- Email: [email protected]
Effect of microstructure of a phase separated sodium-borosilicate glass on mechanical properties
Ceramics International 43 (2017) 11403–11409
Contents lists available at ScienceDirect
Ceramics International journal homepage: www.elsevier.com/locate/ceramint
Effect of microstructure of a phase separated sodium-borosilicate glass on mechanical properties
MARK
⁎
Johannes Häßler, Christian Rüssel
Otto-Schott-Institut, Jena University, Fraunhoferstr. 6, Germany
A R T I C L E I N F O
A BS T RAC T
Keywords: Liquid/liquid phase separation Sodium borosilicate glass Mechanical strength Stress
A glass with the mol% composition 60 SiO2·37 B2O3·30 Na2O was thermally treated at temperatures in the range from 520 to 680 °C for 1–80 h. This led to liquid/liquid phase separation and a droplet phase enriched in Na2O and B2O3 was formed, while the matrix phase was enriched in SiO2. The phase separated glass showed a droplet size distribution which after thermal treatment at comparatively low temperatures showed a lognormal distribution, while higher temperatures resulted in a Brailsford and Wynblatt distribution, which should be expected for Ostwald ripening. The glasses showed two glass transition temperatures and the two phases possessed two different coefficients of thermal expansion. Since the droplet phase has a higher coefficient of thermal expansion, around the droplet radial tensile stresses are formed, while the tangential stresses are compressive. While the Young's Modulus was hardly affected by the phase separation, the hardness was notably smaller for phase separated glasses. The 4-point bending strength increased with the temperature of thermal treatment from 40 MPa for the not treated glass to 115 MPa for a glass thermally treated at 640 °C for 20 h. The stresses formed during cooling were estimated from the elastic properties, the coefficients of thermal expansion of the two glassy phases formed, and the glass transition temperature of the matrix phase as a function of the temperature of thermal treatment. The stresses increase with the temperature of thermal treatment up to a maximum at 620 °C and then decreases rapidly. This is in rough agreement with the 4-point bending strengthhigh stresses lead to high strength.
1. Introduction Liquid-liquid phase separation might occur in multi component liquids if the interaction of a structural unit A with another structural unit B (A-B) is thermodynamically less advantageous than the interactions A-A and B-B. A phase separation which occurs above the liquidus temperature, is denoted as stable phase separation. It is observed in phase diagrams of e.g. CaO-SiO2 [1]. Since the temperature is comparatively high, the viscosity at temperatures phase separation occurs is fairly low and hence due to the different densities, sedimentation occurs. Hence, macroscopically homogeneity can hardly be achieved and chemical compositions which show stable phase separation are not suitable as useful materials. By contrast, metastable phase separation occurs below the liquidus temperature. Here, the temperature is notably lower and hence the viscosity higher. The sedimentation velocity is proportional to the viscosity and the square of the diameter (in the case of droplet phase separation). The droplet coarsening is proportional to the diffusion coefficient and roughly to the reciprocal viscosity. That means, in the case of meta stable phase separation, the droplets are much smaller and the viscosity higher and hence, sedimentation does usually not occur.
⁎
Corresponding author.
http://dx.doi.org/10.1016/j.ceramint.2017.05.349 Received 25 April 2017; Received in revised form 28 May 2017; Accepted 31 May 2017 Available online 02 June 2017 0272-8842/ © 2017 Elsevier Ltd and Techna Group S.r.l. All rights reserved.
Depending on the chemical composition of the glass, two different types of structures may be formed: droplet structures and interpenetrating structures. The type of morphology formed can widely be varied by the chemical composition [2]. The glass forming systems, which show phase separation are quite numerous. The best investigated system is Na2O/B2O3/SiO2 and the other alkali/boronoxide/silica systems. During phase separation, sodium and boron-rich phase as well as a silica rich phase is formed. Here, depending on the chemical compositions, interpenetrating structures can be obtained. Besides, also droplet phase separation is possible with two different structures, a droplet phase enriched in silica as well as a droplet phase enriched in sodium and boronoxide. The phase diagram is shown in Fig. 1, together with the regions in which the three types of phase separations occur [3]. The region, in which the droplet phase is enriched in sodium and boronoxide is in the region, rich in silica which in Fig. 1 is at the bottom right side. The problem with these glass compositions is the high melting point due to the high silica concentrations. The structure is usually small droplets with a comparatively small volume concentration in a silica rich matrix with large volume concentration. The growth
Ceramics International 43 (2017) 11403–11409
J. Häßler, C. Rüssel
In order to ensure an exact temperature, a thermocouple was placed directly above the sample. The temperature accuracy was within ± 1.5 K from the present one. The samples were placed in the pre heated furnace, removed from the furnace after the annealing time and subsequently cooled to room temperature. 2.2. Structural and mechanical analysis
Fig. 1. TEM-replica of an as casted glass sample.
kinetics of such a composition has already been recently reported [4]; the growth exponent is not as large as usually observed. In a material composed of glassy droplets embedded in a glassy matrix, the coefficients of thermal expansion (CTE) are usually different [5]. In the case of droplets with higher CTE, stresses can be relaxed during cooling approximately until the glass transition temperature is reached. During further cooling, tensile stresses are formed in the droplets. The stresses formed in the matrix will later be discussed. This paper presents a study on the mechanical properties of glasses with a droplet phase separation enriched in sodium and boron and a matrix enriched in SiO2. The effect of phase separation, composition difference and droplet size on the mechanical properties is reported. 2. Experimental procedure A glass with of the composition 60 SiO2·37 B2O3·3 Na2O was melted from the raw materials SiO2 (Carl Roth), H3BO3 (Merck) and NaCO3 (Carl Roth) using a platinum-rhodium crucible at temperatures in the range from 1570 to 1580 °C. The melt was kept for 0.5 h at this temperature, stirred for another 1 h and then soaked for 30 min. Subsequently, the glass was casted in a steel mould and then given to a cooling furnace, preheated to 500 °C. The furnace was switched off allowing the sample to cool with a rate of approximately 3 K/min. The resulting glass was homogeneous and clear. The chemical composition of the prepared glass was 62.7 SiO2·35.7 B2O3·1.6 Na2O as analysed by EDX. The glass composition is hence slightly different from batch composition due to the evaporation of borate and sodium. 2.1. Thermal treatment All samples were treated at temperatures in the range from 500 to 680 °C in a laboratory furnace (NABERTHERM).
In order to determine the glass transition temperature, cylindrical samples with a diameter of 8 mm and a length of 15 mm were drilled out and then a dilatometric profile was recorded using a dilatometer DIL 402 PC, NETZSCH. The Young's modulus was determined with an ultrasound technique using a USD 15, KRAUTKRÄMER-BRANSON and cylindric samples with a length of 25 mm and a diameter of 15 mm. The 4-point bending strength was measured using samples with the dimensions 3 × 4 × 45 mm prepared by cutting, grinding and polishing according to DIN EN 843-1, using a mechanical testing machine type ZWICK 1445 equipped with a U2A-load cell with a maximum load of 10 kN. Vickers hardness was tested with 10 × 4 × 3 mm samples prepared by cutting, grinding and polishing, using a Duramin-1 microhardness tester, STRUERS. 3. Results The as melted glass was colorless and visually transparent. The glass transition temperature Tg was 432 °C as determined by dilatometry. There was not any hint at the occurrence of two different glass transition temperatures, which would be typical for phase separated glasses. Fig. 1 shows a TEM-replica micrograph. Here, clearly heterogeneities with sizes in the range from 20 to 30 nm are observed. The observed structures seem to be inclusions of one phase into another one, however, the inclusions are not spherical in all cases. Fig. 2 shows a phase diagram of the system Na2O/B2O3/SiO2. The critical temperature, below which phase separation might occur is 750 °C. The phase separation cupola runs from the right edge (100% SiO2) to the left along the line Na2O:B2O3 = 16:84. Phase separation occurs between around 20% and 75% SiO2. At 50% < [B2O3] < 70%, Na2O/B2O3 rich droplets are formed [6]. The studied glass composition is marked in the phase diagram. According to the tie line, an SiO2 rich composition as well as a Na2O/B2O3 rich composition should be formed. Since the volume concentration of the SiO2 rich phase should be much higher than of the Na2O/B2O3 rich phase, a droplet phase enriched in Na2O and B2O3 embedded in a matrix phase enriched in SiO2 should be formed. It was already shown in Ref [4], that this is really the case. Figs. 3a and b show TEM replica micrographs of glass samples thermally treated at 540 °C for 5 h and at 680 °C for 80 h, respectively. These two samples were chosen in order to demonstrate the variation of the droplet structure obtained during thermal treatment supplying different temperature/time schedules. After thermal treatment at 540 °C, droplets with sizes in the range from 20 to 50 nm are observed, while they are notably larger (80–400 nm), if treated at 680 °C. The data on particle size was obtained by determining the diameter of up to
Fig. 2. Phase diagram in the system Na2O/B2O3/SiO2.
