berthier 2007, Notas de estudo de Engenharia de Produção

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Journal of Non-Crystalline Solids 354 (2008) 1721–1730

New large grain, highly crystalline, transparent glass–ceramics

Thiana Berthier a, Vladimir M. Fokin b, Edgar D. Zanotto a,*

a Vitreous Materials Laboratory, Department of Materials Engineering, Federal University of São Carlos, 13.565-905 São Carlos, SP, Brazil b S.I. Vavilov State Optical Institute, ul. Babushkina 36/1, St. Petersburg 192131, Russia

Received 28 November 2006; received in revised form 13 August 2007 Available online 1 October 2007


Two main reasons assure the transparency in the visible of some glass–ceramics (TGC): their crystal sizes are much smaller than the wavelength of light or the difference between the refractive index of glass matrix and crystal phase is small. The majority of traditional TGC have nano-size crystals and small to moderate crystallized volume fraction, usually between 3% and 70%. In this article we present a new type of transparent glass–ceramics having large (micrometric) grain size and very high crystallized volume fraction, which reaches up to 97%. Their high transparency mainly results from simultaneous variations of the glass matrix and crystal compositions during crys- tallization, which considerably decreases the difference between the respective refractive indexes, and this factor prevails, regardless of crystal size. Preliminary tests of their optical properties indicate that this new family of TGC can be further developed by doping with transition metals and rare-earths.  2007 Elsevier B.V. All rights reserved.

PACS: 61.43.Fs;; 64.60.Q

Keywords: Crystallization; Crystal growth; Glass ceramics; Nucleation; Oxide glasses; Alkali silicates; Silicates; Soda-lime–silica

1. Introduction

Glass–ceramic technology is based on controlled crystal nucleation and growth in certain glasses, and has several advantages over conventional powder-processed ceramics, such as very low or null porosity, as well as uniformity and reproducibility of microstructure. The crystalline phases precipitated in some glass matrices typically enhance and sometimes lead to entirely new combination of properties. Some of the technologically most important glass–ceramics have, for instance, low thermal expansion coefficients coupled with high thermal and chemical stabil- ity, high mechanical strength and optical transparency [1].

Recently, much attention has been devoted to optically transparent glass–ceramics that have improved optical properties, greater thermal stability and strength than their

0022-3093/$ - see front matter  2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2007.08.052

* Corresponding author. Tel.: +55 16 3351 8527; fax: +55 16 3361 5404. E-mail address: (E.D. Zanotto). URL: (E.D. Zanotto).

parent glasses [2,3]. Dozens of papers and patents on trans- parent glass–ceramics have been registered worldwide in the last thirty years (see, e.g. [4]). Applications of these transparent crystalline materials, which are capable of being shaped by fast and flexible glass-forming processes, are numerous and include cooking ware, fire resistant plates, security windows, hosting medium for transition metals and rare-earths among others [5].

This paper focuses on the development and character- ization of a new type of transparent glass–ceramic. The originality of this material is based on a tight control of homogeneous nucleation and growth of solid solution crys- tals with a continuous variation of the compositions of both crystalline and glassy phases during phase transfor- mation. This unique evolution reduces the difference between the refractive indexes of crystals and residual glass. The crystallinity of this new TGC can reach up to 97% (spontaneous cracking takes place for higher crystal- linities) with grain sizes of about 5–7 lm, in contrast to conventional TGC that have nano-metric microstructures

1722 T. Berthier et al. / Journal of Non-Crystalline Solids 354 (2008) 1721–1730

and low to moderate crystallized volume fraction. Some of the characteristic optical properties of these new, large grain transparent glass–ceramics are presented below together with an analysis of their crystallization process.

2. Brief literature review

Some of the most important proposed applications of TGC refer to optical components and devices including: laser media; saturable absorber media; illumination devices using infrared light; heat-resistant materials that absorb ultraviolet light, TGCs that reflect infrared light and are transparent to visible light; substrates for arrayed wave- guide grating (AWG) [6,7]; radiation sources of lamps; laser pumps; substrate materials; wafer stages; mirror sup- port for telescopes; second harmonic generation (optical energy converting elements) [8,9]; front windows in heating furnaces or slow-cooling reactors; precise photolithogra- phy; blue or green state lasers, LCD substrates, optical amplifiers for wavelength up-conversion [10]; ring laser gyroscopes; materials that absorb UV and fluoresce in the red/IR (possibly used as tunable lasers) [11]; solar col- lectors; printed optical circuits; gradient refraction optical lenses; optical waveguides [12–14], etc.

