Journal of the Korean Ceramic Society Vol. 44, No. 4, pp. 19~3, 007. Relationship between Ionic Conductivity and Composition of Glasses Determined from Mixture Design Eun-Tae Kang, Myoung-Joong Kim,* and Jae-Dong Kim** Division of Nano & Advanced Materials Science and Engineering, Engineering Research Institute, Gyeongsang National University, Jinju 660-701, Korea *R&D center, Gonggan Ceramic Co., Ltd., Ansung 456-84, Korea **ATT Ltd., Ansan 45-100, Korea (Received March, 007; Accepted March 6, 007) yw z w k Á½ *Á½ ** w ù Á œw, w œw *œ» **ATT (007 3 ; 007 3 6 ) ABSTRACT The ionic conductivity of glasses has been designed and analyzed on the basis of a mixture design experiment with constraints. Fitted models for the activation energy and the ionic conductivity are as follows: QkJmol ( ) = 54.8565x 1 + 144.85x + 133.846x 3 170.908x 1 x 3 334.338x x 3 logσ( 300K) = 5.0045x 1 1.17876x 15.5173x 3 + 17.45x 1 x 3 The electrical properties are very sensitive to the ratio of O/SiO. The effect of is less than that of this ratio but component attributes to the reduction of the activation energy. The optimal composition for best ionic conduction based on these fitted models is 55 OÁ10 Á35SiO. Its activation energy and ionic conductivity at 300 K are 46.98 kj/mol and 1.08 10 5 Ω 1 Ácm 1, respectively. Key words : Experimental design, Mixture design, glass, Ionic conductivity, Optimal composition 1. p p š w ƒ w. p w, p x» ü pz k ƒ. w w» w wù r p 1) LIPON yd x k. ù RF rl w LIPON -3 +5¾ y k ùkü ³ w w»ƒ š. ) yd ̃ 1000ç 1 7.03 10 6 Ω 1 cm ƒ v w, ƒ Ì w w. 3) Corresponding author : Eun-Tae Kang E-mail : etkang gsnu.ac.kr Tel : +8-55-751-537 Fax : +8-55-758-1987 p» Li ƒ + ƒw w ù, yw ü y. 4,5) ƒ w yw ü y w. Oliveria 6) 30 O 70SiO ƒ yw ü w k š šw. w Miyauchi 7) lithium silicate zirconia ƒƒ ƒ k š w. l d w, w š x ƒ ww ù, w m w z ƒ š. Mazurin 8,9) w š y w w m w ƒ š šw. x p q w» w w w m ƒ ƒ w x z w. x z 19
0 ká½ Á½ Fig. 1. Glass compositions determined by extreme vertices design. w yw z w - SiO q wš, y ww w ü ƒ w.. x x 10) Kitaigorodskii w 10 O 55, 0 14, 35 SiO 60(mol%). ù ww : 30 O 55, 0 14, 35 SiO 60. w yw z w Fig. 1 ƒx Õ 6, ü ƒx Õ 6 ƒx sww 13 w. Table 1 ùkü, y w. CO 3 (Aldrich, 99.99%), (Aldrich, 99.5%), SiO (junsei) w ƒ s w z, 1 yww e. e ƒ» 1400~1600 o C 1~1.5 w z, þƒ q w w. y q w 1µm j» ù ¾ w. r rl w z, HP 419A Impedance Analyzer w 5Hz~10MHz q 50 C¾ y gƒ o d w. d v x 11) fittingw w. 3. š d ü ùkü, σt = σ 0 exp( Q RT). Table 1 ƒ w, y y (Q) š ü 300 K ùkü. y y m q w» w z sƒw. x l 6 w, O,, SiO, ( O ), ( ), ( O ) m z fitw. t y y ( O ) y w 300 K ( O ) ( ) y w. wr z w Table 1. Glass Compositions Determined by DOE, Its Ionic Conduction Parameters (log σ 0 and Q) and Its Conductivities at 300 K O w wz SiO log σ 0 (Ω 1 cm 1 K) Q (kj/mol) Q pred (kj/mol) Log σ 300K Log σ 300K (pred.) Log σ 300K * 41.75 4 54.5 5.63 55.89 55.10 6.581 6.601 6.779 51 14 35 5.71 48.0 48.61 5.14 5.03 5.409 36.75 9 54.5 4.96 54.03 55.16 6.9 6.883 6.455 55 0 45 5.61 49.4 48.65 5.445 5.415 5.6 36.75 11 5.5 5.3 54.65 54.04 6.764 6.75 6.564 49.5 9 41.75 5.38 47.39 47.99 5.345 5.460 5.99 30 14 56 5.00 57.13 57.40 7.49 7.43 6.995 55 10 35 5.69 46.98 46.51 4.97 4.941 5.7 43.5 8 48.5 5.3 5.0 51.09 6.14 6.114 6.104 49.5 4 46.75 5.19 47.63 49.64 5.583 5.747 5.341 47.5 11 41.75 5.65 49.74 48.67 5.484 5.59 5.709 40 0 60 5.94 61.38 61.44 7.30 7.13 7.736 30 10 60 5.8 60.7 60.07 7.690 7.788 7.541