11404
Ceramics International 43 (2017) 11403–11409
J. Häßler, C. Rüssel
Fig. 3. a) TEM-Replica of sample treated at 540 °C for 5 h, b) TEM-Replica of sample treated at 680 °C for 80 h.
1000 particles from images recorded from samples thermally treated under the same conditions. The diameters of the observed droplets are cut planes through a sphere. Therefore, the observed size in the most cases is smaller than the real size of the droplets. Hence, the real particle size distribution is narrower than that in the replica images. For that reason, the particle size distributions was corrected using CSD Corrections [7], based on the sphere unfolding method by Saltikov and further improvements introduced later [8,9]. The Figure clearly shows that the droplet size can well be determined from the replica micrographs. After correction, the droplets have mean size of 109 nm, which increases with the time and temperature of thermal treatment. In Fig. 4a, the droplet size distribution for a sample thermally treated at 540 °C for 5 h is shown. Simple Ostwald ripening in an infinitely diluted system should show the Lifshits Slyozov Wagner (LSW) [10] distribution. The size distribution, P(D), according to the LSW theory, can be expressed by Eq. (1):
⎛ ⎞ 4 −D ⎟⎟ D exp⎜⎜ 3 9 − D ⎝2 ⎠ 2
P (D ) =
1
7
2
11
(1+ 3 D ) 3 (1− 3 D ) 3
(1)
with D = di /d denoting the normalized droplet size. In many cases, this
Fig. 4. a) Normalized particle size distribution of a sample treated at 540 °C for 5 h compared to LSW, B & W and logarithmic normal distribution, b) Normalized particle size distribution of a sample treated at 680 °C for 80 h compared to LSW, B & W and normal distribution.
distribution is only in a poor agreement with the observed distribution. This is caused by the volume concentration which is not infinitely small. Another size distribution, which takes into account larger volume concentrations is that according to the Brailsford and Wynblatt theory (B & W theory) [11] which shows a broadening of the distribution function with the volume concentration (see Eq. (2)).
P (D ) =
⎛ −c ⋅ D ⎞ 3D 2γ⋅exp⎜ ρ − D ⎟ ⎝c ⎠ ⎛ D ⎞a ⎛ D ⎞b1 γ ⎜1− ρ ⎟ ⎜1+ ρ ⎟ c⎠ ⎝ 1⎠ ⎝
(2)
Where the parameters y, c, γ , a, b1, ρc , ρ1 are tabulated as a function of the volume fraction Vs [11]. If the volume fraction of the droplets Vs approaches zero, the B & W distribution gets identical with the LSW distribution function. The observed distributions deviate from the shape expected for Ostwald ripening, this is especially true for low annealing temperatures and short treatment times. For longer treatments at higher tempera-
11405
Ceramics International 43 (2017) 11403–11409
J. Häßler, C. Rüssel
tures, as shown in Fig. 4b, the distribution maximum is shifted to higher values compared to the average diameter, thus approaching the form predicted by the B & W-Theory. Fig. 4a and b also show lognormal distributions fitted to the experimental data. In both cases, the lognormal distributions fit much better than the LSW- or B & Wdistributions. During Ostwald ripening, the particles should grow with time according to an exponential law:
D = const·t 0.33
(3)
It has already been reported that in the case of the presently studied glass composition, the exponent is much smaller than 0.33 [4], and depending on the temperature of thermal treatment in the range from 0.08 to 0.25. This was explained by a depletion of the matrix phase in B2O3 and Na2O, and especially by the formation of a core shell structure with a shell enriched in SiO2 [12]. During the course of the droplet growth, this shell grows and acts as a growth barrier. This interpretation is in analogy to the crystallization of phases such as CaF2 or BaF2 which results in an increase in the transition temperature of the residual glass phase which now is depleted in Ca2+ and F- [13–15]. In these systems, the formation of a core shell structure was proved by Anomaleous Small Angle X-ray Scattering (ASAXS) [16] as well as by TEM in combination with electron energy loss spectroscopy (EELS) [17]. The shell results in a drastic decrease of the crystal growth velocity with time which leads to narrow size distributions [18]. Also according to the phase diagram shown in Fig. 1, a hindrance due to a further silica enrichment in the matrix phase at lower temperatures should occur. It should be noted, however, that the exact position of the tie line changes with temperature. The change in the chemical composition with temperature also results in a change in the coefficient of thermal expansion (CTE) of both formed glassy phases. The change of the SiO2 concentration with temperature, according to the equilibrium concentrations and the tie line from Fig. 2, is schematically shown in Fig. 5. In the SiO2 depleted phase, the SiO2 concentration decreases continuously with decreasing temperature, while a steady increase of the SiO2 concentration should occur in the SiO2 enriched phase. It should be noted that these values are attributed to a state which is reached after a long time of thermal treatment which, however, is not an equilibrium in a thermodynamic sense, because the latter would be the crystalline state. From the respective SiO2 concentration, the CTE was calculated by using the data from Ref [6]. In Fig. 6, the CTEs are shown as a function of the annealing temperature together with the experimentally deter-
Fig. 6. Coefficients of thermal expansion (CTE) of the phases, derived from assumed phase concentrations.
mined coefficient of thermal expansion. The latter values are composed by the CTE of both glassy phases, i.e. the SiO2 rich and the SiO2 depleted ones. The red circles are attributed to the experiment, while the squares represent the calculated values. The upper full squares stand for the sodium borate rich phases; they are all higher than the experimentally determined values and the difference between these two values increases steadily with decreasing temperature. The lower values of the CTE shown as open squares are lower than the experimentally determined values because they represent the SiO2 enriched glassy phase. Hence, the structure of the cooled phase separated glasses is composed by a droplet phase enriched in Na2O and B2O3 which has a CTE in the range from 6.5 and 8.5·10−6 K−1, while the matrix phase is enriched in SiO2 and possesses a coefficient of thermal expansion in the range from 3.0 to 4.0·10−6 K−1. This means, the difference in the CTE of the two glassy phases increases with decreasing temperature of thermal treatment. In Fig. 7, the Young's modulus is shown as a function of the time of thermal treatment of samples thermally treated at 620 °C for up to 80 h. The values are all between 44.5 and 46.5 GPa, the highest value is attributed to the not thermally treated glass. The values do not show a systematic dependency upon the annealing time and are all within the limits of error constant.
Fig. 5. Schematic cut along the tie line showing SiO2-concentrations of both phases depending on temperature.
11406
Fig. 7. Young's modulus of samples annealed at 620 °C for 0–80 h.
Ceramics International 43 (2017) 11403–11409
J. Häßler, C. Rüssel
Fig. 10. 4-point-bending strength as a function of the mean droplet diameter, the point at 0 h represents an untreated sample.
Fig. 8. Vickers Hardness of samples treated at 620 °C for 0–80 h.
Fig. 8 shows the Vickers hardness as a function of the time for samples thermally treated at 620 °C for up to 80 h. While the hardness of the untreated sample is 5.85 GPa, thermal treatment leads to decreasing hardness. After thermal treatment for 40 h, a minimum of 4.6 GPa is reached, increasing the time to 80 h leads to a re-increase of the hardness to 5 GPa. The bending strength of the samples after thermal treatment for 20 h at different temperatures is shown in Fig. 9. The untreated sample possesses a 4-point bending strength of 41 MPa. Thermal treatment for 20 h leads to a bending strength of 71 MPa, a value which is almost constant for thermal treatments up to 580 °C. After thermal treatment at 600 °C, a bending strength of 99 MPa is reached and finally, thermal treatment at 640 °C for 20 h results in a bending strength of 115 MPa. Further increasing temperatures result in decreasing bending strengths. In Fig. 10, the bending strengths of samples thermally treated for different temperatures and for different periods of time are shown. Here, it is clearly shown that a maximum in the bending strength is reached at a mean droplet diameter of around 70 nm. If the droplet size is notably smaller or larger, the values of the 4-bond bending strength were smaller.
