C -H. Chao, H.Y. Lu/Materials Science and Engineering 4328(2002)267-276 ture. In particular when compositions studied in the formation to a-cristobalite, since its content was in- Al2O3-Na2O-SiO2 system could produce both the creased when particle size was reduced to <38 um ternary and binary eutectic liquids at temperatures be-(Fig. 2). This suggests that the relief of the confined tween 740 and 867C [301 particles, which would otherwise be the metastable Liquid-phase sintering at 1100C assisted by the B-cristobalite, from the matrix constraints initiates the eutectic liquids has indeed occurred [19] with the B-+a-phase transformation. However, those particles characteristic rounded grains of a-cristobalite contain- with sizes less than the critical value still retain B- ing twin lamellae and glassy grain-boundary phase of phase. Particles of 300-500 nm have become a continuous nature. Since the ternary eutectic [30] at stabilized in the y= 19.5 samples with 4.65 g 740C is richer in Na,O and leaner in both SiO, Al,O3 and Na,O, even after the relief of matrix con- and Al2O3 than the compositions investigated here, straint by surface grinding(Fig. 5(b)) the crystallization to B-cristobalite incorporating less It may be argued by considering the total thermo amount of Na* is highly possible upon cooling. In dynamic free energy change(AGtotal) for the size-de fact, liquid-phase separation is only observed from pendent phase transformation of the unconstrained samples with y= 13.9 in Al2O3-Na2O-ySiO2, in particles as in ZrO2 [26]. A critical particle size hich the crystalline phase contains only B-cristobalite (rcritical) for just retaining the cubic B-cristobalite phase (as revealed by XRD(Fig. 3)). When phase separa- to room temperature can be determined from the end tion occurs in samples with y= 13.9, solute content in point thermodynamic calculation of AGrotal =0 [26] the separated droplet phase (=13.9 in Fig. 7(c)ap- re pears to have adjusted to favour the crystallization to Poitie=-3(△Gota)/(△7s) B-cristobalite(Fig 4(a)). Nevertheless, the actual con- where AGrotal is the difference in total free energy per tent of(Al,O3+ Na,O)in the retained and untrans- unit volume, and A,sy is the difference in surface-to- formable B-phase can not be deduced from the vapour surface energy of crystal present data before detailed chemical microanalysis ince△Goa=G2- GB is negative for the阝→x The lattice spacing of a-cristobalite diola increases cristobalite phase transformation to occur, A,sv,must with higher contents of Al2O3+ Na2O(Fig. 4(b)), be positive in order to keep Critical rational. Total free contrary to what was previously reported [7]. How energy per unit volume (Gtotal) consists of the chemi ever, it leaves little doubt [9] now that taking up more cal term(Gchemical) and mechanical term(Gstrain) of the stuffing cations [9-ll] has led to the stabilization of crystal. The critical particle size would therefore fall the B-phase. a possible interpretation for the reverse in a range depending on the exact solute content in effect [12] when B-critobalite was obtained is that im- the B-cristobalite crystals (i.e. depending on purities associated with the starting powder may have AGchemical). Indeed, B-cristobalite crystals larger than already stabilized the B-phase chemically ly, but XRD 100 um ha ave been reported [18] in commercial silica failed to differentiate the (a+B)-cristobalite mixture glass containing both Al2O3 and Na,O. For solute (as demonstrated for 101x and lllp in Fig. 1(a) and free particles exceeding raritical to retain p-cristobalite, 2). When the 101 peak at dol=0.4062 nm stops however, sufficient strain energy(AGstrain)would have increasing its intensity and the lllB-peak at dup= to be induced by the differential thermal expansion than that of y=19.5(i.e samples with y 19.5 which negative AGehemlia. ilig.y 0.4110 nm becomes predominant, the sintered sample (of Ax=5x10-6 C-)[25] between B-cristobalite would have incorporated impurities of higher content and the vitreous silica matrix to compensate for a contain both solute oxides greater than 4.65 mol% each and probably also with d-spacing larger than dIola=0.4058 nm, as indicated by Fig. 4(a)). In fact, 5. Conclusions the predominant a-peak (i.e. 101,)could easily ob- scure any chemically stabilized B-cristobalite of a mi The metastable retention of the high temperature nor amount, such as those detected in samples with B-cristobalite to room temperature in sintered col y>19.5(i.e. containing less amount of solute oxides lodal silica ceramics codoped with Na,O+Al,O,can than y=19.5)given in Fig. 1(a)(=19.5)and Fig. 2 be attributed to both the chemical and mechanical factors. Particle size effects similar to the ZrO-con taining ceramics appear to exist also with the stabi- 4.2. Critical particle size for B +a-cristobalite lized B-cristobalite phase embedded matrix a-cristobalite and the residual Na20-Al,O3- Sio2 glass A critical size appears to exist in the present sam- Codoping with Na,O and Al2O3, both at 6.29 mol%, ples for the metastable retention of B-cristobalite, be- has successfully produced crystalline phase of only B- low which the particles have survived the grinding cristobalite in the mixture by sintering at 1100C for stress. Reduction in the particle size favours the trans- 48h.C.-H. Chao, H.-Y. Lu / Materials Science and Engineering A328 (2002) 267–276 275 ture. In particular when compositions studied in the Al2O3 –Na2O–SiO2 system could produce both the ternary and binary eutectic liquids at temperatures be￾tween 740 and 867 °C [30]. Liquid-phase sintering at 1100 °C assisted by the eutectic liquids has indeed occurred [19] with the characteristic rounded grains of -cristobalite contain￾ing twin lamellae and glassy grain-boundary phase of a continuous nature. Since the ternary eutectic [30] at 740 °C is richer in Na2O and leaner in both SiO2 and Al2O3 than the compositions investigated here, the crystallization to