There are several patents on transparent glass–ceramics that contain a major crystalline phase of low thermal expansion coefficient (0.1 · 106–1.0 · 106/K) and thus present high thermal shock resistance [4]. Transparency is usually observed in glass–ceramics containing relatively small to moderate volume fractions of crystals (3–70%) with nanoscale size (1–15 nm) [15]. The majority of these low expansion materials belong to the lithia–alumina–silica family with titanium and/or zirconia as nucleating agents, and a number of minor elements to impart color or to improve processability, and have beta-quartz solid solution as the major phase [16].

3. Theoretical background

There are two distinct ways in which light intensity can be attenuated by a medium: atomic absorption and scatter- ing [17,18]. A combination between these two mechanisms plus light reflection from the external surfaces can be expressed by the following equation:

I ¼ I0ð1 RÞ2 exp½ðb þ SÞx; ð1Þ where

R ¼ n 1 nþ 1

 2 ;

and I0 and I are the initial and transmitted light intensity, respectively, b the linear absorption coefficient (absorption index), S the scattering coefficient, x the optical path length, and n is the refractive index of the TGC.

The scattering coefficient S can be written as

S ¼ Kpr2N ; ð2Þ

or assuming spherical particles, as

S ¼ 3 4 KVr1; ð3Þ

where N and V are the number density and volume fraction of the scattering particles, respectively, and K is a scattering factor.

K increases with particle-size, reaches a maximum when the particle-size is close to k, and decreases for larger par- ticle-sizes, approaching a constant value for r  k. Thus, according to Eq. (3), for a fixed concentration (V) of scat- tering phase the measured scattering coefficient decreases with increasing particle-size (see, e.g. [19]).

If a scattering medium has particles with sizes less than 0.1–0.2 of the typical wavelength of visible light, Rayleigh scattering takes place and the angular distribution of scat- tered light can be written as [3]

I ¼ ð1þ cos 2 hÞ

L2 8p4

k4 r6

M2  1 M2 þ 2

 2 I0; ð4Þ

where h is the scattering angle, L is the distance from the scattering centers of radius r, and M is the ratio of the refractive index of the particle to that of the surrounding medium. According to Eq. (4) the scattered intensity de- pends mainly on the ratio of the particle-size to the wave- length of light, r/k, and the ratio of refractive indexes, M. Thus, for any given value of h, L, and k, the smaller the first ratio and the closer to unity the second, the most transmit- ting is the medium.

If the sizes of the scattering centers are comparable or lar- ger than the wavelength of visible light (as in the case of the micrometric crystals of our TGC), the simple Rayleigh the- ory breaks down. For such relatively large crystal sizes, the dependence of the scattered light intensity on k becomes weaker than that for the Rayleigh scattering, and is given by

I  kp; ð5Þ where p < 4 and decreases with increasing particle-size. Due to the interference of light scattered by different parts of each scattering particle, the I(h) dependence becomes more complicated. With increasing particles sizes forward scattering (acute angles) prevails back scattering (obtuse angles), the so-called Mie effect. This effect may lead to a decrease of the measured scattering coefficient (contrary to the case of small particles) with increasing particle-sizes.

4. Materials and experimental procedures

Sodium and calcium carbonates, and crushed quartz were used as starting materials. After melting the proper mixtures in a platinum crucible at 1300–1500 C for about 4 h, the melts were cast on massive metallic plates to give about 5 mm thick specimens. The compositions of the glasses were close to the pseudo-binary join CaO Æ SiO2–Na2O Æ SiO2 in the interval (Na2O Æ 2CaO Æ 3SiO2(N1C2S3)–Na2O Æ CaO Æ 2SiO2(N1C1S2)) of solid solution formation. Table 1 shows typical compositions of the TGCs here investigated.

