Dynamical and structural properties of undercooled Cu-Ti melts investigated by neutron and x-ray diffraction

We investigate temperature-dependent dynamical and structural properties of Cu-Ti melts within a compositional range of 24–69 at.% Ti. Accurate data of viscosity, density, and structure have been obtained by employing the electrostatic levitation technique, which enables containerlessly processing of the samples. Within the Cu-Ti system, the viscosity features a nonmonotonous trend, with the melt of the highest viscosity located at the compositions with intermediate Ti contents. This compositional trend of the liquid dynamics is not reflected in the average packing fraction derived by the macroscopic density, which is almost independent of the Ti concentration. By studying the melt structure using x-ray and neutron diffraction, particularly the direct access of the concentration-concentration structure factor $S_{\text{CC}}$, we show that the slowdown of the melt dynamics upon mixing is rather due to chemical effects associated with the preferred formation of Cu-Ti pairs. This leads to a contraction of the interatomic distances, whereas the almost ideal mixing behavior in the molar volume of the melt is a result of the simultaneous decrease of the average coordination number.

Figure 1

(a) Normalized radius (red circles) of an undercooled liquid ${\mathrm{Cu}}_{31}{\mathrm{Ti}}_{69}$ sample as a function of time, depicting the decay of the oscillations measured with ESL. The black line is a fit to the data. Inset: Fast-Fourier transformation (FFT) of the decay curve. The peak indicates the excitation and eigenfrequency of the sample. (b) Viscosity $\eta$ calculated via Lamb's law for samples of different masses, which can be described by a single temperature dependence.

Figure 2

(a) Temperature-dependent density of liquid Cu-Ti samples with different compositions (${\mathrm{Cu}}_{31}{\mathrm{Ti}}_{69}, {\mathrm{Cu}}_{50}{\mathrm{Ti}}_{50}, {\mathrm{Cu}}_{54}{\mathrm{Ti}}_{46}$, and ${\mathrm{Cu}}_{76}{\mathrm{Ti}}_{24}$). The solid lines are linear fits to the data according to Eq. (4). The obtained fit parameters are listed in Table 1. The values for pure Cu and Ti correspond to data reported in Refs. [43] and [44], respectively. The respective liquidus temperature of each composition (in the case of ${\mathrm{Cu}}_{31}{\mathrm{Ti}}_{69}$, the solidus temperature) is marked with arrows. (b) Composition dependence of the molar volume of liquid Cu-Ti samples at 1273 K obtained via ESL. In addition, the data reported in Refs. [16, 17], both using EML, are shown for comparison. The dashed line represents the behavior of an ideal mixture, while the dotted line is a fit according to Eq. (5), as explained in the text [16]. The data for liquid Cu and Ti have been extrapolated.

Figure 3

(a) Arrhenius plot of the viscosity. The solid and dashed lines are Arrhenius fits and the extrapolation of the fits, respectively. (b) Viscosity as a function of temperature of liquid Cu-Ti samples with different compositions [same as in (a)]. The solid lines are Vogel-Fulcher-Tammann fits.

Figure 4

(a) Isothermal values for the viscosity at 1030 and 1273 K as well as (b) packing fraction $\varphi$ derived from different density data at 1273 K as a function of the Ti content. The black dashed line represents the here found constant packing fraction of $\sim 0.53$, which is also in good agreement with the data reported by Watanabe et al. [17].

Figure 5

(a) Total x-ray structure factor $S\left(q\right)$ of the studied Cu-Ti alloys at $\sim 1273\mathrm{K}$ with different compositions compared with the structure factors of pure Cu and pure Ti (Cu at approximately 1358 K [51] and Ti at 1845 K [52]). (b) Derived average interatomic distances and coordination numbers of the alloy melt at 1273 K as a function of Ti content, assuming that the total x-ray structure factors closely reassemble the number density structure factor $S_{\text{NN}}$.

Figure 6

(a) Differences between the derived average interatomic distances of the alloys and a weighted average of that of the pure elements. (b) Partial concentration concentration structure factor $S_{\text{CC}}\left(q\right)$ measured by neutron diffraction on the zero-scattering alloy ${\mathrm{Cu}}_{31}{\mathrm{Ti}}_{69}$ at 1273 K compared with its x-ray total structure factor which is close to $S_{\text{NN}}$.

Figure 7

Fourier transformed x-ray total structure factor of ${\mathrm{Cu}}_{31}{\mathrm{Ti}}_{69}$ representing in an approximation of $g_{\text{NN}}$ and $g_{\text{CC}}$ derived from the total and partial $S$ and $S_{\text{CC}}$ measured by x-ray and neutron diffraction, respectively. The $g_{\text{CC}}$ of the ${\mathrm{Zr}}_{64}{\mathrm{Ni}}_{36}$ alloy melt at 1373 K is shown as a comparison.