-cristobalite incorporating less amount of Na+ is highly possible upon cooling. In fact, liquid-phase separation is only observed from samples with y=13.9 in Al2O3 –Na2O–ySiO2, in which the crystalline phase contains only
-cristobalite (as revealed by XRD (Fig. 3)). When phase separa￾tion occurs in samples with y=13.9, solute content in the separated droplet phase (y=13.9 in Fig. 7(c)) ap￾pears to have adjusted to favour the crystallization to
-cristobalite (Fig. 4(a)). Nevertheless, the actual con￾tent of (Al2O3+Na2O) in the retained and untrans￾formable
-phase can not be deduced from the present data before detailed chemical microanalysis. The lattice spacing of -cristobalite d101 increases with higher contents of Al2O3+Na2O (Fig. 4(b)), contrary to what was previously reported [7]. How￾ever, it leaves little doubt [9] now that taking up more stuffing cations [9–11] has led to the stabilization of the
-phase. A possible interpretation for the reverse effect [12] when
-critobalite was obtained is that im￾purities associated with the starting powder may have already stabilized the
-phase chemically, but XRD failed to differentiate the (+
)-cristobalite mixture (as demonstrated for 101 and 111
in Fig. 1(a) and 2). When the 101-peak at d101=0.4062 nm stops increasing its intensity and the 111
-peak at d111
= 0.4110 nm becomes predominant, the sintered sample would have incorporated impurities of higher content than that of y=19.5 (i.e. samples with y19.5 which contain both solute oxides greater than 4.65 mol% each and probably also with d-spacing larger than d101=0.4058 nm, as indicated by Fig. 4(a)). In fact, the predominant -peak (i.e. 101) could easily ob￾scure any chemically stabilized
-cristobalite of a mi￾nor amount, such as those detected in samples with y19.5 (i.e. containing less amount of solute oxides than y=19.5) given in Fig. 1(a) (y=19.5) and Fig. 2 (y=24.6). 4.2. Critical particle size for +-cristobalite A critical size appears to exist in the present sam￾ples for the metastable retention of
-cristobalite, be￾low which the particles have survived the grinding stress. Reduction in the particle size favours the trans￾formation to -cristobalite, since its content was in￾creased when particle size was reduced to 38 m (Fig. 2). This suggests that the relief of the confined particles, which would otherwise be the metastable
-cristobalite, from the matrix constraints initiates the

-phase transformation. However, those particles with sizes less than the critical value still retain
- phase. Particles of 300–500 nm have become fully stabilized in the y=19.5 samples with 4.65 mol% Al2O3 and Na2O, even after the relief of matrix con￾straint by surface grinding (Fig. 5(b)). It may be argued by considering the total thermo￾dynamic free energy change (Gtotal) for the size-de￾pendent phase transformation of the unconstrained particles as in ZrO2 [26]. A critical particle size (rcritical) for just retaining the cubic
-cristobalite phase to room temperature can be determined from the end￾point thermodynamic calculation of Gtotal=0 [26]. rcritical= −3(Gtotal)/(sv) where Gtotal is the difference in total free energy per unit volume, and sv is the difference in surface-to￾vapour surface energy of crystal. Since Gtotal=G−G
is negative for the

- cristobalite phase transformation to occur, sv, must be positive in order to keep rcritical rational. Total free energy per unit volume (Gtotal) consists of the chemi￾cal term (Gchemical) and mechanical term (Gstrain) of the crystal. The critical particle size would therefore fall in a range depending on the exact solute content in the
-cristobalite crystals (i.e. depending on Gchemical). Indeed,
-cristobalite crystals larger than 100 m have been reported [18] in commercial silica glass containing both Al2O3 and Na2O. For solute￾free particles exceeding rcritical to retain
-cristobalite, however, sufficient strain energy (Gstrain) would have to be induced by the differential thermal expansion (of =5×10−6 °C−1 ) [25] between
-cristobalite and the vitreous silica matrix to compensate for a negative Gchemical. 5. Conclusions The metastable retention of the high temperature
-cristobalite to room temperature in sintered col￾loidal silica ceramics codoped with Na2O+Al2O3 can be attributed to both the chemical and mechanical factors. Particle size effects similar to the ZrO2-con￾taining ceramics appear to exist also with the stabi￾lized
-cristobalite phase embedded in a matrix of -cristobalite and the residual Na2O-Al2O3-SiO2 glass. Codoping with Na2O and Al2O3, both at 6.29 mol%, has successfully produced crystalline phase of only
- cristobalite in the mixture by sintering at 1100 °C for 48 h.