Elucidation of the crystallization kinetics for sodium-alumino-silicate glasses containing different...

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Elucidation of the crystallization kinetics for sodium-alumino-silicateglasses containing different amounts of manganese oxideA. A. Solimana; I. Kashifb; E. M. Sakra; A. Ratepa

a Faculty of Girls, Department of Physics, Ain Shams University, Heliopolis, Cairo, Egypt b Faculty ofScience, Department of Physics, Al-Azhar University, Nasr City, Cairo, Egypt

Online publication date: 20 November 2010

To cite this Article Soliman, A. A. , Kashif, I. , Sakr, E. M. and Ratep, A.(2010) 'Elucidation of the crystallization kineticsfor sodium-alumino-silicate glasses containing different amounts of manganese oxide', Phase Transitions, 83: 12, 1096 —1113To link to this Article: DOI: 10.1080/01411594.2010.508459URL: http://dx.doi.org/10.1080/01411594.2010.508459

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Phase TransitionsVol. 83, No. 12, December 2010, 1096–1113

Elucidation of the crystallization kinetics for sodium-alumino-silicate

glasses containing different amounts of manganese oxide

A.A. Solimana*, I. Kashif b, E.M. Sakra and A. Ratepa

aFaculty of Girls, Department of Physics, Ain Shams University, Heliopolis, Cairo, Egypt;bFaculty of Science, Department of Physics, Al-Azhar University, Nasr City, Cairo, Egypt

(Received 17 April 2010; final version received 12 July 2010)

The glass samples [40SiO2þ 5Al2O3þ {55� x}Na2Oþ xMnO2] where x¼ 0.05,0.2, 0.4, 0.6, 0.8, and 1mol% MnO2 before and after being heat treated weresubjected to X-ray diffraction. The diffraction lines provided clear evidence of thenucleation and growth, which are characteristic of sodium silicate phase.Crystallization studies were conducted using differential thermal analysis.Crystallization peak temperatures were identified and the transformed fractionswere determined. Both the rate of growth, K0, and the activation energy, E,depend on the influence of manganese ions in the glass network as a modifier oras a former and the manganese content. The values of the Avrami parameter, n,were calculated using two methods and were in excellent agreement. The processof nucleation and growth rate depends on the manganese content.

Keywords: non-isothermal DTA; crystallization kinetics; nucleation and growth;silicate glasses

1. Introduction

The element of manganese has at least five stable oxidation states with distinctive colors(as is typical of transition metals). It is commonly encountered in the laboratory as thecompound KMnO4 which is a strong oxidizing agent. MnO2 catalyzes the decompositionof H2O2 and is sometimes used for the small scale production of oxygen gas in the lab. Theelectronic structure of the manganese atom is [Ar] 3d54s2 and its stable ionic states areMn2þ. In oxide glasses such as silicate, manganese ions could enter as Mn3þ and Mn2þ

species, so that it is possible that these ions enter both network former and networkmodifier sites [1,2]. Structure studies and mechanical properties of manganese ions insodium-alumino-silicate glasses prepared by adding 0.05–1.0mol% of Mn2O3 in the glasscomposition were performed. Depending on manganese concentrations, both Mn2þ andMn3þ species were present [3]. Crystallization of glass samples involves both nucleationand growth of the crystallites and possibly amorphous phase separation processes [4–6].Knowledge of crystal growth and nucleation rates in glasses at different temperatures isessential for applications in which nucleation must be avoided. The transformation from

*Corresponding author. Email: [email protected]

ISSN 0141–1594 print/ISSN 1029–0338 online

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DOI: 10.1080/01411594.2010.508459

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amorphous to crystalline in glasses can be investigated by isothermal and non-isothermal

methods [7–9]. In the isothermal method, the sample is brought near the crystallization

temperature very quickly and then any physical quantity, which changes drastically,

is measured as a function of time. In the non-isothermal method, the sample is heated at a

fixed rate and the physical quantity is recorded as a function of time or temperature.

A disadvantage of the isothermal method is the impossibility of reaching a test

temperature instantaneously and during the time, which system needs to stabilize, no

measurements are possible. However, the non-isothermal method does not have this

drawback [10,11]. Due to the above-mentioned reason, non-isothermal method has been

used before [11–15] and in this study for the study of crystallization kinetics. The non-

isothermal differential thermal analysis (DTA) was carried out at four different heating

rates in order to elucidate the crystallization mechanism for sodium-alumino-silicate

glasses containing different amounts of manganese oxide. Four different methods of

analysis [16–21] have been used to calculate the parameters of crystallization kinetics of the

investigated glass samples.

