z(˛) function ˛max,z equals 0.632, which isthe so-called “fingerprint” of the JMA model (see Fig. 1). Value ofthe kinetic parameter m itself can then be calculated from the con-version corresponding to the maximum of the y(˛) function ˛max,y

according to [19]:

m = 11 + ln(1 − ˛max,y)

(8)

An alternative way of the parameter m determination is throughthe double logarithm function [8]:

d ln[− ln(1 − ˛)]d(1/T)

= −m · E

R(9)

In addition, linear dependence of this equation is also often con-sidered a satisfactory condition for applicability of JMA model. Suchcondition, however, is not always justified [20].

Second model applied within the framework of this article wasthe autocatalytic AC(M, N) model [21]. This model is empirical, i.e.the model itself or its parameters do not have any physical basisor meaning, the description is purely phenomenological. AC modelcan be expressed through the following equation:

f (˛) = ˛M(1 − ˛)N (10)

According to the algorithm shown in Fig. 1 it can be stated that,except for general boundary condition [22], the only condition forapplicability of the AC model is the value of ˛max,y being lowerthan ˛max,z, which is fulfilled practically for any experimental data.Therefore it is a usual and obvious practice to check the applica-bility of the physically meaningful JMA model first and only in thecase, when JMA equation cannot be used, the empirical AC model

is applied. Parameters of this model can be evaluated on the basisof the following two equations:

M

N= ˛max,y

(1 − ˛max,y)(11)

ln[

exp(

E

RT

)]= ln(�H · A) + N · ln[˛M/N(1 − ˛)] (12)

Final step of the kinetic analysis is determination of the pre-exponential factor A. Its value can be either calculated directly (e.g.according to Eq. (12)) or evaluated by the non-linear curve fitting.Values of A should be, of course, identical regardless of the way oftheir determination.

3. Experimental

The Se70Te30 chalcogenide glass was prepared from pureelements (5 N, Sigma Aldrich) by the classical melt-quenchingtechnique. Corresponding amounts of elements were accuratelyweighted into a fused silica ampoule, degassed and sealed after-wards. Total mass of the batch was approximately 10 g. The batchedampoule was then annealed in the rocking furnace at 650 ◦C for24 h. The glass was prepared from its melt by quenching theampoule in water. The amorphous nature of the glass was checkedby X-ray diffraction, homogeneity of the glass was verified from theposition of the relaxation peak at Tg, which was measured underdefined thermal history for samples taken randomly from the bulkglass.

3.1. DSC measurements

Crystallization behavior of the prepared glass was studied usinga conventional DSC 822e (Mettler, Toledo) equipped with cool-ing accessory. Dry nitrogen was used as the purge gas at a rateof 20 cm3/min. The calorimeter was calibrated through the use ofmelting temperatures of In, Zn and Ga. Baseline was checked daily.For purpose of this study the following powder fractions were pre-pared by grinding: 20–50, 50–125, 125–180, 180–250, 250–300and 300–500 �m. In addition, also bulk samples were prepared bycracking a thin layer of as-prepared bulk glass right after its remov-ing from the ampoule (this way of bulk samples preparation willbe further referred-to in Section 4). Each fraction was studied sepa-rately and its kinetic analysis was performed independently. In thecase of powders a thin layer of particles was spread on the bottomof aluminum pans to improve thermal contact and at the same timeto minimize the variety of the heat transfer processes (crucible-to-glass; glass-to-glass; air-to-glass – with the former being the ideal

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and desired one). By a very careful manipulation with sealed cru-cibles during their transfer to the DSC it was assured that an evenlydistributed thin layer of particles is truly measured and no irre-producible thermal gradients are produced by, e.g. cumulating orpiling of the powder at the crucible wall. The distribution of thepowder was always checked after each measurement when thecrucible was carefully unsealed. For further improving of measure-ments reproducibility the crucibles with pin were used in case ofall measurements in order to precise their positioning in the DSCcell. Masses of the powder samples varied in-between 9 and 10 mg;bulk sample masses were approximately 30 mg.

Regarding the specific DSC temperature program, it was alreadyreported earlier [23] that Se-rich glasses from the Se–Te systemhave a relatively narrow distribution of relaxation times due towhich the structural relaxation phenomena develop into a largeovershoot effect at Tg during the heating of the material. In thecase of an as-prepared or well relaxed Se70Te30 glass this overshoottends to partially overlap with the closely following crystalliza-tion peak, which is of course highly undesirable. For this reasoneach sample was first shortly annealed at temperature just aboveTg (5 min at 70 ◦C) in order to erase previous thermal history andobtain a reproducibly attainable structure of undercooled liquid.This annealing may have also served as a pre-nucleation period,which will be discussed later. In the second step of the temper-ature program the sample was cooled at defined cooling rate of−10 K min−1 to 20 ◦C and then immediately in the last step heatedup to 180 ◦C. The introduced procedure (initial erasing of thermalhistory and subsequent defined and relatively fast cooling) resultedin very small relaxation overshoot effects which no longer influ-enced or interfered with the crystallization process. The heatingrates applied in the measuring scan (the last/third step) were: 1, 2, 3,5, 7, 10, 15, 20 and 30 K min−1. Each measurement was reproducedtwo times in order to estimate experimental errors.

3.2. Data acquisition

Main problem of correct data acquisition is a proper baselinesubtraction. Usually the difference between the heat capacities ofundercooled liquid and crystal is very small and can be neglected– simple linear extrapolation is commonly used in this instance.Nevertheless, in the case of materials for which the aforementioneddifference is not negligible (also the case of Se70Te30 glass) a propersubstitution for the heat capacity transition has to be chosen. Thischoice is usually limited by the possibilities offered by the DSCsoftware; among the most widely used baselines belong varioustangentially or horizontally integrated curves, splines or low-orderpolynomials. Several rigorous derivations concerning the thermalinertia effects are shown in, e.g. [1,21]. Nonetheless, in practice itis still a matter of opinion to decide which function best simu-lates the thermal background under the measured kinetic effect.In our work we decided to use the cubic spline as the most appro-priate baseline. The splines are for interpolations usually superiorto polynomials due to avoiding the Runge’s phenomenon [24]. Asin the case of all methods that include internal calculation of thetangential slope, it is also for the spline utilization extremely impor-tant to correctly choose the data interval in for which the initialtangent will be determined. With respect to the previous, the cal-culated spline baseline was always carefully checked to preciselyimitate the background along the considered crystallization effectin a sufficiently large temperature range.

