A new DTA method for measuring critical cooling rate

Journal of Non-Crystalline Solids 351 (2005) 1350–1358 www.elsevier.com/locate/jnoncrysol

A new DTA method for measuring critical cooling rate for glass formation Chandra S. Ray a,*, Signo T. Reis b, Richard K. Brow b, Wolfram Ho¨land c, Volker Rheinberger c b

a Marshall Space Flight Center, National Aeronautics and Space Administration, Huntsville, AL 35812, USA Graduate Center for Materials Research/Materials Science & Engineering Department, University of Missouri-Rolla, Rolla, MO 65409, USA c Ivoclar Vivadent AG, Bendererstrasse 2, FL-9494 Schaan, Fu¨rstentum, Liechtenstein

Received 24 September 2004; received in revised form 2 March 2005

Abstract A new differential thermal analysis (DTA) experimental method has been developed to determine the critical cooling rate for glass formation, Rc. The method, which is found especially suitable for melts that, upon cooling, have a small heat of crystallization or a very slow crystallization rate, has been verified using a 38Na2O–62SiO2 (mol%) melt with a known Rc (19 C/min), then used to determine Rc for two complex lithium silicate glass forming melts. The new method is rapid, easy to conduct and yields values for Rc that are in excellent agreement with the Rc values measured by standard DTA techniques. 2005 Elsevier B.V. All rights reserved.

1. Introduction The critical cooling rate for glass formation, Rc, is a measure of the ability of a melt to form glass, and is defined as the slowest rate at which a melt can be cooled from its liquidus temperature (Tm) to below the glass transition temperature without detectable crystallization [1,2]. A slower Rc indicates a greater glass forming ability for a melt. Thus, Rc is an important characteristic parameter that should be known for a melt in order to predict the ease or difficulty for glass formation, and, hence, to determine the processing conditions for a glass. Several experimental methods are available for estimating Rc, including ones that are designed to generate

*

Corresponding author. Tel.: +1 256 544 2918; fax: +1 256 544 8762. E-mail address: [email protected] (C.S. Ray).

0022-3093/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2005.03.029

a temperature–time cooling curve by cooling a melt either at a constant temperature (isothermal cooling) or at a constant rate (continuous or non-isothermal cooling). A differential thermal analysis (DTA) apparatus is generally used for melt-cooling experiments. In isothermal cooling, the temperature of an equilibrated melt is quickly decreased from above the melting (or liquidus) temperature, Tm, to a pre-determined temperature, where the melt is held until crystallization occurs, as indicated by an exothermic peak on the isothermal cooling curve. A plot of the isothermal temperature as a function of time needed to crystallize the melt at that temperature results in a nose-shaped temperature–timetransformation (TTT) diagram, shown schematically in Fig. 1. The nose in Fig. 1 corresponds to the temperature (nose temperature, Tn) where the melt, when held isothermally, crystallizes in the shortest possible time (nose time, tn). The slope of the straight line from Tm to the nose of the TTT-curve is a measure of Rc [=(Tm Tn)/tn] for the melt. A melt cooled at a rate R > Rc forms a glass,

C.S. Ray et al. / Journal of Non-Crystalline Solids 351 (2005) 1350–1358

Temperature

Tm

Tn

1351

TTT - Diagram

R RC (Glass) R = RC

tn

RC =

T m-T n tn

Time

Fig. 1. Schematic of a typical nose-shaped temperature–time-transformation or TTT-diagram for a hypothetical melt. Tm: melting temperature, Tn: nose temperature where the melt when held isothermally crystallizes in the shortest possible time, tn (nose time), R: cooling rate, Rc: critical cooling rate for glass formation.