2. Basic theory

The theoretical basis for interpreting the crystallization kinetics of isothermal phase

change can be formally described by Johnson–Mehl–Avrami (JMA) theory [22,23]. This

model predicts that the volume fraction crystallized (x) after a time t, for an isothermal

process, can be expressed by the following equation:

� ¼ 1� expð�ðktÞnÞ, ð1Þ

where n is a characteristic transformation constant, which characterizes the shape of the

transformed domain together with the transformation rate. Alternatively, the logarithmic

transformation of Equation (1) leads to [24]:

ln ln1

1� x

� �� ¼ n lnðkÞ þ n lnðtÞ, ð2Þ

where K is defined as the effective overall reaction rate constant, which reflects the rates of

both nucleation and growth. This is usually assigned to Arrhenion temperature

dependence as

k ¼ k0 exp�E

RT

� �, ð3Þ

where E (kJmol�1) is the effective activation energy describing the overall crystallization

process and R (JK�1) is a gas constant. In a non-isothermal regime, the rate constant K

changes continually with time due to the change of the temperature and Equation (1) can

be rewritten in the form [25]:

�ðtÞ ¼ 1� exp �

Z t

0

K½Tð�tÞ�d �t

� �n� �¼ 1� expð�I nÞ: ð4Þ

Deriving Equation (4) with respect to time, the crystallization rate is obtained as:

_� ¼ nKð1� �ÞI n�1: ð5Þ

Phase Transitions 1097


The maximum rate of crystallization occurs at the peak of the exothermic at

time tp and temperature Tp [26]. The differentiation of Equation (5) with respect to

time yields

€� ¼ nKpðInÞp � ðn� 1ÞKp �

�EIpRT 2

p

¼ 0: ð6Þ

The time integral in Equation (4) is transformed to a temperature integral yielding

IðT Þ ¼K0

�

Z T

T0

exp�E

R �Td �T: ð7Þ

The integral I can be expressed, according to the literature [27], by the sum of the

alternating series:

Sð �yÞ ¼�e� �y

�y2

Xk¼1k¼0

ð�1Þkðkþ 1Þ!

�yk, ð8Þ

where �y ¼ E=R �T. Considering that in this type of series, the error produced is less than the

first term neglected and bearing in mind that in most crystallization reactions�y ¼ E=R �T� 1, it is possible to use only the first two terms of this series, and the error

introduced is not greater than 1%. In addition, if it is assumed that T�T0, (T0 is the

starting temperature), so that �y 0 can be taken as infinity [27], then the last expression of the

integral is

Ip ¼1� 2RTp

nE

� �1=n

: ð9Þ

Substituting for Ip into Equation (6) and taking the logarithmic form, we get

lnðT 2p=�Þ þ lnðK0R=E Þ � E=RTp ¼ ð2RTp=E Þð1� n�2Þ: ð10Þ

It should be noted that for most crystallization reactions, the right-hand side (RHS) of

Equation (10) is generally negligible in comparison to the individual terms on the left-hand

side for common heating rates (�100Kmin�1). Therefore, the approximation in Equation

(10) (RHS¼ 0) might introduce a 3% error in the value of E/R in the worst cases [27], and

Equation (10) becomes

lnT 2p

�

!¼

Ec

RTpþ ln

E

K0R

� �: ð11Þ

Then, the activation energy of crystallization process, Ec, was developed by Kissinger’s

[16], Augis–Bennett’s [19], Matusita–Sakka’s [17,18], and Ozawa–Chen’s [20,21] methods.

In this article, the activation energy of crystallization has been calculated by using the

above different methods that evaluated, E, from different thermograms held at different

heating rates. The first three methods are based on the determination of the fraction of

crystallization, x, for different heating rates using the dependence of peak crystallization

temperature, Tp, on the heating rates, �, while the last method (Ozawa–Chen) is based on

the effect of heating rate, �, on the temperature at which the crystallization fraction, x, is

constant.