Concerning the data acquisition, one more issue related to theextremely fast evolution of heat in the case of bulk samples had tobe solved. For the calculation of crystallization kinetics the actualshape of the peak is crucial, therefore it is not sufficient to evalu-ate just the onset, maximum of the peak, or the amount of enthalpycorresponding to the measured effect. This is, in particular, an issue

in the case of complex or competing processes where only one ofthe involved mechanisms is fast while the heat associated with thesecond (underlying) mechanism evolves slowly. In such case onecan be not only limited by the factual minimum sampling inter-val of the DSC device (in order to obtain enough experimentalpoints along the sharply evolving crystallization peak) but also aproblem of equal distribution of the experimental data comes intoquestion. In other words, if the experimental data are read equidis-tantly along the temperature axis, the ratio between experimentalpoints present in peak tails and those present in the actual body ofthe peak may be unfavorable (bearing in mind that peak tails arelargely influenced by the DSC device artifacts and baseline imper-fections and therefore it is at least for the purposes of curve-fittingdesirable for the most experimental data to come from the body ofthe peak). For this reason an algorithm for nonlinear acquisition ofexperimental data was developed – equidistant readings along thecourse of the curve were applied. In this way each segment of thecrystallization peak has its fitting weighing factor proportional tothe actual amount of evolved heat.

It was found and can be concluded that, when applying all theabove mentioned procedures and conditions, nearly perfect repro-ducibility of the experimental data was achieved. Based on this fact,further studies of influences of various experimental conditionswere possible.

4. Results and discussion

In the main chapter of this article a full procedure of kineticanalysis will be performed for the chosen chalcogenide Se70Te30glass and its each step will be thoroughly commented and dis-cussed with regard to resulting implications and possible sources ofexperimental errors. The chapter will be divided into three Sectionsaccording to the necessary information and data-processing opera-tions needed in order to reach the corresponding level of knowledgeand understanding to the crystallization process. In the first Sectiononly the basic information derivable directly from the raw kineticdata file (the [Ti˛i˚i] triplets for the whole crystallization curve)and characteristic proportions of the crystallization peak – appar-ent activation energy E and the basic crystallization mechanism(bulk/surface) can be revealed in this way. In the second Section thefull description of the kinetic data (including the determination ofthe suitable kinetic model and calculation of the pre-exponentialfactor) will be performed as is usually done in serious kinetic stud-ies. This information is obtained based on various transformationsof the experimental data or from the curve-fitting. Third Sectionwill be focused on interpretations of the results introduced inthe previous two sections and results arising from supplementalmeasurements and tests of the influence of certain experimentalconditions.

4.1. Basic kinetic analysis

In this section basic kinetic analysis that can be derived directlyfrom the raw DSC data for crystallization peaks will be presented.The fundamental assumption of a serious approach to kinetic anal-ysis is a study that involves a number of fractions divided accordingto particle size – only in this way a complex understanding to theinvolved crystallization mechanisms can be achieved. Among thekinetics basics then belongs resolving of first few terms in Eq. (1)as was already suggested in Section 2 – namely evaluation of �H,E and determination of the main crystallization mechanism.

Regarding the former, the enthalpy change associated with crys-tallization process might be, paradoxically, considered a somewhatpeculiar quantity to determine. In Section 2 the crystallizationenthalpy (either specific or molar) is a material constant. However,

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Fig. 2. Determination of apparent activation energy of the crystallization processaccording to the Kissinger method for all studied Se70Te30 particle size fractions.

in practice its value determined from the experimental crystal-lization data may depend on both, particle size and heating rate.The area under the crystallization peak is thus largely influencedby thermal gradients in the sample (usually lower crystalliza-tion enthalpies determined for fine powders in comparison tobulk samples) and by heat dissipation (lower values of �H foundfor slow heating rates). Nevertheless, the value of �H is in thekinetic analysis actually not as important and does not affectany calculations until the final step of the pre-exponential fac-tor A evaluation (where this discussion will be continued). Thevalue of crystallization enthalpy should be though closely moni-tored in order to disclose any deviations from the general pattern,which may indicate, e.g. already starting crystal growth during anyapplied preliminary DSC temperature programme, partially crys-talline structures coming from the unideal glass preparation or,contrariwise, an unfinished crystallization process.

4.1.1. Determination of activation energy EAMain task of the initiating kinetic analysis study is without

question determination of the apparent activation energy of crys-tallization E. In our work the Kissinger [9], Ozawa [10] and Friedman[11] methods already described in Section 2 – Eqs. (2)–(4) – wereemployed in this task. In Fig. 2 the Kissinger dependences forall studied Se70Te30 particle size fractions including bulk samplesare shown. As can be seen, the slope of the dependence (propor-tional to the activation energy E) decreases with increasing particlesize. The values of EKissinger determined from this plot are listed inTable 1.

However, the true reason for plotting the graph in Fig. 2 wasto compare and discuss apparent activation energies calculated for

Table 1Values of pre-exponential factor A and apparent activation energies determined bythe Kissinger, Ozawa and Friedman methods for the studied Se70Te30 particle sizefractions.

Sample size(mm)

EKissinger

(kJ mol−1)EOzawa

(kJ mol−1)EFriedman

(kJ mol−1)ln(A/s)

0.020–0.050 158 ± 2 157 ± 2 150 ± 3 45.5 ± 1.20.050–0.125 147 ± 2 146 ± 2 141 ± 5 41.4 ± 1.10.125–0.180 135 ± 2 135 ± 2 128 ± 6 37.8 ± 0.80.180–0.250 127 ± 2 127 ± 2 120 ± 5 34.7 ± 1.00.250–0.300 125 ± 1 125 ± 1 117 ± 5 32.5 ± 0.10.300–0.500 121 ± 1 122 ± 1 113 ± 3 31.5 ± 0.1Bulk 114 ± 3 115 ± 3 148 ± 8 30.3 ± 0.4

