D 270 (m) = 2.374 X 10“10 e^-6225 m
Z)310 (m) = 5.191 X lO-10 e-03463 m (3)
D 350 (m) = 9.996 X 10“10 e^-2283 ™.
These equations could obviously be applied for the interpolation of the sucrose selfdiffusion at interm ediate concentrations and also for a m od erate extrapolation to the more concentrated side of the diagram. As an example, the data have been extrapolated to 80% w/w sucrose. The additional points inserted at this concentration were obtained from a comparison of the rotational correlation times as obtained from the C-13 Tl studies  as suming that the Debye formula given below is applicable to these solutions.
diffusion coefﬁcient evaluated at a time point at which the VAF crosses zero (at this point D(t) reaches its ﬁrst maximum ) is roughly twice the actual diffusion constant. Figure 3 shows essentially the same information as ﬁgure 2 (b), but with a different normalization, D E from equation ( 3 ). In this case the self-diffusion coefﬁcients approach D E ;0.6 as t ¥ . Somewhat more scattering in D E values is observed compared to D R (compare ﬁgures 2 (b) and 3 ). The oscillations in time-dependent diffusion coefﬁcients are related to the oscillations in the
Fig. 4. Water self-diffusion coefficient, transverse relax ation time and signal amplitude as a function of the hard ening time in an Mg oxychloride cement paste. The fit of an exponential model to the diffusion coefficient decrease shows that the initial decrease is less pronounced than the one observed when the transverse relaxation time is already decreasing more slowly. The big scattering of the diffusion data at long hardening times is mainly due to the very poor signal available for the PFG experiment at these times.
Self-diffusion is one of the basic transport mechanisms in liquids. Its theoretical investigation goes back to the pioneering work of Alder and Wainwright [ 1 , 2 ]. Using molecular dynamics (MD) simulations they found that the velocity autocorrelation function (VACF), which is deﬁned as C t ( ) º á v ( ) · 0 v ( ) t ñ , displays so-called long- time tails being characterized by an asymptotic decay proportional to t - d 2 . Here, the brackets denote a thermal equilibrium average and d = 2, 3 speciﬁes the dimension of the space occupied by the considered liquid. Soon after, this ﬁnding was corroborated by Kawasaki [ 3 ] within mode-mode coupling theory. The long-time tails are caused by hydrodynamic interactions between a tagged particle and the vortex ﬂow induced by the particle motion relative to the rest of the ﬂuid. At the lower dimension d=2, the resulting t 1 long-time tail though is inconsistent within mode-coupling theory. A modiﬁed asymptotics based on a self-consistent argument was suggested in [ 4 – 7 ] leading to a slightly faster decay according to
In conclusion, we provide iron self-diffusion data for liquid iron, Fe 91.3 C 8.7 , and Fe 83.1 C 16.9 . With these, we show that pre- vious literature values from tracer experiments using a long- capillary set-up in Fe –C [ 16 ] are off by a factor of 4 and using a pressure cell in liquid iron [ 19 ] are smaller than factor of about 4 (figure 3 ). In contrast, the conclusions drawn from the previous data sets, that the addition of carbon causes a strong mixing effect on the dynamics in the melt, is not sup- ported: the addition of carbon to iron has only a 10% effect on the iron mobility in the liquid. Furthermore, there is no correlation between the value of the self-diffusion coef- ficient at the liquidus temperature and the onset of glassy dynamics: although the diffusion coefficients in the close-to- eutectic Fe 83.1 C 16.9 approach a value of 10 −9 m 2 s −1 , no onset of glassy dynamics, i.e. a deviation from an Arrhenius-type temper ature dependence of the self-diffusion coefficient or a deviation from a Lorentz-type quasielastic signal could be observed. Quasielastic neutron scattering measurements upon mixing other light elements (e.g. sulfur, boron, and silicon) to liquid iron and nickel are in preparation in order to clarify how generic these findings are.
