Do tunneling states and boson peak persist or disappear in extremely stabilized glasses?

We review and concurrently discuss two recent works conducted by us, which apparently give opposite results. Specifically, we have investigated how extreme thermal histories in glasses can affect their universal properties at low temperatures, by studying: (i) amber, the fossilized natural resin...

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Datum:	2015
Hauptverfasser:	Ramos, M.A., Pérez-Castañeda, T., Jiménez-Riobóo, R.J., Rodríguez-Tinoco, C., Rodríguez-Viejo, J.
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Veröffentlicht:	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2015
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Schlagworte:	10th International Conference on Cryocrystals and Quantum Crystals
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spelling	irk-123456789-1278242017-12-29T03:03:02Z Do tunneling states and boson peak persist or disappear in extremely stabilized glasses? Ramos, M.A. Pérez-Castañeda, T. Jiménez-Riobóo, R.J. Rodríguez-Tinoco, C. Rodríguez-Viejo, J. 10th International Conference on Cryocrystals and Quantum Crystals We review and concurrently discuss two recent works conducted by us, which apparently give opposite results. Specifically, we have investigated how extreme thermal histories in glasses can affect their universal properties at low temperatures, by studying: (i) amber, the fossilized natural resin, which is a glass which has experienced a hyperaging process for about one hundred million years; and (ii) ultrastable thin-film glasses of indomethacin. Specific heat Cp measurements in the temperature range 0.07 K < T < 30 K showed that the amount of two-level systems, assessed from the linear term at the lowest temperatures, was exactly the same for the pristine hyperaged amber glass as for the subsequently rejuvenated samples, whereas just a modest increase of the boson-peak height (in Cp/T³) with increasing rejuvenation was observed, related to a corresponding increase of the Debye coefficient. On the other hand, we have observed an unexpected suppression of the two-level systems in the ultrastable glass of indomethacin, whereas conventionally prepared thin films of the same material exhibit the usual linear term in the specific heat below 1 K ascribed to these universal two-level systems in glasses. By comparing both highly-stable kinds of glass, we conclude that the disappearance of the tunneling two-level systems in ultrastable thin films of indomethacin may be due to the quasi-2D and anisotropic behavior of this glass, what could support the idea of a phonon-mediated interaction between two-level systems. 2015 Article Do tunneling states and boson peak persist or disappear in extremely stabilized glasses? / M.A. Ramos, T. Pérez-Castañeda, R.J. Jiménez-Riobóo, C. Rodríguez-Tinoco, J. Rodríguez-Viejo // Физика низких температур. — 2015. — Т. 41, № 6. — С. 533-540. — Бібліогр.: 45 назв. — англ. 0132-6414 :PACS: 65.60.+a, 64.70.P–, 63.50.Lm, 81.40.Cd http://dspace.nbuv.gov.ua/handle/123456789/127824 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	10th International Conference on Cryocrystals and Quantum Crystals 10th International Conference on Cryocrystals and Quantum Crystals
spellingShingle	10th International Conference on Cryocrystals and Quantum Crystals 10th International Conference on Cryocrystals and Quantum Crystals Ramos, M.A. Pérez-Castañeda, T. Jiménez-Riobóo, R.J. Rodríguez-Tinoco, C. Rodríguez-Viejo, J. Do tunneling states and boson peak persist or disappear in extremely stabilized glasses? Физика низких температур
description	We review and concurrently discuss two recent works conducted by us, which apparently give opposite results. Specifically, we have investigated how extreme thermal histories in glasses can affect their universal properties at low temperatures, by studying: (i) amber, the fossilized natural resin, which is a glass which has experienced a hyperaging process for about one hundred million years; and (ii) ultrastable thin-film glasses of indomethacin. Specific heat Cp measurements in the temperature range 0.07 K < T < 30 K showed that the amount of two-level systems, assessed from the linear term at the lowest temperatures, was exactly the same for the pristine hyperaged amber glass as for the subsequently rejuvenated samples, whereas just a modest increase of the boson-peak height (in Cp/T³) with increasing rejuvenation was observed, related to a corresponding increase of the Debye coefficient. On the other hand, we have observed an unexpected suppression of the two-level systems in the ultrastable glass of indomethacin, whereas conventionally prepared thin films of the same material exhibit the usual linear term in the specific heat below 1 K ascribed to these universal two-level systems in glasses. By comparing both highly-stable kinds of glass, we conclude that the disappearance of the tunneling two-level systems in ultrastable thin films of indomethacin may be due to the quasi-2D and anisotropic behavior of this glass, what could support the idea of a phonon-mediated interaction between two-level systems.