different forms of bulk sample. As was already mentioned in Sec-tion 3, the bulk samples were prepared rather untraditionally, bysimple cracking of a thin as-prepared bulk glass layer right afterits removing from the ampoule. In this way the prepared sam-ples had quite small masses and, most importantly, their surfacewas perfectly smooth and undamaged with absolute minimum ofpotential surface crystallization centres. The same held also for thatside of the sample which was in contact with the inner wall ofthe ampoule – no significant difference was found in-between thetwo sides of the sample slide. In order to make the intended com-parison a set of “common” bulk samples was prepared; these bulksamples will be within the framework of this article denoted as“cylindrical bulk”. The cylindrical bulk samples were prepared ina thin ampoule (3 mm in diameter) which was first filled with analready ground Se70Te30 glassy powder and consequently meltedin a vertical position, so that the melt was positioned in the bottomhalf of the ampoule. After cooling in water the ampoule was cut ona low-speed saw and small cylinders of glass were obtained. Theseflat cylinders were consequently ground using fine Al2O3 grind-ing powders in order to reduce their height to about 0.7–1.0 mm(to lower their mass) and their bases polished to optical quality. Insuch way prepared samples are commonly believed to representa true bulk nature of glass as the polishing is thought to reducethe surface crystallization centres. However, this may not alwaysbe entirely true. At closer look, it is apparent from Fig. 2 that thedata for bulk samples (the cracked thin layer ones) quite well cor-respond with the largest particle size powder fractions – the datafor particular fractions in fact sort of limit with increasing particlesize to the dependence obtained for the bulk sample. Nevertheless,it can be seen that the crystallization process as a whole does notundergo any abrupt changes and continuously follows the influ-ence of increasing particle size. On the other hand, it is clearlyseen that for cylindrical bulk the dependence evidently deviatesfrom the general trend given by the increase in particle size. Thedeviation at high heating rates is clearly caused by increased sam-ple mass (compared to the untreated bulk) and resulting thermalgradients causing a lag and a virtual shift of the crystallizationeffect to higher temperatures. The influence of increased thermalgradient is indeed present also in the case of lower heating rateswhere however, interestingly, the maxima of crystallization peaksare detected at lower temperatures than those for untreated bulk.I.e. some additional influence accelerates the crystallization in thiscase. This is in the authors’ opinion evidence of the “surface” crys-tallization hastening the bulk crystallization mechanism and evengetting it started earlier (further supporting evidence for this state-ment will be given in Section 4.2). Based on this premise it can befurther deduced that the polished cylindrical bulks still have hightendency for surface crystallization. The key idea for understand-ing this contradiction is taking into consideration the influence ofthe preceding grinding of the glassy cylinders. The grinding pro-cedure not only affects the actual surface of the sample but mostprobably introduces large internal strains and stresses into thematerial. The significantly increased number of in this way createddefects/dislocations in the glass then may serve as supplementalcrystallization centres (in order to remove the stress induced bymechanical relaxation the sample would have to be annealed fora relatively long time periods at temperatures above Tg, where,however, the everlasting danger for enhanced nucleation and crys-tal growth processes is already present). Moreover, SEM imagesof a ground surface cross-section showed that the heavily dam-aged surface layer can be as far as several hundreds microns thick.In the light of these facts the authors would like to introduce thefollowing suggestion for the cases when the bulk crystallizationis intended to be studied: the number and intensity of surface-damaging operations should be reduced to minimum even if thepolishing procedure follows; ideally a raw as-prepared untreated

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Fig. 3. Comparison of apparent activation energies determined for Se70Te30 accord-ing to Kissinger and Friedman in dependence on average particle size in particularfractions. Bulk samples were assigned daver = 1 mm. (A) evaluation of EA accordingto Friedman – averaged all applied heating rates; (B) evaluation of EA according toFriedman – averaged following heating rates: 1, 2 and 3 K min−1.

thin plate of glass should be taken in order to minimize the effectsof artificially introduced defects and stresses.

Nevertheless, to continue in the topic of apparent activationenergies determined for the Se70Te30 glass, apart from the Kissingermethod also the Ozawa equation was applied to the experimentaldata. Results from this method are again listed in Table 1 and arequite similar to those obtained by using the Kissinger equation,which is anyhow a very common feature. Third method for eval-uation the apparent activation energy of crystallization applied inour work was the isoconversional Friedman method. The theoreti-cal background of this method was already described in Section 2;here we would like to focus on its flaws, merits and resulting impli-cations. An unambiguous merit is obviously the output in the formof the activation energy E dependence on the degree of conver-sion ˛, which may in certain cases reveal systematic change in thevalue of E representing, i.e. two overlapping or very closely follow-ing processes or a change in the crystallization mechanism. Suchinterpretations based solely on the change in activation energyare, however, often a bit tricky and should always be supportedby additional evidence. Reason for that subsists in unreliability ofthe information corresponding to the crystallization peak onsetand offset. The peak tails are significantly influenced by experi-mental conditions (instability of baseline, minor thermal gradientsin the sample or DSC cell, etc.) which may depend also on heat-ing rate and therefore affect evaluation of the activation energy inthese parts of the peak. Due to this it is a common practice to con-sider only the 0.3–0.7 interval of conversions when calculating, e.g.an average Friedman’s activation energy. The same interval wasapplied also within the framework of this article when calculat-ing the EFriedman listed in Table 1. Full dependencies of activationenergy versus degree of conversion are for the studied particle sizefractions given in Appendix 1.

A complex comparison of the apparent activation energies eval-uated according to Kissinger and Friedman methods is for allstudied fractions (distributed according to the average particle size;value of 1 mm was assigned to the bulk specimen) shown in Fig. 3.It can be seen that the values from both methods correspond quitewell with the activation energies determined according to Fried-man equation being only slightly lower. The only exception fromthis consistency are the bulk values. However, it was already men-tioned earlier that in the case of bulk samples an extremely fastand extensive evolution of heat took place, which due to the large

thermal gradients and resulting lags significantly deformed thecrystallization peak at higher heating rates. The value denoted inFig. 3 as (A) was calculated from the data for all applied heatingrates (even those as high as 20 or 30 K min−1 where the peak shapewas clearly hugely influenced by the inability of the evolved heatto penetrate towards the DSC sensor without cumulative effect oftemperature gradient). The point denoted as (B) then correspondsto the averaged material response to the lowest three heatingrates (1, 2 and 3 K min−1); even in this case the deformation ofthe peak was so substantial that it caused the displayed devia-tion of activation energy from the expected value (that determinedby the Kissinger method). Main point of this discussion pointedat the Friedman method is then a suggestion not to overrate itspotency. One should always bear in mind that if applied blindly,the isoconversional methods may in certain cases provide biasedand unrealistic results due to the natural dependence of thesemethods on evaluation of based solely on mathematical com-putation. Unlike the Kissinger method, where the determinationof E is given by the actual physical essence of the crystallizationprocess (maximum of the heat evolution rate is driven entirely bythe fundamental crystallization mechanism), which in addition isalmost independent of the experimental conditions, the evalua-tion according to the Friedman method is heavily dependent onthe actual shape of the peak (due to the purely mathematical calcu-lation of ˛). Therefore, correspondingly, the results of this methodmay be largely influenced by every possible change in experimentalconditions that can occur either with the change of heating rate orsimply with the long-term duration of the experiments sequence.

4.1.2. Determination of basic crystallization mechanismApart from the determination of activation energy, also the

answer to question which crystallization mechanism (surface orvolume) prevails/dominates in the observed process can be derivedfrom the raw DSC data. A very thorough paper on this topic waspublished by Ray and Day [25], who established several basic crite-ria (˚p – heat flow corresponding to the maximum of the peak, i.e.maximum peak height; �Thh – half-width of the peak, i.e. the widthof the peak in the half of its height) and from the course of theirdependence when plotted against the average particle size theydecided whether the dominant crystallization mechanism is asso-ciated with surface defects and dislocations rather than with bulknuclei. The respective dependencies suggested by these authorsare for the Se70Te30 glass studied in this work shown in Appendix2 (upper index “N” denotes the dependencies normalized withrespect to the value obtained for the finest studied particle sizefraction). Here in the article itself only their final combined cri-terion is shown in Fig. 4. For the lowest heating rate (1 K min−1),where the large influence of thermal gradients on bulk crystal-lization did not manifest yet, a typical sigmoidal dependence wasobtained. In case of the two other displayed heating rates the bulkvalues are already largely influenced by thermal gradients in thesample and DSC crucible. Nevertheless, in all cases an increasing(not decreasing) dependence was obtained, which is an approve-ment for prevailing bulk/volume crystallization mechanism. Sameconclusion results also from the other dependencies introduced inAppendix 2.