1098 A.A. Soliman et al.


3. Experimental work

A series of glass samples of [40SiO2þ 5Al2O3þ {55� x} Na2Oþ xMnO2], where x¼ 0.05,0.2, 0.4, 0.6, 0.8, and 1mol% MnO2, as shown in Table 1, were prepared by using rawmaterials. All of these are chemically pure and they were finally pulverized. Thehomogeneous mixture was melted in a porcelain crucible in an electrically programmableheated furnace, type (VAF 15/10) LENTON thermal designs, equipped with an automatictemperature controller. The samples were melted at about 1100� 20 for 2 h with heatingrate 30�Cmin�1. The molten material was quenched in air and poured at roomtemperature between two steel plates. The quenched samples were annealed at 300�Cfor 20min. The as-made glasses were immediately stored in vacuum desiccators until usedfor measurement. The samples were examined by using Philips analytical X-ray diffraction(XRD) system, Type PW 3710 based with Cu tube anode, which confirms the amorphousnature of the investigated glass samples. Each glass sample is heat treated at around thecrystallization temperature (Tc). The measurements were carried out using a non-isothermal method with DTA techniques. The DTA measurements were carried out usinga SHIMADZU DTA-50 ANALYZER between 25�C and 1100�C (in N2 gas using Al2O3

powder as a reference material), at different heating rates �¼ 15, 25, 35, and 40Kmin�1.

4. Results and discussions

4.1. XRD investigations

XRD pattern of the investigated glass samples {40mol% SiO2þ 5mol%Al2O3þ (55� x)mol% Na2Oþ xmol% MnO2} with x¼ 0.05, 0.2, 0.4, 0.6, 0.8, and1mol% MnO2 before and after heat treatment at about the crystallization temperature areshown in Figure 1(a) and (b), respectively. Figure 1(a) shows a broad halo peak at arounddiffraction angles (2�) 32�, which is characteristic of the fully amorphous structure,confirming that these glass samples are composed of a glassy phase. The glass sampleswere heat treated at about Tp and partly crystallized as shown in Figure 1(b).The diffraction lines are providing a clear evidence of the nucleation process and thegrowth, which are characteristic for the formation of sodium silicate phase in all the glasssamples. The broad XRD diffraction line indicates that the sodium silicate particles areof nano size.

4.2. Composition dependence

The DTA curves of the glass samples {40mol% SiO2þ 5mol% Al2O3þ (55� x) mol%Na2Oþ xmol% MnO2}, where x¼ 0.05, 0.2, 0.4, 0.6, 0.8, and 1mol% MnO2 were

Table 1. Code and silicate glass composition (mol%).

Code SiO2 Al2O3 Na2O MnO2

S1 40 5 54.95 0.05S2 40 5 54.8 0.2S3 40 5 54.6 0.4S4 40 5 54.4 0.6S5 40 5 54.2 0.8S6 40 5 54 1



obtained at four heating rates (�¼ 15, 25, 35, and 40Kmin�1) for each composition.Figure 2 shows the non-isothermal DTA curves for glass sample S6 at chosen heating ratefrom 15 to 40Kmin�1 as an example. It is clear that the peak temperature, which is takenas the crystallization temperature, Tp shifts towards higher temperatures as the heatingrate is increased from 15 to 40Kmin�1 as shown in Table 2. The effect of heating rate onthe variation of Tp with the composition of manganese contents is shown in Figure 3. It isfound that the value of Tp, decreases comparatively in the glass samples containing05 x� 0.4mol% MnO2, and then shows the dramatic change step-wisely inx4 0.4mol% MnO2. The average value of Tp with the manganese content confirmsthis trend as shown in Figure 3 and listed in Table 2. It shows that there is a gradual

S6

S5

S3

S1

S6

S5

S3

S1

18 32 46 60 74

2q

2q

Inte

nsity

(a.

u.)

Inte

nsity

(a.

u.)

Sodium silicate

4 18 32 46 60 74

(a)

(b)

Figure 1. The XRD of the investigated glass samples (a) before heat treated and (b) after heattreated at Tp.



decrease in Tp average values up to 0.4mol% MnO2, followed by a sharp drop in Tp’s

beyond 0.4mol% MnO2. Then the investigated glass samples seem to have two regions

of affect, one up to 0.4mol% MnO2 and another one beyond 0.4mol% MnO2, which

could be attributed to the effect of the different oxidation states of manganese ions in theglass network, since the SiO2/Al2O3 ratio, is constant in all the glass samples and the ratio

of SiO2/Na2O depends on the manganese concentration.

Figure 2. The non-isothermal DTA curves for glass sample S6 at chosen heating rates, as anexample.

