1Absence of fast precursor dynamics of low-density amorphous ice around its hypothetical glass transition temperature
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Absence of fast precursor dynamics of low-density amorphous ice around its hypothetical glass transition temperature
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Elastic fixed window scans have been performed at the high-Q backscattering neutron scattering spectrometer IN13 (ILL) on low-density amorphous (LDA) ice between 2 K and up to 170 K, i.e., above the phase transformation to crystalline ice Ic.
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Within the experimental accuracy no anomaly of the Debye–Waller factor is found below the recrystallization temperature.
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The data rule out the existence of fast precursor processes as they have been predicted by the mode coupling theory of the glass transition and found in molecular glass formers.
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Introduction
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There is a controversial discussion about the physical nature of the two known amorphous ice states, low-density amorphous (LDA) and high-density amorphous (HDA) ice.
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From computer simulations1–3 it has been deduced that LDA and HDA represent the glassy states of two corresponding liquids, low-density water (LDW) and high-density water (HDW), respectively.
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A number of experimental results seem to support this view: Structures similar to LDA and HDA can be produced by extremely fast quenching of microdroplets or the gas phase;4–7 calorimetry experiments8–11 indicate an endothermic “glass transition” around 130–135 K; and from D2O–H2O interlayer mixing upon heating12 of LDA-type vapour deposited water an increased mobility around 150 K has been found.
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On the other hand the above results are neither obtained in bulk samples nor do they constitute unequivocally a glass transition temperature in water.
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In contrast to interlayer mixing effects ion diffusion experiments15 have not shown any higher mobility of guest molecules in the amorphous ice matrix.
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Also, isotopic exchange experiments16 show no translational water motion but rather a defect promoted proton mobility responsible for the endothermic transition.
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Experiment
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The observable, the Debye–Waller factor as measured in neutron scattering, occasionally also called Mössbauer–Lamb factor if incoherent neutron scattering is considered, has been measured by fixed window experiments at zero energy transfer at the thermal backscattering spectrometer IN13 at the ILL Grenoble.23
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For the present experiment, an IN13 standard setting with incident neutron energy of 16.5 meV and an energy resolution of 8 µeV has been used.
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The latter value means that any dynamic process faster than about 10 ns should lead to a decrease of the Debye–Waller factor.
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Most important for the present purpose, IN13 offers the unique possibility to measure the elastic intensity Iel up to Q-values of more than 5 Å–1, thus being highly sensitive at small amplitude dynamics.
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The Q-range is sampled by 32 detectors giving a resolution in Q of ±0.2 Å–1.
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Using this combination of high energy resolution and large accessible Q-values we focus onto eventual glass transition phenomena of LDA in the best possible way.
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In the following, we will present the measured strict elastic intensity Iel(Q,T).
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The sample under consideration has been partially deuterated (60 vol% D2O) water.
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The partial deuteration has been chosen for better control of the sample state due to the pronounced coherent Bragg scattering contributions in the crystalline state as will become obvious in the following section.
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The sample has been prepared by compressing crystalline ice Ih at 77 K (in liquid N2) in a piston-cylinder apparatus up to about 18 kbar.24
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The thus produced HDA is recovered at ambient pressure, filled in aluminium holders used as standard in neutron scattering and placed into a precooled (75 K) standard cryostat.
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After careful removal of remaining N2 the thermal history of the sample has been as follows: (a) Cooling down to 2 K; (b) heating up the HDA sample to 125 K and observing the transformation of LDA.
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(c) Cooling down the LDA sample back to 2 K. (d) Performing a temperature scan up to 170 K where the LDA transformed to ice Ic.
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(e) After cooling down to 2 K a third temperature scan is taken from the ice Ic sample.
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Elastic scans were performed during the heating intervals.
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The temperature was increased in steps of 3.5 K each followed by one hour of data aquisition.
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In the frame of this communication we restrict the discussion below on the results obtained for Iel(Q,T)/Iel(Q, 2 K) from the temperature scan of the LDA sample exclusively.
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The properties of analogous scans on HDA and ice Ic and a general comparison of HDA with LDA will be the subject of a forthcoming publication25.
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Results and discussion
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Being aware of the above controversial discussion the motivation for our present experiments is the following: If LDA and HDA do constitute glasses and if there exists a glass transition around 135 K, one may have a good chance to see dynamic precursor effects as, e.g., postulated by mode coupling theory (MCT) of the glass transition.26
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Such processes can be interpreted as fast overdamped rattling motions with increasing amplitudes as one approaches a critical temperature Tc above Tg.
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They manifest themselves by a pronounced deviation of the Debye–Waller factor from its harmonic behaviour, visible as an excess-loss of elastic intensity, in a temperature range above the glass transition temperature Tg (Fig. 1).
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In favourable cases the onset of these deviations is already observable at temperatures significantly below the glass transition temperature.
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Experimentally, anomalies in the Debye–Waller factor have been found27,28 in several molecular glass formers.
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Fig. 2, top shows the static structure factor obtained for ice Ic.
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In our partially deuterated sample the coherent signal is strongly supressed and the Q-dependence of the normalized elastic intensites is relatively flat (Fig. 2, bottom).
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Nevertheless, the elastic intensity of the crystalline state (solid line) still shows modulations with broad maxima remaining at the Q-values of the Bragg-reflections in the high resolution static structure factor of ice Ic.
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The fact that the elastic intensity of the crystalline state is “oscillating” around the values from the amorphous LDA state will be a central point in the argumentation presented below.
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The results of the present study on LDA are contained in Fig. 3 which shows the temperature dependence of Iel(Q,T)/Iel(Q, 2 K) at those selected Q-values which are marked by arrows in Fig. 2.
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Note that these Q-values have been chosen such that the intensities of the crystallized sample are alternatingly above or below the intensities of the amorphous sample.
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It is clearly seen from the figure that below 135 K the temperature dependence of this normalized elastic intensity behaves as expected for the Debye–Waller factor of a harmonic system, i.e., ln[Iel(Q,T)/Iel(Q, 2 K)] ∝ –T for all Q-values.
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Above 135 K, anomalies occur, and at some Q-values (open symbols in Fig. 3) the elastic intensity indeed decreases for temperatures above the glass transition temperature.
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But from the observation that at those Q-values where the elastic intensity of the crystalline state is above the value of the amorphous state the elastic intensity goes up we can infer that crystallization takes place (shaded temperature interval).
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Note that from all curves shown in Fig. 3 the Q = 1.7 Å–1 data gives the highest evidence for the onset of crystallization because (i) the best S/N-ratio is obtained at small Q-values and (ii) the 1.7 Å–1 coincide with a strong Bragg peak of ice Ic.
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This obviously excludes any other interpretation which at the first sight might be tempting.
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Thus, the conclusion of our work is straightforward:
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Below the onset of recrystallization around 135 K there is no anomaly in the Debye–Waller factor of LDA.
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Clearly, this result cannot be taken as an obvious, unambiguously proof that any glass transition scenario can be excluded.
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But it might be taken as another indication that a glass transition in LDA ice at about 135 K is still questionable and that the amorphous behaviour of LDA ice might be different from that known from other typical glass formers.
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