Although the criteria introduced by Ray and Day are very simpleand relatively easy to evaluate, we would like to introduce here onemore (to the authors’ knowledge original) criterion. This criterion isalso extremely simple to apply but, in addition, it is independent ofthe most negative influences of experimental conditions (like thoseof, e.g. thermal gradients arising from the arrangement of the DSCcell itself or gradients associated with the unideal thermal contactof particular sample grains with the bottom of DSC crucible) due tothe only monitored quantity being Tp, which is from the consideredpoint of view a very robust value to determine. This method is in

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Fig. 4. Normalized crystallization mechanism plot introduced by Ray and Day [25]in order to determine the dominating crystallization mechanism. Data for Se70Te30

glass measured within the framework of this article. See text for details.

fact based on the very essence of the idea of joint influence of bulkand surface crystallization mechanisms. The influence of the pre-vailing mechanism obviously determines/drives the crystallizationprocess and takes control over it already at moderate amounts ofeither surface defects and dislocations (in the case of surface crys-tallization) or bulk nuclei (in the case of volume crystallization).On the other hand, correspondingly, the number of preferred crys-tallization centres has to be very small in order for the secondarycrystallization mechanism to dominate. Implication of this fact canbe well demonstrated, e.g. by help of Fig. 5, where the Kissingerplots for two glasses are compared – Se70Te30 where the volumecrystallization prevails and Ge2Sb2Se5 where the surface crystal-lization mechanism dominates. It is well apparent that in each casethe dependencies sort of “limit” to the one mostly influenced bythe driving mechanism. In order to quantify this phenomenon, it issuitable to plot the value of the temperature corresponding to themaximum of the crystallization peak Tp in dependence on the loga-rithm of the average particle size present in the respective fractionln(daver) – see Fig. 6. In this depiction the dependence limits towardseither bulk or fine powder values accordingly with the dominantcrystallization mechanism.

4.2. Advanced kinetic analysis

This chapter contains results of advanced kinetic analysisapplied to our model Se70Te30 chalcogenide glass. In this contextthe advanced kinetic analysis denotes all procedures where alreadysome kind of transformation or numerical fitting is used to convertor interpret the experimental crystallization curves. In regard toresolving the remaining terms in Eq. (1), finding of an appropriatekinetic model f(˛) and determination of the pre-exponential factorA will be included in this part.

There is a number of suitable methods for estimation or deter-mination of a kinetic model best describing the experimentalcrystallization data – see Ref. [5] and references there. In our workwe chose the method introduced by Málek [12,13], which is basedon a very simple transformation of the DSC crystallization curvesinto the so-called z(˛) and y(˛) functions. Based on the values of˛max,z and ˛max,y (the values of corresponding to the maximaof the respective functions) an appropriate model and its param-eters may be determined. The y(˛) and z(˛) functions are for allapplied heating rates and chosen three particle size fractions shownin Fig. 7, where each row corresponds to one particular fraction. Full

Fig. 5. Comparison of Kissinger plots for a set of particle size fractions measured fortwo chalcogenide glasses. Se70Te30 – dominating bulk crystallization mechanism;Ge2Sb2Se5 – dominating surface crystallization mechanism.

set of y(˛) and z(˛) functions for all studied fractions including bulksample can be found in Appendix 3.

4.2.1. Characteristic kinetic functionsLooking first at the z(˛) functions it can be seen that their max-

imum at least roughly corresponds to the value typical for the JMAmodel (see algorithm at Fig. 1, theoretical value for this model is0.632). The slight systematic deviation of the functions maxima tohigher values of will be commented later in this Section. It can befurther seen that the z(˛) functions are completely invariant withrespect to the applied heating rate and other experimental con-ditions. These conclusions both suggest and confirm applicabilityof the JMA model. On the other hand, the course of y(˛) functionsclearly shows several significant dependencies. The most evidenttrend in the course of y(˛) functions is the shift of their maxi-mum towards higher values of with increasing particle size. Aswas already shown in Section 3.1 the prevailing/dominant crystal-lization mechanism in Se70Te30 glass is associated with the bulkprocesses. Nevertheless, the maximum of the y(˛) function corre-sponding to the finest particle size fractions clearly indicates theJMA kinetic exponent m = 1(˛max,y ∼ 0; linear decrease), which isusually attributed to the surface crystallization mechanism. How-ever, with the increasing particle size this surface mechanismrecedes and the second y(˛) “peak” arises with ˛max,y equal toapproximately 0.5–0.6 corresponding to the bulk crystallizationmechanism. This interpretation is perfectly consistent with theidea of both crystallization mechanisms (surface and bulk) being

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Fig. 6. Normalized crystallization mechanism plot introduced in this work inorder to determine the dominating crystallization mechanism. Results for twochalcogenide glasses – Se70Te30 (dominating bulk crystallization mechanism) andGe2Sb2Se5 (dominating surface crystallization mechanism) – are compared. See textfor details.

present, where the intensity/representation of each particular pro-cess is given by the ratio of the number of surface defects ordislocations to volume nuclei. I.e. for the finest fractions, where dur-ing the grinding procedure a large number of surface defects actinglike crystallization centres was created and, moreover, the actualsurface area was significantly increased, the prevailing mechanismis the surface crystallization. On the other hand, in the case of coarsefractions the grinding was not so intensive (not applied at all inthe case of bulk), the result of which was low amount of surfacedefects and a much more favorable ratio of the bulk/surface crys-tallization centres for the crystallization mechanism to be driven bythe volume nucleation and continuing crystal growth. In the caseof middle-sized powder fractions there are both factors present,quite large number of surface defects resulting from the grindingand sample-preparation procedures and, at the same time, rela-tively high number of bulk nuclei due to the glass particles havinglarger size. Another evidence for this interpretation is also the factthat the surface crystallization mechanism (mJMA = 1) entirely dis-appears only for the bulk sample, which only was not processed inany way that could cause creation of a significant/increased numberof surface defects.

The second trend visible in Fig. 7 is the shift in crystalliza-tion mechanism with the applied heating rate. It is apparent thatfor low heating rates the bulk mechanism is more pronounced(due to the normalization of characteristic functions in Fig. 7 this

effectively looks like a depression of the surface crystallization).There are several ways how to interpret this phenomenon. Accord-ing to the authors’ opinion the most probable one is to imply theconclusion resulting from Fig. 3, i.e. to employ the difference inactivation energies for the two crystallization mechanisms into theexplanation of the effect discussed in this paragraph. It is clearlyapparent from Fig. 3 that the surface crystallization appears to haveslightly but still significantly higher activation energy than the bulkprocess. The same conclusion can be made also from the course ofapparent activation energies with the degree of conversion shownfor the studied powder fractions in Appendix 1. On the other hand,the three-dimensional kinetics is axiomatically slower and can befurther decelerated by, e.g. steric reasons. As can be seen alreadyfrom Fig. 7 (and as will be proven later) the first process that takesplace is always the surface crystallization that corresponds to theearliest heat evolution. Therefore during the fast heating the start-ing primary surface crystallization mechanism takes control overthe larger partition of the complex crystallization process (withmore than enough energy being provided by the faster heatingand thermal gradients causing the whole process to be allocatedto higher temperatures), while the slower bulk mechanism doesnot have enough time to fully develop (in accordance with the con-cept of competing processes). Correspondingly at low heating ratesit is the difference in activation energies that determines the out-come. Although it is still the surface crystallization that starts thecomplex crystallization, the energy input (caused by the factualtemperature increase plus heat evolved during the crystallization)is relatively low and an actual competition based on the differencein energy barriers (represented by the apparent activation energyEA) takes place causing the bulk process to be more pronouncedwhile “consuming” larger part of the provided energy.