format	Article
author	Ramos, M.A. Pérez-Castañeda, T. Jiménez-Riobóo, R.J. Rodríguez-Tinoco, C. Rodríguez-Viejo, J.
author_facet	Ramos, M.A. Pérez-Castañeda, T. Jiménez-Riobóo, R.J. Rodríguez-Tinoco, C. Rodríguez-Viejo, J.
author_sort	Ramos, M.A.
title	Do tunneling states and boson peak persist or disappear in extremely stabilized glasses?
title_short	Do tunneling states and boson peak persist or disappear in extremely stabilized glasses?
title_full	Do tunneling states and boson peak persist or disappear in extremely stabilized glasses?
title_fullStr	Do tunneling states and boson peak persist or disappear in extremely stabilized glasses?
title_full_unstemmed	Do tunneling states and boson peak persist or disappear in extremely stabilized glasses?
title_sort	do tunneling states and boson peak persist or disappear in extremely stabilized glasses?
publisher	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate	2015
topic_facet	10th International Conference on Cryocrystals and Quantum Crystals
url	http://dspace.nbuv.gov.ua/handle/123456789/127824
citation_txt	Do tunneling states and boson peak persist or disappear in extremely stabilized glasses? / M.A. Ramos, T. Pérez-Castañeda, R.J. Jiménez-Riobóo, C. Rodríguez-Tinoco, J. Rodríguez-Viejo // Физика низких температур. — 2015. — Т. 41, № 6. — С. 533-540. — Бібліогр.: 45 назв. — англ.
series	Физика низких температур
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first_indexed	2025-07-09T07:48:36Z
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fulltext	© M.A. Ramos, T. Pérez-Castañeda, R.J. Jiménez-Riobóo, C. Rodríguez-Tinoco, and J. Rodríguez-Viejo, 2015 Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 6, pp. 533–540 Do tunneling states and boson peak persist or disappear in extremely stabilized glasses? M.A. Ramos and T. Pérez-Castañeda Laboratorio de Bajas Temperaturas, Departamento de Física de la Materia Condensada Condensed Matter Physics Center (IFIMAC) and Instituto de Ciencia de Materiales “Nicolás Cabrera” Universidad Autónoma de Madrid, Cantoblanco, Madrid E-28049, Spain E-mail: miguel.ramos@uam.es R.J. Jiménez-Riobóo Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC), Cantoblanco, Madrid E-28049, Spain C. Rodríguez-Tinoco and J. Rodríguez-Viejo Nanomaterials and Microsystems Group, Physics Department, and MATGAS Research Centre Universitat Autónoma de Barcelona, Bellaterra E-08193, Barcelona, Spain Received September 4, 2014, published online April 23, 2015 We review and concurrently discuss two recent works conducted by us, which apparently give opposite re- sults. Specifically, we have investigated how extreme thermal histories in glasses can affect their universal prop- erties at low temperatures, by studying: (i) amber, the fossilized natural resin, which is a glass which has experi- enced a hyperaging process for about one hundred million years; and (ii) ultrastable thin-film glasses of indomethacin. Specific heat Cp measurements in the temperature range 0.07 K < T < 30 K showed that the amount of two-level systems, assessed from the linear term at the lowest temperatures, was exactly the same for the pristine hyperaged amber glass as for the subsequently rejuvenated samples, whereas just a modest increase of the boson-peak height (in Cp/T 3 ) with increasing rejuvenation was observed, related to a corresponding in- crease of the Debye coefficient. On the other hand, we have observed an unexpected suppression of the two-level systems in the ultrastable glass of indomethacin, whereas conventionally prepared thin films of the same material exhibit the usual linear term in the specific heat below 1 K ascribed to these universal two-level systems in glasses. By comparing both highly-stable kinds of glass, we conclude that the disappearance of the tunneling two-level systems in ultrastable thin films of indomethacin may be due to the quasi-2D and anisotropic behavior of this glass, what could support the idea of a phonon-mediated interaction between two-level systems. PACS: 65.60.+a Thermal properties of amorphous solids and glasses: heat capacity, thermal expansion, etc.; 64.70.P– Glass transitions of specific systems; 63.50.Lm Glasses and amorphous solids; 81.40.Cd Solid solution hardening, precipitation hardening, and dispersion hardening; aging. Keywords: low-temperature thermal properties of glasses; specific heat; glass transition; tunneling two-level sys- tems; ultrastable glasses 1. Introduction Glasses and amorphous solids, in general, and even some disordered crystalline solids, exhibit thermal and acoustic properties at low temperatures anomalously dif- ferent from those found in crystalline solids [1,2]. Fur- thermore, these low-temperature glassy properties show a remarkable degree of universality for any glass, irrespec- tive of the type of material, chemical bonding, etc. Hence the low-temperature properties of noncrystalline solids are said