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 -0 (د المغنیســـیوم تتـــراوح بــــینفـــة مـــن فلوریـــات مختلعلـــى كمیـــ مغنیســـوم منیـــوم الســـیلیكات االللزجـــاج ا حتـــويی 13.2.%( معتمــد بشــكل يزجــاج الســیرامیكنمــاذج الللزجــاج االساســي و الدقیقــةتمــدد الحــراري والصــالبة یالحــظ ان معامــل ال نوعــا مـا مــع زیــادة ویالحــظ ان السـلوك معقــد تــدخل فـي التركیــب، یــدةعدتـداخلي علــى بعضـهما لكــون هنــاك مركبـات .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 o f Some Properties of Magnesium Aluminum Silicate Glass Ceramic A. J. Ibrahiem Departme nt of Physics., College of Education – Ibn Al-Haitham , Unive rsity of Baghdad Abstract M agnesium aluminum silicate of glass ceramic having different amounts of magnesium fluoride in the range (0-13.2)%. Thermal exp ansion coefficient and micro hardness of the base glass and glass ceramic samples are seen to be interdep endent but due to t he multi – comp onent sy st em, the behaviour is seen to be somewhat complex, with an increase in M g F2 content. The thermal exp ansion coefficient increase and micro harness decrease, numerical simulation of thermal exp ansion and hardness is useful in this study , L 2 – regression is used to calculate the two p arameters associated with each glass comp onent, by comp aring the measured p arameters and the calculated p arameters ,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 (M AS) sy st em belong to an imp ortant class of advanced technological material, having a wide range of app lications[1] .Some of their interesting features are mach inability , st ability , high electrical insulation, vacuum comp atibility , etc. Coeff, conductivity … etc depend on the comp osition and microstructure, [2] in some p apers carried out some st udies on thermal p rop erties of Li2O-M gO – Al2O3 – SiO2 glass and glass ceramic, [3] in the preparation and st udy of thermal exp ansion and micro hardness of (M AS) glass and glass ceramic having different comp osition p repared under different conditions [4], the concentration of M gF2 was varied from 0-13.2% mole. Due to t he multi comp onent nature of material the behavior was found t o be some what comp lex. The knowledge of thermal and mechanical p rop erties of glass ceramic needed for the app lication in the field of glass ceramic to metal, generally the glass ceramic exhibits a wide range of thermal exp ansion depending up on the comp osition the consolidated st udy of thermal exp ansion coefficient, and micro hardness of M AS glass ceramic of a function of p rocessing temp erature which seems not to be rep orted. The average thermal exp ansion (30-300)C of base glass samples decreases from (8.387.93610 6 ), with the increase of M gF2,the content of the micro hardness of base glass without M gF2 is higher than (6.822 Gp a) as compared to 13.2% mole of M gF2 (6.32 Gp a). In all cases, thermal exp ansion coefficient (TEC) increases & micro hardness decreases when glass is transformed to glass ceramic by controlled cryst allization at different p rocessing temp erature. Numerical simulation In some research[4], simple model is used to interp ret the contribution. of glass comp onent to the thermal exp ansion of certain temp erature, the model assumes linear contribution of glass comp onent to glass p rop erty i.e. thermal exp ansion and hardness chemical The simulation model at hand (L 2 - regression) related linearity the glass p rop erty to weight p ercentage or mole fraction of each chemical comp onent of glass, to fundamental of linear algebra are essential p resenting matrices model. IBN AL- HAITHAM J . FO R PURE & APPL. SC I VO L. 23 (1) 2010 Reliance on such model comes from that, t his st udy aims to assist in solving p roblems 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 t he chemical comp osition that contributes to the glass p rop erty P as follows  n i iixaP >…………………………………………..(1) where xi are numerical coefficients and n is t he number of comp osition components. If there are m measures for the p rop erty , each for different comp osition for the glass tehn  mn ji ixjiajP , , ,, ……………………………………….(2) Where j = runs on the composition numbers aij is the value of the ith comp onent of the jth comp osition and Pj is the value of the glass p rop erty fo jth composition in matrix notation, the sy st em of linear equation can be exp ressed 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 p i 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 sy st em linear sy st em equ (4) utilizing L 2 – regression is as follows: X= (C T .C) -1 C T P ………………………………….(5) Where C T = the transp ose of matrix C (C- T C) -1 is the inverse of matrix resulting form the dot – p roduct C T C. The exp erimental data is used to comp ose the materials, a comp uter p rogram for mathematical op eration M atlab installed on Pc comp uter has been used to handle matrix op eration and obtaining the coefficient table and p lots are done by using M icrosoft excel, the measured coefficient of TEC & hardness, and the calculated are p lott ed for different batches at different temp . Re sults The thermal exp ansion and micro hardness for different batches samples after p rocessing at different temp eratures 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 exp ansion & the micro hardness by using L 2 - regression. Table (1) represents the batches used to calculate the two p arameters and tables (2-5) represent each batch with different temp eratures, and we can see the measure p arameters and the calculated p arameters. While the tables (6-10) show the two p arameters both measured and calculated at constant t emp erature 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 excep ted due to the measurement occurring for chemical comp osition, 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 . Re ferences 1.Crossman,D. Q., (1972) M achinable 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). Exp ansion characterist ic of some Li2O-M gO –Al2O3-SiO2 glasses and glass ceramic, cerma. Int.17: 25-29, 3.Goswami, M .; M irza, T.and Sarka, A. ..etc. (2002). Prep aration and characterization of magnesium –aluminum –silicate glass ceramics, Bull. M ater 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) M cGraw – Hill Book of Company third edition., Table (1):Nominal composi tion of diffe rent batch samples Batch SiO2/M -Oxide M gO (mol%) M gF2 (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+M g. Table (2-5): S hows the difference between the measure and calculation of the two paramete rs (TEC & mi cro hardne ss) Table (2) Batch1 T O C M icro Hardness M eas (Gp a) Har TEC M eas 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 paramete rs (TEC) and hard ne ss at constant temperature with different batches Table (6) At 600C (Op a) M icro Hardness M eas (Gp a) Hard (Calc) TEC M eas 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 (Op a) M icro Hardness M eas (Gp a) Hard (Calc) TEC M eas 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 (Op a) M icro Hardness M eas (Gp a) Hard (Calc) TEC M eas 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 (Op a) M icro Hardness M eas (Gp a) Hard (Calc) TEC M eas 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 (Op a) M icro Hardness M eas (Gp a) Hard (Calc) TEC M eas 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 (Op a) M icro Hardness M eas (Gp a) Hard (Calc) TEC M eas 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 (Op a) M icro Hardness M eas (Gp a) Hard (Calc) TEC M eas 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 (Op a) M icro Hardness M eas (Gp a) Hard (Calc) TEC M eas 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