A spherical particle in a solid matrix which has another CTE than the matrix and which do not show stresses at a certain elevated temperature, will form stresses during cooling. In the case of a glassy matrix, the stress formation starts at that temperature, where the stresses can no longer relax, i.e. below Tg. The stresses in the spherical inclusion according to Selsing [19] can be calculated by Eq. (4):
P =
ΔCTE ⋅ ΔT ⎛1 ⎜ ⎝
+ μm 2Em
+
1 − 2μi ⎞ ⎟ Ei ⎠
P = stress in the inclusion, ΔCTE = CTE(inclusion) – CTE(matrix). ΔT = difference between the upper temperature the stresses can relax and the final temperature (usually room temperature), Em and Ei = Young's moduli of the matrix and the inclusion, µm and µi = Poisson's ratio of the matrix and the inclusion. If both the matrix and the particle are isotropic, then the pressure is isostatic within the particle. In the matrix, the stresses decrease with increasing distance from the particle. At the interface matrix/particle, the radial stresses are identical, while the tangential stresses inside the matrix are twice as high as the radial stresses. It should be noted that the maximum stresses do not depend on the diameter of the spheres, i.e. not on the droplet size.
σr = − 2σt = − P⋅
Fig. 9. 4-point-bending strength of samples treated at 500–680 °C for 20 h, the point at 0 h represents an untreated sample.
(4)
R3 r3
(5)
σr = stresses in the matrix, σt = tangential stresses in the matrix, P= isostatic pressure in the spherical particle, R = radius of the particle, r = distance from the center of the particle. In the case of a Na2O/B2O3 enriched droplet phase embedded in an SiO2 enriched matrix, the CTE of the droplet is much larger than that of the matrix. The difference between the two CTE is, however, a function of the temperature of thermal treatment. Tg of the matrix is higher than that of the droplets, and hence at temperatures below Tg of the matrix, formed stresses cannot relax. The behaviour during cooling and the formation of stresses is schematically shown in Fig. 11. During cooling, in between the Tg values of the matrix and the droplet, the difference in the thermal expansion coefficients is very large, because the droplet is still above its Tg. Below Tg of the droplet, the difference in the coefficients of thermal expansion is by far not as large. ΔT in Eq. (4) should be Tg of the silica rich phase minus the room temperature, i.e. the numerator of Eq. (4) should be:
11407
Ceramics International 43 (2017) 11403–11409
J. Häßler, C. Rüssel
Fig. 12. Δα·ΔT as function of the temperature of thermal treatment. Fig. 11. Schematic of stress formation above and below the glass transition temperatures.
ΔT ΔCTE· = (CTEi(T >Tgi)−CTEm)·(Tgm −Tgi) + (CTEi(T
(6)
With: CTEm and CTEi are the CTEs of the matrix and the droplet phase, respectively; Tgi and Tgm are the glass transition temperatures of the droplet and the matrix phase, respectively. CTEi(T > Tgi) and CTEi(T < Tgi) are the coefficients of thermal expansion of the droplet phase above and below Tgi, respectively; Table 1, columns 2 and 3 summarize the CTEs and columns 4 and 5 the glass transition temperatures of the droplet and the matrix phase, respectively obtained for different temperatures of thermal treatments. Column 6 presents ΔCTE·ΔT, which is a measure of the stresses around the particle and was calculated using Eq. (6). After thermal treatment at 730 °C, phase separation does not yet occur and therefore, no stresses are formed. After thermal treatment at 720 °C, phase separation takes place and the CTEs of droplet and matrix are 5.5 and 4.25· 10−6 K−1, respectively. Tg of the matrix phase already showed a slight increase and ΔCTE·ΔT is 0.66 10−3. Decreasing temperature of thermal treatment led to larger differences in the CTEs of droplet and matrix phase and to increasing Tg of the matrix phase. Both contribute to an increase in ΔCTE·ΔT. Since the CTE of the droplet phase is much larger above Tg, the difference in the Tg values of the two phases has a large effect on the formed stresses (see also Fig. 11). According to Ref [6], for the droplet phase, CTE above Tg of 22 10−6 K−1 was estimated. With decreasing temperatures of thermal treatment, the stresses increase, because both the differences in the CTEs increase and the differences in the Tg values increase. At a temperature of thermal treatment of 580 °C, a maximum in the differences of the two Tg-values is reached Table 1 CTEm, CTEi: CTE of the matrix and the inclusion; ΔCTE: difference of CTEm and CTEi; Tgm, Tgi; Tg of the matrix and the inclusion; ΔT* ΔCTE: the numerator of Eq. (4) as a function of the temperature of thermal treatment. T in °C
CTEm in 10−6 K−1
CTEi in 10−6 K−1
ΔCTE in 10−6 K−1
Tgm in °C
Tgi in °C
ΔT*ΔCTE in 10−6
730 720 700 680 660 640 620 600 580 560 540
4.8 4.3 4 3.6 3.5 3.3 3.25 3.3 3.3 3.3 3.3
4.8 5.5 6.3 6.6 6.8 7.1 7.2 7.4 7.6 7.7 7.9
0 1.2 2.3 3 3.3 3.8 3.95 4.1 4.3 4.4 4.6
434 440 446 452 459 465 505 494 534 493 469
434 432 430 429 427 425 432 431 427 420 420
0 656 1267 1695 1999 2360 3141 2988 3976 3271 2846
and also ΔCTE·ΔT reaches a maximum of 3.97·10−3. Further decreasing temperatures of thermal treatment resulted in re-increasing Tg of the matrix phase and also decreasing ΔCTE·ΔT. At a first glance, this is surprising, because according to the phase diagram, the composition of the respective phases should shift continuously and hence also the CTE should become increasingly different as well as the glass transition temperatures. Both should result in increasing ΔCTE·ΔT and hence increasing stresses around the droplets. However, if the experiment is performed in the way as described in the section experimental procedure, i.e. the quenched glass is heated to a certain “heat treatment temperature”, then the kinetics of the phase separation process are too slow to reach a state where compositions near those of the phase separation cupola of the phase diagram are reached. Fig. 12 shows a plot of ΔCTE·ΔT versus the temperature of thermal treatment. A comparison of the Figs. 9 and 12 shows that the dependencies of the 4-point bending strength and the formed stresses both upon the temperature of thermal treatment show some similarities. They exhibit fairly broad maxima. At higher temperatures, the strengths and the stresses show a steep decrease. In analogy also at lower temperatures, a decrease in both curves is observed. A rough estimation of the stresses formed was done by approximating the denominator of Eq. (4) with µm ≈ 0.3, µi ≈ 0.275 [20], Em ≈ 60 GPa and Ei ≈ 60 GPa [20]. The denominator is then 0.0183/GPa, which results in a maximum stress of 3.97·10−3 GPa/0.0183 = 217 MPa. It should be noted that both Young's moduli and Poisson's ration are only rough approximations. Nevertheless, the stresses are high enough to justify the observed increase in strength. In the MgO/Al2O3/SiO2 system with the nucleation agents TiO2, ZrO2 or a mixture of both, volume crystallization is observed. In certain compositions, such as 21.2 MgO·21.2 Al2O3·51.9 SiO2·5.7 ZrO2 (in mol %), in a first step, tetragonal zirconia is formed during thermal treatment and in a second step a high quartz solid solution with around 10 mol% MgO and 10 mol% Al2O3 is crystallized. If such a glass ceramic is cooled to room temperature, it still contains the high quartz solid solutions and shows accordingly a comparatively small coefficient of thermal expansion of typically 4·10−6 K−1. If the crystallization temperature is higher or the crystallization time much longer, then the quartz phase formed contains only minor concentrations of both MgO and Al2O3 (around 1 mol% each) and additionally spinel (MgAl2O4). During subsequent cooling, a phase transitions from the high to the low temperature phase of quartz takes place which runs parallel to volume contraction (pure phases: 0.8%) and results in a thermal expansion (25–500 °C) of 12.8·10−6 K−1 [21,22]. The mechanical strengths which can be achieved by low quartz containing glassceramics exhibit high strengths of usually around 450 MPa [23,24], recently even values of up to 1 GPa were reported. By contrast, the 4point bending strength of the high quartz containing glass ceramics is
