2010) 1( 23مجلة ابن الھیثم للعلوم الصرفة والتطبیقیة المجلد التمثیل العددي لبعض خصائص سیلیكات االلمنیوم المغنیسیوم للسیرامیك الزجاجي ایسر جمعة ابراهیم جامعة بغداد ، ابن الهیثم –كلیة التربیة ، قسم الفیزیاء الخالصة ـة مـــن فلوریـــات مختلعلـــى كمیـــ مغنیســـوم منیـــوم الســـیلیكات االللزجـــاج ا حتـــويی -0 (د المغنیســـیوم تتـــراوح بــــینفــ 13.2.%( ـةتمــدد الحــراري والصــالبة یالحــظ ان معامــل ال ـاج االساســي و الدقیقـ معتمــد بشــكل يزجــاج الســیرامیكنمــاذج الللزجـ ـا مـا مــع زیــادة ویالحــظ ان السـلوك معقــد تــدخل فـي التركیــب، یــدةعدتـداخلي علــى بعضـهما لكــون هنــاك مركبـات نوعـ .فلورید المغنیسیوممحتوى Lطریقـة خدمتمـع نقصـان الصـالبة، والتمثیـل فـي هـذه الدراسـة اسـت ادزدیـمعامـل التمـدد الحـراري ن ا 2 -regress .والمحسوبة بالطریقة الریاضیة عملیا للتمثیل العددي لهذین المتغیرین للمقارنة بین الكمیة المقاسة IBN AL- HAITHAM J. FO R PURE & APPL. SC I. VOL. 23 (1) 2010 Numerical Estimation of Some Properties of Magnesium Aluminum Silicate Glass Ceramic A. J. Ibrahiem Department of Physics., College of Education – Ibn Al-Haitham , University of Baghdad Abstract Magnesium aluminum silicate of glass ceramic having different amounts of magnesium fluoride in the range (0-13.2)%. Thermal expansion coefficient and micro hardness of the base glass and glass ceramic samples are seen to be interdependent but due to the multi – component system, the behaviour is seen to be somewhat complex, with an increase in Mg F2 content. The thermal expansion coefficient increase and micro harness decrease, numerical simulation of thermal expansion and hardness is useful in this study, L2 – regression is used to calculate the two parameters associated with each glass component, by comparing the measured parameters and the calculated parameters ,it is useful to use such a method to calculate the quantity of the component used in manufacturing the glass & class ceramic. Introduction The glass ceramics based on the magnesium aluminum silicate (MAS) system belong to an important class of advanced technological material, having a wide range of applications[1] .Some of their interesting features are mach inability , stability, high electrical insulation, vacuum compatibility , etc. Coeff, conductivity… etc depend on the composition and microstructure, [2] in some papers carried out some studies on thermal properties of Li2O-M gO – Al2O3 – SiO2 glass and glass ceramic, [3] in the preparation and study of thermal expansion and micro hardness of (MAS) glass and glass ceramic having different composition prepared under different conditions [4], the concentration of MgF2 was varied from 0-13.2% mole. Due to the multi component nature of material the behavior was found to be some what complex. The knowledge of thermal and mechanical properties of glass ceramic needed for the application in the field of glass ceramic to metal, generally the glass ceramic exhibits a wide range of thermal expansion depending upon the composition the consolidated study of thermal expansion coefficient, and micro hardness of MAS glass ceramic of a function of processing temperature which seems not to be reported. The average thermal expansion (30-300)C of base glass samples decreases from (8.387.93610 6), with the increase of MgF2,the content of the micro hardness of base glass without MgF2 is higher than (6.822 Gpa) as compared to 13.2% mole of MgF2 (6.32 Gpa). In all cases, thermal expansion coefficient (TEC) increases & micro hardness decreases when glass is transformed to glass ceramic by controlled crystallization at different processing temperature. Numerical simulation In some research[4], simple model is used to interpret the contribution. of glass component to the thermal expansion of certain temperature, the model assumes linear contribution of glass component to glass property i.e. thermal expansion and hardness chemical The simulation model at hand (L 2 - regression) related linearity the glass property to weight percentage or mole fraction of each chemical component of glass, to fundamental of linear algebra are essential presenting matrices model. IBN AL- HAITHAM J. FO R PURE & APPL. SC I VO L. 23 (1) 2010 Reliance on such model comes from that, this study aims to assist in solving problems in glass industry which is mainly originated from minor change in composition of Iraqi ores. Let ai be the ith component (e.g Wt%) of the chemical composition that contributes to the glass property P as follows  n i iixaP >…………………………………………..(1) where xi are numerical coefficients and n is the number of composition components. If there are m measures for the property , each for different composition for the glass tehn  mn ji ixjiajP , , ,, ……………………………………….(2) Where j = runs on the composition numbers aij is the value of the ith component of the jth composition and Pj is the value of the glass property fo jth composition in matrix notation, the system of linear equation can be expressed in term of matrix C. Cx = p………………………………………………(3) C is the matrix of numerical values aij X is a column factor containing the coefficient xi and p is also a column vector containing the measurement value pi So in order to obtain the values of the coefficients xi the above equation can be written as [5]. X= C -1 P……………………………………………(4) The solution of the linear system linear system equ (4) utilizing L2 – regression is as follows: X= (C T.C)-1 CTP ………………………………….