whereas the melt crystallizes when cooled at a rate R < Rc (Fig. 1). Constructing a TTT-curve from isothermal cooling experiments is time-consuming. In addition, the isothermal cooling approach does not replicate common glass manufacturing processes. A more realistic approach, which is less time-consuming, is to analyze the crystallization event (temperature and time) for a melt cooled from Tm at different, continuous rates. Three commonly used methods for measuring Rc by analyzing crystallization peaks from continuously cooled melts are briefly described here. (a) Method 1: Identifying the cooling rate curve for which no crystallization peak is observed. When a melt is cooled at a sufficiently slow rate, an exothermic crystallization peak appears at a certain temperature, Tc, in the cooling curve as the melt crystallizes. With increasing cooling rate (R), Tc occurs at progressively lower temperatures, and the size of the crystallization peak becomes less intense, as shown schematically in Fig. 2. The cooling rate at which the crystallization peak just disappears is taken as Rc. (b) Method 2: Continuous-cooling-temperature or CCT diagram. A plot of Tc in Fig. 2 versus the time a melt takes to crystallize when cooled from the melting temperature, Tm, at a rate R produces a curve, known as continuous-cooling-temperature or CCT diagram [1] that resembles the upper portion of a TTT diagram, see the inset in Fig. 2. Since, temperatures lower than those represented by the solid curve in the CCT diagram (inset in Fig. 2) cannot

Fig. 2. Schematic of typical temperature–time cooling curves for a hypothetical melt when cooled at different rates, R. The melt crystallizes, as exhibited by exothermic peaks, when cooled at rates less than the critical cooling rate for glass formation, Rc. The onset temperature for crystallization, Tc, and the height of the peak, h, decrease with increasing R, and the R for which the crystallization peak just disappears is the Rc. Tm: melting temperature. The inset shows a continuous-cooling-temperature diagram based on the temperature–time cooling curves.

be approached by continuous cooling without crystallizing the melt, only the upper half can be experimentally determined for a CCT diagram. The lower half, shown as dashed line, is a mirror image of the experimental curve, which has been drawn intentionally to make the CCT diagram look like a TTT diagram so that a nose temperature, Tn, and a nose time, tn, can be identified. The CCT curve is then analyzed [1] like the TTT curve in Fig. 1 to determine Rc using the relation Rc = (Tm Tn)/tn. (c) Method 3: An empirical equation for evaluation of cooling curves. The crystallization temperature Tc for a melt (Fig. 2) has been related [3–5] to the corresponding cooling rate R as ln R ¼ ln Rc B=ðT m T c Þ2 ;

ð1Þ

where B is a constant. A plot of ln R versus 1/(Tm Tc)2 yields a straight line and the critical cooling rate, Rc, for the melt is determined from the intercept of the straight line with the lnR axis. Each of the methods discussed above require a detectable crystallization peak during cooling to determine Rc. However, certain melts, particularly silicarich melts, exhibit crystallization peaks during cooling that are difficult to discern, either due to slow crystallization kinetics or because of small heats of crystallization. The determination of Rc for such melts using the methods described above poses an experimental

1352


challenge. However, a new DTA method has been developed for determining Rc for glass forming melts, which is based on analyzing the relatively larger exothermic crystallization peaks that result when glasses with well-defined thermal histories are re-heated at a constant rate. 1.1. A new experimental method for determining Rc As mentioned above, many melts, particularly those with high silica contents, do not exhibit significant crystallization peaks in a DTA experiment when cooled. However, upon re-heating, many of these glasses do exhibit detectable crystallization peaks. An example is shown in Fig. 3, which shows the DTA heating and cooling curves for a glass designated as VP2212. The glass sample was initially heated to 140–200 C above the crystal melt temperature (Tm 920 C), held for 3 min to equilibrate the homogeneous melt, then cooled at the indicated rate (R 7.8 C/min) to room temperature before re-heating at 15 C/min. On cooling at this slow rate, a small, nearly undetectable, crystallization exotherm is observed, whereas two, much larger, exothermic peaks are present in the re-heating cycle. The barely detectable crystallization peak (on cooling the melt) such as one shown in Fig. 3, can introduce a larger error in Rc measured by any of the standard methods (Methods 1–3). This problem led us to develop an alternative method, which does not require using the crystallization peak that occurs on cooling the melt, rather uses the crystallization peak that occurs on re-heating the solidified melt. This new method, which just requires repeating the complete heating–cooling cycle (e.g., Fig. 3) by changing only the cooling rate