11408
Ceramics International 43 (2017) 11403–11409
J. Häßler, C. Rüssel
around 150 MPa. This was explained by the high mechanical stresses which were formed during cooling. In this case, the residual glassy phase is set under axial tensile stresses and tangential compressive stresses. In the present case that of the amorphous droplet embedded in an amorphous matrix, the situation is quite similar. It can hence be concluded, that the increased 4-point bending strength of the phase separated glasses is due to the stresses formed during cooling. The concept of high strength glass-ceramics can hence be transferred to liquid/liquid phase separated glasses. It should, nevertheless, be mentioned, that most liquid/liquid phase separated glasses reported in the literature contain SiO2 enriched droplets, which show smaller CTE than the matrix they are embedded. These glasses are not assumed to show increased strength after phase separation. In Ref [25]., a glass with the composition 0.5 Li2O 0.5 K2O 2 SiO2 was studied with respect to phase separation. It was found, that the mechanical strength decreases with increasing size of the droplets. In the studied glass composition, the droplets are enriched in silica and should have a smaller CTE. The flaw size according to Griffith equation was calculated from the strength and a good correlation with the size of the droplets was obtained. Hence the formation of the droplets had just the opposite effect as in the present paper where the droplets had a higher CTE than the matrix. 4. Conclusion Thermal treatment of a glass with the mol% composition 60 SiO2·37 B2O3·3 Na2O at temperatures in the range from 520 to 680 °C for 1– 80 h led to liquid/liquid phase separation. A droplet phase enriched in Na2O and B2O3 embedded in a matrix phase enriched in silica is formed. The droplet size distribution after thermal treatment at comparatively low temperatures can be well described by a lognormal distribution, while thermal treatment at higher temperatures leads to a Brailsford and Wynblatt distribution as expected from Ostwald ripening. During the course of the phase separation, the viscosity of the matrix phase increases which should lead to the formation of a core shell structure, i.e. to a highly viscous layer around the droplets which hinder further growth. The droplet phase possesses a much higher CTE than the matrix phase. At lower temperatures of thermal treatments, the differences in the CTE increases and also the Tg of the matrix phase. Simple models according to Selsing enable the calculations of stresses formed during cooling assuming that stresses can no longer relax at temperatures below Tg of the matrix phase. At comparatively low temperatures, the compositions of the formed phases are no longer in agreement with the phase separation cupola. The stresses hence first increase with increasing temperature of thermal treatment, reach then a maximum at 620 °C kept for 20 h, and then decrease again. The latter is attributed to lower Tg of the matrix and smaller differences in the CTE. The 4-point bending strength exhibits a maximum after thermal treatment at 640 °C for 20 h and decreases again at higher tempera-
tures. In analogy to the formed stresses, also a decrease at lower temperature is observed. It can hence be concluded that the stresses formed during cooling are responsible for the increase in the 4-point bending strength. References [1] W. Vogel, Glaschemie, 3rd ed., Springer, Berlin, 1992. [2] M. Suzuki, T. Tanaka, Composition dependence of microstructures formed by phase separation in multi-component silicate glass, ISIJ Int. 48 (2008) 405–411. [3] O. V. Mazurin, E. A. Porai-Koshits, N. S. Andreev, N. S. Phase separation in glass, North-Holland, Amsterdam, New York, 1984. [4] J. Häßler, C. Rüssel, Self-organized growth of sodium borate-rich droplets in a phase-separated sodium borosilicate glass, Int. J. Appl. Glass Sci. 8 (2017) 124–131. [5] J.E. Shelby, Thermal expansion of alkali borate glasses, J. Am. Ceram. Soc. 66 (1983) 225–227. [6] T. Abe, Borosilicate glasses, J. Am. Ceram. Soc. 35 (1952) 284–299. [7] M.D. Higgins, Quantitative Textural Measurements in Igneous and Metamorphic Petrology, Cambridge University Press, Cambridge, 2006. [8] J. Gegner, Stereological cross-sectional micrograph analysis for the calculation of real particle size distributions, Prakt. Metallogr. 43 (2006) 224–236. [9] S. A. Saltikov, in "Stereology", edited by H. Elias, Springer, Berlin, Heidelberg, 1967, pp. 163–173. [10] I.M. Lifshitz, V.V. Slyozov, The kinetics of precipitation from supersaturated solid solutions, J. Phys. Chem. Solids 19 (1961) 35–50. [11] R.N. Stevens, C.K.L. Davies, Self-consistent forms of the chemical rate theory of Ostwald ripening, J. Mater. Sci. 37 (2002) 765–779. [12] I. Avramov, C. Bocker, C. Rüssel, Topology and numerical simulation of phase separation in sodium silicate glasses, J. Phys. Chem. Solids 78 (2015) 8–11. [13] C. Rüssel, Nanocrystallization of CaF2 from Na2O/K2O/CaO/CaF2/Al2O3/SiO2 Glasses, Chem. Mater. 17 (2005) 5843–5847. [14] C. Bocker, C. Rüssel, Self-organized nano-crystallisation of BaF2 from Na2O/K2O/ BaF2/Al2O3/SiO2 glasses, J. Eur. Ceram. Soc. 29 (2009) 1221–1225. [15] V.S. Raghuwanshi, A. Hoell, C. Bocker, C. Rüssel, Experimental evidence of a diffusion barrier around BaF2 nanocrystals in a silicate glass system by ASAXS, CrystEngComm 14 (2012) 5215–5223. [16] A. Hoell, Z. Varga, V.S. Raghuwanshi, M. Krumrey, C. Bocker, C. Rüssel, ASAXS study of CaF2 nanoparticles embedded in a silicate glass matrix, J. Appl. Crystallogr. 47 (2014) 60–66. [17] S. Bhattacharya, C. Bocker, T. Heil, J.R. Jinschek, T. Höche, C. Rüssel, H. Kohl, et al., Experimental evidence of self-limited growth of nanocrystals in glass, Nano Lett. 9 (2009) 2493–2496. [18] C. Bocker, S. Bhattacharyya, T. Höche, C. Rüssel, Size distribution of BaF2 nanocrystallites in transparent glass ceramics, Acta Mater. 57 (2009) 5956–5963. [19] J. Selsing, Internal Stresses in Ceramics, J. Am. Ceram. Soc. 44 (1961) 419. [20] S.P. Jaccani, L. Huang, Understanding sodium borate glasses and melts from their elastic response to temperature, Int. J. Appl. Glass Sci. 7 (2016) 452–463. [21] M. Dittmer, C.F. Yamamoto, C. Bocker, C. Rüssel, The effect of yttria on the crystallization and mechanical properties of MgO/Al2O3/SiO2/ZrO2 glass-ceramics, Solid State Sci. 13 (2011) 2146–2153. [22] M. Dittmer, C. Rüssel, Colorless and high strength MgO/Al2O3 /SiO2 glass-ceramic dental material using zirconia as nucleating agent, J. Biomed. Mater. Res. Part B, Appl. Biomater. 100 (2012) 463–470. [23] A. Hunger, G. Carl, C. Rüssel, Crystallization of ZnO/MgO/Al2O3/TiO2/ZrO2/SiO2Glasses, Solid State Sci. 12 (2010) 1570–1574. [24] A. Hunger, G. Carl, A. Gebhardt, C. Rüssel, Young's moduli and microhardness of glass-ceramics in the system MgO/Al2O3/TiO2/SiO2 containing quarz nano crystals, Mater. Chem. Phys. 122 (2010) 502–506. [25] J.F. Sproull, G.E. Rindone, Correlation between strength of glass and glassy microphases, J. Am. Ceram. Soc. 56 (1973) 102–103.
