Glassy Dynamics versus Thermodynamics: The Case of 2

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Glassy Dynamics Versus Thermodynamics : The Case of 2- Adamantanone Daria Szewczyk, Andrzej Jezowski, George A Vdovichenko, Alexander I Krivchikov, Francisco Javier Bermejo, Josep Lluis Tamarit, Luis Carlos Pardo, and John W Taylor J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b04240 • Publication Date (Web): 15 Jun 2015 Downloaded from http://pubs.acs.org on June 18, 2015

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The Journal of Physical Chemistry

Glassy dynamics versus thermodynamics : the case of 2-adamantanone D. Szewczyk,† , A. Je»owski G.A.,† Vdovichenko,‡ A. I. Krivchikov,‡ F.J. Bermejo,¶ J. Ll. Tamarit,∗ § L. C. Pardo,§ and J. W. Taylor ,

Institute for Low Temperature and Structure Research, Polish Academy of Science, Poland, B. Verkin Institute for Low Temperature Physics and Engineering of NAS Ukraine, 47 Lenin Ave., Kharkov 61103, Ukraine, Instituto de Estructura de la Materia, Consejo Superior de Investigaciones Cientícas, CSIC, Serrano 123, 28006 Madrid, Spain, Grup de Caracterització de Materials, Departament de Física i Enginyieria Nuclear, ETSEIB, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona, Catalonia, Spain, and Rutherford Appleton Lab, ISIS Facility, Didcot OX11 0QX, Oxon, England

E-mail: [email protected]

Phone: +34 93 401 6564. Fax: +34 93 401 6564

To whom correspondence should be addressed INTIBS ‡ ILT ¶ Madrid § Barcelona ISIS ∗ †

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)>IJH=?J The heat capacity and thermal conductivity of the monoclinic and the fully ordered orthorhombic phases of 2-adamantanone (C10 H14 O) have been measured for temperatures between 2 K and 150 K. The heat capacities for both phases are shown to be strikingly close regardless of the site disorder present in the monoclinic crystal which arises from the occupancy of three nonequivalent sites for the oxygen atom. The heat capacity curves are also well accounted for by an evaluation carried out within the harmonic approximation in terms of the g(ω) vibrational frequency distributions measured by means of inelastic neutron scattering. Such spectral functions show however a signicant excess of low frequency modes for the crystal showing statistical disorder. In contrast, large dierences are found for the thermal conductivity which contrary to what could be expected, shows the substitutionally disordered crystal to exhibit better heat transport properties than the fully ordered orthorhombic phase. Such an anomalous behavior is understood from examination of the crystalline structure of the orthorhombic phase which leads to very strong scattering of heat-carrying phonons due to grain boundary eects able to yield a largely reduced value of the conductivity as well as to a plateau-like feature at intermediate temperatures which contrasts with a bell-shaped maximum shown by data pertaining the disordered crystal. The relevance of the present ndings within the context of glassy dynamics of the orientational glass state is nally discussed. Introduction

The most widely accepted denition of a glass portraits it as

a condensed state of matter

which has become non-ergodic by virtue of the continuous slow-down of one or more of its degrees of freedom.

A wide class of materials compliant with such a denition has been shown to exhibit glassy behaviour apart from the well documented case of structural glasses, namely those disordered or amorphous solids formed by rapid quenching of the liquid state. The phenomenology exhibited by this class of materials is astoundingly rich and in fact 2


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the routes to attain a glassy state comprise mechanisms as varied as trapping of colloidal particles by their neighbors as happens in concentrated colloidal solutions, cold compression of a crystal or decompression of a crystal that was stable at high pressure etc. Such pathways most of the time involve a somewhat strong departure from the initial state and in many cases, a characteristic temperature signaling the ergodicity-breaking transitions leading to freezing-in into a structural state with built-in disorder and/or frustration may be dened. 2 Such a characteristic temperature would correspond, in the case of structurally-disordered matter, to that signaling the canonical liquid

→

glass transition.