(R) of the melt, is straight forward, rapid, and yields reasonably accurate results in addition to its capability for measuring Rc for a wide variety of melts. The area of the DTA peak on re-heating is directly proportional to the amount of heat evolved during crystallization, and, hence, to the amount of residual glass present after cooling the equilibrated melt, which, in turn, depends upon the initial cooling rate of the melt. If the solidified melt is partially crystallized (for a sufficiently slow R, for example), the subsequent re-heated DTA peak area will be smaller than those for a crystal-free glass cooled at a faster R, since the partially crystallized sample contains less residual glass that is available for crystallization on re-heating. A solid sample produced at R P Rc should be crystal-free, and the area of the subsequent re-heated DTA peak should be a maximum. This means that no further increase in the area of the DTA peak would be observed for samples prepared by cooling the melt at rates greater than Rc. The primary task in determining Rc by this method, therefore, is to identify a cooling rate which produces a sample whose subsequent rate-heated DTA yields a crystallization peak with maximum area. Schroers and Johnson [6] recently reported a somewhat similar method to determine Rc for a Pd43Ni10Cu27P20 bulk metallic glass using differential scanning calorimetry (DSC). They calculated volume fraction crystallized on cooling 100–300 lm diameter molten particles dispersed in a mixture of Al2O3 and B2O3 powder by directly measuring the heat release on subsequent heating in DSC. The minimum cooling rate for which the crystallized volume fraction became zero (heat release on re-heating was maximum) was the Rc. 1.2. Calculation of DTA peak area

4

Tp

VP2212

heating rate o

15 C/min

o

hold at 1125 C for 3min

0

o

∆ T ( C), Exo

2

cooling rate

-2

o

T m =920 C

o

R= 7.8 C/min o

T c=822 C

-4 0

200

400

600

800

1000

1200

o

Temperature ( C ) Fig. 3. DTA heating curve at a rate of 15 C/min for the solidified melt of VP2212 composition after cooling the melt at a rate of 7.8 C/min. The melt was held at 1125 C for 3 min before cooling. Tm melting temperature, Tc crystallization temperature on the cooling curve, Tp: crystallization temperature on the heating curve. Note: nearly undetectable crystallization signature on cooling compared to that on heating the solidified melt.

The area under a DTA peak was calculated using the Pyris software package (1996) provided by Perkin– Elmer Corporation. The method for calculating DTA peak area is shown in Fig. 4, as an example, using a peak obtained at rate of 10 C/min for a glass designated as VP2076. In practice, the digitized data for the thermal profile were compared to select an initial and a final temperature. The temperature differential (DT on vertical axis) generally shows a constant value within some temperature range (T on horizontal axis) before it starts increasing as the crystallization peak is approached, and the initial temperature is selected from this range. Similarly, DT becomes constant for a certain temperature range after completion of the peak, and the final temperature is selected from that temperature range (Fig. 4). Based on these inputs, the software calculates a sigmoidal base line, and the area between the peak profile and the sigmoidal base line is displayed as the DTA peak area.


1353

Fig. 4. Method of calculating DTA peak area using a calculated sigmoidal base line under the peak. The DTA crystallization peak at a heating rate of 10 C/min for the VP2076 glass is used to show the calculations. See text for a description of the calculation procedure.

2. Experimental methods The new experimental technique for measuring the critical cooling rate for glass formation (Rc) was developed while attempting to measure Rc for two complex lithium disilicate (Li2O Æ 2SiO2)-based glass compositions developed by Ivoclar Vivadent AG,1 and designated as VP2212 and VP2076. Both compositions, designed for glass–ceramic applications, contained 81– 83 wt% Li2O Æ 2SiO2, about 4 wt% P2O5 as a nucleating agent, and several other oxide components such as, K2O, ZnO, La2O3, and Al2O3. The primary difference between the compositions was that VP2212 contained about 1.1 wt% Al2O3, but VP2076 was alumina-free. In addition to the Li-disilicate melts, a 38Na2O– 62SiO2 (mol%) glass with a known Rc (19 C/min [7]) was also characterized. About 50 g of this Na-silicate glass was prepared by mixing appropriate amounts of reagent grade crystalline Na2CO3 and SiO2 powders, and melting the mixture at 1150 C for 2 h in an alumina crucible. The melt was stirred three times with an alumina rod to ensure homogeneity and cast between two steel plates. The as-cast glass was ground (400– 600 lm) for subsequent use in the DTA experiments. A Perkin–Elmer DTA-7 apparatus was used to characterize the critical cooling rates for the glass-forming melts. The experiments were conducted in platinum containers in a flowing (30 mL/min) nitrogen gas using high purity (99.999%) Al2O3 powder as a reference material supplied by Perkin–Elmer. The DTA apparatus was periodically calibrated using indium (mp. 156.6 C), alu-