It is further interesting to plot the maxima ˛max,z and ˛max,y

of the two characteristic functions in dependence on the averageparticle size – see Fig. 8. The depicted values were in all cases cal-culated as an average for all applied heating rates. Dashed linein the ˛max,z–daver dependence suggests the theoretical “finger-print” value for the JMA model. Large errors associated with themean value for the bulk sample are obviously a result of the ther-mal gradients deforming the crystallization peaks measured athigher heating rates (see Appendix 3). Looking at the ˛max,y–daver

dependence it is well apparent for which particle sizes the criticalsurface-defects-to-bulk-nuclei ratio is achieved. Large error bars incase of these powder fractions of course correspond to averaging ofthe two mechanisms with mJMA = 1 and mJMA = 3–4. Another inter-esting conclusion can be obtained when plotting the values of bothmaxima types against each other – so called “kinetic plot” [26];see Fig. 9. It is clearly apparent that except for the finest powdersall points lie outside the suggested interval where JMA model isrecommended and its usage tested. Nevertheless, as will be shownlater in this chapter, the JMA formula describes reasonably wellalmost all experimental data despite the fact that two competingmechanisms are included in the overall manifestation of the crys-tallization process. Based on this fact, the authors would like tosuggest for consideration widening of the applicability interval forthe JMA model. The exact borderline is, certainly, hard to accuratelydetermine – at this stage our intention is only to demonstrate thatJMA model may be successfully used even outside the formerly sug-gested application range. The actual quality of the final fit will ofcourse be still dependent on many additional factors besides thevalue of ˛max,z alone.

4.2.2. Kinetic modelsRegarding the very description of the experimental crystalliza-

tion peaks the both previously mentioned models – physicallymeaningful Johnson–Mehl–Avrami JMA(m) nucleation/growthmodel and empiric autocatalytic AC(M, N) model – were tested.

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Fig. 7. Normalized y(˛) and z(˛) functions corresponding to non-isothermal measurements of chosen particle size fractions of Se70Te30 glass. Particular rows match theindividual studied fractions. Full set of y(˛) and z(˛) functions for all studied fractions including bulk sample can be found in Appendix 3.

The JMA model is with respect to crystallization in glasses prob-ably the only physical model that is currently being consideredroutinely and if it cannot be for some reason applied, the AC modelis automatically used. In case of both models the essential task is tocorrectly determine their parameters, the consequent calculationof the pre-exponential factor A is rather automatic and stronglydepends on the prior evaluations.

The JMA model was to our experimental data applied in com-pliance with Eq. (7). Suitability of its usage was confirmed by thevalues of ˛max,z being very close to the value 0.632 (which is acharacteristic “fingerprint” for this model). Determination of themodel parameter m was done in two ways. First applied equationwas that derived by Málek [19] – Eq. (8) in Section 2 – where the

determination is based on the value of ˛max,y. It is probably obvi-ous that no average quantification of the JMA parameter m can bemade in the case of Se70Te30 glass. If two or more mechanismsare apparent in the y(˛) plot, the correct way of their descriptionis certainly to evaluate them separately and then, possibly, plotthem in dependence on the factor associated with the change oftheir course (solution for our particular case would be to plot theparameter m versus daver – converted plot from Fig. 8). Thereforeit can be only said that in the case of Se70Te30 glass manifesta-tion of two different crystallization mechanisms can be observed.The first one can be associated with the surface crystallization andan average value of the parameter m is for this process close tounity (m = 1). The second process then corresponds to bulk/volume

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Fig. 8. Particle size dependence of the characteristic kinetic functions maxima ˛max,z

and ˛max,y for the Se70Te30 glass. Bulk samples were assigned daver = 1 mm.

crystallization mechanism and the averaged JMA parameter ism ≈ 3–4. In addition to the Málek’s equation, there is one moreway how to determine the JMA kinetic parameter, which is rep-resented by Eq. (9). Though the usage of Eq. (9) is probably much

Fig. 9. So called “kinetic plot” evaluated for the Se70Te30 glass. Theoretical appli-cability of the JMA model as suggested by Málek [12] is displayed. The solid curveguides eyes in direction of the increasing particle sizes in particular fractions.

more common and widespread, it has to be stated that for com-plex processes this equation fails. The double logarithm functionaverages the contributions of both present processes as a result ofwhich none of them is properly recognized or described by a cor-responding physically meaningful JMA parameter. For this reasoncaution should be taken when multiple simultaneous, overlappingor combined crystallization processes are expected. Nonetheless,appropriate credit has to be given to the double logarithm becauseat least in the marginal cases where one of the processes is beingcompletely dominant also Eq. (9) gives reasonable and physicallymeaningful values of mJMA similar to those provided by the Málek’sequation. Moreover, the linearity of the double logarithm depen-dence can also serve as an additional independent confirmation ofthe JMA model applicability. Nevertheless, it is not recommendedto use solely this method [20].

We would like to, however, clearly state that in this case ofthe two mutually interacting processes (mechanisms) even thedetermination of the JMA parameter according to Eq. (8) may beburdened with a relatively large error. The value of ˛max,y andresulting parameter m of the surface process were not signifi-cantly shifted for any combination of experimental conditions. Anegligible change in the position of ˛max,y occurred for severalheating rates and fractions, which was, however, a completelyrandom effect probably associated with slight differences in grainmorphology and number of defects generated by powder samplepreparation for each particular measured sample. One more remarkregarding the surface mechanism should be made, namely that ofthe value of ˛max,y not being equal exactly zero (as is assumed forthe true first order kinetics) due to the thermal gradients in thesample and resulting lag in the material response to the temper-ature program. On the other hand, it is well apparent from Fig. 7and Appendix 3 that the ˛max,y value associated with the bulk pro-cess is considerably influenced by the mutual overlapping with thesurface crystallization. In addition, as follows from Eq. (8) thereis an exponential accumulation of discrete integer m values withthe increase of ˛max,y, which results in an increased error in deter-mination of the JMA parameter for the bulk mechanisms. In theparticular case of Se70Te30 glass this issue is further complicatedby the interaction with a preceding surface process. Two types ofdeformation arising from this interaction can be recognized. Thefirst one is strictly limited to the y(˛) plot where a small shiftof the bulk maximum towards lower values of is caused by aheat flow “coupling” at the place of transition in-between the twoevincing mechanisms. This unideality caused by thermal gradientsinside the glass particles is in the authors’ opinion a more plausibleexplanation than would be, e.g. a positive influence of the surfacecrystallization on development of the initial bulk process conver-sion rate or, conversely, retardation of the surface crystallizationby the bulk process. Second deformation arising from the interac-tion between the surface and bulk crystallization mechanisms isassociated with physical separation of these two processes, moreprecisely with their sequentiality. Although the surface crystalliza-tion acts as a primer/catalyst for the bulk process, the processes donot start simultaneously and a significant delay occurs in the caseof bulk process (which is, as we would like to remind, the dom-inating crystallization mechanism). As a result the correspondingmaxima are for both characteristic functions y(˛) and z(˛) slightlyshifted towards higher values of ˛, which may of course causedetermination of incorrect values of the JMA kinetic parameter.This phenomenon should be therefore always taken into accountwhen dealing with complex processes and their kinetics and onlyphysically meaningful solutions should be sought.