Over the last few decades, interest has been focused onto nding some common features exhibited by such a diverse class of materials which concern measurable properties such as the specic heat, thermal conductivity, anomalies in the temperature dependence of the sound velocity, etc. 37 Between those features, the presence of tunneling systems has been studied for a long time. In fact, our current understanding of the anomalies shown by the thermal and transport properties of glasses at low temperatures, heavily relies on the concept of tunneling systems which may execute incoherent transitions or perform interactions between them. Detailed studies on the entities executing such tunneling motions were carried out on mixed crystals allowing to identify the microscopic entities executing such motions. 8 In contrast, work concerning structural glasses can only be carried out on phenomenological grounds and no widely accepted answers concerning the identity of particles executing such motions have been given. The thermal properties of glassy matter at low temperature such as the rise up of

Cp /T 3

as the temperature decreases or the presence of a plateau in the

thermal conductivity have been considered as a glaring evidence of universal behaviour, and are usually modeled by recourse to the tunneling model. Here we report on a study of the specic heat and thermal conductivity of a crystal which can be prepared with a controlled amount of disorder. It pertains to a material such as 2-Oadamantane or 2-adamantanone (C 10 H14 O, hereinafter referred to as 2O-A), a derivative of the plastic crystal adamantane with C 2v symmetry 9,10 which by means of thermal treatments

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can be prepared into dierent phases on cooling down the liquid below 557 K. This may rst lead to a plastic- rotator- or orientational-(OD) state which exhibits a high-symmetry (Fm3m) lattice where molecules are disordered only with respect to their orientational degrees of freedom. Further cooling below ca. 178 K leads to a metastable monoclinic (P2 1 /c) low-temperature phase which comes back to the OD phase upon heating at 205 K. 9,10,12 Such a metastable phase shows intrinsic statistical disorder concerning the site occupancy of the oxygen atom. Such atomic positions of the oxygen atoms have fractional occupancies of 25%, 25%, and 50% regarding three dierent sites which, interestingly enough do not show any marked temperature dependence. Interconversions among such sites by means of large-angle angular excursions have been proven by dielectric spectroscopy 9 which for such a relatively ordered crystal shows processes akin to those usually found in structurally disordered matter, 1315 namely α- and β -relaxations. The former displays a relaxation time that reaches 102 s at a temperature T ≈ 132 K, where a change in slope of the temperature dependence of the unit cell volume has been reported. On the other hand, the latter process was clearly assigned to strongly hindered reorientational motions taking place within the crystal lattice and displayed properties commonly considered as those of the Johari-Goldstein

β -relaxation. 9 Finally, a true fully-ordered ground state of this material can also be prepared by means of thermal cycles between ca. 100 K and 220 K (i.e., around the low-temperature to OD phase transition) . The crystalline phase coming out of such an annealing procedure corresponds to an orthorhombic (Cmc2 1 ) stable and fully ordered crystal. The shapes of the crystals so prepared have been analyzed by means of scanning electron microscopy which shows welldened regions with at surfaces and sharp edges having fused grain sizes of some 20 μm. 10 Such a well ordered crystal made of the same material provides us with a reference onto which the dynamic and thermodynamic features of the metastable phase can be referred to. On such grounds we have carried out a study on the thermal and transport properties of such a material such as the specic heat and thermal conductivity at low and intermediate

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temperatures.

Furthermore, the vibrational frequency distributions for both crystals as

determined by inelastic neutron scattering are also reported. Our purpose here is thus to report on how inferences based upon the thermodynamic measurements for the two crystal phases of 2O-A need to be scrutinized against data pertaining the microscopic dynamics since incorrect conclusions may otherwise be derived. The results are on the other hand relevant to understand the origin of some reported anomalies in the thermal and transport properties of some materials sometimes interpreted as evidence of new condensed matter states. $

