基于时域有限差分法的ESP玻璃的钾离子浓度分布的模拟

doi:10.15541/jim20180028

摘要/Abstract

摘要：

由于特殊的交换离子浓度分布,工程应力分布玻璃(ESP玻璃)的强度呈现集中分布的特性。为了预测其钾离子浓度的分布,运用了时域有限差分法对其扩散过程进行数值模拟。该模拟是基于测量的扩散系数、玻璃表面浓度以及第一步交换后的钾离子浓度分布进行的。模拟计算的结果与使用能谱仪测量的实验结果相吻合。基于模拟计算的结果,讨论了ESP玻璃的强度与钾离子浓度分布的关系。

关键词: 离子交换, 工程应力分布玻璃（ESP玻璃）, 时域有限差分法, 强度

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

中图分类号:

TQ174

郑国源, 李家成, 宋力昕, 张涛. 基于时域有限差分法的ESP玻璃的钾离子浓度分布的模拟[J]. 无机材料学报, 2018, 33(6): 693-698.

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.

图/表 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

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