International Journal of Academic Engineering Research (IJAER) ISSN: 2000-001X Vol. 2 Issue 2, February – 2018, Pages: 18-23 www.ijeais.org/ijaer 18 Anisotropy of Different Types of Alloys Assoc. Prof. Dr. Fae'q A. A. Radwan Faculty of Engineering, Near East University, KKTC – Lefkosa, Mersin – 10, TURKEY faeq.radwan@neu.edu.tr or frdwnk@gmail.com Abstract: The norm of elastic constant tensor and the norms of the irreducible parts of the elastic constants of the alloys IronSilicon at different percentages of Silicon, Lead-Indium at different percentages of Indium, Molybdenum-Rhenium at different percentages of Rhenium, NiobiumHydrogen at different percentages of Hydrogen, Niobium-Molybdenum at different percentages of Molybdenum, Niobium-Oxygen at different percentages of Oxygen, Niobium-Zirconium at different percentages of Zirconium, Palladium-Rhodium at different percentages of Rhodium, PalladiumRhodium at different percentages of Rhodium, and Palladium-Silver at different percentages of Silver are calculated. The relation of the scalar parts norm and the other parts norms and the anisotropy of the alloys are presented. The norm ratios are used as a criterion to present the anisotropy degree of the properties of the alloys. Keywords: Norm, Anisotropy, Elastic Constant, Irreducible, and alloys. 1. INTRODUCTION An alloy is a mixture of metals or a mixture of a metal and another element, the term alloy is used to describe a mixture of atoms in which the primary constituent is a metal. The primary metal is called the base, the matrix, or the solvent. The secondary constituents are often called solutes Alloys are used in a wide variety of applications. In some cases, a combination of metals may reduce the overall cost of the material while preserving important properties. In other cases, the combination of metals imparts synergistic properties to the constituent metal elements such as corrosion resistance or mechanical strength, the mechanical properties of alloys will often be quite different from those of its individual constituents. A metal that is normally very soft (malleable), such as aluminum, can be altered by alloying it with another soft metal, such as copper. Although both metals are very soft and ductile, the resulting aluminum alloy will have much greater strength, Alloying a metal is done by combining it with one or more other elements that often enhance its properties. For example, the combination of carbon with iron produces steel, which is stronger than iron, its primary element, The alloy constituents are usually measured by mass, Alloys are usually classified as substitutional or interstitial alloys, depending on the atomic arrangement that forms the alloy. They can be further classified as homogeneous (consisting of a single phase), or heterogeneous (consisting of two or more phases) or intermetallic. The decomposition of the elastic constant tensor to its irreducible parts and the norm concept and its relation to anisotropy are given in [1]. 2. ALLOYS: The elastic constants of Cubic systems Alloys are given in the following table, [2,3]. Table 1. Elastic constants in GPa Alloy C 11 C44 C12 Iron-Silicon, Fe-Si, 216.4 124.6 134 at % Si 8.59 11.68 215.5 126.7 137 12.91 25.1 217.0 238 127.9 136 137 138 Lead-Indium, Pb-In, at % In 5.5 9.0 20.7 49.32 59.70 48.70 14.43 13.90 16.60 42.51 33.70 18.90 Molybdenum-rhenium, Mo-Re at % Re 7.0 16.6 26.9 466.5 465.0 460.7 114.8 123.7 132.3 172.9 185.8 195.9 International Journal of Academic Engineering Research (IJAER) ISSN: 2000-001X Vol. 2 Issue 2, February – 2018, Pages: 18-23 www.ijeais.org/ijaer 19 Niobium-Hydrogen, Nb-H at % H 0.1 1.06 3.06 246.8 247.0 245.8 28.2 28.6 29.6 133.2 134.4 133.8 Niobium-Molybdenum, Nb-Mo 271.0 29.47 133.4 at % Mo 16.8 23.3 286.0 32.02 134.8 33.9 315.7 36.29 136.8 51.6 363.6 62.63 143.4 75.2 422.3 68.59 153.0 92.1 454.0 102.3 159.6 Niobium-Oxygen, Nb-O at % O 0.59 9.60 247.2 249.4 28.2 30.0 133.4 134.0 Niobium-Zirconium, Nb-Zr at % Zr 69.6 74.7 79.7 127.1 120.4 116.4 33.76 33.42 32.56 91.9 88.5 