11409
Contents lists available at ScienceDirect
Ceramics International journal homepage: www.elsevier.com/locate/ceramint
Effect of microstructure of a phase separated sodium-borosilicate glass on mechanical properties
MARK
⁎
Johannes Häßler, Christian Rüssel
Otto-Schott-Institut, Jena University, Fraunhoferstr. 6, Germany
A R T I C L E I N F O
A BS T RAC T
Keywords: Liquid/liquid phase separation Sodium borosilicate glass Mechanical strength Stress
A glass with the mol% composition 60 SiO2·37 B2O3·30 Na2O was thermally treated at temperatures in the range from 520 to 680 °C for 1–80 h. This led to liquid/liquid phase separation and a droplet phase enriched in Na2O and B2O3 was formed, while the matrix phase was enriched in SiO2. The phase separated glass showed a droplet size distribution which after thermal treatment at comparatively low temperatures showed a lognormal distribution, while higher temperatures resulted in a Brailsford and Wynblatt distribution, which should be expected for Ostwald ripening. The glasses showed two glass transition temperatures and the two phases possessed two different coefficients of thermal expansion. Since the droplet phase has a higher coefficient of thermal expansion, around the droplet radial tensile stresses are formed, while the tangential stresses are compressive. While the Young's Modulus was hardly affected by the phase separation, the hardness was notably smaller for phase separated glasses. The 4-point bending strength increased with the temperature of thermal treatment from 40 MPa for the not treated glass to 115 MPa for a glass thermally treated at 640 °C for 20 h. The stresses formed during cooling were estimated from the elastic properties, the coefficients of thermal expansion of the two glassy phases formed, and the glass transition temperature of the matrix phase as a function of the temperature of thermal treatment. The stresses increase with the temperature of thermal treatment up to a maximum at 620 °C and then decreases rapidly. This is in rough agreement with the 4-point bending strengthhigh stresses lead to high strength.
1. Introduction Liquid-liquid phase separation might occur in multi component liquids if the interaction of a structural unit A with another structural unit B (A-B) is thermodynamically less advantageous than the interactions A-A and B-B. A phase separation which occurs above the liquidus temperature, is denoted as stable phase separation. It is observed in phase diagrams of e.g. CaO-SiO2 [1]. Since the temperature is comparatively high, the viscosity at temperatures phase separation occurs is fairly low and hence due to the different densities, sedimentation occurs. Hence, macroscopically homogeneity can hardly be achieved and chemical compositions which show stable phase separation are not suitable as useful materials. By contrast, metastable phase separation occurs below the liquidus temperature. Here, the temperature is notably lower and hence the viscosity higher. The sedimentation velocity is proportional to the viscosity and the square of the diameter (in the case of droplet phase separation). The droplet coarsening is proportional to the diffusion coefficient and roughly to the reciprocal viscosity. That means, in the case of meta stable phase separation, the droplets are much smaller and the viscosity higher and hence, sedimentation does usually not occur.
⁎
Corresponding author.
http://dx.doi.org/10.1016/j.ceramint.2017.05.349 Received 25 April 2017; Received in revised form 28 May 2017; Accepted 31 May 2017 Available online 02 June 2017 0272-8842/ © 2017 Elsevier Ltd and Techna Group S.r.l. All rights reserved.
Depending on the chemical composition of the glass, two different types of structures may be formed: droplet structures and interpenetrating structures. The type of morphology formed can widely be varied by the chemical composition [2]. The glass forming systems, which show phase separation are quite numerous. The best investigated system is Na2O/B2O3/SiO2 and the other alkali/boronoxide/silica systems. During phase separation, sodium and boron-rich phase as well as a silica rich phase is formed. Here, depending on the chemical compositions, interpenetrating structures can be obtained. Besides, also droplet phase separation is possible with two different structures, a droplet phase enriched in silica as well as a droplet phase enriched in sodium and boronoxide. The phase diagram is shown in Fig. 1, together with the regions in which the three types of phase separations occur [3]. The region, in which the droplet phase is enriched in sodium and boronoxide is in the region, rich in silica which in Fig. 1 is at the bottom right side. The problem with these glass compositions is the high melting point due to the high silica concentrations. The structure is usually small droplets with a comparatively small volume concentration in a silica rich matrix with large volume concentration. The growth
Ceramics International 43 (2017) 11403–11409
J. Häßler, C. Rüssel
In order to ensure an exact temperature, a thermocouple was placed directly above the sample. The temperature accuracy was within ± 1.5 K from the present one. The samples were placed in the pre heated furnace, removed from the furnace after the annealing time and subsequently cooled to room temperature. 2.2. Structural and mechanical analysis
Fig. 1. TEM-replica of an as casted glass sample.
kinetics of such a composition has already been recently reported [4]; the growth exponent is not as large as usually observed. In a material composed of glassy droplets embedded in a glassy matrix, the coefficients of thermal expansion (CTE) are usually different [5]. In the case of droplets with higher CTE, stresses can be relaxed during cooling approximately until the glass transition temperature is reached. During further cooling, tensile stresses are formed in the droplets. The stresses formed in the matrix will later be discussed. This paper presents a study on the mechanical properties of glasses with a droplet phase separation enriched in sodium and boron and a matrix enriched in SiO2. The effect of phase separation, composition difference and droplet size on the mechanical properties is reported. 2. Experimental procedure A glass with of the composition 60 SiO2·37 B2O3·3 Na2O was melted from the raw materials SiO2 (Carl Roth), H3BO3 (Merck) and NaCO3 (Carl Roth) using a platinum-rhodium crucible at temperatures in the range from 1570 to 1580 °C. The melt was kept for 0.5 h at this temperature, stirred for another 1 h and then soaked for 30 min. Subsequently, the glass was casted in a steel mould and then given to a cooling furnace, preheated to 500 °C. The furnace was switched off allowing the sample to cool with a rate of approximately 3 K/min. The resulting glass was homogeneous and clear. The chemical composition of the prepared glass was 62.7 SiO2·35.7 B2O3·1.6 Na2O as analysed by EDX. The glass composition is hence slightly different from batch composition due to the evaporation of borate and sodium. 2.1. Thermal treatment All samples were treated at temperatures in the range from 500 to 680 °C in a laboratory furnace (NABERTHERM).
In order to determine the glass transition temperature, cylindrical samples with a diameter of 8 mm and a length of 15 mm were drilled out and then a dilatometric profile was recorded using a dilatometer DIL 402 PC, NETZSCH. The Young's modulus was determined with an ultrasound technique using a USD 15, KRAUTKRÄMER-BRANSON and cylindric samples with a length of 25 mm and a diameter of 15 mm. The 4-point bending strength was measured using samples with the dimensions 3 × 4 × 45 mm prepared by cutting, grinding and polishing according to DIN EN 843-1, using a mechanical testing machine type ZWICK 1445 equipped with a U2A-load cell with a maximum load of 10 kN. Vickers hardness was tested with 10 × 4 × 3 mm samples prepared by cutting, grinding and polishing, using a Duramin-1 microhardness tester, STRUERS. 3. Results The as melted glass was colorless and visually transparent. The glass transition temperature Tg was 432 °C as determined by dilatometry. There was not any hint at the occurrence of two different glass transition temperatures, which would be typical for phase separated glasses. Fig. 1 shows a TEM-replica micrograph. Here, clearly heterogeneities with sizes in the range from 20 to 30 nm are observed. The observed structures seem to be inclusions of one phase into another one, however, the inclusions are not spherical in all cases. Fig. 2 shows a phase diagram of the system Na2O/B2O3/SiO2. The critical temperature, below which phase separation might occur is 750 °C. The phase separation cupola runs from the right edge (100% SiO2) to the left along the line Na2O:B2O3 = 16:84. Phase separation occurs between around 20% and 75% SiO2. At 50% < [B2O3] < 70%, Na2O/B2O3 rich droplets are formed [6]. The studied glass composition is marked in the phase diagram. According to the tie line, an SiO2 rich composition as well as a Na2O/B2O3 rich composition should be formed. Since the volume concentration of the SiO2 rich phase should be much higher than of the Na2O/B2O3 rich phase, a droplet phase enriched in Na2O and B2O3 embedded in a matrix phase enriched in SiO2 should be formed. It was already shown in Ref [4], that this is really the case. Figs. 3a and b show TEM replica micrographs of glass samples thermally treated at 540 °C for 5 h and at 680 °C for 80 h, respectively. These two samples were chosen in order to demonstrate the variation of the droplet structure obtained during thermal treatment supplying different temperature/time schedules. After thermal treatment at 540 °C, droplets with sizes in the range from 20 to 50 nm are observed, while they are notably larger (80–400 nm), if treated at 680 °C. The data on particle size was obtained by determining the diameter of up to
Fig. 2. Phase diagram in the system Na2O/B2O3/SiO2.
