ARTICLE https://doi.org/10.1038/s42005-023-01398-4 OPEN Depletion of two-level systems in highly stable glasses with different molecular ordering Manuel Moratalla 1,2, Marta Rodríguez-López3,4, Cristian Rodríguez-Tinoco 3,4, Javier Rodríguez-Viejo 3,4, Rafael J. Jiménez-Riobóo 5 & Miguel A. Ramos 1,2 ✉ Recent findings of structural glasses with extremely high kinetic and thermodynamic stability have attracted much attention. The question has been raised as to whether the well-known, low-temperature “glassy anomalies” (attributed to the presence of two-level systems [TLS] and the “boson peak”) persist or not in these ultrastable glasses of much lower configura- 1234567890():,; tional entropy. To resolve previous contradictory results, we study a particular type of ultrastable glass, TPD, which can be prepared by physical vapor deposition in a highly-stable state with different degrees of layering and molecular orientation, and also as a conventional glass and in crystalline state. After a thorough characterization of the different samples prepared, we have measured their specific heat down to 0.4 K. Whereas the conventional glass exhibits the typical glassy behaviour and the crystal the expected Debye cubic dependence at very low temperatures, a strong depletion of the TLS contribution is found in both kinds of ultrastable glass, regardless of their layering and molecular ordering. 1 Departamento de Física de la Materia Condensada, Condensed Matter Physics Center (IFIMAC), Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain. 2 Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, 28049 Madrid, Spain. 3 Departamento de Física, Facultad de Ciencias, Universitat Autònoma de Barcelona, Bellaterra 08193 Barcelona, Spain. 4 Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Bellaterra 08193 Barcelona, Spain. 5 Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC), 28049 Madrid, Spain. ✉email: miguel.ramos@uam.es COMMUNICATIONS PHYSICS | (2023)6:274 | https://doi.org/10.1038/s42005-023-01398-4 | www.nature.com/commsphys 1 ARTICLE COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-023-01398-4 A fter more than one century of intense research, the phe- “orientational glasses”), and even many other more or less dis- nomenon of the glass transition (the solidification of a ordered crystals, were found to exhibit this ubiquitous and liquid without crystallization) and many of the physical striking “glassy behavior” at low temperatures14. properties of glasses continue to be the subject of controversy and Since the 1970’s, many experiments were devoted to investi- lively discussions1–14. gating whether those low-temperature anomalous excitations Glasses are liquids that have been supercooled out of ther- would gradually decrease or even disappear, when decreasing modynamic equilibrium, avoiding crystallization. The glass enthalpy and entropy of the glass by means of typical annealing transition in the laboratory is a kinetic transition. However, when or aging stabilization processes. Due to the obvious limitations of thermodynamic magnitudes are measured, the glass transition time (many millions of years are expected to be necessary to looks like a second-order phase transition, with finite dis- stabilize a glass with minimal entropy), the obtained results from continuities in second derivatives of the Gibbs free energy, such as those modest thermal treatments were usually unclear or even the specific heat. Hence, in contrast to the first-order divergence contradictory. for the melting of a crystal, glass transitions are typically observed Nevertheless, highly-stable glasses have recently been identified as a jump in heat capacity with a small overshoot depending on or prepared, raising interest and hope of successfully addressing the employed heating rate. Nonetheless, there are complicated these issues. Previous works on amorphous silicon films unsolved questions related to this apparent phase transition. For reported20 an absence of the glassy features at low temperatures instance, if one cools the liquid at a slower rate, the deviation mentioned above, that were later shown to be dependent on from the equilibrium curve occurs at a lower glass-transition deposition conditions21,22. Furthermore, ultrastable glasses temperature Tg. This is a serious problem to consider it a proper obtained by physical vapor deposition (PVD) of typically organic phase transition temperature. Furthermore, since the glass is in a molecular substances, by employing particular deposition rates non-equilibrium state, it exhibits time-dependent relaxation. So, (~0.1 nm/s) and temperatures (≈0.85 Tg), were demonstrated to by isothermal annealing of a glass below Tg (or simply by aging at exhibit extremely high thermodynamic and kinetic room temperature), the thermodynamic magnitudes can be stability17,23–26. Then, specific-heat measurements of ultrastable relaxed to lower, more stable values. indomethacin (IMC) glasses prepared by PVD were published27, There is not a unique, widely accepted theory of the glass where the linear term attributed to TLS was completely sup- transition. The essential reason of the problem is probably that pressed in samples deposited under high stability conditions, the glass transition is a complex combination of kinetics and while a usual linear term was observed for samples of the same thermodynamics. There is, nevertheless, a very useful framework material with ordinary deposition conditions. This behavior has often