Table 1 Examples of some our TGC compositions in mol%


TGC-0a 50.2 19.2 30.6 TGC-1b 49.0 18.8 32.3 TGC-2a 50.0 16.7 33.1

a By analysis. b This TGC was doped with 0.2 and 0.5 wt% Er.

0.0 0.5 1.0 1.5 2.0 2.5





ln (I

/I o)

x, mm

Fig. 1. ln (I/I0) versus x typical plot for TGC-0 with about 3% of crystallinity fitted by a linear function.

400 800 1200 1600 -1







ex o


425 450 475 500 525






μV /m


T, oC

en do

Fig. 2. Typical DSC heating and cooling curves for glass TGC-0. The dotted and solid lines refer to heating and cooling with rates ±10 K/min, respectively. Arrows denote the characteristic temperatures: glass transi- tion, Tg, crystallization during heating, Tcr-h, and cooling, Tcr-c, liquidus, TL, and the reversible phase transition, Tpm. The ‘pre-melting’ peak is likely caused by the peculiarities of the s/s melting between solidus and liquidus. It should be noted that this peak is typical for compositions that are shifted relative to stoichiometric composition N1C2S3. The inset shows DSC heating and cooling curves for a fully crystallized TGC-2.

T. Berthier et al. / Journal of Non-Crystalline Solids 354 (2008) 1721–1730 1723

The degree of crystallinity and crystal sizes were mea- sured by optical microscopy with a pattern analyzer. The crystal and glassy matrix compositions were estimated via energy dispersive spectroscopy (EDS) using Stereoscan 440 Link/Oxford. The excitation volume of the electron beam was about 2–3 lm in diameter. The parent glass and a fully crystallized glass were employed as standards. About six measurements were performed for both glassy and crystalline phases to evaluate the average values.

Spectra of the partly and fully crystallized glasses, shaped as parallel-sided polished plates, were recorded in the range of 200–1100 nm to characterize their transmit- tance as a function of crystallinity. To estimate the param- eters P1 = (1  R)2 and P2 = (b + S) of Eq. (1) characterizing the energy loss due to light reflection, absorption and scattering, respectively, the transmittance I/I0 was measured as a function of sample thickness, x. Fig. 1 shows a ln (I/I0) versus x plot approximated by a lin- ear function Y = A  Bx where A = ln(P1) and B = P2.

The refractive indexes of the parent glasses and TGCs were measured with an Abbe refractometer using the NaD line (k = 589 nm). The Abbe numbers (td) were calcu- lated by the following equation

td ¼ ðnd  1Þ ðnf  ncÞ

; ð6Þ

where nd, nf, and nc are the refractive index at k = 589, 486, and 643 nm, respectively [20].

A Netzsch DSC 404 equipment was employed for the determination of the characteristic temperatures in the heating and cooling curves using bulk samples of about 20–30 mg.

5. Results

The crystals grown in the present glasses are solid solu- tions (s/s) having the chemical formula Na4+2x- Ca4x[Si6O18] (0 6 x 6 1). These s/s are formed by replacement of 1Ca by 2Na [21–23].

At a temperature Tpm, well below the glass transition temperature, Tg, the solid solutions with 0 < x < 0.5 reveal a reversible polymorphic transition, which is accompanied by a clear thermal effect in the DSC curves (Fig. 2) also reported in Ref. [24]. The value of Tpm strongly decreases with decreasing sodium content (see Fig. 3) and thus can be employed to characterize the crystal composition, see Ref. [25].

Depending on the parent glass composition, the crystals are approximately spheric or cubic shaped, such as those shown in Fig. 4. Crystals with mixed shapes were occasion- ally observed as has been already noted in Ref. [26]. Excess of SiO2 relative to the metasilicate composition favors spherical crystals, while a deficit in SiO2 favors the forma- tion of cubic shaped crystals.

Fig. 5 shows the XRD patterns of almost fully crystal- lized samples TGC1 and TGC2 with crystals of cubic and spherical morphologies, respectively. Both morphologies refer to solid solutions based on the hexagonal structure

16 17 18 19 20 21 22





T pm

Na2O, mol%

Fig. 3. Temperature of reversible polymorphic transition in fully crystal- lized glasses taken from DSC hitting curves versus sodium oxide content in the parent glasses. Solid and opened circles refer to analyzed and nominal sodium contents, respectively. The line is placed just to guide the eyes.

