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Study on elastic deformation of substitution alloy ab with interstitial atom C and BCC structure under pressure

The analytic expressions of the free energy, the mean nearest neighbor distance between two atoms, the elastic moduli such as the Young modulus E, the bulk modulus K, the rigidity modulus G and the elastic constants C11, C12, C44 for substitution alloy AB with interstitial atom C and BCC structure under pressure are derived from the statistical moment method. | TẠP CHÍ KHOA HỌC SỐ 20 2017 55 STUDY ON ELASTIC DEFORMATION OF SUBSTITUTION ALLOY AB WITH INTERSTITIAL ATOM C AND BCC STRUCTURE UNDER PRESSURE Nguyen Quang Hoc1 Nguyen Thi Hoa2 and Nguyen Duc Hien3 1 Hanoi National University of Education 2 University of Transport and Communication 3 Mac Dinh Chi High School Abstract The analytic expressions of the free energy the mean nearest neighbor distance between two atoms the elastic moduli such as the Young modulus E the bulk modulus K the rigidity modulus G and the elastic constants C11 C12 C44 for substitution alloy AB with interstitial atom C and BCC structure under pressure are derived from the statistical moment method. The elastic deformations of main metal A substitution alloy AB and interstitial alloy AC are special cases of elastic deformation for alloy ABC. The theoretical results are applied to alloy FeCrSi. The numerical results for alloy FeCrSi are compared with the numerical results for main metal Fe substitution alloy FeCr interstitial alloy FeSi and experiments. Keywords Substitution and interstitial alloy elastic deformation Young modulus bulk modulus rigidity modulus elastic constant Poisson ratio. Email hoanguyen1974@gmail.com Received 02 December 2017 Accepted for publication 25 December 2017 1. INTRODUCTION Thermodynamic and elastic properties of interstitial alloys are specially interested by many theoretical and experimental researchers 1-7 10 12 13 . In this paper we build the theory of elastic deformation for substitution alloy AB with interstitial atom C and body-centered cubic BCC structure under pressure by the statistical moment method SMM 8-10 . 56 TRƯỜNG ĐẠI HỌC THỦ ĐÔ HÀ NỘI 2. CONTENT OF RESEARCH 2.1. Analytic results In interstitial alloy AC with BCC structure the cohesive energy of the atom C in face centers of cubic unit cell with the atoms A in body center and peaks of cubic unit cell in the approximation of three coordination spheres with the center C and the radii r1 r1 2 r1 5 is .