88.7 Palladium-Rhodium, Pd-Rh at % Rh 1 5 20 222.7 227.2 249.0 72.1 76.0 90.25 172.0 172.4 173.8 Palladium-Silver, Pd-Ag at % Ag 2 10 220.3 207.7 71.8 75.5 170.0 159.6 By using table 1, the decomposition of the elastic constant tensor and the norm concept we can calculate the norms and the norm ratios of the given alloys as in the following table. Table 2. The norms and norm ratios (the anisotropy degree). Alloy Ns N d Nn N N s / N N d / N N n / N Iron-Silicon, Fe-Si, at % Si 8.59 571.1528 0 152.8747 591.2581 0.965996 0 0.258558 11.68 576.3232 0 160.2985 598.2006 0.963428 0 0.267968 12.91 579.3866 0 161.1234 601.373 0.96344 0 0.267926 25.1 614.6089 0 157.6406 634.5035 0.968645 0 0.248447 Lead-Indium, Pb-In, at % In 5.5 1.383895 0 20.20916 139.8572 0.989505 0 0.144498 9 134.8001 0 1.649727 134.8102 0.999925 0 0.012237 20.7 101.3418 0 3.116151 101.3897 0.999528 0 0.030734 Molybdenum-rhenium, Mo-Re, at % Re 7 915.9316 0 58.65697 917.8079 0.997956 0 0.06391 16.6 941.2604 0 29.14518 941.7115 0.99521 0 0.030949 26.9 958.8581 0 0.183303 958.8581 1 0 0.000191 Niobium-Hydrogen, Nb-H, at % H International Journal of Academic Engineering Research (IJAER) ISSN: 2000-001X Vol. 2 Issue 2, February – 2018, Pages: 18-23 www.ijeais.org/ijaer 20 0.1 529.7725 0 52.42467 532.36 0.995139 0 0.098476 1.06 532.3243 0 50.77494 534.7404 0.995482 0 0.094953 3.06 530.3967 0 48.392 532.5997 0.995864 0 0.09086 Niobium-Molybdenum, Nb-Mo, at % Mo 16.8 558.3048 0 72.09308 562.9402 0.991766 0 0.128065 23.3 579.3029 0 79.88346 584.7848 0.990626 0 0.136603 33.9 619.4446 0 97.44389 627.0621 0.987852 0 0.155398 51.6 704.4832 0 87.01395 709.8366 0.992458 0 0.122583 75.2 793.5522 0 121.09 802.7378 0.988557 0 0.150846 92 870.0146 0 82.30306 873.8988 0.995555 0 0.094179 Niobium-Oxygen, Nb-O, at % O 0.59 530.5804 0 52.60797 533.1821 0.99512 0 0.098668 9.6 535.0383 0 50.77494 537.4422 0.995527 0 0.094475 Niobium-Zirconium, Nb-Zr, at % Zr 69.6 323.8126 0 29.62177 325.1646 0.995842 0 0.091098 74.7 310.0515 0 32.02304 311.7008 0.994709 0 0.102736 79.7 305.3446 0 34.296 307.2646 0.993751 0 0.11617 Palladium-Rhodium, Pd-Rh, at % Rh 1 593.7306 0 85.69417 599.8829 0.989744 0 0.142851 5 601.9746 0 89.08527 608.5307 0.989226 0 0.146394 20 639.2115 0 96.50904 646.456 0.988794 0 0.149289 Palladium-Silver, Pd-Ag, at % Ag 2 587.3658 0 85.51086 593.5576 0.989568 0 0.144065 10 557.4961 0 94.30941 565.4168 0.985991 0 0.166796 International Journal of Academic Engineering Research (IJAER) ISSN: 2000-001X Vol. 2 Issue 2, February – 2018, Pages: 18-23 www.ijeais.org/ijaer 21 International Journal of Academic Engineering Research (IJAER) ISSN: 2000-001X Vol. 2 Issue 2, February – 2018, Pages: 18-23 www.ijeais.org/ijaer 22 International Journal of Academic Engineering Research (IJAER) ISSN: 2000-001X Vol. 2 Issue 2, February – 2018, Pages: 18-23 www.ijeais.org/ijaer 23 3. CONCLUSION: From table (2) and the figures shown above we can conclude that Molybdenum-rhenium, Mo-Re, at 26.9 % Re is the most isotropic alloy with highest value of Ns / N and lowest value of Nn / N , and Iron-Silicon, Fe-Si, at 11.68 % Si is the most anisotropic alloy with highest value of Nn / N and with lowest value of Ns / N . From table (2) and the figures shown above we can conclude that as the isotropy increases the anisotropy decreases and vice versa. Which means that as Nn / N increases the anisotropy increases and isotropy decreases and as Ns / N increases isotropy increases and anisotropy decreases. And also the strongest material is Molybdenum-rhenium, Mo-Re, at 26.9 % Re, which has the highest value of N . From table (2) and the figures shown above we can notice that the alloys have different isotropy behavior as the percentage of the associated materials increases. 4. REFERENCES 1. Fae'q A. A. Radwan, 'Norm Ratio and Anisotropy Degree', Journal of Applied Sciences, Vol. 1, No. 3., 2001, PP, 301-304. 2. Landolt-Börnstein, Group III, "Crystal and Solid State Physics", Volume, 11,Springer-Verlag. 3. Raymond Chang, 'Chemistry', Fifth Edition, 1994, McGraw-Hill, Inc.