The flow rate of the outer solution was (2.0 ± 0.1) mms-1, which with the self-diffusion co efficient 1.952 x 10"9 m2 s ' 1 of CI" in 0.1 M NaCl2 resulted in an effective capillary length of 25.38 mm. Instead, with the rate (1.0±0.1) mms-1, e.g., the effective length of the capillary was 25.83 mm (Al- effect!).
At high temperatures and for 0.6 q 1.0 A ˚ 1 , a q-rescaling of U(q, t) as ^ Uðq; ^tÞ ¼ ½Uðq; t=hs q iÞ c=f q holds well with a mean b q ¼ 1 [Fig. 3(a) ]. Furthermore, in the tem- perature range of some 300 K, a time-temperature-superposi- tion (TTS) holds also with a simple exponential decay [Fig. 3(b) ]. Thus, in this temperature and q-range, the self- motion of gold atoms in the Au 81 Si 19 melt can be described via Brownian diffusion, consistent with the predictions of hydrodynamics in the small q limit. 7 , 26 However, TTS is violated at 713 K by the pronounced stretching of U(q, t) [Fig. 3(b) ]—an indication that the hydrodynamic regime is no longer reached on the spatial length scale probed here by the smallest accessible q; i.e., 2p/q 10 A ˚ . Although struc- tural relaxation at 713 K deviates significantly from the sim- ple exponential predicted by hydrodynamic theory, the hs q i, nonetheless, obeys a q 2 proportionality, allowing us to extract an apparent self-diffusion coefficient commensurate with the QENS data at higher temperatures [Fig. 1(b) ]. Thus,
10 5 m 2 =s (error: log
10 D 0 ¼ 1.5).
This comparably high value of 4.4 eV indicates that the activation energy of diffusion has to be composed of a migration and a defect formation part. In literature, data on activation energies of diffusion are very limited. A theo- retical study on self-diffusion in amorphous silicon can be found which was done between 627 and 1027 °C by classical molecular dynamics  . An activation energy of silicon migration between 0.86 and 0.95 eV is derived. In a different study  , a migration energy of only 0.23 eV is calculated at low temperatures between 27 and 327 °C. Mirabella et al.  give an activation energy of dangling bond migration (as the underlying diffusion defect) of 2.6 eV as derived from boron diffusion in a-Si. Further information on activation energies in a-Si can be found in experiments investigating structural relaxation, e.g., by resistivity measurements. This process involves point defect annihilation during annealing, necessitating a move- ment of atoms. According to various literature work  , activation energy spectra are found, ranging between 0.2 and 2.7 eV, which should at most represent the migration part of our activation energy given above. The spectral aspect of the activation energies for structural relaxation hints at a complex diffusion process with varying local coordination and orientation.
reported evidence for a wall effect. Diffusion coefficients calculated for samples held in capillaries of 0.83 mm I. D. were considerably lower than those calculated for samples held in 1.60 mm capillaries. These data are shown in Fig. 1. In the course of studies underway in our laboratory, it became necessary to know ac curately the self-diffusivity in liquid indium. Con sequently an investigation over a limited temperature range was undertaken by use of techniques different from those employed in Ref. 1 and 2. The method used was analogous to the standard “thin layer” slicing method in the solid state. Following L a r s s o n and L o d d i n g ’s technique3 of preparing samples, a small
reﬂectometry might be such a method. 49
Our measurements provided the ﬁrst tracer self-diﬀusivities in LiNbO 3 single crystals at temperatures below 773 K.
However, in the literature some high-temperature data above 1073 K are available, which were also obtained by tracer methods about 25 years ago. 24 The data are also shown in Fig. 4. A higher activation enthalpy of 1.98 eV was found. This can be explained by the fact that in this temperature range signiﬁcant vacancy formation according to reaction (5) takes place. The activation enthalpy is then given by DH = DH m +