employed for interpreting the complex phenomenology of been recently supported by swap Monte Carlo computer simu- glasses and supercooled liquids: the potential-energy landscape lations, which have found a depletion of the TLS in computer (PEL)15,16, illustrated, for instance, in Fig. 3 of ref. 17. In brief, the glasses with increasing stability28,29. Nonetheless, the very nature PEL is a schematic topographic view of the potential-energy of computer glasses is not straightforwardly related to that of real hypersurface of any glass-forming material. It is plenty of local structural glasses. minima and saddle points for thermal energies below the melting It should be noted, however, that there is a notable exception point (Tm) of the crystalline state, which is associated with the to this behavior in highly stable glasses. A significant linear absolute energy minimum. Much has been speculated about the coefficient on the specific heat at the lowest temperatures, existence of an “ideal glass” which should correspond to the best ascribed to the “universal” presence of TLS in glasses, was found and most stable possible glass achievable, associated with the to persist invariant in geologically hyperaged glasses of amber (a lowest relative minimum, of course still above the energy of the typical polymer glass)30–32, when comparing the pristine sam- crystalline absolute minimum. Moreover, this "ideal glass" may ples (up to 110 My aged) to the rejuvenated samples. One well correspond to the limiting case of zero configurational possible difference to take into account between standard glasses entropy of a liquid eventually supercooled down to the Kauz- and PVD glasses is that the former are essentially homogeneous mann temperature18, where an underlying thermodynamic phase and isotropic, whereas the latter typically exhibit anisotropic transition might occur. packing and layered structures33–36 that can play a role in dif- Besides the abovementioned supercooled-liquid to glass-state ferent properties37–42. In fact, the anisotropy of IMC ultrastable transition and related relaxational effects at higher temperatures, glasses was argued in ref. 27 as a possible origin of the sup- also in the solid state at very low temperatures the situation is pression of TLS in opposition to the case of highly-stable amber complex and not well understood. It is well likely that the origin glasses. of such complexity is that most of the “anomalous” glassy features Beyond the fundamental interest of this topic in condensed are interrelated. Among the particular physical properties of non- matter physics, the presence and behavior of TLS in disordered crystalline solids, one of the most conspicuous issues is that of the solids have recently been found most relevant for quantum low-temperature properties of glasses (comprising thermal, technological applications, such as superconducting qubits for vibrational, acoustic or dielectric properties), unexpectedly very quantum computation or gravitation wave detectors43–47. Speci- different from those found in their crystalline counterparts, and at fically, the major source of noise and decoherence in super- the same time very similar among themselves. For instance, the conducting circuits typically made from aluminum or niobium, specific heat at the lowest temperatures is dominated by a linear comes from the losses generated by these TLS or atomic tun- term ascribed to the existence of tunneling states or two-level neling excitations within the amorphous oxide layers systems (TLS) in glasses, whereas the thermal conductivity encasing them. exhibits a quadratic T2 dependence, followed by a plateau, both Therefore, the natural conclusion is that more experiments on behaviors clearly deviating from the Debye theory fulfilled by this matter are needed, mainly where the issue of anisotropy or crystalline solids1,14. Most of these properties are independent of any other variable deemed relevant could be controlled inde- the type of substance or its chemical bonding, hence the usual pendently. To shed light on this issue, we have identified a sub- reference to “universal properties of glasses”1,2,14,19. These stance, namely N,N—bis(3-methylphenyl)_N,N-bis(phenyl)- “anomalies” were initially only ascribed to structural glasses, i.e., benzidine (TPD), an organic molecular solid, where various amorphous solids, but soon other materials such as mixed crystals relevant parameters can be tuned separately. Besides, it presents a or orientationally-disordered crystals (often also named as very convenient Tg slightly above room temperature48,49. 2 COMMUNICATIONS PHYSICS | (2023)6:274 | https://doi.org/10.1038/s42005-023-01398-4 | www.nature.com/commsphys COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-023-01398-4 ARTICLE Results and discussion been related to the existence of layering in the z direction50. The As described in Methods more in detail, we have studied TPD sample grown at 0.9 Tg has the peak maximum at 2θ = 5.340° glasses grown by PVD in three different conditions: anisotropic which accounts for an average vertical distance of 16.55 Å, while glass with the highest stability (deposited at 285 K); isotropic glass the sample grown at 0.85 Tg has the maximum at 6.15° which but also with high stability (deposited at 300 K); and isotropic, translates into 14.35 Å of vertical separation. The low-angle fea- conventional glass (deposited at Tg = 333 K). Control samples ture of the former Tdep = 300 K sample is also more