to exhibit a universal “glassy behavior”. In particular, below about 1 K the specific heat of glasses depends quasilinearly on temperature, Cp T 1+ , and the thermal conductivity almost quadratically, T 2− , in clear con- mailto:miguel.ramos@uam.es M.A. Ramos, T. Pérez-Castañeda, R.J. Jiménez-Riobóo, C. Rodríguez-Tinoco, and J. Rodríguez-Viejo 534 Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 6 trast with the cubic dependences successfully predicted by Debye theory for crystals. On the other hand, the thermal behavior of glasses above 1 K and their corresponding low-frequency vibrational properties around 1 THz, are dominated by another universal but most controversial feature of glasses: the so-called “boson peak” [2,3] arising from a noteworthy excess in the vibrational density of states (VDOS) over that predicted by Debye’s theory g( ) 2 . Such an excess in the low-frequency VDOS appears as a broad peak in g( )/ 2 , which produces a cor- responding broad maximum in Cp/T 3 , observed in glasses at typically 3−10 K [2]. The formerly mentioned thermal properties of glasses below 1 K, as well as related acoustic and dielectric pro- perties of amorphous solids at low temperatures [2], were since long successfully accounted for [4,5] by the Tun- neling Model (TM). The core idea of the TM is the ubiq- uitous existence of atoms or groups of atoms in amor- phous solids due to the intrinsic atomic disorder, which can perform quantum tunneling between two configura- tions of very similar energy, usually named tunneling states or two-level systems (TLS). Nevertheless, a very few authors [6,7] raised later strong criticisms against the standard TM, pointing out how improbable was that a ran- dom ensemble of independent tunneling states would pro- duce essentially the same universal constant for the ther- mal conductivity or the acoustic attenuation in any sub- stance. Most experimentalists, however, have continued to trust the TM, given its both simplicity and apparent suc- cess to account for the experimental data. As said above, the thermal properties of glasses above 1 K and their low- frequency vibrational spectrum dominated by the boson peak at 1 THz, are still much more controversial and poor- ly understood [3]. In this article we present and discuss together two re- cent experimental works [8,9] conducted by us, aimed at investigating whether this universal behavior of glasses persists or not in glasses subjected to unusually strong pro- cesses of thermodynamic and kinetic stabilization. Specifi- cally, we have studied two very different kinds of extreme- ly stable glasses. First, we have measured the specific heat of 110 million-year-old amber samples from the cave of El Soplao (Spain), both at very low temperatures and around the glass transition Tg [8]. Amber is essentially a fossilized tree resin that polymerized millions of years ago. Of inter- est here, amber is a unique example of a (polymer) glass that has aged far longer than any system accessible in the laboratory, thus reaching a state (of lower enthalpy and entropy) which is not accessible under normal experi- mental conditions. In other words, it is an amorphous solid or glass which has experienced an extreme thermodynamic stabilization process (hyperageing) [10]. Second, we have also studied the specific heat of ultrastable glasses of in- domethacin [9]. So-called ultrastable glasses, showing un- precedented thermodynamic and kinetic stability, have recently been synthesized by physical vapor-deposition of several organic molecules in short-time scales [11 16]. An appropriate deposition rate in combination with an opti- mal substrate temperature (typically around 0.85 Tg) have proved to drastically favour two-dimensional mobility and, as a consequence, access to local minima of very low energy in the potential-energy landscape [17,18]. An ordinary glass obtained by supercooling the liquid should theoretically be aged for 10 3 10 9 years in order to achieve the same stability and density of these vapor- deposited glasses [19]. Interestingly, we have found clear-cut but opposite re- sults in the two cases. Although this makes it more difficult to draw a simple conclusion, it certainly provides us with complementary information to shed light on the long- standing mystery of the nature of low-energy excitations in glasses, responsible for the universal glassy behavior at low temperatures. 