11404
Ceramics International 43 (2017) 11403–11409
J. Häßler, C. Rüssel
Fig. 3. a) TEM-Replica of sample treated at 540 °C for 5 h, b) TEM-Replica of sample treated at 680 °C for 80 h.
1000 particles from images recorded from samples thermally treated under the same conditions. The diameters of the observed droplets are cut planes through a sphere. Therefore, the observed size in the most cases is smaller than the real size of the droplets. Hence, the real particle size distribution is narrower than that in the replica images. For that reason, the particle size distributions was corrected using CSD Corrections [7], based on the sphere unfolding method by Saltikov and further improvements introduced later [8,9]. The Figure clearly shows that the droplet size can well be determined from the replica micrographs. After correction, the droplets have mean size of 109 nm, which increases with the time and temperature of thermal treatment. In Fig. 4a, the droplet size distribution for a sample thermally treated at 540 °C for 5 h is shown. Simple Ostwald ripening in an infinitely diluted system should show the Lifshits Slyozov Wagner (LSW) [10] distribution. The size distribution, P(D), according to the LSW theory, can be expressed by Eq. (1):
⎛ ⎞ 4 −D ⎟⎟ D exp⎜⎜ 3 9 − D ⎝2 ⎠ 2
P (D ) =
1
7
2
11
(1+ 3 D ) 3 (1− 3 D ) 3
(1)
with D = di /d denoting the normalized droplet size. In many cases, this
Fig. 4. a) Normalized particle size distribution of a sample treated at 540 °C for 5 h compared to LSW, B & W and logarithmic normal distribution, b) Normalized particle size distribution of a sample treated at 680 °C for 80 h compared to LSW, B & W and normal distribution.
distribution is only in a poor agreement with the observed distribution. This is caused by the volume concentration which is not infinitely small. Another size distribution, which takes into account larger volume concentrations is that according to the Brailsford and Wynblatt theory (B & W theory) [11] which shows a broadening of the distribution function with the volume concentration (see Eq. (2)).
P (D ) =
⎛ −c ⋅ D ⎞ 3D 2γ⋅exp⎜ ρ − D ⎟ ⎝c ⎠ ⎛ D ⎞a ⎛ D ⎞b1 γ ⎜1− ρ ⎟ ⎜1+ ρ ⎟ c⎠ ⎝ 1⎠ ⎝
(2)
Where the parameters y, c, γ , a, b1, ρc , ρ1 are tabulated as a function of the volume fraction Vs [11]. If the volume fraction of the droplets Vs approaches zero, the B & W distribution gets identical with the LSW distribution function. The observed distributions deviate from the shape expected for Ostwald ripening, this is especially true for low annealing temperatures and short treatment times. For longer treatments at higher tempera-
11405
Ceramics International 43 (2017) 11403–11409
J. Häßler, C. Rüssel
tures, as shown in Fig. 4b, the distribution maximum is shifted to higher values compared to the average diameter, thus approaching the form predicted by the B & W-Theory. Fig. 4a and b also show lognormal distributions fitted to the experimental data. In both cases, the lognormal distributions fit much better than the LSW- or B & Wdistributions. During Ostwald ripening, the particles should grow with time according to an exponential law:
D = const·t 0.33
(3)
It has already been reported that in the case of the presently studied glass composition, the exponent is much smaller than 0.33 [4], and depending on the temperature of thermal treatment in the range from 0.08 to 0.25. This was explained by a depletion of the matrix phase in B2O3 and Na2O, and especially by the formation of a core shell structure with a shell enriched in SiO2 [12]. During the course of the droplet growth, this shell grows and acts as a growth barrier. This interpretation is in analogy to the crystallization of phases such as CaF2 or BaF2 which results in an increase in the transition temperature of the residual glass phase which now is depleted in Ca2+ and F- [13–15]. In these systems, the formation of a core shell structure was proved by Anomaleous Small Angle X-ray Scattering (ASAXS) [16] as well as by TEM in combination with electron energy loss spectroscopy (EELS) [17]. The shell results in a drastic decrease of the crystal growth velocity with time which leads to narrow size distributions [18]. Also according to the phase diagram shown in Fig. 1, a hindrance due to a further silica enrichment in the matrix phase at lower temperatures should occur. It should be noted, however, that the exact position of the tie line changes with temperature. The change in the chemical composition with temperature also results in a change in the coefficient of thermal expansion (CTE) of both formed glassy phases. The change of the SiO2 concentration with temperature, according to the equilibrium concentrations and the tie line from Fig. 2, is schematically shown in Fig. 5. In the SiO2 depleted phase, the SiO2 concentration decreases continuously with decreasing temperature, while a steady increase of the SiO2 concentration should occur in the SiO2 enriched phase. It should be noted that these values are attributed to a state which is reached after a long time of thermal treatment which, however, is not an equilibrium in a thermodynamic sense, because the latter would be the crystalline state. From the respective SiO2 concentration, the CTE was calculated by using the data from Ref [6]. In Fig. 6, the CTEs are shown as a function of the annealing temperature together with the experimentally deter-
Fig. 6. Coefficients of thermal expansion (CTE) of the phases, derived from assumed phase concentrations.
mined coefficient of thermal expansion. The latter values are composed by the CTE of both glassy phases, i.e. the SiO2 rich and the SiO2 depleted ones. The red circles are attributed to the experiment, while the squares represent the calculated values. The upper full squares stand for the sodium borate rich phases; they are all higher than the experimentally determined values and the difference between these two values increases steadily with decreasing temperature. The lower values of the CTE shown as open squares are lower than the experimentally determined values because they represent the SiO2 enriched glassy phase. Hence, the structure of the cooled phase separated glasses is composed by a droplet phase enriched in Na2O and B2O3 which has a CTE in the range from 6.5 and 8.5·10−6 K−1, while the matrix phase is enriched in SiO2 and possesses a coefficient of thermal expansion in the range from 3.0 to 4.0·10−6 K−1. This means, the difference in the CTE of the two glassy phases increases with decreasing temperature of thermal treatment. In Fig. 7, the Young's modulus is shown as a function of the time of thermal treatment of samples thermally treated at 620 °C for up to 80 h. The values are all between 44.5 and 46.5 GPa, the highest value is attributed to the not thermally treated glass. The values do not show a systematic dependency upon the annealing time and are all within the limits of error constant.
Fig. 5. Schematic cut along the tie line showing SiO2-concentrations of both phases depending on temperature.
11406
Fig. 7. Young's modulus of samples annealed at 620 °C for 0–80 h.
Ceramics International 43 (2017) 11403–11409
J. Häßler, C. Rüssel
Fig. 10. 4-point-bending strength as a function of the mean droplet diameter, the point at 0 h represents an untreated sample.
Fig. 8. Vickers Hardness of samples treated at 620 °C for 0–80 h.
Fig. 8 shows the Vickers hardness as a function of the time for samples thermally treated at 620 °C for up to 80 h. While the hardness of the untreated sample is 5.85 GPa, thermal treatment leads to decreasing hardness. After thermal treatment for 40 h, a minimum of 4.6 GPa is reached, increasing the time to 80 h leads to a re-increase of the hardness to 5 GPa. The bending strength of the samples after thermal treatment for 20 h at different temperatures is shown in Fig. 9. The untreated sample possesses a 4-point bending strength of 41 MPa. Thermal treatment for 20 h leads to a bending strength of 71 MPa, a value which is almost constant for thermal treatments up to 580 °C. After thermal treatment at 600 °C, a bending strength of 99 MPa is reached and finally, thermal treatment at 640 °C for 20 h results in a bending strength of 115 MPa. Further increasing temperatures result in decreasing bending strengths. In Fig. 10, the bending strengths of samples thermally treated for different temperatures and for different periods of time are shown. Here, it is clearly shown that a maximum in the bending strength is reached at a mean droplet diameter of around 70 nm. If the droplet size is notably smaller or larger, the values of the 4-bond bending strength were smaller.