Experimental 2-Adamantanone was purchased from Aldrich with purity 99+ % and used as provided. Thermal conductivity measurements were performed by means of the uniaxial stationary steadystate method on a specially designed bath cryostat % within temperature range from 5 to 260 K. The original powder sample was transformed into a convenient cylindrical shaped solid of 5 mm diameter by mechanical pressing (ca. 1500 kg cm −2 ) for thermal conductivity measurements. Scanning Electron Microscopy pictures (see ref. ) enables us to assure the homogeneity of the prepared material without possible air inclusions. The upper error bound (≈

10

%)

mainly arises from systematic errors incurred in the measurement of geometri-

cal parameters (e.g. the inner container cross section and spacing between thermometers), whereas the statistical error in the thermal conductivity coecient was below 3 % for the whole temperature range. The heat capacity measurements were carried out using the Physical Property Measurement System (PPMS) from Quantum Design Inc. operated in the Heat Capacity Option. Accuracy for the heat capacity measurements was better than 1 %. The sample was cooled from room temperature down to 5 K at the rate of

≈

3 K min−1 and the

heat capacity of the so-obtained monoclinic phase was measured on heating. Measurements of thermal conductivity and heat capacity of the stable orthorhombic phase were performed

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on heating after the sample was quickly cycled ve times between 5 and ≈ 220 K. Heat capacity and thermal conductivity were performed up to 150 K due to the noticeable vapor pressure at higher temperatures which produced sublimation of the sample. Inelastic neutron scattering measurements were performed using the direct geometry spectrometer MARI at the ISIS facility, Rutherford Appleton laboratory. The instrument has continuous detector coverage from 3.5 -135 degrees and views the 100K liquid methane moderator on target station one. The sample of 2O-A was loaded into a aluminium sample holder with an annular geometry designed specically for liquid scattering. The sample was cooled using a top loading closed cycle refrigerator system with a temperature range of 5600K. The ordered orthorhombic phase of the material was prepared in-situ by thermally cycling the sample 5 times from 100K to 220K before nally cooling to 5K. Inelastic neutron measurements were taken at 5K with an incident energy of 18meV, selected using a fermi chopper system with a Gd foil chopper pack rotating at 200Hz. The chosen conguration of the instrument gave an elastic line resolution of 3% δE/Ei and a |Q| range of ≈0.4 ◦

−1

5A . The experimental data were treated using the MANTID software framework & using a standard method to calculate the density of states.

Results The Figure 1 shows the heat capacity as a function of temperature for the metastable monoclinic phase and for the stable orthorhombic phase. The gure highlights that at lowtemperatures the dierences in heat capacity for the aforementioned phases are negligible (see upper left inset of Figure 1) as well as the small eect on the heat capacity at the dynamical glass transition at ca. 132 K. Some measurable dierences in heat capacity for both phases are apparent at temperatures above some 100 K, that is the region where dielectric spectroscopy has shown a clear feature reminiscent of the glass transition temperature (T g ≈ 132 K). Moreover, it can be seen that the heat capacity jump at the glass transition (lower

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right inset in Figure 1) is really subtle.

102 101

104

100 10-1

103

C / mJ·mol-1·K-1

103

105

T/K 2

4

6

8 10

10 9

C / J·mol-1·K-1

Heat Capacity / mJ K-1 mol-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2

10

101

8 7 6 5 4 3

10

T/K

110

0

1

10

120

T/K

130

140

150

100

Figure 1: (Color online) Heat capacity of the monoclinic (black circles) and orthorhombic (red circles) phases as a function of temperature in a log-log scale. Blue line are values from

reference Bazyleva et al. Upper left inset is a log-log representation of the heat capacity at the lowest temperature range. Lower right inset is a magnication around the glass transition temperature of the monoclinic phase to highlight the small change of the heat capacity at the dynamical glass transition.