Table 2. The crystallization temperature Tp with different heating rates and the parameters A and Bof Equation (1).

Tp (K)The average

valuesThe valuesof A and B

Code15

(Kmin�1)25

(Kmin�1)35

(Kmin�1)40

(Kmin�1) Tp (K)Heatingrate A B

S1 912 929.02 941 948 932.51 28.75 814.07 35.967S2 892 916 933.5 939.5 918.75 28.75 759.76 48.739S3 884.4 910 929.5 940 915.97 28.75 732.31 55.78S4 835.4 861 873.5 889.4 864.83 28.75 695.34 51.471S5 804 826.25 844 853.5 831.94 28.75 668.42 49.66S6 797.01 823.86 837.5 847.5 826.47 28.75 661.91 49.977



4.3. Calculation of rate constant of crystallization process (K0)

To get information about the morphology of the nucleation and growth, the following

equation from the Gao–Wang model [28] has been used to calculate the value of the rateconstant K0 at peak crystallization temperature (Tp) for a constant heating rate:

K0 ¼ ð�E Þ=RT2p : ð12Þ

The calculated values of K0 at constant heating rate for all the glass samples are shownin Figure 4(a). Augis and Bennett [19] is another method which has been used to calculate

the values of the rate constant, as shown in Figure 4(b). The two figures are shown in thesame trend at which K0 is decreased rapidly up to 0.4mol% MnO2 reaching a minimum

value at S3 (0.4mol% MnO2) and then increased gradually beyond 0.4mol% MnO2. Thisbehavior could be used to interpret the trend of the variation of Tp. Since K0 is measuringthe growth rate, it can be seen that the growth rate decreases for the glass samples

containing manganese up to 0.4mol% MnO2 and then increases by the addition of moremanganese. As far as is known, the application of controlled crystallization process

required that attention be paid to both nucleation and growth rates. Therefore, the reasonfor this behavior could be due to the fact that the investigated glass samples are highlynucleated initially, and the nucleation decreases by increasing the MnO content up to

0.4mol% MnO2, reaching a minimum at 0.4mol% MnO2. Beyond 0.4mol% MnO2, ahigh amount of manganese contents can induce a high crystal growth rate and increase the

nucleation process resulting in the glass samples. Then, the rate of constant K0 has twoaffected regions as Tp. The structural and chemical local order within the network insilicate glasses can be characterized by the concentration of various types of Si

environment, typically expressed as Qn species, where n varies between 0 and 4 anddenotes the number of bridging oxygens [29]. Therefore, in the concentration

region�0.4mol% MnO2, the manganese ions may mostly exist in Mn2þ state, occupynetwork forming positions with MnO4 structural units and in turn increase the bridgingoxygen, which increases the polymerization of the silicate glass network and weakens the

crystallization process at this region of manganese content [1,2]. Above 0.4mol% MnO2,the manganese ions may change to Mn3þ state and occupy modifying positions with

790

810

830

850

870

890

910

930

950

970

0 0.2 0.4 0.6 0.8 1 1.2MnO2 (mol%)

Tp

(K)

Tp K at 15Kmin–1

Tp at 25Tp at 35Tp at 40Taverage

Figure 3. The effect of heating rates on the variation of Tp with the Manganese contents.



increasing the manganese content which in turn increases the NBO and helps thecrystallization process [1] and growth rate. Then it could be concluded that the rate ofgrowth for the investigated glass samples depends on the influence of the manganese ionson the glass network. The values of Tp are affected by the crystal growth and thecrystallization process as well.

4.4. Avrami index n

The fraction of crystallization at constant temperature for different heating rates isassumed to be proportional to the amount of heat evolved during crystallization which isproportional to the area under the exothermic peak, and the Avrami exponent, is relatedto the directionality of crystal growth. The value of n can be determined from the slope ofplotting the relation between ln[ln(1� x)�1] versus ln�, as shown in Figure 5(a)–(c)according the relation [30]

d ln½�lnð1� xÞ�

d ln�¼ �n: ð13Þ

At a particular temperature (T ), x is calculated by dividing the partial area up to thattemperature by the total area of the exothermic peak. The transformed volume fraction xat three different temperatures of each sample for the chosen heating rates has beencalculated. The obtained volume fraction for all the glass samples at the chosen heating

(a)

0.3

0.35

0.4

0.45

0.5

0.55

0.6

MnO2 (mol%)

Rat

e co

nsta

nt (

K0)