A spherical particle in a solid matrix which has another CTE than the matrix and which do not show stresses at a certain elevated temperature, will form stresses during cooling. In the case of a glassy matrix, the stress formation starts at that temperature, where the stresses can no longer relax, i.e. below Tg. The stresses in the spherical inclusion according to Selsing [19] can be calculated by Eq. (4):
P =
ΔCTE ⋅ ΔT ⎛1 ⎜ ⎝
+ μm 2Em
+
1 − 2μi ⎞ ⎟ Ei ⎠
P = stress in the inclusion, ΔCTE = CTE(inclusion) – CTE(matrix). ΔT = difference between the upper temperature the stresses can relax and the final temperature (usually room temperature), Em and Ei = Young's moduli of the matrix and the inclusion, µm and µi = Poisson's ratio of the matrix and the inclusion. If both the matrix and the particle are isotropic, then the pressure is isostatic within the particle. In the matrix, the stresses decrease with increasing distance from the particle. At the interface matrix/particle, the radial stresses are identical, while the tangential stresses inside the matrix are twice as high as the radial stresses. It should be noted that the maximum stresses do not depend on the diameter of the spheres, i.e. not on the droplet size.
σr = − 2σt = − P⋅
Fig. 9. 4-point-bending strength of samples treated at 500–680 °C for 20 h, the point at 0 h represents an untreated sample.
(4)
R3 r3
(5)
σr = stresses in the matrix, σt = tangential stresses in the matrix, P= isostatic pressure in the spherical particle, R = radius of the particle, r = distance from the center of the particle. In the case of a Na2O/B2O3 enriched droplet phase embedded in an SiO2 enriched matrix, the CTE of the droplet is much larger than that of the matrix. The difference between the two CTE is, however, a function of the temperature of thermal treatment. Tg of the matrix is higher than that of the droplets, and hence at temperatures below Tg of the matrix, formed stresses cannot relax. The behaviour during cooling and the formation of stresses is schematically shown in Fig. 11. During cooling, in between the Tg values of the matrix and the droplet, the difference in the thermal expansion coefficients is very large, because the droplet is still above its Tg. Below Tg of the droplet, the difference in the coefficients of thermal expansion is by far not as large. ΔT in Eq. (4) should be Tg of the silica rich phase minus the room temperature, i.e. the numerator of Eq. (4) should be:
11407
Ceramics International 43 (2017) 11403–11409
J. Häßler, C. Rüssel
Fig. 12. Δα·ΔT as function of the temperature of thermal treatment. Fig. 11. Schematic of stress formation above and below the glass transition temperatures.
ΔT ΔCTE· = (CTEi(T >Tgi)−CTEm)·(Tgm −Tgi) + (CTEi(T
(6)
With: CTEm and CTEi are the CTEs of the matrix and the droplet phase, respectively; Tgi and Tgm are the glass transition temperatures of the droplet and the matrix phase, respectively. CTEi(T > Tgi) and CTEi(T < Tgi) are the coefficients of thermal expansion of the droplet phase above and below Tgi, respectively; Table 1, columns 2 and 3 summarize the CTEs and columns 4 and 5 the glass transition temperatures of the droplet and the matrix phase, respectively obtained for different temperatures of thermal treatments. Column 6 presents ΔCTE·ΔT, which is a measure of the stresses around the particle and was calculated using Eq. (6). After thermal treatment at 730 °C, phase separation does not yet occur and therefore, no stresses are formed. After thermal treatment at 720 °C, phase separation takes place and the CTEs of droplet and matrix are 5.5 and 4.25· 10−6 K−1, respectively. Tg of the matrix phase already showed a slight increase and ΔCTE·ΔT is 0.66 10−3. Decreasing temperature of thermal treatment led to larger differences in the CTEs of droplet and matrix phase and to increasing Tg of the matrix phase. Both contribute to an increase in ΔCTE·ΔT. Since the CTE of the droplet phase is much larger above Tg, the difference in the Tg values of the two phases has a large effect on the formed stresses (see also Fig. 11). According to Ref [6], for the droplet phase, CTE above Tg of 22 10−6 K−1 was estimated. With decreasing temperatures of thermal treatment, the stresses increase, because both the differences in the CTEs increase and the differences in the Tg values increase. At a temperature of thermal treatment of 580 °C, a maximum in the differences of the two Tg-values is reached Table 1 CTEm, CTEi: CTE of the matrix and the inclusion; ΔCTE: difference of CTEm and CTEi; Tgm, Tgi; Tg of the matrix and the inclusion; ΔT* ΔCTE: the numerator of Eq. (4) as a function of the temperature of thermal treatment. T in °C
CTEm in 10−6 K−1
CTEi in 10−6 K−1
ΔCTE in 10−6 K−1
Tgm in °C
Tgi in °C
ΔT*ΔCTE in 10−6
730 720 700 680 660 640 620 600 580 560 540
4.8 4.3 4 3.6 3.5 3.3 3.25 3.3 3.3 3.3 3.3
4.8 5.5 6.3 6.6 6.8 7.1 7.2 7.4 7.6 7.7 7.9
0 1.2 2.3 3 3.3 3.8 3.95 4.1 4.3 4.4 4.6
434 440 446 452 459 465 505 494 534 493 469
434 432 430 429 427 425 432 431 427 420 420
0 656 1267 1695 1999 2360 3141 2988 3976 3271 2846
and also ΔCTE·ΔT reaches a maximum of 3.97·10−3. Further decreasing temperatures of thermal treatment resulted in re-increasing Tg of the matrix phase and also decreasing ΔCTE·ΔT. At a first glance, this is surprising, because according to the phase diagram, the composition of the respective phases should shift continuously and hence also the CTE should become increasingly different as well as the glass transition temperatures. Both should result in increasing ΔCTE·ΔT and hence increasing stresses around the droplets. However, if the experiment is performed in the way as described in the section experimental procedure, i.e. the quenched glass is heated to a certain “heat treatment temperature”, then the kinetics of the phase separation process are too slow to reach a state where compositions near those of the phase separation cupola of the phase diagram are reached. Fig. 12 shows a plot of ΔCTE·ΔT versus the temperature of thermal treatment. A comparison of the Figs. 9 and 12 shows that the dependencies of the 4-point bending strength and the formed stresses both upon the temperature of thermal treatment show some similarities. They exhibit fairly broad maxima. At higher temperatures, the strengths and the stresses show a steep decrease. In analogy also at lower temperatures, a decrease in both curves is observed. A rough estimation of the stresses formed was done by approximating the denominator of Eq. (4) with µm ≈ 0.3, µi ≈ 0.275 [20], Em ≈ 60 GPa and Ei ≈ 60 GPa [20]. The denominator is then 0.0183/GPa, which results in a maximum stress of 3.97·10−3 GPa/0.0183 = 217 MPa. It should be noted that both Young's moduli and Poisson's ration are only rough approximations. Nevertheless, the stresses are high enough to justify the observed increase in strength. In the MgO/Al2O3/SiO2 system with the nucleation agents TiO2, ZrO2 or a mixture of both, volume crystallization is observed. In certain compositions, such as 21.2 MgO·21.2 Al2O3·51.9 SiO2·5.7 ZrO2 (in mol %), in a first step, tetragonal zirconia is formed during thermal treatment and in a second step a high quartz solid solution with around 10 mol% MgO and 10 mol% Al2O3 is crystallized. If such a glass ceramic is cooled to room temperature, it still contains the high quartz solid solutions and shows accordingly a comparatively small coefficient of thermal expansion of typically 4·10−6 K−1. If the crystallization temperature is higher or the crystallization time much longer, then the quartz phase formed contains only minor concentrations of both MgO and Al2O3 (around 1 mol% each) and additionally spinel (MgAl2O4). During subsequent cooling, a phase transitions from the high to the low temperature phase of quartz takes place which runs parallel to volume contraction (pure phases: 0.8%) and results in a thermal expansion (25–500 °C) of 12.8·10−6 K−1 [21,22]. The mechanical strengths which can be achieved by low quartz containing glassceramics exhibit high strengths of usually around 450 MPa [23,24], recently even values of up to 1 GPa were reported. By contrast, the 4point bending strength of the high quartz containing glass ceramics is
