The 3DAP is a very powerful tool that provides atomic scale elemental mapping of chemical heterogeneities in materials. Recently, it has been successfully employed to identify the presence of liquid phase separation in metallic glasses [14, 19]. For example, Hono’s group [14] revealed that nanoscale phase separation from the melt into Cu-enriched and was observed, since Ag−Cu has a positive heat of mixing (∆HAg−Cu= +2 kJ mol−1). Figure 5.4 (a) displays an atom map of the as-cast Nb0 metallic glass. It can be seen that the map exhibits an almost homogenous contrast. Apart from four constituent elements (Zr, Cu, Ni and Al), oxygen was also detected, mainly in the form of ZrO. In the current study, the needle-shaped specimens were prepared by electropolishing technique, which allows a possible route for oxygen uptake. Oxygen, being a mobile species, is able to diffuse further into the bulk specimen during process. It is expected that a part of oxygen in the map was from the process of specimen preparation. In order to get more details on local compositional variation, atom probe concentration depth profiles obtained from the Nb0 specimen are displayed in Figure 5.4 (b). One can see that all the constituent elements are uniformly distributed in the matrix, indicating that no phase separation occurred in the as-cast Nb0 alloy. We tried to run Nb0.5 alloy specimens several times, but unfortunately the data quality is not as good as Nb0. The specimens had quite thick oxides on the top which is
Metallic glasses Tg Tx ΔTx Tl (at. %) (K) (K) (K) (K) Zr68Cu16-Ni7.5Al8.5 635 704 69 1213 0.523 0.381 < 2 Zr68Cu13Ni10.5Al8.5 625 701 76 1190 0.526 0.386 2.5 Zr68Cu10Ni13.5Al8.5 632 703 71 1198 0.528 0.384 2 Figure 6.2 displays the DSC and DTA curves of the Zr68Cu(16-x)Ni(7.5+x)Al8.5 (x=0, 3, 6) metallic glasees. Table 6.1 summarizes Dc, Tg, Tx and Tl as well as three common GFA indicators (ΔTx=Tx−Tg, Trg= Tg/Tl and γ= Tx/(Tg+Tl)). It can be observed that all the alloys display one endothermic peak related to glass transition, followed by two exothermic peaks due to crystallization. The ΔTx increases from 69 K to 76 K with decreasing Cu content from 16 at.% to 13 at.%. With further decreases in Cu content to 10 at.%, the ΔTx decreases to 71 K. The γ parameter also shows the same trend as that of ΔTx. Thus, all of the indicators for the Zr68Cu16-Ni7.5Al8.5 glassy alloy exhibit the lowest among the alloy series, confirming the poorest GFA of this alloy composition. Although the Zr68Cu13Ni10.5Al8.5 glassy alloy does not exhibit the highest Trg, it has the largest ΔTx and γ parameter, which indicates that it is the best glass-forming composition. It can be concluded that the high GFA, characterized by critical size dc, is well reflected by the higher ΔTx and γ values. Since the Zr68Cu13Ni10.5Al8.5 alloy shows the best GFA, we will focus on its thermal, kinetic and mechanical properties in the following section.