(b)

–1.2

–1.1

–1

–0.9

–0.8

–0.7

–0.6

–0.5

0 0.2 0.4 0.6 0.8 1 1.2

0 0.2 0.4 0.6 0.8 1 1.2MnO2 (mol%)

lnK

0

Figure 4. The calculated values of K0 by using (a) Gao–Wang model and (b) Augis and Bennett.



rates shows the same trend and lies in the range of 0.1–0.9 as shown in Figure 5 at

�¼ 40Kmin�1 as an example. Alternatively, the obtained volume fraction for each

sample at chosen heating rates signifies that the rate of crystallization process

increases with increasing the heating rate as shown in Figure 5(a) for the sample S6, as

an example. Then, the values of n for each glass sample have been determined at three

different temperatures, as shown in Figure 6(a)–(c). The correlation coefficients r of the

plots are all greater than 0.99, indicating good linear relationships. These values of

the Avrami index n are given in Table 3 with the average value for each sample. Also,

from the shape of crystallization exothermic peak, another method could be used to

determine the crystallization mechanism n, using the equation [19]

n ¼2:5

DT

� �RT 2

p

E, ð14Þ

where DT is the width of the crystallization exothermic peak at half maximum, R is the gas

constant, Tp at heating rate 40Kmin�1 is in Table 2 and E average is in Table 4. The

obtained values of n are given in Table 3. Based on the values of n which were obtained

from the two mentioned methods, it is reasonable to say that the different values of n are

indication for the different crystallization mechanisms and the non-integer values of n

mean that two crystallization (2- and 3-D growth) mechanisms are working

At heating rate 40K min–1(a)

(b)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

790 820 850 880 910 940

Temperature (K)

Fra

ctio

n x

S1S2S3S4S5S6

S6

0

0.2

0.4

0.6

0.8

1

1.2

760 780 800 820 840 860Temperature (K)

Fra

ctio

n x

b =15b =25b =35b =40

Figure 5. The volume fraction of crystals for all the glass samples at 40Kmin�1 as an example(a) the volume fraction of crystals for S6 at chosen heating rates.



simultaneously during the amorphous-to-crystalline transformation of the studied glasssamples [31,32].

4.5. Dependence of Tp on the heating rate

There are several approaches which were used to analyze the dependence of crystallizationtemperature, Tp on the heating rate (�). The first approach used the empirical relationship,which had been used before, for phase transformation from glass to amorphous [3,33,34]to analyze the dependence of Tg on the heating rate. In this study, we try to use it for phase

–4

–3

–2

–1

0

1

2(a)

(b)

(c)

ln b

ln[ln

(1–x

)–1]

S1 at 943 KS2 at 893 KS3 at 913 KS4 at 833 KS5 at 793 KS6 at 813 K

–4

–3

–2

–1

0

1

ln b

ln[ln

(1–x

)–1]


–4–3.5

–3–2.5

–2–1.5

–1–0.5

00.5

1

2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9

2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9

2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9

ln b

ln[ln

(1–x

)–1]


Figure 6. (a–c) The relation between ln[ln(1�x)�1] vs. ln�.



Table

3.Avramiindex,n,in

thestudiedglass

samples.

Theinvestigatedglass

samples

S1

S2

S3

S4

S5

S6

T(K

)n

T(K

)n

T(K

)n

T(K

)n

T(K

)n

T(K

)n

Thevalues

ofnfrom

theslope

893

1.6

893

1.84

883

3.08

833

1.35

793

2.48

803

1.56

918

1.2

913

0.96

893

2.11

863

0.89

813

1.79

813

1.72

943

1.7

943

0.67

913

2.14

883

1.13

828

2.12

833

2.02

n(average)

n(average)

n(average)

n(average)

n(average)

n(average)

1.5

1.16

2.44

1.12

2.13

1.77

Thevalues

ofDT

(K)

59.015

56.491

60.501

83.23

69.31

61.04

Thevalues

ofnfrom

calculations

1.737

2.401

2.648

1.799

2.053

2.314



transformation from amorphous to crystallization phase, using Tp instead of Tg to analyzethe dependence of Tp on the heating rate that can be written in the following form:

