Measuring the dynamical critical exponent of an ordering alloy using x-ray photon correlation spectroscopy

The dynamics of the order fluctuations in the ${\mathrm{AuAgZn}}_2$ close to the critical point ($T_c\simeq 609$ K) was observed by coherent x-ray scattering. With the high beam intensity of the ID10 ESRF beamline and with the new pixel detector, the dynamics was measured with a few tens of millisecond resolution. The intensity connected to the diffuse scattering corresponding to fluctuations was unambiguously distinguished from the surface pretransitional ordering occurring in this system close to $T_c$. The variations of the fluctuation time with temperature and wave vectors were measured in this system belonging to the universality class of Ising second order transition with a nonconserved order parameter. The direct observation of the critical slowing down in the vicinity of the second-order transition led to an estimate of the dynamic exponent $z\simeq 1.96\left(11\right)$, in rough agreement with theory (model “A” of Hohenberg and Halperin [Rev. Mod. Phys. 49, 435 (1977)]).

Figure 1

(a) B2 and (b) ${\mathrm{L}2}_1$ ordered structures of the ${\mathrm{AuAgZn}}_2$ alloy near $T=609$ K. The lattice parameter $a$ of the B2 phase is close to 3.17 Å at 603 K.

Figure 2

(a) Measured scattering at 609.35 K ($T_c+0.188$ K) and (b) the mask used and the typical circular rings where the dynamics was observed. Both figures show the same $100\times 100$ pixel area; each pixel is $1.29\times {10}^{-4}{\AA }^{-1}$.

Figure 3

Determination of the critical temperature by fitting intensity profiles to Eq. (2). (a) from the variation of $S^{-1/\gamma }(q=0)$ with $\gamma =1.241$. (b) from the variation of ${\xi }^{-1/\nu }$ with $\nu =0.63$.

Figure 4

Time correlations obtained for various $q$ vectors at $T=T_c+0.113\mathrm{K}$. Curves are shifted vertically for sake of visibility. Symbols correspond to values of the ${\mathrm{g}}_2(q,t)$ function and solid lines to a least-square fits with Eq. (3).

Figure 5

(a) Fluctuation times $\tau (q,T)$ for various temperatures and the Lorentzian fits. (b) Temperature variations of ${\tau }_0\left(T\right)$. An estimate of the exponent yielded $z\nu =1.235\left(70\right)$.