As was already suggested in Section 2, apart from thenucleation-growth JMA model there are several other optionsfor description of crystallization behavior in glasses. It is thougha common practice to apply the autocatalytic Sesták–Berggren

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Fig. 10. Particle size dependence of the parameters M and N of the Sesták–Berggrenautocatalytic model for the Se70Te30 glass. Bulk samples were assigned daver = 1 mm.

model in the case when the process does not follow the JMAkinetics. Main advantage of the AC model is its flexibility. How-ever, the AC model is empirical and its parameters do nothave physical meaning. Although our model Se70Te30 glass waspossible to be very well described by the JMA kinetics, theAC(M, N) model was in our study applied too in order toinvestigate its merits and flaws for the case of dealing with complexcrystallization behavior. The AC model was applied in compliancewith Eq. (10) and its parameters were evaluated according to theprocedure described in Section 2. It should be remarked that theevaluation is again based on the value of ˛max,y, which may be bur-dened with an error, the origin of which was described in the previ-ous paragraph. Nevertheless, in the case of complex processes thereis one additional much more complicated issue associated withdetermination of the M and N parameters. Due to the very essenceof the model, where each parameter is “responsible” for one side ofthe crystallization peak (the significance of particular parametersdepends on the degree of conversion ˛), the evaluation accordingto Eq. (12) may decouple into two dependencies with dissimilarslope. Each of these two dependencies then represents “part” ofthe process corresponding to one crystallization mechanism andaccording to which slope is chosen for evaluation the correspond-ing part of the curve is described more precisely. From this pointof view, even the universal AC model has a significant drawback.In order to choose the best solution, the dependence/mechanismcovering most of the experimental data was always selected (basedon the better RSS criterion). The averaged evaluated parameters Mand N are for all studied particle size fractions shown in Fig. 10; nosignificant trends with heating rate were observed. It can be seenthat while the parameter N remains roughly constant there is anapparent trend in the parameter M evolution. It is evident from Eq.(10) and can be also shown by simulations that significance of theparameter M increases with (hence its change affects the finalpart of the crystallization peak) and, contrariwise, the shape of theleading edge of the peak determines the parameter N. The obviousimplication of this fact is that with increasing particle size (thuswith the crossover from the surface to bulk mechanism) it is thedescending side of the peak which is influenced significantly, whileshape of the initial/leading peak edge remains identical. This will befurther commented in the following paragraph. It has to be noted,however, that the value of the parameter M for bulk is already out-side of the theoretical limits for the model (M ≤ 1), which is anotherevidence for the large distortion of the bulk crystallization peaksdue to thermal gradients within the sample.

4.2.3. Fit of experimental dataLast step in the kinetic analysis is determination of the pre-

exponential factor A. As was already suggested earlier, it isadvantageous to confirm the value of this parameter by inde-pendent evaluation within the framework of different models (ifpossible). In our work the values of A were determined by curve-fitting for the JMA model (input parameters were E and m) andby calculation according to Eq. (12) for the AC model. The resultsare listed in Table 1; several chosen experimental crystallizationcurves fitted by JMA model are then shown in Fig. 11 (full set ofall particle size fractions fitted by the JMA model is to be foundin Appendix 4). Fits by the AC model (not displayed explicitly inthis work) were slightly better, mostly for coarse fractions wherethe deviation from the surface first order kinetics due to the evinc-ing bulk crystallization started to take effect. This is, however, anexpected finding as in the case of JMA model it is the sole parameterm, which is responsible for the shape of the crystallization peak andany deviation from the kinetics defined by this parameter showsitself instantly, while in the case of the AC model each parameter(M and N) “controls” one edge of the peak, thus higher flexibil-ity is granted. Nonetheless, even the AC fits were not perfect asthe steeply developing bulk crystallization overlapping the back-ground surface kinetics produced an abruptly digressive peak edgewhile the leading edge was still driven by the first order kinetics(see Fig. 11). In consequence the data corresponding dominantlyto the bulk kinetics cover a relatively narrow range and there-fore the parameter M still results from averaged response of bothinvolved mechanisms.

One more very interesting fact arises from the curves in Fig. 11and Appendix 4. It can be seen that although in case of coarsefractions the surface crystallization mechanism does not evincemarkedly (see Fig. 7) it is still this mechanism which is crucialfor the overall shape of the crystallization peak, i.e. with the onlyexception of pure bulk samples each set of crystallization curvesmeasured within one particle size fraction had a similar leadingpeak edge, which is a “fingerprint” of first order kinetics and theonly difference caused by ascending bulk crystallization was to beseen in the steepness of the digressive peak edge. Only in the caseof bulk samples the peaks were significantly shifted in temperaturerepresenting true bulk kinetics. Similar trend may also be observedfor slowest heating rates and coarse fractions, where the numberof surface defects in combination with higher activation energy forthis type of crystallization does not suffice to initiate the bulk crys-tallization, which in this case starts to manifest independently. Thepresented conclusion is also in agreement with the rather signifi-cant shift of crystallization temperatures with particle size, whichcannot be attributed only to the thermal gradients arising fromlarger grain sizes but is an evident result of the initiating process(surface crystallization) having less pronounced effect.

As was shown in this chapter, even in the case of complex oroverlapping processes it is possible to perform detailed kineticstudies and obtain solid conclusions. Apart from the obvious needfor a very precise experimental performance the authors would liketo further stress the importance of a simultaneous interpretationof the characteristic kinetic functions z(˛) and y(˛), which are verysensitive to the peak shape, and of the raw DSC data, which on theother hand provide information about the actual peak positions intemperature, plus can also confirm certain conclusions arising fromthe characteristic kinetic functions.

4.3. Interpretations and supplemental measurements

In this chapter a set of independent studies aimed at explor-ing of an influence of certain experimental conditions in orderto demonstrate further possibilities that differential scanning

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Fig. 11. Crystallization peaks corresponding to non-isothermal measurements of chosen particle size fractions of Se70Te30 glass fitted by JMA model. Particular rows matchthe individual studied fractions. Full set of experimental curves fitted by JMA model for all studied fractions including bulk sample can be found in Appendix 4.