20 40 60 80








21 1 2


40 4

24 0

20 2

R el

at iv

e In

te ns

ity (

a. u


2θ (Degree)

00 3

Fig. 5. XRD patterns of TGC1 (a) and TGC2 (b) with about 97% crystallinity – solid solutions with hexagonal structure N1C2S3. Crystals have cubic (a) and spherical (b) morphologies. XRD spectrums are close to JCPDS (card 22-1455) for sodium calcium silicate Na2Ca2Si3O9.

1724 T. Berthier et al. / Journal of Non-Crystalline Solids 354 (2008) 1721–1730

of sodium calcium silicate Na2Ca2Si3O9 (JCPDS card 22- 1455) [23].

Crystal morphology is one of the factors which affect the transparency of crystallized glasses. Fig. 6 shows examples of a typical transmission spectrum and micrographs of some TGCs with spherical and cubic shaped crystals. The volume fraction crystallized is close to 1.0 in both cases. It is clear that the cubic form favors the transparency of our TGC.

The transmittance of our TGC strongly depends on the degree of crystallinity. Fig. 7 shows a typical plot of trans- mittance versus volume fraction crystallized together with the reduced specific area of the crystal/glass interface esti- mated via the following equation [27]:

SR ¼ 2NL=SmaxV ; ð7Þ

Fig. 4. Optical micrographs of the typical crystal morphologies in glasses hav composition. Scale bars denote 100 lm.

where NL is the average number of intersections of an arbi- trary secant at the crystal/glass interface per unit length and SmaxV is maximal value of SV.

The parameter P1, which takes into account reflection losses, was estimated in the way described in Section 4. P1 slightly decreases with crystallized volume fraction (Fig. 8(a)) owing to the increase of the effective refractive index of TGC (Fig. 8(b)). Calculation of P1 via Eq. (1) with experimental values of refractive index, denoted by stars in Fig. 8(a), corroborates the direct measurements of P1.

The variation of P1 is very small (0.915–0.907) as com- pared with changes of the parameter P2 = (b + S), which characterizes absorption and scattering – and is shown in Fig. 9 as a function of a. According to Fig. 9, the lowest values of P2 correspond to volume fractions crystallized a  0.90–0.96. The transmittance in this a interval varies from 86% to 83% for a 1mm thick plate sample.

For samples containing about 97% crystallized fraction the measured Abbe number is 52.6. Ref. [28] reports a study of mechanical properties of these TGC.

ing a deficit (left) and an excess (right) of silica relative to the metasilicate

300 400 500 600 700 800








90a b

c T

ra ns

m itt

an ce

a t x

= 1

m m

in %

λ, nm

Fig. 6. Transmittance spectra of TGCs with different crystal shapes (a). Optical micrographs of TGC with cubic (TGC-0) (b) and spherical (TGC-2) (c) crystals. The sample thickness is 4 mm (b) and 2 mm (c). The volume fraction crystallized is close to unity in both cases.

0.0 0.2 0.4 0.6 0.8 1.0














T ra

ns m

itt an

ce a

t x =

1 m

m in


1 2


Fig. 7. Transmittance at k = 800 nm (1), and reduced specific area of the crystal/glass interface SR (2) versus volume fraction crystallized for TGC-0.

T. Berthier et al. / Journal of Non-Crystalline Solids 354 (2008) 1721–1730 1725

6. Discussion

In contrast to most of the traditional TGCs, which are based on nano-crystallization, the distinguishing features of the new TGCs above described are their very high degree of crystallinity and micrometric crystal sizes. To under- stand why such high crystallinity combined with relatively large crystal sizes do not lead to a significant loss of trans- mittance we must consider the details of the nucleation- growth process in the parent glasses.

As we already mentioned in Section 4, the compositions of the present glasses are close to the metasilicate join N1C2S3–N1C1S2, which leads to the formation of solid solutions (s/s) [21] with a continuous compositional varia- tion during crystallization [29]. The densities and corre- sponding refractive indexes of crystals and glasses

belonging to this join do not strongly differ. Indeed, the dif- ference between the refractive indexes of N1C2S3 crystal and glass of respective stoichiometric composition is only 0.015. Another interesting factor is that the optical birefrin- gence of 1-2-3 crystals is also very low. These similarities favor a low light scattering.