To account for the astoundingly close heat capacities of both crystal phases, the spectral frequency distribution or vibrational density of states (DOS) was determined at 5 K. The DOS depicted in Figure 2 shows the Debye behaviour for both phases is only followed at energies below ca. 1.5 meV, a feature common to most molecular crystals. A comparison of both distributions shows that the orthorhombic phase displays sharper low frequency features than the monoclinic crystal within the 4 to 12 energy range. Such a dierence is also understood on the basis of studies on rotator-phase crystals where molecular rotations become strongly hybridized within the phonon environment. 9,20 On the grounds of such studies we tentatively assign the sharp feature appearing at about 5 meV in the orthorhombic phase to excitations having a mixed acoustic-rotational character. The appearance of a smoother distribution for the monoclinic phase provides an additional insight into the presence of molecular motions of mostly single-particle character which may take place even at such low temperatures. A calculation of the vibrational specic heat in the harmonic approximation was carried

7



out using the experimental DOS values. The results are shown in Figure 3 where they are compared with experiment in terms of the C p /T3 form. The lowest temperature region where Cp /T3 values are constant tells that the Debye temperatures for both the disordered monoclinic and the ordered orthorhombic phases are very close and in fact yield a common value of θD =124.4 K. Because of the restricted range of temperatures available, it has not been possible to explore the region well below 1 K where a linear term characteristic of two-level systems could be expected to appear. 0.10

0.8 0.6

0.6

go

0.00

-gm

0.8

0.05

/ meV

0.4

2

4

6

0.4

)

0

g(

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0.2

0.2

0.0

0.0 0

2

4

6

8

10

12

/ meV

Figure 2: (Color online) Density of states for monoclinic (black circles) and orthorhombic (red circles) phases determined at 5 K by means of MARI spectrometer. Blue triangles correspond to the Debye approximation. Upper inset shows the dierence between densities of states of the orthorhombic and monoclinic phases in the low-energy region. Thermal conductivities for both phases are shown in Figure 4 in a log-log scale. The results coming out from such measurements are highly counterintuitive. In fact, despite the built-in disorder of the monoclinic phase, κ(T ) exhibits a temperature dependence reminiscent of an ordered crystal, although the low temperature κ(T ) ∝ T 3 dependence is absent. The maximum of κ(T ) appears at about 20 K yielding 0.78 W m −1 K−1 . This peak is a consequence of a change in the dominant phonon scattering mechanisms, from defect or boundary scattering mechanisms at low temperatures to Umklapp scattering at high temperatures which limit the thermal conductivity. In stark contrast, the conductivity of the orthorhombic phase displays values which are at least one order of magnitude lower. Fur8


0.1

0.1

C

/T p

3

/ mJ·mol

-1

·K

1

1

0.01

1

0.01 100

10 T / K

Figure 3: (Color online)Calculated (full symbols) and experimental (empty symbols) heat capacity divided by T3 for the monoclinic (black symbols) and orthorhombic (red symbols) phases in a log-log plot. thermore, the low-temperature region exhibits a dependence of T 1.38 , virtually the same as to that of some glacial-phase crystals. $ A remarkable plateau also develops at temperatures between 20 and 80 K, then leading to a strong increase.

1

-1

K

-1

Monoclinic

m

/W

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-1

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T1.38

0.1

0.01

1

Orthorhombic

10

T/K

100

Figure 4: (Color online) Thermal conductivity as a function of temperature for the monoclinic (black symbols) and orthorhombic (red symbols) phases of 2-adamantanone in a log-log plot. Continuous and dashed lines are ts (see text). Blue diamonds represent the thermal conductivity for n-butanol in the glacial phase. $