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calorimetry offers in regard to the studying of crystallizationkinetics.

4.3.1. Influence of pre-nucleation periodFirst examined effect was that of a pre-nucleation influence on

the DSC crystallization peaks of complex processes. A very niceworks on the topic of studying the nucleation processes by usingDSC are, e.g. [27,28]. However, this problem is obviously a lot morecomplicated in the case of complex processes. On the other hand,additional information about the nature of the particular involvedmechanisms can be derived from such study. Before any specificresults will be discussed, the authors would like to mention thatthis is by no means a complete nucleation-effect study; the fol-lowing text should more likely only suggest various possibilitiesof the DSC instrument engagement into the study of nucleation inglasses. The first question to answer is associated with choice ofthe pre-nucleation temperature. In the case of Se70Te30 glass thereis a relatively narrow temperature interval, in which this prelimi-nary treatment can take place. Due to the very close vicinity of thecrystallization and glass transition phenomena the pre-nucleationtemperature was restricted from below to 70 ◦C, as this tempera-ture is the closest limit at which the relaxation overshoot of glasstransition is fully developed and finalized, i.e. it cannot consid-erably influence any eventual nucleation process. On the otherhand, at all tested higher temperatures (75, 80 and 85 ◦C) therewas a considerable decrease of the crystallization enthalpy after a30 min annealing at the respective temperatures, which indicatedan already proceeding crystal growth. These higher temperatureswere therefore excluded from further testing of the influence ofnucleation of the very crystallization process. Thus the effect ofnucleation was examined for various nucleation times (0, 5 and30 min) at 70 ◦C, when the sample was afterwards regularly heateduntil the crystallization peak was recorded (the experiment with5 min long pre-nucleation period is in fact the standard crystal-lization measurement performed within the framework of thispublication – see Section 3). Full sets (with regard to applied heatingrates) of y(˛) and z(˛) functions and actual experimental crystal-lization curves fitted by JMA model are for all three nucleation timesand particle size fraction 125–180 �m shown in Appendix 5. Thisparticular fraction was chosen for the supplemental studies due tothe both involved mechanisms being represented roughly equallythe consequence of which is the highest sensitivity to even slightchanges in any of the mechanisms.

In order to concretize individual quantities from Eq. (1) the valueof �H was (and had to be in order to examine sole effect of nucle-ation) similar for all three nucleation times. Also the Kissinger plotswere exactly the same, no change in positions of Tp or in the veryvalue of activation energy were observed in-between the threestudied experimental sets. Regarding the z(˛) plot no change wasnoted, however, in the y(˛) function a slight shift was observableimplying an actual influencing of the overall crystallization pro-cess by nucleation period. As was already mentioned several times,shape of the y(˛) function reflects intensity and consequentialityof involved kinetic mechanisms. It was found that the ˛max,y cor-responding to surface crystallization did not change at all and wasperfectly reproducible for all nucleation times. This implies thatthe surface mechanism is associated exclusively with structuraldefects and surface dislocations the number of which originatesfrom preparation treatment and which do not further change atsub-crystal-growth temperatures. On the other hand, there is anapparent change in the y(˛) data corresponding to the bulk process.The bulk crystallization response is considerably more developedwith increasing nucleation time, especially for higher heating rates.Here both processes (surface and bulk) are truly competing dueto the higher activation energy of the surface mechanism on oneside and short time (due to the fast heating) to create adequate

number of sufficiently large nuclei on the other side. This effectwas, however, expected as it was assumed that the nucleation ratepeak does not perfectly overlap with that for crystal growth rateand, furthermore, that the nucleation starts at lower temperaturesthan are then optimal for the consequent crystal growth (which isthe usual case). Similar conclusions can be derived also from the fit-ted crystallization curves (see Appendix 5), where the peaks turnto be higher and sharper with increasing nucleation time, againindicating a more pronounced bulk mechanism.

4.3.2. Influence of glass preparation procedureSecond studied effect was that associated with the way of prepa-

ration of the Se70Te30 glass itself. Apart from the results obtained bythe classical melt-quenching technique using a standard ampoulewith inner diameter ∼15 mm and thickness of the wall being1.5 mm, three more different cooling experimental settings wereapplied. The same ampoule with similar batch was also cooled onair. In addition, the Se70Te30 glass was also prepared in two thinampoules (inner diameter 3 mm, wall thickness 1 mm), when onewas again cooled by quenching in water and the second was letfreely cool down on air. Results obtained for the former mentionedsetting (wide ampoule cooled in water) were in fact a reproductionof work presented in this article and therefore served as a refer-ence glass sample. In the case of the wide ampoule being let freelycool on air several visible crystals were formed on the surface ofthe bulk glass extracted from the broken ampoule. The value of�H was also considerably lower in comparison with our referenceglass, indicating that a significant part of the material is alreadycrystalline most probably due to a very low cooling rate throughthe critical region of maximum nucleation and crystal growth rates– the glass prepared in this way was therefore excluded from fur-ther comparisons. Full sets (with regard to applied heating rates)of y(˛) and z(˛) functions and actual experimental crystallizationcurves fitted by JMA model are for the two glasses prepared in thinampoules and for the reference glass (particle size fractions were20–50 �m and 125–180 �m) shown in Appendix 6.

The 125–180 �m fraction will be commented first. This particu-lar fraction was again chosen due to the both involved mechanismsbeing represented roughly equally the consequence of which wasthe highest sensitivity to even slight changes in any of the mech-anisms. Regarding the description of crystallization kinetics in thecase of the three glasses prepared in different ways and describedin the previous paragraph, it was found that no change in �H, posi-tions of Tp or in the very value of activation energy evaluated fromthe Kissinger plot occurred in-between the three studied exper-imental sets. However, when looking closer at the characteristickinetic functions significant differences have been found. If theglass prepared in thin ampoule cooled in water is compared tothe reference material, it can be clearly seen that for the low heat-ing rates the bulk mechanism is markedly pronounced (due to thenormalization of characteristic functions optically restraining thesurface mechanism). Moreover, even in the case of higher heat-ing rates the surface mechanism seems to be slightly depressedon account of the bulk crystallization. This observation is veryinteresting. Quenching of melt placed in a narrow as well as thin-walled ampoule obviously provides one of the fastest cooling ratesachievable without special laboratory equipment; however, thecrystallization kinetics suggests that the number of bulk crystal-lization centres is higher than in the case of the reference glassprepared in a standard thick ampoule. It is the authors’ opinion thatin this case it is not the higher number of volume nuclei formed dur-ing cooling or pre-nucleation period that is responsible for morepronounced bulk crystallization. One of the differences betweenthe two ampoules subsists also in the influence of the ampoule-glass boundary itself. In the wide ampoule the melt is spread whilehaving free fluid-level, whereas the thin ampoule is filled by the