Tp ¼ Aþ B ln�, ð15Þ

where A and B are constants for a given glass composition and � is the rate of heating.Then the plot of Tp versus ln� gives a straight line, the slope of which gives B. The plot ofthe results shown in Figure 7(a) indicated the validity of Equation (14) for the investigatedglass samples. The obtained values of A and B are given in Table 2. For a betterunderstanding of the variation of the values B, let us think of the variation of B withdifferent concentrations of MnO2 which is shown in Figure 7(b). It shows that the trend ofthe variation of values of B is exactly in the direction opposite to that of the values of K0

(rate of crystallization process) with the manganese content, which is shown in Figure 3(a)and (b). It is obvious that the values of B are increased as the manganese content isincreased up to 0.4mol% at which it has a decrease in the values of the rate constant K0.Beyond 0.4mol% MnO2, the value of B shows a decrease while the rate of crystallization,K0 shows an increase. Then the slope B is related to the crystal growth and thecrystallization process, where the lower value of B, corresponds to the higher the rate ofcrystallization and crystal growth and vice versa. This signifies that B is related with theresponse of the construction changes within the crystallization transition region Tp.

4.6. Activation energy of crystallization process (E)

The second approach which was used is the determination of the activation energy ofcrystallization process of each glass sample to analyze the dependence of crystallizationtemperature on the heating rate (�). It has been calculated by four different methods usedin the literature and the correlation coefficients r of the plots in four methods are allgreater than 0.99, indicating good linear relationships. The first method used is Kissinger’smethod [16], according to which the peak temperature of crystallization Tp is expressed asa function of heating rate by the following equation:

lnT 2p

�

!¼ ln

E

R

� �� lnAþ

E

RTp, ð16Þ

where A is constant which depends on the material and R is the gas constant. Plots oflnðT 2

p=�Þ as a function of 1000/Tp have been made as shown in Figure 8(a) for the

Table 4. The crystallization activation energy Ec (kJmol�1) in the investigated glass systems.

Crystallization activation energy Ec (kJmol�1)

Sample (a) Kissinger (b) Matusita–Sakka (c) Augis–Bennett (d) Ozawa–Chen Ec (average)

S1 177.296 192.203 174.877 184.513 182.222S2 129.757 145.212 151.315 137.414 135.263S3 108.339 122.074 113.369 114.766 114.637S4 102.611 116.928 110.052 109.637 109.807S5 100.259 114.002 104.258 107.126 106.411S6 97.972 110.809 108.315 105.629 105.681



investigated glass samples. The activation energy of crystallization process, E, has been

derived from the slopes of these plots and the results are given in Table 4.Another method used is based on the Matusita–Sakka theory [17,18] according to

which Tp and the heating rates (�) are given by

lnð�Þ ¼�E

RTpþ const: ð17Þ

Matusita–Sakka studied the relation between ln� versus 1000/Tp, as shown in

Figure 8(b) for all studied glass samples. The slope of which gives E and the results are

given in Table 4.The third method used is based on the method of Augis and Bennett [19], according to

which Tp as a function of � is given by the following equation:

lnTp � T0

�

� �¼ �lnK0 þ

E

RTp, ð18Þ

where T0 is the onset crystallization temperature. Figure 8(c) shows the relationship

between ln(DT/�) and 1000/Tp, from which the activation energy was calculated and

tabulated in Table 4.Finally, the Ozawa–Chen method [20,21] studied ln(Tp/�) versus 1000/Tp at constant

crystallization fraction according to equation:

lnTp

�

� �¼ �

1

nlnK0þ

E

RTp: ð19Þ

780800820840860880900920940960(a)

(b)ln b

Tp

(K)

S1S6S2S3S4S5

2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9

30

35

40

45

50

55

60

MnO2 (mol%)

The

slo

pe B

0 0.2 0.4 0.6 0.8 1 1.2

Figure 7. (a) The plot of Tp vs. ln� and (b) the variation of B with the different concentrations ofMnO2.



Kissinger’s method

9.6

9.8

10

10.2

10.4

10.6

10.8

11

1.03 1.08 1.13 1.18 1.23 1.28

1000/Tp (K–1)

ln(T

p2 /b

)

S1S2S3S4S5S6

(b)

(a)

2.5

2.7

2.9

3.1

3.3

3.5

3.7

3.9

1000/Tp (K–1)

lnb S1

S2 S3 S4 S5 S6

Matusita–Sakka

(c)

2

2.2

2.4

2.6

2.8

3

3.2

1000/Tp (K–1)

ln(Δ

Tp/

b)

S1S2S3S4S5S6

Augis and Bennett’s method

(d) Ozawa–Chen

3

3.2

3.4

3.6

3.8

4

4.2

1.05 1.1 1.15 1.2 1.25 1.3

1.03 1.08 1.13 1.18 1.23 1.28

1.03 1.08 1.13 1.18 1.23

1000/Tp (K–1)

ln(T

p/b

)

S1S2S3S4S5S6

Figure 8. (a) The Plots of lnðT 2p=�Þ vs. 1000/Tp, (b) the relationship between ln � vs.