Another feature of these glasses is very important for TGC formation. As we have shown in a previous publica- tion [30], the compositions of the critical nuclei in glasses belonging to the N1C2S3–N1C1S2 interval are close to N1C2S3 and hence they are enriched in sodium as com- pared with the parent glasses. The reasons for this compo- sitional deviation, discussed in detail in ref. [30], is the decrease in the thermodynamic barrier for nucleation caused by the possible reduction of the interfacial energy due to the increase of sodium in critical nuclei. This sce- nario agrees with Ostwald’s rule of stages, generalized in Ref. [31] for nucleation as ‘In phase transformation pro- cesses the structure and properties of the critical nucleus may differ qualitatively from the properties both of the ambi-

ent and of the newly evolving macrophases. Those classes of

critical clusters determine the transformation process, which

correspond to a minimum work of critical cluster formation –

as compared with all other possible alternative structures and

compositions, which may be formed at the given thermody-

namic constraints’. Another interpretation for the precipita- tion of crystals containing more sodium than the s/s corresponding to the equilibrium phase diagram in deeply undercooled liquids (which are highly viscous) was pro- posed in Ref. [32]. Those authors connected this composi- tional deviation from stoichiometry with the high diffusivity of sodium, which exceeds that of calcium by about two orders of magnitude. In any case, for the consid- ered problem it is important that nuclei enriched in sodium continuously grow throughout the phase transformation leading to a depletion of sodium in the glass matrix. This depletion impairs the kinetics of growth and nucleation

0.0 0.2 0.4 0.6 0.8 1.0






P 2 =

(β +

S) , m

m -1


Fig. 9. Absorption and scattering coefficient (b + S) of TGC-0 versus volume fraction crystallized.









0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.70






1.00 P 1

= (

1- R



a b

Fig. 8. Value of P1 = (1R)2 – light loss due to reflection (a), and refractive index (b) versus volume fraction crystallized. The stars denote P1 calculated via Eq. (1) using the experimental value of n. The dashed line refers to linear approximations of experimental data.

1726 T. Berthier et al. / Journal of Non-Crystalline Solids 354 (2008) 1721–1730

up to the termination of the latter. During phase transfor- mation the average crystal composition approaches that of the parent glass. Therefore, in the advanced stages of crys- tallization the vitreous matrix (occupying a very small vol- ume fraction) has much less sodium than the crystals.

Such complex crystallization pathway was corroborated by an analysis of the overall crystallization kinetics with the JMAK equation:

aðtÞ ¼ 1 expfBtnAg; ð8Þ

where a is the volume fraction transformed, nA is the Avrami coefficient, and B is a parameter that includes the number of crystals (or the crystal nucleation rate) and their growth rate [33]. The Avrami coefficient can be approxi- mately written as

nA ¼ k þ 3m; ð9Þ

where k and m are taken from the formulas N  tk and a  tm describing the variation of the crystal number (N) and size (a) with time.

Fig. 10(a) and (c) show the volume fraction of crystals and the size of the largest crystals as a function of heat treatment time at T = 628 C for a glass of composition TGC-0 (see Table 1). To estimate the values of nA and m the data of Fig. 10(a) and (c) were reploted in Avrami (Fig. 10(b)) and logarithmic (Fig. 10(d)) coordinates, respectively. Beginning from approximately 90–110 min the phase transformation occurs solely due to crystal growth, since nA ffi 3m and k ffi 0 (according to Eq. (9)).

The evolution of the glass matrix and crystal composi- tions during phase transformation was corroborated by direct EDS measurements, whose results for the same TGC are shown in Fig. 11. According to these data, the sodium content in the crystalline phase is always higher than that in the corresponding glassy matrix. This compo- sitional difference is one of the main reasons for the improved transparency of the present TGC. Analyzing the data of Fig. 11 together with the compositional depen- dencies of the refractive indexes of glass and crystal (s/s), shown in Fig. 12(a), one realizes that sodium enrichment of the crystalline phase relatively to that of the parent glass approximates the refractive indexes of crystal and glassy phase. Knowing the compositional variations of the glassy matrix and the crystals, and the functions nðCNa2OÞ for both crystal and glass, one can estimate the evolution of refrac- tive indexes during glass crystallization. An example of such evolution is shown in Fig. 12(b). The solid and dashed lines refer to the crystal and the glassy matrix. The top and bottom horizontal lines show the refractive indexes for par- ent glass and fully crystallized sample, respectively.

