Ab initio alloy theory, formulated within the exact muffin-tin orbitals method in combination with the coherent-potential approximation, is used to determine the effect of long range order on the elastic properties. The lattice parameters and single-crystal elastic constants of Cu3Au are calculated for different partially ordered structures ranging from the fully ordered L12 to the random face centered cubic lattice. Special attention is put on the chemical and magnetic effects and on the interplay between these two degrees of freedom. For non-magnetic Cu3Au, it was found that the lattice parameters and single-crystal elastic constants follow a clear trend with the degree of chemical order: namely, C11 and C12 decrease slightly, whereas C44 remains nearly constant with increasing disorder. As none of the single-crystal elastic constants were modified significantly due to the long-range-order, the polycrystalline elastic moduli of Cu3Au also keep nearly constant upon ordering. The Debye temperature does not show a strong chemical order dependence either. Using the calculated Debye temperatures, we find that for the entropy change upon order-disorder transition varies between −0.018 kB and 0.022 kB, the upper value being surprisingly close to 0.023 kB observed in experiments. However, some of the elastic constants of ferromagnetic Ni3Fe, adopting the same crystal lattice as Cu3Au, were affected considerably. For the lattice parameter a, the main effect of magnetism is concentrated in the chemically dis-ordered region, with long-range order parameter S below ∼ 0.6 and the effect gradually disappears with increasing S. In the ferromagnetic state, the lattice parameter is almost constant as a function of the degree of order. Out of the three single-crystal elastic constants, only C11 and C12 are found to be affected by magnetism in the ordered state, however, their combined effect results in a nearly constant bulk modulus as a function of S. C44 changes slightly with S and magnetic state. The tetragonal shear elastic constant C´ , the Young’s modulus E and the shear modulus G increase significantly with the degree of order in the ferromagnetic state, but the effect becomes weak as the system approaches the random regime. Especially the C´ shear elastic constant depends strongly on the magnetic state and the degree of order. As a result, the Zener anisotropy ratio C44/C´ and the Possion’s ratio are strongly affected by the long-range order in the ferromagnetic state. Nevertheless, the actual values for the Pugh ratio and the Cauchy pressure remain far from their critical values, indicating that the ductility of Ni3Fe is not influenced by the chemical/magnetic ordering. Interestingly, the ferromagnetic L12 system possesses ∼5.4% larger elastic Debye temperature than the paramagnetic one, which in turn has similar ΘD as the chemically disordered face centered cubic phase being in either ferro-or paramagnetic state. The implications of the chemical/magnetic order on the mechanical properties and order-disorder transition is discussed. / <p>QC 20140929</p>
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:kth-152529 |
| Date | January 2014 |
| Creators | Wang, Guisheng |
| Publisher | KTH, Tillämpad materialfysik, Stockholm |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Licentiate thesis, comprehensive summary, info:eu-repo/semantics/masterThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
Page generated in 0.0025 seconds