heating rate, ϕ, is much greater than that in characteristic temperature, T. Compared to other reported Zr-based metallic glasses, such as Eg = 191 kJ mol−1 and Ex = 171 kJ mol−1 for Zr55Cu30Al10Ni5 BMG [16], the current alloy exhibits higher thermal stability. In addition, the Tx and Tp are considered associated with the nucleation and growth of the crystalline phase precipitated from the glassy alloy, respectively [17]. The results shown in Table 3 imply that the nucleation process is more difficult than the growth process for both first and second stages of crystallization. Methods Eg (kJ mol−1) Ex1 (kJ mol−1) Ep1 (kJ mol−1) Ex2 (kJ mol−1) Ep2 (kJ mol−1) Kissinger 432 251 239 331 289 Ozawa 442 263 250 344 302 According to the concept of fragility introduced by Angell [18], glassy materials can be classified into two groups, namely “strong” or “fragile” glasses. Generally, the “strongly bonded” glass-formers, such as SiO2, exhibit small changes in viscosity during heating, and the temperature dependence of viscosity obeys Arrhenius equation. Conversely, glasses with “fragile” bonding structure deviate considerably from the Arrhenius behavior. The kinetic fragility is defined as the slope of the logarithm of viscosity η (or the average structural relaxation time, τ) dependence on Tg/T near Tg:
6.4 summaries the fracture angle in various BMGs [21−29]. It is observable that the fracture angle is generally in the range of 39−44° for compression and 50−60° for tension. However, according to the classical von Mises or Tresca criterion, this angle would be expected to lie at 45° to the compression axis. Thus both criterions cannot satisfactorily explain the fracture behaviour of metallic glasses, which consider only the shear stresses in polycrystalline metals. Donvan [30] recently demonstrated that yielding/fracture follows the Mohr-Coulomb criterion by investigating a Pd40Ni40P20 metallic under different loading modes. He suggested that shear fracture of BMGs depends not only on the shear stress but also on the stress normal to the shear plane. The general form of the criterion can be described as with τy the effective shear fracture stress, τ0 and σ0 the shear and normal stresses on the shear plane, respectively, and α a empirical constant. Using the mechanical date of σf =1552 MPa and θ =44°, τ0 and σ0 can be calculated by following expression: The fracture angles θc and θt were to be closely related to the constant α by [31] Thus the constant α is determined to be 0.035. By substituting τ0, σ0 and α into Eq. (6.5), the effective shear fracture stress τy for the current Zr-based BMG can be obtained
II. Symbols B = bulk modulus C = constant Cp = heat capacity dc = critical casting diameter D = stress concentration factor E = Young’s modulus Eg = activation energy of glass transition Ex = activation energy of crystallization Ep = activation energy of peak crystallization f = volume fraction f0 = frequency of atomic vibration G = shear modulus Gmix = Gibbs free energy of the liquid K = thermal conductivity kB = Boltzmann constant Lsb = length of shear band m = fragility parameter nD = number of required to annihilate a free volume Q = activation energy associated with serration R = gas constant
ϕ = heating rate T = temperature Tr = room temperature Tg = glass transition temperature Tx = onset temperature of crystallization Tm = melting temperature Tl = liquids temperature Tp = peak temperature Tf = temperature in the liquid region of the shear band Trg = reduced glass transition temperature v* = hard sphere volume vf = average free volume of an atom vs = shear velocity vg = growth velocity of the shear band νl = longitudinal velocity vR = velocity of a Rayleigh wave vs = displacement velocity w = thickness of shear band xi = atomic fraction Vm = molar volume α = plastic work converted to heat β = ratio of the dilatation to the shear strain γ0 = characteristic strain of an STZ ω = interaction parameter between two constituent elements
Appendix B (Thermodynamic Calculation) The thermodynamic calculation was carried out to identify whether the potential composition would undergo phase separation in the liquid state during rapid solidification. Using a subregular solution model, the Gibbs free energy of the liquid (Gmix) can be obtained from the expression Here the first term refers to the contribution purely from elemental properties without interaction, xi is the atomic fraction of the component i (Zr, Cu, Al, and Nb), and Gi is the free energy of component i in the reference state. The second term refers to the ideal mixing contribution, and R is the gas constant (8.314 J mol−1k−1). The third term refers to the excess free energy, υ is the order of the term considered, and ωij is the interaction parameter between the i and j components, which can be obtained from Thermo-Calc software. (1) Pure elements contribution
f[0.472, 0.465, 0.055] Plot[Exp.(16),{T,650,1250}] (as seen Figure 4.3.(a)) ii) Compositional dependence of (dGmix/dx) f[xzr_, xCu_, xAl_]=D[Gmix, xzr]; f[0.472, 0.465, 0.055] Plot[Exp.(17),{T, 650, 1250}] (as seen Figure 4.3.(b))