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Discussion As mentioned in the introductory paragraphs, due account of the crystal structure of the monoclinic phase of 2O-A require to position the Oxygen atoms occupying three dierent positions with rened occupancy factors of 25 %, 25% and 50%. Such an intrinsic disorder leads to large-angle molecular rotations as proven by the dielectric susceptibility ' which follow the common glassy pattern including a secondary β -relaxation. Taken at its face value, the relaxation parameters would match those for a strong glass with m ≈ 20, and a stretching exponent β KW W for the α-relaxation showing a value as low as ca. 0.5 at the temperature where the slope of the cell volume shows a kink. The case at hand strikingly contrasts with that of most disordered solids which within the low-temperature region, i.e. below 10 K, show a heat capacity well above that of the parent crystal, whereas the thermal conductivity is several orders of magnitude smaller. ! The larger heat capacity of the glass is usually associated with an excess of low-frequency vibrational excitations as proven by the vibrational density of states g( ω) and yields in the g(ω)/ω2 form to the feature known as the boson peak. In turn, thermal conductivity of disordered states tend to be lower than that of its ordered counterparts due to the sources of phonon scattering brought-in by disorder. Some recent works " however state that the main dierence between glass and crystal states arises from dierences in mass density because, at a given pressure, the specic volume for glasses is larger than that of the crystalline phase. The present data however constitutes a counterexample to such a hypothesis since the density dierences between the glass-like monoclinic phase and the fully ordered orthorhombic come to be a mere 2% over the 90-200 K range. ' Despite such a small dierence, the measured DOS reveal diverse patterns for both crystal forms. In fact, while one would expect to nd for the monoclinic phase less pronounced features in g(ω) than those apparent for the full ordered phase as a direct consequence of partial orientational disorder, a glance to Figure 3 shows that an excess of low energy vibrational states with a maximum at 4.6 meV (1.11 THz) is readily apparent. The frequency region where such excess states appear suggests that 10


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they should be coupled to sound waves # and therefore should, at low enough temperatures, behave much alike like tunneling systems known to be responsible of the anomalous thermal and transport properties of disordered matter. At this point it is pertinent to recall that tunneling systems are known to exist in crystals since long and are due to the presence of substitutional atoms which cannot easily accommodate within the crystal lattice structure. Usually, such defects dier in size and shape from the rest of atoms constituting the host crystal, " the net result of which is the generation of fairly strong strain elds. The well studied case of cubic alkali halide crystals and in particular the presence of Li or CN ions within a lattice of octahedral symmetry lead to the formation of a multi-valley potential energy landscape.

At low temperatures, the available thermal energy is not enough to

overcome the potential barriers separating the wells and tunneling through such barriers is neatly observed in its contribution to an excess of the specic heat over the Debye value. Moreover, the response to an applied DC electric eld yields a measurable dielectric loss even at millikelvin temperatures or the anomalous variation with temperature of the sound velocity. In fact, the term

orientational glass state

was coined to describe the properties of

systems such as (KBr) 1−x (KCN)x for concentrations of randomly oriented CN ions within the rage

0.05 < x < 0.55. & Detailed studies on such crystals have thus enabled the understanding

of phenomena common to those shown by amorphous materials in terms of the motion of microscopic entities such as the CN ions which execute either low angle librations or large amplitude motions, $ . % In doing so, our understanding of glassy dynamics has gone beyond the phenomenological realm where nearly all research on the properties of glassy matter is conned to. The case of 2O-A provides a promising opportunity to deepen into the nature of entities originating the anomalous low frequency response observed in the

g(ω)

vibrational

frequency distribution of the monoclinic crystal is compared to that of the fully ordered phase. As a nal remark, let us mention that the present data pertaining the specic heat seem to be at odds with some proposed correlations established between the magnitude of the excess

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heat capacity associated to the boson peak and the fragility index 28 where large values for the latter appear to correlate with low excess heat capacity as measured with respect to the Debye value Cexe . On the grounds of such a proposed correlation, one would expect for a system with a fragility value of 20 such the monoclinic phase of 2O-A an excess C exe as large as 4.5 time the reference Debye value. Our current data however set such an excess (see Fig. 3) to a gure well below 1.73C D . As a consequence, this would mean that the kind of glassy material here studied does not follow the proposed correlation. One should however notice that such an excess specic heat comes to be strikingly close to that shown by the well-ordered phases which show no feature identiable with a boson peak. A phenomenological analysis of the thermal conductivity for the monoclinic phase κm (T ) can be carried out using two competing terms, m κm (T ) = κm ph (T ) + κmin (T )

