Simulation on Potassium Ion Concentration Profile of Engineered Stress Profile Glass by FDTD Method

doi:10.15541/jim20180028

Abstract

Abstract:

Strength of Engineered Stress Profile glass has been proved narrowly distributed owing to its particular exchanged ion profile. In order to predict the K⁺ concentration profile, Finite-Difference Time-Domain method was introduced to simulate the diffusion processes. Simulation procedures were conducted based on detected diffusion coefficients, surface concentrations, and ion profile subjected to single step ion exchange. The calculated results show a reasonable agreement with the experimental measurements (Energy Dispersive Spectroscopy). According to the simulation results, the relation between K⁺ profile and strength performance were interpreted.

Key words: ion-exchange, Engineered Stress Profile glass, Finite-Difference Time-Domain method, strength

CLC Number:

TQ174

ZHENG Guo-Yuan, LI Jia-Cheng, SONG Li-Xin, ZHANG Tao. Simulation on Potassium Ion Concentration Profile of Engineered Stress Profile Glass by FDTD Method[J]. Journal of Inorganic Materials, 2018, 33(6): 693-698.

Figures/Tables 9

Table 1 The various treatments of the samples

Batch Code	First-step process (Salt 1)	Second-step process (Salt 2)
P0	-	-
P1	450℃, 42 h	400℃, 15 min
P2	450℃, 42 h	400℃, 30 min
P3	450℃, 42 h	400℃, 1 h
P4	450℃, 42 h	400℃, 2 h
D1	450℃, 42 h	-
D2	-	400℃, 12 h
D3	-	350℃, 12 h

Fig. 1 HF treatment for the glass samples

Fig. 2 The K+ profile of glass subjected to the first-step ion exchange (immersed in Salt 1 at 450℃ for 42 h)

Fig. 3 K+ concentration profiles of the sample P1, D1, D2 and the Boltzmann fittings

Table 2 Diffusion coefficients at 450℃, 400℃ and 350℃

Temperature/℃	450	400	350
D/(m²•s^-1)	2.27×10^-14	4.25×10^-15	9.63×10^-16

Fig. 4 Diffusion coefficients of different K+ concentration at 400℃

Fig. 5 Measured and calculated K+ profiles in two-step ion-exchanged glass with different processing time of the second step(a) 15 min; (b) 30 min; (c) 1 h; (d) 2 h

Table 3 The relation between peak value, general gradient g (numerical simulation results) and strength property of the ESP glass

Code	Simulation result^*1		Bend strength (16 pieces)	Variation coefficient^*2	Weibull modulus
Code	Peak value	g/µm^-1	Bend strength (16 pieces)	Variation coefficient^*2	Weibull modulus
P0	-	-	100.32 MPa	18.0%	8.38
D1	-	-	471.28 MPa	5.28%	22.98
P1	0.90129	0.031292	469.16 MPa	4.05%	28.34
P2	0.86847	0.019208	468.88 MPa	2.08%	54.51
P3	0.83794	0.012338	460.61 MPa	2.55%	45.43
P4	0.80203	0.007056	430.86 MPa	2.74%	42.32

Fig. 6 Failure probability, F, as a function of the applied stress. Weibull modulus of the strength are corresponding slopes of the fitting lines