2. Experimental techniques The samples of amber used in these experiments [8] were obtained from a new amber deposit discovered quite recently in the northern region of Spain, in Cantabria, within El Soplao territory [20], and have been dated to be 110–112 million years old. When necessary, raw pieces of amber were cleaved or slowly cut with a diamond wheel, and then simply cleaned with distilled water. After being completely measured and characterized, some pris- tine samples of amber were either partially or totally re- juvenated, by means of an isothermal annealing process at Tg = 423 K during 2 hours or by heating the sample well above Tg followed by cooling at 1 K/min, respec- tively [8]. Other different thermal treatments conducted to study in detail the calorimetry and thermodynamics around the glass transition can also be seen in [8]. The Debye contribution to the specific heat was independent- ly determined for the three samples studied at low tem- peratures from the experimental values of the sound ve- locity and mass density. The longitudinal sound velocity was measured in the temperature range 80 K ≤ T ≤ 300 K using High Resolution Brillouin Spectroscopy (HRBS), with excitation wavelength λ0 = 514.5 nm, and extrapo- lated to 0 K with a least-squares fit, as shown in Fig. 1 and in Table 1. Polished plan-parallel slabs of amber, less than 0.5 mm thick were employed. Both backscattering (180º) and right-angle (90ºA) geometries were simultane- ously used, the former implying a refractive-index de- pendent acoustic wave vector and the latter being inde- pendent of it. Given the high background signal intro- duced by the luminescence of the samples at these wavelenghts, the transverse sound velocities vT could not be measured by HRBS. However, the zero-temperature values vT (0) could be approximately obtained by means of the generalized Cauchy equation [8,21], and are also Do tunneling states and boson peak persist or disappear in extremely stabilized glasses? Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 6 535 displayed in Table 1. The mass density of the three sam- ples was measured at room temperature by means of the Archimedes method with a Mettler Toledo AB 265-S balance, using distilled water as a fluid. Linear extrapola- tion of the mass densities to zero temperature were done by recourse to the Lorenz–Lorentz relation between mass density ρ(T) and refractive index n(T) for a transparent medium, after our HRBS measurements as a function of temperature in the range 80 K < T < 300 K. Indomethacin (C19H16ClNO4, Tg = 315 K, Tm = 428 K) crystalline powders with 99% purity were purchased from Sigma–Aldrich. The fabrication of the ultrastable glass of indomethacin (IMC) [9] was done under ultrahigh-vacuum conditions P < 10 –8 mbar, by vapor-depositing the organic molecule onto a silicon substrate kept isothermally at tem- perature Tsubs = 0.85·Tg = 266 K. The deposition rate for the samples presented here was kept constant at ~0.1 nm/s, which was observed to produce samples with optimal sta- bility. The growth rate was (0.15 ± 0.05) nm/s. The thick- ness of the films ranged from 50 to 80 μm, in order to en- hance the signal-to-noise ratio in the low-T specific-heat measurements. All samples were stored in vacuum-sealed bags with desiccant in a freezer to minimize aging prior to the low-T specific heat measurements. Low-temperature data of the ultrastable glasses in high vacuum was acquired few days after preparation, with the exception of a sample stored in those conditions for two months, named “degrad- ed” ultrastable glass. We also carried out x-ray diffraction (XRD) measurements using an X’Pert diffractometer from Phillips in the Bragg–Brentano configuration with Cu Kα radiation, in order to confirm the glassy nature of the as- grown samples. The samples were scanned in Bragg–Bren- tano geometry from 2θ = 2° to 300 with an angular step of 0.025° (0.05°) and time per point of 18 (12) s for the ultrastable and conventional IMC glasses, respectively. We also conducted experiments at the beamline ID28 of the European Synchrotron Radiation Facility (ESRF), with the energy of the x rays set to 23.725 eV. Photons were detect- ed with a photodiode with the sample aligned parallel (in- plane) or perpendicular (out-of-plane) to the detector axis (see Fig. 3 of Ref. 9). Calorimetric characterization of amber through the dif- ferent stages of rejuvenation (thermodynamic destabiliza- tion) was performed using a commercial DSC Q100 from TA Instruments. The technique employed was tempera- ture-modulated differential scanning calorimetry (TM- DSC), which allowed us to independently determine ther- modynamic and kinetic stability via reversing and non- reversing contributions to the heat capacity, as well as the total heat capacity [8]. Heating and cooling rates employed were always ±1 K/min, and modulating signals ±0.5 K every 80 s. To characterize the calorimetric behavior of different glasses and crystals of IMC, a DSC Perkin Elmer 7 was used with heating scans at a rate of 10 K/min on IMC thin films with masses of the order of 8 11 mg. Whereas the first scan usually corresponds to an ultrastable glass, the second upscan is characteristic of a conventional glass obtained by cooling the liquid at 10 K/min. Table 1. Calorimetric data for amber: Glass-transition temperatures * gT and fictive temperatures Tf obtained after the different ther- mal histories applied to the studied samples. 