11408
Ceramics International 43 (2017) 11403–11409
J. Häßler, C. Rüssel
around 150 MPa. This was explained by the high mechanical stresses which were formed during cooling. In this case, the residual glassy phase is set under axial tensile stresses and tangential compressive stresses. In the present case that of the amorphous droplet embedded in an amorphous matrix, the situation is quite similar. It can hence be concluded, that the increased 4-point bending strength of the phase separated glasses is due to the stresses formed during cooling. The concept of high strength glass-ceramics can hence be transferred to liquid/liquid phase separated glasses. It should, nevertheless, be mentioned, that most liquid/liquid phase separated glasses reported in the literature contain SiO2 enriched droplets, which show smaller CTE than the matrix they are embedded. These glasses are not assumed to show increased strength after phase separation. In Ref [25]., a glass with the composition 0.5 Li2O 0.5 K2O 2 SiO2 was studied with respect to phase separation. It was found, that the mechanical strength decreases with increasing size of the droplets. In the studied glass composition, the droplets are enriched in silica and should have a smaller CTE. The flaw size according to Griffith equation was calculated from the strength and a good correlation with the size of the droplets was obtained. Hence the formation of the droplets had just the opposite effect as in the present paper where the droplets had a higher CTE than the matrix. 4. Conclusion Thermal treatment of a glass with the mol% composition 60 SiO2·37 B2O3·3 Na2O at temperatures in the range from 520 to 680 °C for 1– 80 h led to liquid/liquid phase separation. A droplet phase enriched in Na2O and B2O3 embedded in a matrix phase enriched in silica is formed. The droplet size distribution after thermal treatment at comparatively low temperatures can be well described by a lognormal distribution, while thermal treatment at higher temperatures leads to a Brailsford and Wynblatt distribution as expected from Ostwald ripening. During the course of the phase separation, the viscosity of the matrix phase increases which should lead to the formation of a core shell structure, i.e. to a highly viscous layer around the droplets which hinder further growth. The droplet phase possesses a much higher CTE than the matrix phase. At lower temperatures of thermal treatments, the differences in the CTE increases and also the Tg of the matrix phase. Simple models according to Selsing enable the calculations of stresses formed during cooling assuming that stresses can no longer relax at temperatures below Tg of the matrix phase. At comparatively low temperatures, the compositions of the formed phases are no longer in agreement with the phase separation cupola. The stresses hence first increase with increasing temperature of thermal treatment, reach then a maximum at 620 °C kept for 20 h, and then decrease again. The latter is attributed to lower Tg of the matrix and smaller differences in the CTE. The 4-point bending strength exhibits a maximum after thermal treatment at 640 °C for 20 h and decreases again at higher tempera-
tures. In analogy to the formed stresses, also a decrease at lower temperature is observed. It can hence be concluded that the stresses formed during cooling are responsible for the increase in the 4-point bending strength. References [1] W. Vogel, Glaschemie, 3rd ed., Springer, Berlin, 1992. [2] M. Suzuki, T. Tanaka, Composition dependence of microstructures formed by phase separation in multi-component silicate glass, ISIJ Int. 48 (2008) 405–411. [3] O. V. Mazurin, E. A. Porai-Koshits, N. S. Andreev, N. S. Phase separation in glass, North-Holland, Amsterdam, New York, 1984. [4] J. Häßler, C. Rüssel, Self-organized growth of sodium borate-rich droplets in a phase-separated sodium borosilicate glass, Int. J. Appl. Glass Sci. 8 (2017) 124–131. [5] J.E. Shelby, Thermal expansion of alkali borate glasses, J. Am. Ceram. Soc. 66 (1983) 225–227. [6] T. Abe, Borosilicate glasses, J. Am. Ceram. Soc. 35 (1952) 284–299. [7] M.D. Higgins, Quantitative Textural Measurements in Igneous and Metamorphic Petrology, Cambridge University Press, Cambridge, 2006. [8] J. Gegner, Stereological cross-sectional micrograph analysis for the calculation of real particle size distributions, Prakt. Metallogr. 43 (2006) 224–236. [9] S. A. Saltikov, in "Stereology", edited by H. Elias, Springer, Berlin, Heidelberg, 1967, pp. 163–173. [10] I.M. Lifshitz, V.V. Slyozov, The kinetics of precipitation from supersaturated solid solutions, J. Phys. Chem. Solids 19 (1961) 35–50. [11] R.N. Stevens, C.K.L. Davies, Self-consistent forms of the chemical rate theory of Ostwald ripening, J. Mater. Sci. 37 (2002) 765–779. [12] I. Avramov, C. Bocker, C. Rüssel, Topology and numerical simulation of phase separation in sodium silicate glasses, J. Phys. Chem. Solids 78 (2015) 8–11. [13] C. Rüssel, Nanocrystallization of CaF2 from Na2O/K2O/CaO/CaF2/Al2O3/SiO2 Glasses, Chem. Mater. 17 (2005) 5843–5847. [14] C. Bocker, C. Rüssel, Self-organized nano-crystallisation of BaF2 from Na2O/K2O/ BaF2/Al2O3/SiO2 glasses, J. Eur. Ceram. Soc. 29 (2009) 1221–1225. [15] V.S. Raghuwanshi, A. Hoell, C. Bocker, C. Rüssel, Experimental evidence of a diffusion barrier around BaF2 nanocrystals in a silicate glass system by ASAXS, CrystEngComm 14 (2012) 5215–5223. [16] A. Hoell, Z. Varga, V.S. Raghuwanshi, M. Krumrey, C. Bocker, C. Rüssel, ASAXS study of CaF2 nanoparticles embedded in a silicate glass matrix, J. Appl. Crystallogr. 47 (2014) 60–66. [17] S. Bhattacharya, C. Bocker, T. Heil, J.R. Jinschek, T. Höche, C. Rüssel, H. Kohl, et al., Experimental evidence of self-limited growth of nanocrystals in glass, Nano Lett. 9 (2009) 2493–2496. [18] C. Bocker, S. Bhattacharyya, T. Höche, C. Rüssel, Size distribution of BaF2 nanocrystallites in transparent glass ceramics, Acta Mater. 57 (2009) 5956–5963. [19] J. Selsing, Internal Stresses in Ceramics, J. Am. Ceram. Soc. 44 (1961) 419. [20] S.P. Jaccani, L. Huang, Understanding sodium borate glasses and melts from their elastic response to temperature, Int. J. Appl. Glass Sci. 7 (2016) 452–463. [21] M. Dittmer, C.F. Yamamoto, C. Bocker, C. Rüssel, The effect of yttria on the crystallization and mechanical properties of MgO/Al2O3/SiO2/ZrO2 glass-ceramics, Solid State Sci. 13 (2011) 2146–2153. [22] M. Dittmer, C. Rüssel, Colorless and high strength MgO/Al2O3 /SiO2 glass-ceramic dental material using zirconia as nucleating agent, J. Biomed. Mater. Res. Part B, Appl. Biomater. 100 (2012) 463–470. [23] A. Hunger, G. Carl, C. Rüssel, Crystallization of ZnO/MgO/Al2O3/TiO2/ZrO2/SiO2Glasses, Solid State Sci. 12 (2010) 1570–1574. [24] A. Hunger, G. Carl, A. Gebhardt, C. Rüssel, Young's moduli and microhardness of glass-ceramics in the system MgO/Al2O3/TiO2/SiO2 containing quarz nano crystals, Mater. Chem. Phys. 122 (2010) 502–506. [25] J.F. Sproull, G.E. Rindone, Correlation between strength of glass and glassy microphases, J. Am. Ceram. Soc. 56 (1973) 102–103.
11409