yw z w 1 Table. Estimated Regression Coefficients for Activation Energy Term Coef. SE Coef. T P VIF O 43.6.680 * * 13.69 55.09 5.019 * * 16.17 SiO 74.6.646 * * 13.34 O 0.94 8.776.39 0.044 11.88 40.96 11.146 3.67 0.006 14.54 S=1.17839 R =96.7% R a =94.40% Coef.: Least square estimator of regression coefficient, T: Test statistic, P: p-value, VIF: variance inflation factor, s= MSE (error mean of squares), R p : predicted R, R a : adjusted R Table 3. Analysis of Variance for Activation Energy Source DF Seq SS Adj SS Adj MS F P Regression Linear Quadratic 4 86.569 58.04 8.57 86.569 170.918 8.57 71.64 85.459 14.64 51.59 61.54 10.7 0.006 Residual error 8 11.109 11.109 1.389 - - Total 1 97.678 - - - - DF: Degrees of freedom, SS: Sum of squares, MS: Mean square, F: Test statistic, P: p-value» x 1, x, x 3 ƒ» O,, SiO. l d y y 300 K» Table 1 6 8 ùkü. Table 1 5 7 d d ew. Tables ~5 d z m t ùkü. z w ùkü R. y y 300 K w ƒ» 96.7% 99.18%. y y 300 K l ƒ» 96.7% 99.18%ƒ z w. v w w ƒ j R f, w m R w. d š w d w R w. y y 300 K w z ƒ» 94.40% 98.91% w š. z l dw w R d R y y 300 K w ƒ» 91.1% Table 4. Estimated Regression Coefficients for Ionic Conductivity at 300 K Term Coef. SE Coef. T P VIF O 4.71 0.1833 * * 9.188 5.51 0.808 * * 7.66 SiO 8.698 0.1833 * * 9.188 O.138 0.7306.93 0.017 11.80 S=0.098 R =99.18% R a =98.91% Table 5. Analysis of Variance for Conductivity at o C Source DF Seq SS Adj SS Adj MS F P Regression Linear Quadratic 3 1 10.5466 10.4637 10.5466 10.539 3.5155 5.665 363.45 544.46 8.56. x x z fitting (pseudo) w, l z y g. z. QkJmol ( ) = 54.8565x 1 + 144.85x + 133.846x 3 170.908x 1 x 3 334.338x x 3 0.017 Residual error 15 0.0871 0.0871 0.0097 - - Total 18 10.6336 - - - - logσ( 300K) = 5.0045x 1 1.17876x 15.5173x 3 +17.45x 1 x 3 Fig.. Cox response trace plots for (a) activation energy and (b) log σ at 300 K. 44«4y(007)
ká½ Á½ Fig. 3. Mixture contour plots for (a) activation energy and (b) log σ at 300 K. 98.15%. fit de sƒ w 1) m VIF(variance inflation factor)ƒ. Marquardt VIFƒ 10 j deƒ š 13) w ù, Cornell j VIF z d e x ü d w ù d t x w j VIF w š w. y y 300 K w 10 w ù j š ù, (response trace) ùkü ù š ùkü š. t F wwš l p w z m w z w w. y y 300 K w z y y 300 K z ƒ w. Tables 3 5 α=0.05 w p 0.05 z w š. Fig. x» w ƒ e w. O SiO ƒ» j z ùkü w z ƒ j. w ƒ» w z ùký š. Fig. 3 y y 300 K š. Ow 65 mol% w š ƒ ƒ w p š dw, t ü x ƒ w w O w w p w š. z» p yw w w. w z yw D- y 14) w x ü w. 55 O 10 35SiO, y y 300K ƒ» 45.40 kj/mol 1.15 10 5 Ω 1 cm 1. d t w (desirability) 0.993. d y y 300K ƒ» 46.98 kj/mol 1.08 10 5 Ω 1 cm 1. y d x ü û y y w. 4. w, 30 O 55, 0 14, 35 SiO 60 w p x z yw z w m w. y y 300 K z ù, m. z w m O SiO w p j w e w O SiO w p w» w. y mw d 55 O 10 35SiO, y y 300 K ƒ» 45.40 kj/mol 1.15 10 5 Ω 1 cm 1 d 46.98 kj/mol 1.08 10 5 Ω 1 cm 1 yw ew. w wz
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