0 0( )/f f fT T T displays the relative decrease of the fictive temperature Tf in relation to the canonical reference glass obtained after fully rejuvenation and cooling at 10 K/min. Elastic data: measured mass density at room tem- perature ρRT and zero-temperature extrapolated ρ(0), longitudinal vL(0) and transverse vT(0) sound velocity, average Debye velocity in the zero-temperature limit vD and correspondingly calculated cubic Debye coefficient cD for the specific heat. Sample State *, KgT Tf, K 0 0( )/f f fT T T RT, kg/m 3 (0), kg/m 3 vL(0), m/s vT(0), m/s vD, m/s cD, J·g 1 ·K 4 Pristine (hyperaged) 438 384 7.7% 1045 1055 3175 1635 1831 18.9 Partially rejuvenated rejuvenated 436 391 6.0% 1038 1049 3160 1625 1820 19.3 Fully rejuvenated (canonical glass) 423 416 0% 1024 1035 3115 1596 1788 20.7 Fig. 1. Temperature dependence of the longitudinal sound veloci- ties in amber from El Soplao with decreasing stability, measured by High Resolution Brillouin Spectroscopy. Least-squares fits of the experimental data in the temperature range 80 K ≤ T ≤ 300 K are used to calculate the zero-temperature extrapolation prs Lv (0 K) = 3175 m/s, ann Lv (0 K) = 3160 m/s and rej Lv (0 K) = 3115 m/s, for the pristine, annealed (= partially rejuvenated) and fully rejuvenated samples, respectively. M.A. Ramos, T. Pérez-Castañeda, R.J. Jiménez-Riobóo, C. Rodríguez-Tinoco, and J. Rodríguez-Viejo 536 Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 6 In all cases, the low-temperature specific heat in the temperature range from 0.07 K to 30 K was measured by means of thermal relaxation calorimetry [20]. Low- temperature specific-heat measurements in the range 1.8 K <T <30 K were performed in a double-chamber in- sert, placed in a 4 He cryostat. Measurements in the range 0.07 K <T <3 K were performed in a dilution refrigerator Oxford Instruments MX400. In the case of amber samples, calorimetric cells consisted of a sapphire disc, on which a small calibrated thermometer (either Cernox or RuO2, re- spectively) and a resistive chip as a Joule heater were glued diametrically opposed using cryogenic varnish GE7301. The sapphire substrate is suspended from a cop- per ring acting as thermally-controlled sink. In the case of IMC samples, those used for the low-temperature specific- heat measurements were all grown on silicon substrates of dimension 12×12 mm, and with typical masses m ≈ 0.1g, what enabled us the handling of the samples, as well as optimal attachment and thermal contact to the calorimetric cell. The main thermal contact between the calorimetric cell and the thermal bath is a thin metallic wire through which heat is released. The heat capacity of the empty ad- denda was independently measured in each case and sub- tracted from the total data points. Excellent agreement was found between experimental data from both experimental setups in the overlapping temperature range. 3. Experimental results 3.1. Amber The first and most important characterization of the amber samples was to perform DSC experiments to con- firm their presumed hyperaging and corresponding ther- modynamic stabilization. As can be seen in Fig. 2(a) of Ref. 8, a huge endothermic peak is observed for the pris- tine amber at the calorimetric glass-transition (strictly speaking, devitrification) temperature gT = 438 K (here determined by the inflection point of the reversing Cp jump). gT is well above the genuine glass transition tem- perature Tg = 423 K obtained for the rejuvenated sample, or alternatively from the second or third heating runs for any sample, when the cooling and heating rates are canoni- cally the same. This unusual increase of the calorimetric gT for the stabilized amber compared to the canonical glass (see Table 1) is also observed in the case of ultrastable glasses of IMC, and has been ascribed [11] in ultrastable glasses obtained from physical vapor deposition to a high kinetic stability, indicating that much higher tem- peratures are needed to dislodge the molecules from their glassy configurations. From the calorimetric curves, the enthalpy as a function of temperature was obtained by direct integration. It is tra- ditional and useful to determine the so-called fictive tem- perature Tf, defined as the temperature at which the nonequilibrium (glass) state and its equilibrium (super- cooled liquid) state would have the same enthalpy. The obtained values of Tf for the pristine, partially rejuvenated and fully rejuvenated samples are displayed in Table 1. The observed extraordinary decrease Tf = −32 K (ther- modynamic stability) for the pristine amber compared to the rejuvenated glass is similar or even superior to the ef- fects seen in some ultrastable thin films of organic glasses [11,19,23]. Such an extraordinary reduction 8% of the fictive temperature due to the extremely long aging of am- ber