1

Bendererstrasse 2, FL-9494 Schaan, Fu¨rstentum Liechtenstein.

minum (mp. 660.4 C), and gold (mp. 1064.4 C) standards. The mass of each glass sample, initially 40–45 mg, was re-measured at the conclusion of each experimental set; no mass loss was observed indicating that the composition of the glass remained unchanged throughout an experiment. All DTA results were normalized to the initial sample mass. It was observed that the actual cooling rate (R) differed from the cooling rate programmed for the experiment. Therefore, R was measured for each experiment by recording the time required to decrease the measured sample temperature by 50 C, covering the temperature range around Tc. The reported value of R is the average of at least three such measurements.

3. Results and discussion 3.1. New method Three DTA heating curves, collected at 15 C/min, for the 38Na2O–62SiO2 (mol%), VP2212 and VP2076 melts are shown in Figs. 5–7, respectively. These are examples of the typical experiments carried out using the new method for determining the critical cooling rates for the melts. These curves were obtained after cooling each melt at different rates (R) indicated in the figures. Similar DTA results were obtained for all three melts cooled at other rates, and the DTA peak areas are plotted as a function of R in Fig. 8. Fig. 8 shows that the DTA peak areas for all the samples increase initially with increasing R, indicating an increase in the fraction of residual glass in the cooled samples. The DTA peak area becomes a maximum at a certain R and remains

1354

C.S. Ray et al. / Journal of Non-Crystalline Solids 351 (2005) 1350–1358 3.5

4.5

38Na 2 O-62SiO 2

VP2212 o

o

Heating rate: 15 C/min

3.0

o

∆T ( C), Exo

o

1.5 0.0

o

2.0

o

∆T ( C), Exo

2.5

1.5

-1.5 o

(a)

o

Prior cooling rate: 5 C/min

(a)

o

peak area: 6.0 C/mgx C/s

o

peak area: 0.8 C/mg x C/s

1.0 400


3.0


-3.0

600

800

200

1000

400

600

800

1000

o

Temperature ( C)

Temperature ( o C) 4.5

VP2212

3.5

38Na 2 O - 62SiO 2 o

o

2.5 2.0

0.0

-1.5

(b) (b)

3.5

600

200

800

400

600

4.5

VP2212

o

o

∆T ( C), Exo

3.0

2.5

o

2.0 1.5

1.5

0.0 -1.5

o


(c)

o


o

Heating rate: 15 C/min o


3.0

1000

Temperature ( C)

o


800 o

1000

38Na2 O - 62SiO 2

o


(c) -3.0

1.0 400

o


-3.0

o


400

o

o

1.5

1.5 1.0

∆T ( C), Exo


o


∆T ( C), Exo

o

∆T ( C), Exo

3.0

o


o

3.0

o


600

800

1000

o

Temperature ( C)

200

400

600

800

1000

o

Temperature ( C)

Fig. 5. DTA heating curves (15 C/min) for the solidified melts of a 38Na2O–62SiO2, mol%, composition after cooling the melts at a rate of (a) 5 C/min, (b) 20 C/min, and (c) 25 C/min. The area and height of the crystallization peak increased as the prior cooling rate increased from (a) 5 C/min to (b) 20 C/min, but no such increase in their values is observed when the prior cooling rate exceeded the critical cooling rate, Rc for this melt, compare (b) and (c).