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Fig. 12. “Kinetic plot” evaluated for the basic and supplemental crystallizationkinetics measurements of Se70Te30 glass. The area of JMA model applicability issuggested. The solid curve guides eyes in direction of the increasing particle sizes inparticular fractions. Basic dataset (similar to that shown in Fig. 9) is updated withsupplemental measurements performed for glasses (particularly their 20–50 �mand 125–180 �m fractions) prepared in thin ampoules either quenched in water orfreely cooled on air.

melt across its whole cross-section. During the fast cooling of theampoule when bulk glass is formed the contracting/freezing liq-uid can change its volume adequately with no restrains in the caseof the wide ampoule. On the other hand the glass formed in thethin ampoule still fills its whole cross-section even though theoriginal liquid had considerably higher specific volume (possiblereason being the interfacial tension). In the author’s opinion thismay lead to mechanical strains and bulk dislocations resulting fromthe negative pressure in the glass structure. These defects mightconsequently act like crystallization centres thus accelerating thewhole bulk mechanism. In the case of thin ampoule cooled on airthe influence of strained structure was then most probably fur-ther strengthened by increased number of true bulk nuclei formedduring substantially slower cooling.

Regarding the second studied fraction 20–50 �m and influenceof different ways of glass preparation it can be said that all threeexperimental sets were similar implying that the intense grindingprocedure wipes the difference in the initial number of bulk nucleiand the dominating crystallization mechanism is again utterly thesurface one. Visual quantification of the differences is for bothfractions and the three different ways of glass preparation demon-strated in Fig. 12, which is in fact an extended kinetic plot fromFig. 9. For detailed information see legends of Figs. 9 and 12.

The last studied topic was that of reproducibility of experi-mental data. It was already mentioned that for the basic set ofcrystallization measurements perfect overall reproducibility wasachieved. For any prepared fraction the superposition of kineticcurves (both, characteristic functions and raw DSC data) obtainedduring repeated experiments was excellent, thus indicating thatunder perfectly similar conditions of the sample preparation (untilnow always set of samples from identical powder batch was taken)the DSC instrument error and errors associated with the mea-surement alone are negligible. The following step was verifying ofreproducibility for “similarly” prepared raw bulk glasses, i.e. forseveral ampoules which were treated in exactly same way duringthe glass and consequent powder fractions preparation. In this caseagain a very good reproducibility was achieved. However, slighttrends were already observed in this case. Namely those of repro-ducibility being dependent on particle size of the prepared powderfraction. It was found that coarser fractions have slightly worse

reproducibility, suggesting that while fine grinding of the glassseems to be a very well reproducible operation in the sense of intro-ducing constantly high enough number of mechanical defects forthe surface crystallization to dominate and manifest reproducibly,conversely the very preparation of the glass (cooling of the meltin ampoule) is the limiting factor for the overall reproducibilityof achieved results as the number of nuclei/bulk crystallizationcentres appears to vary with each ampoule, even though similarpre-nucleation period was applied in all cases. This implies that thecritical factor seems to be the cooling rate and associated thermalgradients during the glass preparation, where even slight changesof experimental conditions can evince in reproducibility worsen-ing, however small. In order to further investigate this influenceone more series of experiments was performed.

4.3.3. Influence of annealing temperature during glasspreparation

In the last supplemental study, an effect of the temperature fromwhich the original melt is cooled in order to prepare the raw glassbulk was examined. As was mentioned in Section 3 all ampoulesprepared within the framework of this article were annealed at450 ◦C and then cooled in water. For this supplemental study twomore ampoules (one thick and one thin) were prepared by anneal-ing at 650 ◦C and then cooling in water. Aim of this experimentwas to reveal possible influences of different initial structure of theglass, irreproducible thermal gradients during quenching or exactposition of the nucleation rate maximum. The results for the twoannealing temperatures were for both ampoule types (thick andthin) again very well reproducible – within the experimental errorassociated with slightly worsened reproducibility correspondingto repeatedly prepared raw bulk glass. This suggests that: (a) pos-sible different initial structure of the higher-temperature melt(length of selenium/tellurium chains; ratio of chain crosslinking;implementation of the tellurium atoms into selenium chains – ran-dom/preferred) does not have any recognizable influence on thecrystallization behavior; (b) higher thermal gradients arising fromthe larger temperature difference of the melt and cooling mediumdo not in this case have significant influence on the resultingquenching rate and consequent number of formed bulk crystal-lization centres, similar limiting heat-removal rates in the criticaltemperature region were probably achieved; (c) more probableposition of the nucleation rate maximum is at lower/similar tem-peratures compared to the crystal growth rate maximum, theirreverse position would have been indicated by significantly dif-ferent crystallization kinetics due to dissimilar quenching rates athigher temperatures caused by large additional amount of energyneeded to be dissipated in the case of cooling from 650 ◦C.

5. Conclusions

Crystallization kinetics of the Se70Te30 glass was studied undernon-isothermal conditions by using differential scanning calorime-try – main aim of the study was to demonstrate the potentialDSC for the kinetic studies of complex processes. Concerning thebasic kinetic information an extensive investigation of the parti-cle size influence on apparent activation energy was made. Forpurposes of the sample form influence interpretation both, ther-mal gradients and effect of grinding procedures were considered.Couple of recommendations regarding minimization of errors aris-ing from experimental set-up was suggested. A new criterion forquick determination of the dominating crystallization mechanism– surface or bulk – was introduced.

The complete kinetic analysis was performed in terms of theJohnson–Mehl–Avrami and Sesták–Berggren models. Complexityof the competing surface and bulk mechanisms was explained both,

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qualitatively and quantitatively. The obtained DSC data allowedexplaining of the mutual interaction of the processes as well asof the origin of their sequentiality. Discussion over the observedeffects, shifts in temperature and deviations from ideal modelbehavior was conducted on the basis of thermal gradients, sur-face crystallization centres arising from the sample preparationtreatments and amount of volume nuclei originating from the com-bination of pre-nucleation period and the very glass preparationphase. The presented conclusions are thus general and qualitativelyvalid for all similar types of complex processes.

In addition several supplemental studies were performed inorder to demonstrate further possibilities of the DSC instrumentin regard to the complex kinetic studies and an extensive amountof information that can be derived from the DSC data under theassumptions of maximum precision being dedicated to the exper-imental set-up and consequently a careful analysis of the resultsbeing performed with respect to all possible involved additionalinfluences.

As a concluding remark the authors would like to note thatalthough advanced interpretation of the DSC curves provides evenin the case of complex processes answers to a number of fundamen-tal kinetic questions, differential scanning calorimetry itself is notan ultimate technique and always should be accompanied by sup-plemental information about molecular structures (XRD, EXAFS,etc.) and/or crystal growth kinetics (optical or electron microscopy)in order to give full and consistent picture of crystallization behav-ior in the studied material.

Acknowledgement

This work has been supported by the Czech Science Foundationunder project no. P106/11/1152.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.tca.2011.10.005.

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