is indeed the consequence of extremely prolonged sub- sub-Tg structural relaxations [24]. In Fig. 2, we present our consecutive specific-heat measurements for an amber sample in three different states: pristine, partially-rejuvenated (after annealing at 423 K for 2 h) and fully-rejuvenated. Fig. 2(a) is a log-log plot at the lowest temperatures, which emphasizes that the TLS-dominated specific heat below 1 K, remains invaria- ble within experimental error. On the other hand, above 1 K the specific heat moderately increases with rejuvena- tion around the “boson peak” in Cp/T 3 , see Fig. 2(b), fol- lowing the same trend as the elastic Debye coefficient ob- tained from both Brillouin-scattering sound velocity (Fig. 1) and mass-density measurements (see Table 1). However, the position of the peak remains fixed at (3.4 0.1) K in all cases. 3.2. Indomethacin We measured the specific heat of the two above- mentioned ultrastable glasses (USG) of 50 μm- (USG-1) and 80μm- (USG-2) thin films, grown under slightly dif- ferent conditions, as well as of a conventionally prepared glass and of the crystalline state (in this case, we measured only above 2 K, since the cubic Debye limit had been al- ready reached, allowing a direct extrapolation to lower temperatures). Finally, also a degraded ultrastable glass, after being stored for two months in poor vacuum condi- tions, hence absorbing water and losing its ultrastability, was measured. Similarly to the case of amber samples, we display the low-temperature specific heat measurements of different states of IMC in two complementary plots: Fig. 3(a) depicts the whole specific-heat data in the Debye- reduced Cp/T 3 representation, where as Fig. 3(b) amplifies the very-low-temperature region in the usual Cp/T vs T 2 Table 2. Coefficients and statistical errors obtained from least-squares linear fits at low temperatures to the function Cp = = cTLS·T + cD·T 3 for indomethacin (see Fig. 3) cTLS, J/g·K 2 cD, J/g·K 4 Crystal 15.0 0.3 Conventional glass 13.7 0.3 49.4 0.2 Ultrastable glass #1 0.2 0.9 46.4 0.6 Ultrastable glass #2 0.02 0.8 36.9 0.4 Degraded USG 13.0 0.7 40.6 0.5 Do tunneling states and boson peak persist or disappear in extremely stabilized glasses? Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 6 537 plot where a least-squares linear fit provides the TLS linear term (the intercept with the y axis) and the Debye coeffi- cient (the slope). The crystal of indomethacin exhibits the expected Cp T 3 below 8 K. The same shoulder-like be- havior (a very shallow boson peak, as typically occur in other fragile glass formers [25]) is observed in both ultrastable and ordinary glasses below ~5 K in Fig. 3(a). Nevertheless, the most surprising behavior found in both ultrastable glasses is the full suppression of the linear term of the specific heat ascribed to the tunneling TLS. This is demonstrated in Fig. 3(b), where the intercept with the ordinate axis goes to zero within experimental error (see Table 2), in clear contrast with the case of convention- al glass, or even for the degraded ultrastable glass. 4. Discussion Whether or not the low-temperature universal “anoma- lies” of glasses (dominated by low-energy excitations not present in crystals, i.e., tunneling TLS and the boson peak) could be eventually suppressed by much stronger and longer annealing or ageing processes, and hence whether they are or not intrinsic properties of the glass state, has been an unsolved question during the last forty years. In- deed, different experiments [26 32] have been reported Fig. 2. Specific-heat data for three different states (pristine, par- tially-rejuvenated and fully-rejuvenated) of the same amber sam- ple at very low temperatures, 0.05–2 K. The upper dashed line shows the best quasilinear fit Cp T 1 to the experimental data below 0.4 K given by Cp T 1.27 , hence faster than the simple linear dependence indicated by the lower dashed line (a). Cp /T 3 plot of the same data in (a), displayed in a wider temperature range. The height of the boson peak is observed to further in- crease with rejuvenation, though the values of both the minimum and the maximum of Cp/T 3 remain constant: Tmin = (1.2 0.1) K and Tmax = (3.4 0.1) K, respectively. The corresponding Debye levels determined from the sound velocity and density data (Ta- ble 1) are indicated by solid lines, and exhibit the same trend as the boson-peak height (both sets follow the same order as the symbols in the legend) (b). Fig. 3. Low-temperature specific-heat data for two differently pre- pared ultrastable glasses of indomethacin: 50 μm- (USG-1) and 80μm- (USG-2) thin films, compared to the crystalline phase (De- bye extrapolated at lower temperatures) and the conventional glass. A degraded ultrastable glass (see Experimental techniques) has also been measured and is presented. Dashed lines show the correspond- ing linear fits CP = cTLS·T + cD·T 3 for