Fig. 6. DTA heating curves (15 C/min) for the solidified melts of VP2212 after cooling the melts at a rate of (a) 20 C/min, (b) 34 C/ min, and (c) 37 C/min. The area and height of the crystallization peak (first peak in this case) increased as the prior cooling rate increased from (a) 20 C/min to (b) 34 C/min, but no such increase in their values is observed when the prior cooling rate exceeded the critical cooling rate, Rc for this melt, compare (b) and (c).

constant with further increase of R. The critical cooling rate for glass formation, Rc, is taken as the value of R where the crystallization peak area on the subsequent re-heating cycle is maximized, i.e., when the solidified melt transforms completely to glass. As shown in Fig. 8, the value of Rc was determined from the intersection of the tangent drawn at the inflection point of the ascending curve and the straight line produced by backward extrapolation of the plateau region. The method of determining the inflection point and, hence, Rc, is further illustrated in Fig. 9 using the data points from Fig. 8(a) for the 38Na2O–62SiO2, mol%, glass. A numerical fit to the experimental results was obtained and the inflection point of the curve was determined from the first derivative of the fit. The derivative of the curve was generated using a EasyPlot SoftwareTM with filler points [8]. The intersection of the curve containing the data points with the vertical straight line

from the maximum of the derivative curve is the point of inflection. The tangent at the inflection point was extended to intersect the extrapolated horizontal straight line from the plateau region, and this intersection defines Rc. The values of Rc for all three glasses shown in Fig. 8 were determined using this method. For the 38Na2O–62SiO2, mol%, melt, analysis of Fig. 9 (and also Fig. 8(a)) predicts a critical cooling rate (Rc) of 19 ± 1 C/min. This is in excellent agreement with the value of 19 C/min determined for this composition by standard techniques [7], and this agreement strongly justifies the validity and usefulness of the newly developed method for measuring critical cooling rates for glass forming melts. The Rc values for the VP2212 (Fig. 8(b)) and VP2076 (Fig. 8(c)) melts are 33 ± 1 C/min and 41 ± 2 C/min, respectively. However, since these are new compositions and no other data on Rc for these

6

VP2076 o

Heating rate: 15 C/min o

o

peak area: 6.4 C/mg x Cxs

2

o

∆T ( C), Exo

4

0 o


(a)

-2 200

400

600

800

1000

o

Temperature( C)

DTA Peak Area (oC/mg x oC/s )


1355

2.0

38Na 2O - 62SiO2, mol% 1.8 1.6 1.4 1.2 1.0

(a)

R C=19 ±1 oC/min

0.8 5

10

15

20

25

30

6 o

VP2076

o

o

2

o

0 o


(b)

-2 200 6

400

600

VP2076

800

o

peak area: 8.0 C/mg x

o

1000

o

C/s

VP2212 7.6 7.2 6.8 6.4

(b)

6.0 15

2

o

∆T ( C), Exo


8.0

4

0

(c)

o


-2 200

400

600 o Temperature ( C)

800

1000

Fig. 7. DTA heating curves (15 C/min) for the solidified melts of VP2076 composition after cooling the melts at a rate of (a) 37 C/min, (b) 45 C/min, and (c) 47 C/min. The area and height of the crystallization peak increased as the prior cooling rate increased from (a) 40 C/min to (b) 45 C/min, but no such increase in their values is observed when the prior cooling rate exceeded the critical cooling rate, Rc for this melt, compare (b) and (c).

melts are available, these melts were also characterized using conventional methods, and the results are described below.


∆T ( C), Exo


4



8.0

R C =33 ±1 o C/min 20

25

30

35

40

VP2076

7.5 7.0 6.5 6.0

(c) 5.5

o

R C =41 ±2 C/min 28

32

36

40

44

48

o

Cooling Rate (R) C/min

Fig. 8. Plots of DTA crystallization peak area (on heating) for the solidified melts of (a) 38Na2O–62SiO2, mol%, (b) VP2212, and (c) VP2076 compositions, as a function of the cooling rate (R) used to solidify the melts. The area of the crystallization peak in these plots was obtained from results similar to those shown in Figs. 4–6. Rc was determined by tangent-intersecting method indicated by the dashed lines.

