Some Properties of Copper – Gold and Silver – Gold Alloys at Different % of Gold Fae`q A. A. Radwan * Abstract: The norm of elastic constant tensor and the norms of the irreducible parts of the elastic constants of Copper, Silver and Gold metals and Copper-Gold and Silver-Gold alloys at different percentages of Gold are calculated. The relation of the scalar parts norm and the other parts norms and the anisotropy of these metals and their alloys are presented. The norm ratios are used to study anisotropy of these metals and their alloys. Index Terms -Copper, Silver, Gold, Alloys, Anisotropy, Elastic Constants. I. ELASTIC CONSTANT TENSOR DECOMPOSITION The constitutive relation characterizing linear anisotropic solids is the generalized Hook’s law [1]: kl ijkl ij C    , kl ijkl ij S    (1) Where ij  and kl  are the symmetric second rank stress and strain tensors, respectively ijkl C is the fourth-rank elastic stiffness tensor (here after we call it elastic constant tensor) and ijkl S is the elastic compliance tensor. There are three index symmetry restrictions on these tensors. These conditions are: jikl ijkl C C  , ijlk ijkl C C  , klij ijkl C C  (2) Which the first equality comes from the symmetry of stress tensor, the second one from the symmetry of strain tensor, and the third one is due to the presence of a deformation potential. In general, a fourth-rank tensor has 81 elements. The index symmetry conditions (2) reduce this number to 81. Consequently, for most asymmetric materials (triclinic symmetry) the elastic constant tensor has 21 independent components. Elastic compliance tensor ijkl S possesses the same symmetry properties as the elastic constant tensor ijkl C and their connection is given by [2,3,4,5]: klmn ijkl S C =   jm in jn im      2 1 (3) * Faculty of Engineering - Near East University KKTC – Lefkosa: P.O. Box: 670, Mersin 10 - TURKEY (email: faeq@neu.edu.tr) Where ij  is the Kronecker delta. The Einstein summation convention over repeated indices is used and indices run from 1 to 3 unless otherwise stated. By applying the symmetry conditions (2) to the decomposition results obtained for a general fourth- rank tensor, the following reduction spectrum for the elastic constant tensor is obtained. It contains two scalars, two deviators, and one-nonor parts:       1 ; 2 2 ; 0 1 ; 0 ijkl ijkl ijkl ijkl C C C C        1 ; 4 2 ; 2 ijkl ijkl C C   (4) Where:   ppqq kl ij ijkl C C   9 1 1 ; 0  , (5)     kl ij jk il jl ik ijkl C       2 3 3 90 1 2 ; 0      ppqq pqpq C C  3 (6)     ipkp jl jpkp il iplp jk jplp ik ijkl C C C C C         5 1 1 ; 2   pqpq jk il jl ik C       15 2 (7)       ipjp ijpp kl kplp klpp ij ijkl C C C C C 4 5 7 1 4 5 7 1 2 ; 2           ipkp ikpp jl jplp jlpp ik C C C C 4 5 35 2 4 5 35 2           iplp ilpp jk iplp jkpp il C C C C 4 5 35 2 4 5 35 2         kl ij jl ik il jk       5 2 2 105 2      pqpq ppqq C C 4 5  (8)   ) ( 3 1 1 ; 4 iljk ikjl ijkl ijkl C C C C         jplp jlpp ik kplp klpp ij C C C C 2 2 21 1       Proceedings of the International MultiConference of Engineers and Computer Scientists 2011 Vol II, IMECS 2011, March 16 - 18, 2011, Hong Kong ISBN: 978-988-19251-2-1 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online) IMECS 2011