(1)

which account for propagation of acoustic phonons with long relaxation times τR (ω, T ), i.e., with mean free path larger than the lattice parameters, and for short-wave length acoustic phonons with the minimum value of τ M IN = π/ω . 2931 Both contributions give rise to the bell-like shape for κ(T ) in a double-log scale. Such a common maximum for a dielectric crystal features the change from an increase of the density of high-energy phonons at low-temperature to a rapid increase of intensity of three-phonon scatterings by the so-called Umklapp processes which strongly limit the thermal conductivity of the crystal. 32,33 The κph (T ) or Debye term is written as k4 T 3 κph (T ) = B2 3 2π h ¯ cs

ΘD /T 0

τR (x)

x4 e x dx (1 − ex )2

(2)

where x = h ¯ ω/kB T , ΘD is the Debye temperature, τR (x) is an eective relaxation time for phonon scattering, and cs is a sound velocity averaged over longitudinal and transverse polarizations. Values of ΘD and cs are obtained from the Debye behavior of heat capacity at low 12


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temperature. The contributions of the dierent phonon-scattering processes are introduced into the relaxation time

τR (x)

by means of the Mattiessen's rule,

−1 −1 + τimp τR (ω, T )−1 = τU−1 + τdis

(3)

where the individual terms are given by,

τU−1

2

= Bω T exp

−EU T

(4)

corresponding to Umklapp processes,

τd−1 = Dd ω

(5)

−1 = Cimp ω 4 τimp

(6)

for dislocations and

for Rayleigh scattering (i.e. scattering due to impurities). Within the last equations the activation energy of the Umklapp processes for which B is a frequency factor, scattering strength for dislocations, and scattering. The

κm min (T )

A

and

D,

κ(T )

is the

is the parameter accounting for the Rayleigh

at temperatures beyond the maximum. This term can

κm min (T ) = A/T +D .

By plotting

κ(T )·T

as a function of T, the constants

accounting for three-phonon Umklapp processes and all scattering mechanisms

leading to the deviation of the

κph (T )

is

contribution is derived from the Cahill-Pohl model, which provides

the temperature dependence of be parametrized as

Cimp

Ddis

EU

T −1

dependence beyond the phonon maximum, respectively,

can be determined by subtraction to the experimental

κ(T ).

Subsequently,

κm ph (T )

was tted according to Eq. 2 by inserting Eq. 3 and Eqs 4, 5 and 6. Results are consigned in Table I and ts are depicted in Figure 4. As far as the orthorhombic phase is concerned,

13

κo (T ) looks like the shape of very defective



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crystals, 6,34,35 very dierent from that of a typical stable crystalline phase. It shows a smeared out maximum at ca. 30 K and from the lowest temperature to such a maximum it grows as T 1.38 . On these grounds, thermal conductivity is analyzed by considering two contributions:

κo (T ) = κoph (T ) + κoh (T )

(7)

where (i) the rst term accounts for the classical phonon-phonon or Debye scattering, and (ii) the second accounts for hopping of localized vibrations via a thermally activated hooping process. The last contribution, within the simplest model, is described by a single activation energy Ea as:

κoh (T ) = κoho exp(−Ea /T )

(8)

where κoho is a constant. The data of thermal conductivity for the orthorhombic phase was analyzed by means eq. 7, where the κoph (T ) was tted according to 2 and Eq. 3 to 6 and κoh (T ) according to eq. 8. The so-obtained parameters of the excellent t (see Figure 4) are gathered in Table 1. The gures quoted in Table 1 show that the Umklapp process is, as expected, virtually independent of the analyzed phase. Similar results were obtained for stable and metastable phases of Cyclohexanol 36 and that the large dierence for the Debye contribution concerns the term accounting for dislocations, Ddis (two-dimensional defects mainly at the grain boundaries). This result matches perfectly the morphology of the orthorhombic phase. We should recall here that orthorhombic phase is obtained by cycling (between 77 and 220 K) and that such a procedure gives rise to small crystals with at surfaces and sharp edges of a size smaller than 20 μm, which act as strong acoustic scatterers. 10 Thus the thermal conductivity variation with temperature is reminiscent of defective crystals (as indicated by the quoted value of Ddis and published 10 SEM pictures). Figures also show up a dierence for the Rayleigh term, due to the presence of local defects. Similar results were found for the so-called glacial phase of n-butanol (see gure 4 in which for sake of comparison thermal conductivity of such phase is shown). For n-butanol, a mixture of nano-crystalline grains