3.2. Conventional methods 3.2.1. Method 1: Observing the cooling curve Fig. 10(a) and (b) shows DTA cooling and heating curves for the glass VP2212. The sample in Fig. 10(a) was cooled from the melt at 29.4 C/min, before being re-heated at 15 C/min and the sample in Fig. 10(b) was first cooled at 34 C/min before the 15 C/min re-heat. Fig. 11 shows comparable data sets for the VP2076 glass. For the VP2212 melt, a small crystallization exotherm is still detectable when the melt is cooled at a rate of 29.4 C/min (see inset in Fig. 10(a)), but no exotherm is observed when the melt is cooled at 34 C/min (inset in Fig. 10(b)). There is no clear distinction in the DTA cooling curves collected for intermediate cooling rates. Based on these results, it is estimated that Rc for the

VP2212 melt is between 30 and 34 C/min. Similar analyses of the cooling curves for the VP2076 melt (Fig. 11) indicate that Rc for this composition is between 40 and 45 C/min.

3.2.2. Method 2: CCT diagram The values of Tc determined from the DTA cooling curves, the corresponding cooling rate, R, and the time, t, taken to decrease the temperature from Tm to Tc are given in Tables 1 and 2 for the VP2212 and VP2076 melts, respectively. The values of t and Tc were used to construct the CCT diagrams shown in Fig. 12(a) and (b) for the VP2212 and VP2076 melts, respectively. The nose temperature (Tn) and nose time (tn)


DTA Peak Area ( oC/mg x oC/s )

1.8

0.16

38Na2O - 62SiO2, mol%

1.6

0.12

inflection point

1.4

0.08

1.2

0.04

1.0

0.00

Derivative of Peak Area Curve

1356

RC=19 oC/min

0.8

-0.04

5

10

15

20

25

30

Cooling Rate (R) oC/min

Fig. 9. Calculation of Rc for the new method using a tangent intersection procedure. Results for the 38Na2O–62SiO2, mol%, glass from Fig. 8(a) have been used to show the calculations. See text for a detailed description of the procedure.

Fig. 11. DTA heating curves (15 C/min) for the VP2076 glass resulting after initially cooling melts at a rate of (a) 39.7 C/min and (b) 45 C/min. The corresponding cooling curves, from 1050 C, are also shown and are enlarged in the insets. A small, nearly undetectable, shoulder is observed as a signature of crystallization when this melt is cooled at 39.7 C/min, inset (a). No such crystallization event is observed when the melt is cooled at 45 C/min, inset (b).

Table 1 Cooling rate, R, crystallization temperature, Tc, and the time, t, taken to crystallize when cooled at R from the melting temperature (Tm = 920 C) for the VP2212 melt

Fig. 10. DTA heating curves (15 C/min) for the VP2212 glass resulting after initially cooling melts at a rate of (a) 29.4 C/min and (b) 34 C/min. The corresponding cooling curves, from 1125 C, are also shown and are enlarged in the insets. A small, nearly undetectable, shoulder is observed as a signature of crystallization when this melt is cooled at 29.4 C/min, inset (a). No such crystallization event is observed when the melt is cooled at 34 C/min, inset (b).

R (C/min)

t (min)

Tc (C)

1.0 2.9 5.0 7.8 9.8 14.5 19.7 29.4

68.0 27.2 17.6 12.6 10.5 8.2 6.8 4.9

852 841 832 822 817 801 786 776

as estimated from Fig. 12(a) and (b) are 775 C and 5 min for the VP2212 melt, and 818 C and 2 min for the VP2076 melt. Based on these results, Rc for the VP2212 melt is 30 C/min, and 42 C/min for the VP2076 melt.

C.S. Ray et al. / Journal of Non-Crystalline Solids 351 (2005) 1350–1358 Table 2 Cooling rate, R, crystallization temperature, Tc, and the time, t, taken to crystallize when cooled at R from the melting temperature (Tm = 910 C) for the VP2076 melt t (min)

Tc (C)

3.0 8.0 12.3 15.5 18.4 25.9 34.0 36.8 39.7

13.7 6.8 4.6 3.8 3.5 2.9 2.4 2.4 2.3

869 862 854 851 845 835 827 820 819

0

VP2212

(a)

-1

ln (R)

R (C/min)

1357

-2

-3

-4

Rc ~ 41oC/min

0.00

1.00

2.00

3.00

4.00

5.00

10,000/(Tm-Tc)2 0

Tm 920

VP2076 VP2212

(b)