experimental data below 2 K. Debye-reduced CP/T 3 vs T representation (a); CP/T vs T 2 plot at very low temperatures to determine the TLS and Debye coeffi- cients, which are shown in Table 2 (b). M.A. Ramos, T. Pérez-Castañeda, R.J. Jiménez-Riobóo, C. Rodríguez-Tinoco, and J. Rodríguez-Viejo 538 Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 6 about the possible influence of the thermal history on these low-temperature properties, but with contradictory conclu- sions (see a more detailed discussion on those experiments in Ref. 8). Besides, there have been a few reports [33 36] claiming the absence of TLS in some particular amorphous solids. Angell et al. [37] proposed the designation of “superstrong liquids” for some “tetrahedral liquids” which could be potential “perfect glasses”, with a residual entro- py near zero, and where the defect-related boson peak and TLS excitations were weak or absent. Specifically, they identified two examples where TLS had been reported to be absent: (i) amorphous silicon; (ii) low-density amor- phous water. Let us begin with the boson peak. From our experi- ments in amber, it is clear that this vibrational excess over the Debye level persists in such a hyperaged glass. Notice that its position does not vary with rejuvenation, though a modest increase of its height is observed following the increase of the elastic Debye level. In addition, a strong boson peak in Cp/T 3 had already been observed by us in (20 million years old) Dominican amber [10], though ap- parent residual curing or repolymerization, occurring around the glass transition temperature when rejuvenating those amber samples, hindered a reliable quantitative in- vestigation. Although some authors have tried to correlate the boson peak feature in glasses [38], and even in crystals [39], with transformations of the elastic continuum only, such a Debye-scaling rule is not hold quantitatively in our case. The height of the Cp/T 3 boson peak in the hyperaged amber has decreased a 22% from the standard rejuvenated glass, whereas a Debye scaling [38] 3( ,D with D being the Debye frequency) would predict only a 7.4% reduction. Unfortunately, a similar discussion on the boson peak in ultrastable glasses of indomethacin is not possible since this feature is hardly seen in the specific-heat curves of this glass. Nevertheless, the best fingerprint of the universal glassy anomalies is surely the density of TLS, measured from the corresponding quasilinear contribution to the specific heat, since the influence of Debye-like lattice vibrations be- comes less and less important below 1 K. In this respect, our experimental results are conclusive: pristine, partially- rejuvenated and fully-rejuvenated amber glasses have the same specific heat below 1 K, within experimental error. Therefore, the boson peak and, especially, the tunneling TLS are robust and intrinsic properties of glasses which remain “fossilized” in 110-million-year stabilized glasses of amber. After this finding, our later results in ultrastable glasses of indomethacin were quite unexpected. As clearly demonstrated in Fig. 3 and Table 2, these USG exhibited a full suppression (within experimental error) of the TLS contribution to the specific heat, whereas similar glasses of the same substance lacking such ultrastability exhibited a typical contribution. Without the experiments on amber, one would be tempted to ascribe the found suppression of the TLS in ultrastable glasses of IMC to the extraordinary stability (either thermodynamic or structural) of these par- ticular glasses, and its corresponding large reduction in enthalpy or entropy, in the line of the “perfect glasses” mentioned above. An alternative approach is the Random First Order Theory (RFOT) that explains the “universality” of TLS behavior at low temperature by the universality of the dy- namical correlation length at Tg [40,41]. As such RFOT predicts that ultrastable glasses [42] should have a dimin- ished density of two level systems. With the argument about the faster relaxation at glass surfaces that allows the correlation length to grow, the expected reduction in TLS should be roughly by a factor of between 4 and 8 [43]. This would go in the line of our experiments, though a full sup- pression is not explained. Rather, we believe that the reason should be sought in some particularities of the ultrastable glass of indometha- cin. In fact, some glasses obtained by physical vapor depo- sition show evidence of molecular anisotropy which is partly due to the growth method of thin films from the va- por phase. In particular, ultrastable IMC glasses exhibit an extra, low-q, peak in wide-angle x-ray scattering (WAXS) spectra [44] and birrefrigence in ellipsometric measure- ments [45]. In our experiments [9] we have shown that the low-q peak appears indeed in the WAXS pattern of our vapor-deposited ultrastable glass, whereas it