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embedded in a disordered matrix gives rise to a similar thermal conductivity variation. In other words, phonon scattering is dominated by the scattering at the grain boundaries.

Table 1: Parameters of the U-processes, dislocations and Rayleigh obtained from the ts of thermal conductivity data for monoclinic and orthorhombic forms of 2adamantanone as well as the energy for the thermally activated hooping process Ea . Specic volumes were obtained from at 100 K Property

v Cs θD Ddis · 104 Cimp · 1040 B · 1016 EU Ea

Units Monoclinic Orthorhombic (cm3 · mol−1 ) 119.3 117.1 (m · s−1 ) 2280 2250 (K) 124.4 124.4 46 510 ( s3 ) 0.2 2.0 (s · K −1 ) 3.8 3.8 (K) 30 30 (K) 700

To wrap up this section it is worth pointing out the close similarity of exponents yielding the power law dependence of the conductivity below some 10 K of the ordered crystal and the allegedly glacial state of some materials such as n-butanol. $ Our results thus add further support to the interpretation of such anomaly in thermal transport as due to the presence of a mixture of two dierent coexisting phases as proposed by some of us. $

Conclusions The experiments here reported on provide some contrasting evidence pertaining to properties which characterize disordered matter either in the dynamic or thermodynamic realms. In fact, spectroscopic data derived from neutron scattering lend further support to dielectric and microstructural data, all showing clear signatures of glassy dynamics on a crystal showing minimal disorder. In contrast, if one were led to infer the presence of dynamic features brought forward by disorder from the two thermodynamic properties at prima facie could easily entail wrong conclusions. The results reported here thus warn against using oversimplied statements and conjectures concerning the thermal properties of disordered matter versus those of their parent crystals. Here we have shown that well known sources of 15 ACS Paragon Plus Environment


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phonon scattering in nely divided matter may yield deceptive results which may led to infer from data regarding highly-defective crystals the presence of some new phases of matter (i.e. glacial states). The material studied here opens up an interesting opportunity for further studies at lower temperatures to explore whether the large-angle rotations evidenced at higher temperatures may transform into tunneling entities in the low temperature realm as happens for bulky CN or ionic moieties 26,27 in alkali halide crystals. Although the origin of the excess of vibrational modes giving rise to the deviation of the Debye dependence of the density of states, and thus to the deviation of the specic heat Debye law are generally attributed to the presence of disorder in glasses with the appearance of the Boson peak, this work, together with some other recent publications 24,37 questions such belief. In these works it is proposed that the propose that the Boson peak in the phonon density of states of crystals and glasses appears due to the existence of low-energy phonons and that thermal conductivity is probably intrinsically associated with the existence of disorder. In our case, we also clearly demonstrate that glassy features can also appear in thermal conductivity of well-ordered crystals and that for crystals with well-dened disorder can display the common crystalline behavior. Whatever the case, phonon density of states reveals the existence of low-energy excitations. Thus, the study of simple systems, i.e., with subtle and controlled disorder, and their ordered counterparts open a great opportunity to address the topical and the unsolved problem of the glass state.

Acknowledgement This work was supported by the Spanish Ministry of Science and Innovation (Grant FIS201124439) and the Catalan Government (Grant 2014SGR-00581). One of us (A.I.K.) thanks the Spanish Ministry (SB2011-0070) for an invited position at the Universitat Politècnica de Catalunya.

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Glassy Dynamics versus Thermodynamics: The Case of 2

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