1000/Tp, (c) ln(DT/�) and 1000/Tp, and (d) the variation of ln(Tp/�) vs. 1000/Tp.



Figure 8(d) shows this relationship for different heating rates from which the activationenergy has been calculated and tabulated in Table 4. It can be observed that the values ofthe activation energy for crystallization of the Na2SiO3 phase, which are obtained by fourmethods, are reinforcing each other. The values of the activation energy obtained from theKissinger method have found to be much smaller than those obtained from other methodsand those obtained by Matusita–Sakka are larger than others. There is a noticeabledifference between the results obtained by the Kissinger model and those obtained byOzawa–Chen’s, Matusita–Sakka’s, and Augis–Bennett’s methods (the Kissinger method iscommonly used, which is one of the most used methods for crystallization kinetic studies).The activation energy of crystallization can be determined by using the Kissinger equation,which could be attributed to the applicability of the Kissinger equation to non-isothermalkinetics and this activation energy is deduced without taking into account thecrystallization mechanisms [24]. In some cases, surface and bulk crystallization occursimultaneously. The Kissinger equation is valid only when crystal growth occurs on a fixednumber of nuclei during crystallization process [24]. Incorrect values for the activationenergy can be obtained if a majority of the nuclei are formed during crystallization.A comparison among all the above different calculation methods for the activation energyand its average value has been made from which it can be deduced that all the usedmethods are valid to determine the activation energy for the studied glasses with differentlevels of accuracy. The most accurate method deduced according to this study is suggestedto be Ozawa–Chen’s method, since it has shown the minimum deviation from the average.The average values of the obtained values of the crystallization transition activation energyEc (average) from the above models were plotted as a function of MnO2 content andshown in Figure 9(a). It shows that the activation energy for the crystallization transition,Ec (average), decreases rapidly in the glass samples containing 05 x� 0.4mol% MnO2,and then shows the comparative change in x4 0.4mol% MnO2. From energy point ofview, the state of a crystallization system, which has the lowest energy, is the best of thecrystallization process and growth rate. Larger levels of activation energy for thecrystallization transition correspond to a low level of nucleation and growth rate system,which is consistent with the results of the rate constant K0. Then, this confirms that theinvestigated glass samples have a weakening crystallization process and a growth rate inlow manganese oxide content up to 0.4mol% MnO2, and beyond 0.4mol% MnO2

the crystallization process has been improved by increasing the manganese content. Also,the activation energies involved in crystallization process, Ec, were compared with theactivation energies of glass transition process from the dependence of Tg on the heatingrate, Eg, shown in Figure 9(b) [3]. It is found that they are closely inverse related i.e.,the maximum value of Ec at 0.05mol% MnO2 is related to a minimum value of Eg

and the maximum value of Eg at 1mol% MnO2 records a minimum value of Ec.Accordingly, the minimum value of Ec gives an indication of the retardation of thecrystallization with high thermal relaxation helping rearrangement of the atoms aroundTg, while the lower Eg is attributed to the stability and glass-forming ability (GFA) [35].

5. Conclusions

The effect of different amounts of manganese on the crystallization kinetics of heat-treated40SiO25Al2O355Na2O glasses has been studied using non-isothermal DTA at four heatingrates. The crystallization kinetic parameters Ec, K0, and n have been calculated usingdifferent methods, from which it can be deduced that all the used methods are valid to



determine the values of activation energy for the studied glasses with different levels ofaccuracy. The most accurate method deduced according to this study is suggested to be

Ozawa–Chen’s method, since it has shown the minimum deviation from the average.The values of the Avrami parameter, n, were calculated using two methods and both

indicated a mixed mechanism of 2- and 3-D growth. The rate of growth, K0, and Ec depend

on the influence of manganese ions in the glass network as a modifier or as a former and

the manganese content.

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100

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190(a)

(b)

0 0.2 0.4 0.6 0.8 1

MnO2 (mol%)

Ec

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