is absent in the conventionally prepared glass. The presence of this peak for the ultrastable glass should be related to some sort of molecular order along the growth direction, perpendicu- lar to the substrate, as clearly revealed in the in-plane/out- of plane diffraction experiments [9]. This orientation may be enabled by the high mobility of the indomethacin mole- cules when they impinge the substrate surface from the vapor [44]. The layered and anisotropic character of the USG of IMC could hence be the key of the observed be- havior. As mentioned in the Introduction, it has been stressed [6,7] that, in addition to the unexplained universality of the TM fitting parameters, the model in its original form ne- glects the fact that as a result of interaction with the strain (phonon) field, the tunneling TLS must acquire a mutual interaction. It can be shown [6,7] that the effective interac- tion between two TLS separated by a distance r is dipolar elastic and the interaction strength goes as g/r 3 , with g = = γ 2 /ρv 2 , where γ is the TLS-phonon coupling constant, ρ is the mass density and v is the sound velocity of a given substance. An ensemble of independent, noninteracting TLS would not be possible nor could justify the observed quantitative universality. Instead, the observed astonishing universality could emerge as the general result of some renormalization process of (almost) any ensemble of de- fects or manybody energy levels and stress matrix ele- ments, interacting through the usual bath of thermal pho- nons, implying the existence of some crossover length Do tunneling states and boson peak persist or disappear in extremely stabilized glasses? Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 6 539 scale r0. Therefore, we think that the picture of a spherical volume of size 3 0r comprising an isotropic random distri- bution of structural defects (TLS) embedded in a 3D vibra- tional lattice, allowing the interaction between resonant defects via the acoustic-phonon bath, may fail in the case of these layered and anisotropic ultrastable glasses of IMC. We suggest that a possible interpretation of the found sup- pression of TLS in ultrastable IMC thin-film glasses grown at 0.85 Tg could then be related to the modification of the molecular interaction in vapor-deposited USG films, through a decrease of free hydrogen bonds and an en- hancement of π–π interactions between chlorophenyl rings. Further, water absorption seems to take place by occupying free sites of the IMC glass where water can hydrogen bond. Thus, without modifying the intrinsic structure of the layer, absorbed water molecules are able to bridge IMC molecules through hydrogen bonds, so feeding the inter- connection of the dynamical network, and hence recover- ing the interacting TLS excitations, as we indeed observe in the “degraded” USG sample. Therefore, the found sup- pression of the two-level-systems would not be related to the extraordinary stability of the glass, but rather to the particular molecular arrangement ruled by the deposition conditions in this ultrastable glass. Finally, highly-stable “ideal glasses” can be associated in our view with a negligible excess in configurational entropy, whereas non-crystalline solids lacking low-energy excitations (TLS, boson peak...) could be associated with a low vibrational entropy. Both features may be related sometimes, but they are not automatically connected, as the case of hyperaged amber shows. 5. Conclusions To the best of our knowledge, no study had been per- formed up to date to investigate the possible effects that the dramatic increase in thermodynamic and kinetic stabil- ity of unique and selected kinds of glass could have on the universal low-temperature anomalies of glasses. In the discussed experiments, we have studied two dif- ferent kinds of extremely stabilized glasses, ideally ap- proaching the “ideal glass” state with zero configurational entropy. Our experiments on hyperaged glasses of amber undoubtedly demonstrate that the low-temperature “anom- alous” properties of glasses (TLS and the boson peak) per- sist essentially unchanged in ideal-like glasses, subjected to a dramatic thermodynamic and kinetic stabilization. Therefore, they are robust and intrinsic properties of glass- es. In contrast, tunneling TLS unexpectedly dissappear in ultrastable glasses of IMC, what we attribute to its very anisotropic and layered character. We speculate that it may lend support to the arguments by Leggett and others [6,7] which have claimed against the standard TM assuming independent, non-interacting TLS. Similar experiments in nonlayered ultrastable glasses would be most interesting to confirm this interpretation. 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Do tunneling states and boson peak persist or disappear in extremely stabilized glasses?

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