intense which grown simultaneously with the ones for low-temperature mea- may be indicative of stronger layering in this sample. We note surements were characterized by Differential scanning calori- that the conventional glass exhibits a similar diffraction pattern to metry (DSC), X-ray diffraction (XRD), ultraviolet/visible (UV/ that of the sample grown at 285 K (0.85 Tg) in terms of intensity, Vis) spectroscopy and high-resolution Brillouin spectroscopy with the lowest angle peak maximum at 2θ = 5.340°. This is (HRBS). indicative of a similar level of layering as the most stable glass. Differential scanning calorimetry. Figure 1 shows the calori- metric scans obtained at 10 K/min from the two most stable Ultraviolet/visible spectroscopy. For TPD, two main electronic samples, deposited at 285 K (0.85 Tg) and 300 K (0.9 Tg), transitions can be observed in the UV-Vis spectra, at 355 nm respectively. The small difference in the onset of devitrification (3.50 eV) and 315 nm (3.95 eV), as shown in Fig. 3a. The lower (built by intersection of the dashed lines as shown) of the sample energetic transition is associated to the HOMO-LUMO transi- grown at 0.9 Tg (Ton = 360 K) with respect to the one grown at tion. The HOMO state of the molecule is electronically dis- 0.85 Tg (Ton = 363.3 K) indicates its slightly lower kinetic stabi- tributed along the molecule, having contributions from the lity. The left wing of the devitrification peak of the 285 K sample amines, the biphenyl core and the C rings at the peripheral ends is caused by the front transformation initiating at the many of the molecule. The LUMO of this low energetic transition is surfaces that emerge from cracking when the Al foil is wrapped to heavily centered on the biphenyl core, implying that the transi- fit it in the Al pan. This is more evident in the more stable glass tion dipole moment of the molecule will be oriented along the due to its retarded bulk glass transition temperature. The long axis of the molecule. On the other hand, the higher energetic respective second upscans, measured after the previous heating to transition comprises two almost degenerated transitions, arising 380 K and immediate cooling down at −10 K/min, are also from HOMO-(LUMO + 2) and HOMO-(LUMO + 3). In this shown, which correspond to the conventional glass state, where case, (LUMO + 2) and (LUMO + 3) are electronically localized at the devitrification onset Ton shifts down about 30 K and the big the peripheral C rings of the molecule. This transition has two overshoot due to the huge enthalpy release characterizing stable different associated transition dipole moments, both oriented in glasses has disappeared, as expected. the perpendicular plane of the long axis and having opposite directions51,52. For this reason, the intensity of this transition at 355 nm (3.50 eV) is used to determine the molecular orientation X-ray diffraction. The glassy nature of the sample and the pre- of the molecule in comparison to an isotropic sample. The sence of layering was investigated by Wide angle X-ray Scattering absorption of this electronic transition is associated to the degree (WAXS) as shown in Fig. 2. The most remarkable feature of the of horizontal orientation of the molecules with respect to the XRD spectra is the difference in the intensity and position of the substrate. low-angle peak (vertical dotted blue lines) located at around We use the order parameter, Sz, to quantify the degree of 2θ ≈ 5−6° from samples grown at 285 and 300 K. This peak has orientation of the molecules53–55. Sz is generally derived from the angle between the transition dipole moment and the surface normal, θ, but can be simplified to a simple fraction between Fig. 1 Differential Scanning Calorimetry. DSC curves for stable glasses deposited at 0.85 Tg (black lines) and 0.9 Tg (red lines), where Tg is the glass transition temperature. Both first upscans at 10 K/min up to 380 K −exposing the thermodynamic history of the stable glass− and second Fig. 2 Diffraction patterns for conventional and ultrastable glasses. upscans −after the sample has transformed into the conventional glass by Wide-angle XRD spectra for the two stable glasses with the corresponding cooling the liquid at −10 K/min− are depicted. The corresponding deposition temperatures indicated in the legend and the one of the devitrification temperatures Ton of each case (assessing the degree of conventional glass (CG) deposited at Tg = 333 K. Blue dotted lines mark the kinetic stability) are graphically shown. positions of the main diffraction peaks. COMMUNICATIONS PHYSICS | (2023)6:274 | https://doi.org/10.1038/s42005-023-01398-4 | www.nature.com/commsphys 3 ARTICLE COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-023-01398-4 Fig. 3 Order parameter Sz from UV/Vis spectra. a Ultraviolet/Visible spectra for glasses grown at different deposition temperatures as indicated in the legend. See Sample preparation in Methods for more details. b Solid black squares (left scale): Sz obtained from UV/Vis spectra of samples grown at temperatures spanning 235 to 333 K. Open black squares: Sz values measured by ellipsometry in refs. 50,55. Solid red squares (right scale): devitrification onset temperature (Ton) measured by calorimetry on TPD glasses grown at different deposition temperatures. Solid stars correspond to samples obtained by cooling from the liquid state. Dashed lines are guides to the eye. The uncertainty in the Sz value is obtained from the standard deviation of three absorption measures per each deposition temperature, after error propagation of the maximum absorption value in the UV-Vis spectra. absorbances56: slightly different colors) are depicted together, showing good reproducibility. 