(a)

880

ln (R)

Tc (oC)

-1 840

800

-2

o

Tn ~ 775 C tn ~ 4.9min

760 720

-3

Rc ~ 53oC/min

o

Rc ~ 30 C/min 680 0

10

20

30

40

1.00

50

2.00

Time (min.) 920

910oC

Tm

VP2076

(b)

Tc (oC)

tn~ 2.2 min

760

Rc ~ 42oC/min 0

2

4

6

8

5.00

6.00

7.00

10,000/(Tm-Tc)

Tn ~ 818oC

800

4.00 2

880

840

3.00

10

12

14

Time (min.) Fig. 12. Continuous-cooling-temperature (CCT) diagrams for melts of the (a) VP2212 and (b) VP2076 compositions. The solid curve in each figure is a guide to the eye fitting the experimental data points (solid circles). A broken curve, which is a mirror image of the solid curve, has been drawn intentionally to make the combined curve, solid and broken, look like a TTT-diagram. The combined curve shows a nose temperature and nose time of (a) 775 C and 5 min, respectively, for the VP2212 melt, and (b) 818 C and 2 min, respectively, for the VP2076 melt. The values of Rc calculated from these data are shown in each figure.

3.2.3. Method 3: Empirical equation The values of R and Tc given in Tables 1 and 2 were used to produce the ln R versus 1/(Tm Tc)2 plots (Eq. (1)) shown in Fig. 13(a) and (b) for the VP2212 and VP2076 melts, respectively. The scatter in the data points for the VP2212 melt is larger (correlation factor,

Fig. 13. Plots of ln R versus 1/(Tm Tc)2, Eq. (1), for the (a) VP2212 and (b) VP2076 melts. Values of Rc determined from the intercept of the straight lines fitting the data points on the ln R – axis are shown in the figures.

0.989) than that for the VP2076 melt (correlation factor, 0.998). This is primarily the result of smaller, less sharp crystallization peaks (on cooling) for the VP2212 melt. The values of Rc determined from the intercept of the straight lines in Fig. 13(a) and (b) on the lnR axis are 41 and 53 C/min for the VP2212 and VP2076 melts, respectively. The values of Rc determined by the different methods are summarized in Table 3, along with an estimated error associated with each method. The error occurs Table 3 Critical cooling rate for glass formation, Rc, as measured by different methods for the VP2212, VP2076, and 38Na2O–62SiO2 (mol%) compositions Methods

Rc (C/min) VP2212

VP2076

38Na2O–62SiO2, mol%

New Method

33 ± 1

41 ± 2

Conventional Method 1 Conventional Method 2 Conventional Method 3

32 ± 2 30 ± 2 41 ± 3

43 ± 2 42 ± 2 53 ± 3

19 ± 1 19 [Ref. [7]] Not measured Not measured Not measured

See text for description of the methods.

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primarily from the uncertainty in determining the exact temperature for crystallization (±2 C) from the cooling curves (Methods 1–3), or the peak area for crystallization (±0.1 C/mg · C/min) from the heating curves (New Method). Table 3 clearly shows that the values of Rc determined by the different methods are in excellent agreement with each other, with the exception of Method 3. The value of Rc determined by Method 3 (Eq. (1)) is greater than that determined by any other method for reasons that are not clearly understood. However, the values of Rc obtained by the new method are in good agreement with those obtained by the more conventional cooling rate analyses.

measurement of Rc for compositions with melts that produce very small or undetectable crystallization peaks on cooling, such that Rc cannot be readily measured by standard methods.

Acknowledgement The authors wish to thank Mr Harald Buerke of Ivoclar for preparing VP2076 and VP2212 glass samples for this investigation.

References 4. Conclusions A new and straight-forward experimental method that uses differential thermal analysis (DTA) has been developed for measuring the critical cooling rate, Rc, for glass forming melts. The justification and usefulness of the method has been established by comparing Rc measured by this method with those measured by other DTA methods. Unlike the standard methods, which determine Rc through the analysis of crystallization peaks obtained by cooling a melt at different rates, this new method utilizes crystallization peaks obtained by heating solidified melts produced at different cooling rates. As a result, the proposed method will allow the

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