The Investigation Of The TiAl Based Co₂TiAl Alloy By First Principle Calculations

The investigation of the TiAI based Co₂TiAl alloyby first principle calculationsSpecialty: Atomic and Molecular PhysicsPostgraduate: Fu Hongzhi Tutor: Professor Yang XiangdongThe TiAl based alloys have many desirable properties, such as, lower density,higher melting temperatures and higher yield strength, etc. But in many cases, theyhave a few defects, for example, lacking ductility, which prevent them from beingused to quite important practical applications. Therefore, it is considerableinteresting to investigate the structures and performance of the TiAl basedmaterials. The experiments and electronic structure calculations have shown thatthe properties of these compounds depend strongly on crystal structure and theelemental composition, and that their electronic structure plays an important rolein their properties. Then, there exists strong motivation to understand thecontrolling elements of their behavior from a fundamental, microscopic theory ofelectronic structure. However, especially for some of the more importantaluminide intermetallic compounds, very little is known from a fundamental pointof view about the underlying physics which governs strength, ductility, andresistance to fracture and thermal failure.Co₂ TiAl belongs to a large group of the L2₁-structure compounds commonlyreferred to as Hume-Rothery (H-R) alloys with the general formula X₂YZ, inwhich X and Y are transition metals(TM) and Z is a nonmagnetic sp element. TheL2₁-structure compounds have long been known as an important stable structurefor certain ternary alloys, and have a unique close-packed cubic structure unit cellcomposed of eight simple bcc (B2) unit cells. In recent years, many attemptshave been mainly focused on the magnetism of Co and give little attentions to the role of the non-magnetic atom Al, the thermodynamic properties of Co₂TiAl, theequations of states, chemical bindings and the influence of the doping elements onthe electronic structure of Co₂TiAl, which we have discussed in the paper.Firstly, we have used the full potential linearized augmented plane wave(FLAPW) theory employing generalized gradient approximation (GGA) to studythe ternary electronic structure of the L2₁ type X₂TiAl (X=Fe, Co, Cu, Ni) crystals.We focus on the influence of the X atoms and Al 3p occupied states in AITiX₂(X=Fe, Cu, Co, Ni) intermetallics. The results show that the total DOS dependsstrongly not only on electronegativity of TM atoms, but also on the positions ofTM atoms, and the TM d DOS not only connects with the pseudo-gap which is theindication of the stability of the intermetallic ternary Hume-Rothery(H-R) alloys,but also plays a crucial role in hybridization with other element valence electrons.Although the Al 3p states take small proportion in the total DOS for all studiedsamples, the Al 3d states are far more extended-like in the character than the dstates. And the Al 3p states are more sensitive than d states to change in theelectronic interactions, and the total DOSs in all the studied samples are modulatedby Al 3p states.Secondly, thermodynamic properties of the Co₂TiAl are investigated by ab initioplane-wave pseudopotential density functional theory and by the quasi-harmonicDebye model. The lattice constant a, the bulk modulous B_o and the first orderpressure derivative of the bulk modulous B_o are obtained. We have calculated thedependences of the relative (X-X_o)/X_o (X=Debye temperature O, volume V or heatcapacity Cv) on the different pressure P and temperature, the heat capacity Cv on thedifferent pressure P and temperature T, the difference of the heat capacity Cp, and Cv,on temperature, and the bulk modulus B on temperature T and pressure P. It can befound that Cv increases with T³ at lower temperature, and when temperature T＞800K, the increasing is suppressed and approaches the Dulong-Petit limit. At agiven temperature T, the bulk modulous B increases linearly with applied pressures.And the bulk modulous B decreases almost linearly with the increase of temperatureT at the fixed pressure P. By fitting the data to second-order polynomials, we haveobtained the relationships of B-T and 0-T. The thermal expansion coefficientα increases with T³ at lower temperatures and gradually approaches to a linearincreasing at higher temperatures (＞600℃). At higher pressures, the Gruneisenparameterγis almost invariant with temperatures. At lower pressures (＜30Gpa), theGruneisen parameterγincreases non-linearly with the temperatures, and the effectsof pressure on the Gruneisen parameterγare more important than temperature. Thecalculated Poisson's ratio a of Co₂TiAl is 0.246, very close to 0.25, which meansthat the Co₂TiAl has predominantly central inter'atomic forces. The Co₂TiAl has notonly great shear modulus G, but also great bulk modulus B, representing the higherresistance to the plastic deformation and fracture, respectively. The obtained G/B is0.6116, showing that the Co₂YiAl alloy is brittle. The shear anisotropic factors A ofthe [100] plane, [010] plane and [010] plane are also 1.769, indicating the elasticanisotropic.Finally, using the full potential linearized augmented plane wave (FLAPW)theory employing generalized gradient approximation (GGA), we have studied theinfluence ofX (X=Si, C, and Zr) on the Co₂TiAl alloy. The effects of X (X=Si, C,and Zr) on lattice parameters, bulk modulus, chemical bindings and electrondensity contour are investigated. The solutes studied in the present work are X(X=Si, C, and Zr) which are in the second, third and fifth line of the periodic table, andoften used as hardening (C and Si) and softening (Zr) solutes in metals,respectively. It is shown that the X (X=Si, C, and Zr) shrink the unit cell by1.794ï¼…, 0.478ï¼…and 0.137ï¼…. On the other hand, the Si and C increase the bulkmodulus by 1.1ï¼…and 1.3ï¼…, respectively. On the contrary, the Zr decreases bulkmodulus by 0.56ï¼…. Among the chemical bonds Al-Co, Al-Ti, Co-Ti, Al-X andCo-X (X=C, Si and Zr)), the chemical bonds Co-C are the biggest, followed by thechemical bonds Co-Si. In order to learn more clearly, we have plot the electroniccontour which cut though the [011] for the studied alloys Co₂TiAl,Co₂AlTi_0.75Zr_0.25, Co₂AlTi_0.75Si_0.25 and Co₂AlTi_0.75C_0.25. The characters of thechemical bonds are mainly metallic in Co₂TiAl and Co₂AlTi_0.75Zr_0.25 alloys, andthey have the smaller bulk modulus than Co₂AlTi_0.75Si_0.25 and Co₂AlTi_0.75C_0.25which have not only chemical bonds, but also covalent bonds, i.e. the covalentbonds appear between Co-Si and Co-C bonds.