Indeed, the difference between the refractive indexes of the crystalline and glassy phase is about four times lower than that if the crystal and glassy matrix compositions were

0 400 800 1200 1600






1.0 α

t, min 0 200 400 600 800






a, μ


t, min

4.5 5.0 5.5 6.0 6.5 7.0 7.5








n A =2.61+ 0.15

n A =1.09 +0.05

ln (-

ln (1

-α ))

ln(t,min) 4.0 4 .5 5.0 5.5 6.0 6.5 7.0










m=0.75+ 0.08

m=0. 32+0.04

ln (a

, μ m



a b

c d

Fig. 10. Volume fraction of crystals (a, c) and size of the largest crystals (b, d) in TGC-0 versus time of heat treatment at 628 C. The dashed lines refer to linear approximations.

T. Berthier et al. / Journal of Non-Crystalline Solids 354 (2008) 1721–1730 1727

equal. Moreover there is a (slight) further reduction of this difference with increasing degree of crystallinity. This phe- nomenon results in a significant decrease of the refractive

index dependent term, M 21


h i2 , which provides a good

description of the scattered light intensity also in the case

of large particles. Fig. 13 shows M 21


h i2 for different vol-

ume fractions crystallized. Thus, a TGC with about 95–97% crystallinity consists of

relative large crystals having a composition very close to that of the (initial) parent glass, and thin areas of glassy phase with a composition close to the stoichiometric N1C2S3 (for TGC-0 and TGC-1). In other words, the resid- ual glassy phase is depleted in sodium as compared with the crystalline phase. Here it should be noted that we are deal- ing with average compositions. Possible compositional gra- dients are expected, especially within crystals, and noticeably complicate this picture.

In addition to the similarity of the refractive index of the crystals and surrounding glassy matrix, the scattering coef-

ficient, S, is affected by the average crystal size. Therefore, the thermal history leading to crystallization is of great importance. Fig. 14 shows the transmission spectra of partly crystallized glasses (42% crystallinity) caused by single and double heat-treatments.

According to Eq. (3) the increased transmittance shown in curves 1, 2 result from an increased average crystal size from 7.5 to 47 lm at a fixed crystallized volume fraction. This crystal size increase also weakens the I(k) dependence (see Section 3). Indeed, one can observe that the transmis- sion curve 2 in Fig. 14 is flatter than curve 1, which is related to smaller crystal sizes.

The scattering theory deals with isolated particles in a surrounding medium. In the early and middle stages of phase transformation isolated crystals indeed represent such particles. Their total volume and size increases dur- ing crystallization. In the advanced stages of crystalliza- tion isolated areas of glass embedded within the crystalline phase act as scattering particles whose volume and size decreases during crystallization. This evolution is

0.0 0.2 0.4 0.6 0.8 1.0 0.0





[( M

2 - 1)

/( M

2 + 2)



Fig. 13. Parameter M 21


h i2 that gives the scattering due to the difference

between the reflective indexes of crystals and glass matrix versus volume fraction crystallized. The dotted line refers to crystals and glassy matrix having same composition.

0.0 0.2 0.4 0.6 0.8 1.0 10






a , a



1 2 3 4

Fig. 11. Average sodium content in the crystalline phase (1) and glassy matrix (2) versus volume fraction crystallized of TGC-0. The solid line (3) is a linear fit to experimental data. The dashed line (4) was calculated from the crystal and parent glass compositions. The dotted line shows the sodium content in the parent glass and in the fully crystallized sample.

1728 T. Berthier et al. / Journal of Non-Crystalline Solids 354 (2008) 1721–1730

reflected by the dependence of specific interface area, which reveals a maximum (see Fig. 7, curve 2). Since the scattering coefficient depends on the volume and size of the particles, the ‘switch’ of the microstructure (from crystals in a glassy matrix to glassy ‘lakes’ in a crystalline matrix) results in the minimum of the curve of TGC transmittance versus volume fraction crystallized (Fig. 7, curve 1).