References 27

[1]	LAWN B R.Fracture of Brittle Solids. Cambridge, UK: Cambridge Univ. Press, 1993.
[2]	GRIFFITH A A.The phenomona of rupture and flow in solid.Phil. Trans. R. Soc. Lond. A, 1920, 221(4): 163-190.
[3]	WEIBULL W.A statistical distribution function of wide applicability.J. Appl. Mech.-Trans. ASME, 1951, 18(3): 293-297.
[4]	DENG B, JIANG D.Determination of the weibull parameters from the mean value and the coefficient of variation of the measured strength for brittle ceramics.Journal of Advanced Ceramics, 2017, 6(2): 149-156.
[5]	RAO M P, SANCHEZ-HERENCIA A J, BELTZ G E,et al. Laminar ceramics that exhibit a threshold strength. Science, 1999, 286(5437): 102-105.
[6]	FILLERY S P, LANGE F F.Ion-exchanged glass laminates that exhibit a threshold strength.J. Am. Ceram. Soc., 2007, 90(8): 2502-2509.
[7]	FAIR G E, LANGE F F.Ceramic composites with three-dimensional architectures designed to produce a threshold strength - I. Processing.J. Am. Ceram. Soc., 2005, 88(5): 1158-1164.
[8]	FAIR G E, HE M Y, MCMEEKING R M,et al., Ceramic composites with three-dimensional architectures designed to produce a threshold strength - II. Mechanical observations. J. Am. Ceram. Soc., 2005, 88(7): 1879-1885.
[9]	KARLSSON S, JONSON B, STALHANDSKE C.The technology of chemical glass strengthening - a review.Glass Technol.-Eur. J. Glass Sci. Technol. Part A, 2010, 51: 41-54.
[10]	VARSHNEYA A K.Chemical strengthening of glass: lessons learned and yet to be learned.Int. J. Appl. Glass Sci., 2010, 1: 131-142.
[11]	TANDON R, GREEN D J.Crack stability and t-curves due to macroscopic residual compressive stress profiles.J. Am. Ceram. Soc., 1991, 74(8): 1981-1986.
[12]	GREEN D J, TANDON R, SGLAVO V M.Crack arrest and multiple cracking in class through the use of designed residual stress profiles.Science, 1999, 283(5406): 1295-1297.
[13]	SGLAVO V M, LARENTIS L, GREEN D J.Flaw-insensitive ion-exchanged glass: I, Theoretical aspects.J. Am. Ceram. Soc., 2001, 84(8): 1827-1831.
[14]	SGLAVO V M, GREEN D J.Flaw-insensitive ion-exchanged glass: II, Production and mechanical performance.J. Am. Ceram. Soc., 2001, 84(8): 1832-1838.
[15]	GREEN D J.Critical parameters in the processing of engineered stress profile glasses.J. Non-Cryst. Solids, 2003, 316(1): 35-41.
[16]	ABRAMS M B, GREEN D J.Prediction of crack propagation and fracture in residually stressed glass as a function of the stress profile and flaw size distribution.J. Eur. Ceram. Soc., 2006, 26(13): 2677-2684.
[17]	COOK R F, CLARKE D R.Fracture stability, r-curves and strength variability.Acta Metall., 1988, 36(3): 555-562.
[18]	SHETTY D K, WANG J S.Crack stability and strength distribution of ceramics that exhibit rising crack-growth-resistance (r-curve) behavior.J. Am. Ceram. Soc., 1989, 72(7): 1158-1162.
[19]	VARSHNEYA A K.Mechanical model to simulate buildup and relaxation of stress during glass chemical strengthening.J. Non-Cryst. Solids, 2016, 433: 28-30.
[20]	SHEN J W, GREEN D J.Prediction of stress profiles in ion exchanged glasses.J. Non-Cryst. Solids, 2004, 344(1/2): 79-87.
[21]	VARSHNEYA A K, OLSON G A, KRESKI P K,et, al. Buildup and relaxation of stress in chemically strengthened glass. J. Non-Cryst. Solids, 2015, 427: 91-97.
[22]	SHIDFAR A, AZARY H.An inverse problem for a nonlinear diffusion equation.Nonlinear Anal.-Theory Methods Appl., 1997, 28(4): 589-593.
[23]	FATULLAYEV A.Determination of unknown coefficient in nonlinear diffusion equation.Nonlinear Anal.-Theory Methods Appl., 2001, 44(3): 337-344.
[24]	SHEN J W, GREEN D J, PANTANO C G.Control of concentration profiles in two step ion exchanged glasses.Phys. Chem. Glasses, 2003, 44(4): 284-292.
[25]	MEHRER H.Diffusion in Solids: Fundamentals, Methods, Materials, Diffusion-controlled Processes. Berlin Heidelberg: Springer-Verlag, 2007.
[26]	LI X Y, JIANG L B, WANG Y, et al. Correlation between K+-Na+ diffusion coefficient and flexural strength of chemically tempered aluminosilicate glass. J. Non-Cryst. Solids, 2017, 471: 72-81.
[27]	MATANO C.On the relation between diffusion-coefficients and concentrations of solid metals.Japanese Journal of Physics, 1933, 8: 109-113.