(5) Where CT = the transpose of matrix C (C- T C) -1 is the inverse of matrix resulting form the dot – product C T C. The experimental data is used to compose the materials, a computer program for mathematical operation Matlab installed on Pc computer has been used to handle matrix operation and obtaining the coefficient table and plots are done by using Microsoft excel, the measured coefficient of TEC & hardness, and the calculated are plotted for different batches at different temp. Results The thermal expansion and micro hardness for different batches samples after processing at different temperatures are summarized in tables from (1- 10) and the measuring data of such kind of base glass and ceramic [4]– glass have been used for calculating thermal expansion & the micro hardness by using L 2- regression. Table (1) represents the batches used to calculate the two parameters and tables (2-5) represent each batch with different temperatures, and we can see the measure parameters and the calculated parameters. While the tables (6-10) show the two parameters both measured and calculated at constant temperature with different batches. Conclusion From the tables (2-9) result for both of the measurements of the calculated data, it can be seen that the differences are too small which were excepted due to the measurement occurring for chemical composition, therefore, it is always better to have alarge amount of IBN AL- HAITHAM J. FO R PURE & APPL. SC I VO L. 23 (1) 2010 data and optimizing the solution by using an advance technique such as L 2 –regression used in this study. References 1.Crossman,D. Q., (1972) Machinable glass Ceramics based on tetrasilicamica, J. Am, Cerma, Soc. 55: 446-450. 2.El- Shennawi, A. W. A.; Omar, A. A.and El – Channam, A. R., (1991). Expansion characteristic of some Li2O-MgO –Al2O3-SiO2 glasses and glass ceramic, cerma. Int.17: 25-29, 3.Goswami, M.; Mirza, T.and Sarka, A. ..etc. (2002). Preparation and characterization of magnesium –aluminum –silicate glass ceramics, Bull. Mater Sci. 23: 377-382, 4.Gawley,J. D.and Lee, W. E., (1994) material science and technology, 11: 69. 5.Conte, S. D.and Carl de Boor, (1980) McGraw – Hill Book of Company third edition., Table (1):Nominal composition of different batch samples Batch SiO2/M-Oxide MgO (mol%) MgF2 (mol %) Batch I 1.137 12.85 0.00 Batch II 1.127 12.85 6.6 Batch III 1.129 12.82 13.2 Batch IV 0.764 25.7 6.6 M= Al+B+K+Mg. Table (2-5): Shows the difference between the measure and calculation of the two parameters (TEC & micro hardness) Table (2) Batch1 TOC Micro Hardness Meas (Gpa) Har TEC Meas TEC (30-300) (10 -6 / O C) (Calcu) 600 5.84 5.81 7.936 7.84 725 5.74 5.67 8.211 8.101 850 5.67 5.56 8.266 8.230 950 5.57 5.51 8.413 8.391 1050 5.43 5.20 8.6 8.621 IBN AL- HAITHAM J. FO R PURE & APPL. SC I VO L. 23 (1) 2010 Table (3) Table (4) Table (5) Table from (6-10) shows the difference of the two parameters (TEC) and hard ness at constant temperature with different batches Table (6) At 600C (Opa) Micro Hardness Meas (Gpa) Hard (Calc) TEC Meas TEC (30-300) (10 -6 /C) (Calc) B1 5.84 5.81 7.963 7.84 B2 6.03 5.98 8.53 8.56 B3 6.32 6.24 9.285 9.311 B4 6.82 6.752 7.463 7.352 Batch2 TC (Opa) Micro Hardness Meas (Gpa) Hard (Calc) TEC Meas TEC (30-300) (10 -6 /C) (Calc) 600 6.03 5.98 8.53 8.56 725 5.82 5.79 9.255 9.311 850 5.74 5.71 9.553 9.492 950 4.59 5.10 9.591 9.583 1050 4.25 4.42 9.618 9.611 Batch3 T C (Opa) Micro Hardness Meas (Gpa) Hard (Calc) TEC Meas TEC (30-300) (10 -6 /C) (Calc) 600 6.32 6.24 9.285 9.311 725 6.25 6.134 9.56 9.461 850 5.02 5.131 9.821 9.793 950 4.67 4.63 9.873 9.821 1050 4.22 4.31 10.159 10.063 Batch4 T C (Opa) Micro Hardness Meas (Gpa) Hard (Calc) TEC Meas TEC (30-300) (10-6/C) (Calc) 600 6.82 6.752 7.463 7.352 725 6.38 6.27 7.583 7.471 850 5.22 5.20 9.376 9.151 950 5.37 5.29 9.587 9.643 1050 5.36 5.34 9.643 9.512 IBN AL- HAITHAM J. FO R PURE & APPL. SC I VO L. 23 (1) 2010 Table (7) T= 725C (Opa) Micro Hardness Meas (Gpa) Hard (Calc) TEC Meas TEC (30-300) (10-6/C) (Calc) B1 5.74 5.67 8.211 8.101 B2 5.82 5.79 9.255 9.311 B3 6.25 6.13 9.56 9.461 B4 6.38 6.27 7.583 7.471 Table (8) T=850C (Opa) Micro Hardness Meas (Gpa) Hard (Calc) TEC Meas TEC (30-300) (10-6/C) (Calc) B1 5.67 5.56 8.266 8.230 B2 5.74 5.7 9.553 9.492 B3 5.02 5.131 9.84 9..793 B4 5.22 5.202 9.376 9.151 Table (9) T= 950C (Opa) Micro Hardness Meas (Gpa) Hard (Calc) TEC Meas TEC (30-300) (10-6/C) (Calc) B1 5.57 5.51 8.413 8.56 B2 4.59 5.10 9.591 9.583 B3 4.67 4.36 9.873 9.82 B4 5.37 5.29 9.587 9.643 Table (10) T=1050C (Opa) Micro Hardness Meas (Gpa) Hard (Calc) TEC Meas TEC (30-300) (10 -6 /C) (Calc) B1 5.43 5.20 8.6 8.621 B2 4.25 4.42 9.618 9.611 B3 4.22 4.31 10.159 10.063 B4 5.36 5.34 9.643 9.512