To summarize, the TGC transmittance is affected by the continuous compositional changes of both glassy matrix

5 10 15 20 25 30 35 1.54











CNa2O, w%

a b

Fig. 12. (a) Refractive indexes of crystal and glass versus of sodium oxide conte Dashed lines resulted from a polynomial fit to the experimental data. Black poi of the parent glass, respectively. The arrows show the direction of the compo indexes of crystals (solid line) and glassy matrix (dashed line) versus volume indexes of the parent glass (a = 0) and fully crystallized sample (a = 1).

and crystalline phase. Crystallization leads to an approxi- mation of the refractive indexes of the crystalline and glassy phases. Such changes determine the TGC transmit- tance, and this could be one of the reasons why the position of the minimum on curve 1 does not coincide with that of the maximum on curve 2. It should be also noted that before impingement the crystals have more or less isometric shape, while the shapes of the glassy ‘lakes’ in a crystalline matrix at advanced and final stages of phase transforma- tion are more complex. A decrease of transmittance in the very final stage (for crystallinities higher than about

0.0 0.2 0.4 0.6 0.8 1.0








nt. Stars refer to our TGC. Open circles refer to data taken from Ref. [34]. nts 1 and 2 correspond to the critical nucleus composition and composition sition evolution during phase transformation. (b) Evolution of refractive fraction crystallized. Dotted and dashed-dotted lines show the refractive

0.0 0.1 0.2 0.3 0.4 0.5 350




T pm

, T g

Er, w %

- 1 - 2

Fig. 15. Temperature of reversible polymorphic phase transition (1) and glass transition temperature (2) versus Er content.

200 400 600 800 1000 1200








1 2

% tr

an sm

itt an

ce f

or x

= 1

m m

λ, nm

Fig. 14. Transmission spectra of partly crystallized glass of composition TGC-2 containing about 42% crystal phase by single (2) and double (1) heat treatments, having crystal number densities about 1.2.104 and 2Æ106 mm-3 and crystal diameters of 47 and 7.5 lm, respectively.

T. Berthier et al. / Journal of Non-Crystalline Solids 354 (2008) 1721–1730 1729

97%) is caused by the appearance of spontaneous micro cracks in these TGC, since the blockaded glassy areas are exposed to high stresses [35].

As we already mentioned, the crystals in our TGCs are Na4+2xCa4x[Si6O18] s/s which are based on the hexagonal structure of sodium calcium silicate Na4Ca4[Si6O18]. This structure has cation sites only partly occupied by Na and Ca ions [22]. Thus we expect that transition metals or rare-earth elements could be inserted as substitutional sites in these structures. Fig. 15 shows that, indeed, first attempts to introduce Er in our TGC resulted in a pro- nounced increase in the reversible isomorphous phase tran- sition temperatures Tpm of the s/s crystals. This result can be interpreted as an evidence for Er insertion in s/s.

The Abbe number of our TGC is similar to that of com- mercial soda-lime–silica glass and is surprising for a mate- rial containing 97% crystallized fraction. Just for

comparison purposes, the Abbe number of the human eye is approximately 45, and thus any lens with smaller Abbe number can compromise the vision quality. This Abbe number, 52.6, indicates that our TGC does not suffer strong light dispersion.

7. Conclusions

As opposed to the typical traditional transparent glass– ceramics, which have nano-size crystals and low to moder- ate crystallinity, we developed a new type of TGC having large (micrometric) grain size and high crystallized volume fraction. Their high transmittance mainly results from simultaneous variations of the glass-matrix and s/s-crystal compositions during crystallization, which lead to a consid- erable decrease in the difference between the respective refractive indexes of the two phases. Therefore the differ- ence between the respective refractive indexes prevails regardless of crystal size when the aim is to improve trans- mittance. Preliminary tests indicate that this new family of TGC can be further developed by doping them with tran- sition metal and rare-earth elements and perhaps be used as optical components.


We are indebted to Fapesp – The São Paulo State Re- search Foundation (Brazil) for funding this research, and to CAPES (Brazil) for a doctoral grant to TB.


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