3 cos2 θ  1 A It is important to stress at this point that HRBS measurements Sz ¼ ! Sz ¼ 1  ð1Þ 2 Aiso do not average in all three directions of the sample as calorimetric methods do. HRBS measures the elastic properties in the where A is the absorption of the deposited film and Aiso is the direction of the acoustic wave vector (see Supplementary Fig. 1). absorption of a film that has exactly the same number of If the sample under study is really isotropic, as usually canonical molecules as the original one, but randomly oriented. This is glasses are, this difference in averaging will become irrelevant, but obtained after annealing the vapor deposited film during 30 s at if the sample is anisotropic, then discrepancies can arise, because 350 K (Tg + 27 K) in Ar atmosphere. A value of Sz = −0.5 the averaging is different. Therefore, the absolute values for the corresponds to a transition dipole moment of the molecule different samples in Fig. 4, especially for the more anisotropic aligned parallel to the substrate, then indicating horizontal glass (0.85 Tg), must be taken with caution. orientation of the molecule; Sz = 0 means that the molecules The testing of the elastic isotropy in the sample/substrate plane are randomly oriented, and Sz = 1 that molecules are preferen- of a TPD sample grown at 300 K is shown in Supplementary tially aligned with the long axis perpendicular to the substrate. Fig. 2a. It is to see that there is no relevant indication of According to Fig. 3b the sample grown at the lowest anisotropy in the longitudinal phonon, the data show random temperature has an order parameter Sz (UV/Vis) of −0.029 dispersion about f 110A = 7.859 ± 0.013 GHz. The acoustic wave while for the one grown at 0.9 Tg is −0.002. This indicates that vector performed a circular path in the plane with 10° steps. The the sample grown at 0.85 Tg has on average a slightly larger face- 2αA scattering geometry was used, with a scattering angle of 55º on orientation with molecules lying with their long axis parallel to (2α = 110º). Supplementary Fig. 2b shows the film TPD sample the substrate compared to the sample deposited at 300 K that is with the schematics of the different directions of the q2αA in the much more isotropic, as also shown from HRBS experiments in sample/substrate plane. Supplementary Fig. 2a. These results are slightly lower but Not surprisingly, the most stable glass (the rather anisotropic compatible with previous ellipsometry (open squares in Fig. 3b) ultrastable glass deposited at 0.85 Tg) exhibits the hardest elastic and Grazing-Incidence Wide-Angle X-ray Scattering measure- constants, i.e., the highest sound velocities, whereas the conven- ments on TPD or closely related organic semiconductor tional glass (the one deposited at Tg) has the lower. Interestingly, molecules50,55. the intermediate glass grown at 300 K (0.9 Tg) behaves closer to Overall, the thermokinetic and structural investigation of the the latter than to the former. It seems, therefore, that the two stable samples leads to the following conclusions: samples molecular orientation in the structural network plays a more grown at 0.85 Tg have slightly larger thermodynamic and kinetic leading role to determine the sound velocity than the degree of stability, lower layering (similar to the conventional glass) but stability53. This finding will be supported by the specific heat data more molecular anisotropy towards face-on orientation with to be discussed below. respect to the sample grown at Tdep = 300 K (0.9 Tg), which is essentially isotropic, as depicted in Fig. 3b. Low-temperature specific heat. Specific-heat Cp data, obtained Sound velocity. In Fig. 4, longitudinal (vL) and transverse (vT) after low-temperature measurements of the heat capacity sound velocity for the three different glasses, determined from employing the thermal-relaxation method and carefully sub- HRBS measurements down to low temperatures, are presented. tracting the contribution of the addenda (see Methods), are As usual, transverse sound waves give much weaker Brillouin presented in Figs. 5−7. We have measured the specific heat for peaks with lower frequency shifts, thereby resulting in more three different glasses grown as thin films on 1 cm2 sapphire scattered data points than for longitudinal sound waves. Data substrates, following the procedure detailed in Methods. In every obtained from both cooling and heating runs (same symbols with case, three twin samples were put together on the calorimetric cell 4 COMMUNICATIONS PHYSICS | (2023)6:274 | https://doi.org/10.1038/s42005-023-01398-4 | www.nature.com/commsphys COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-023-01398-4 ARTICLE Fig. 5 Debye-reduced Cp/T3 specific heat. Specific heat for the three different glasses (conventional, isotropic ultrastable glass and anisotropic ultrastable glass) and the reference crystal of TPD (see the symbols in the legend) plotted in a Debye-reduced Cp/T 3 plot. Error associated with the data points was calculated using one standard deviation and is of the size of the data points. As mentioned above, in Fig. 5 the whole of our specific-heat data is plotted as Cp/T 3 versus temperature in a log scale. This is the well-known Debye-reduced plot, where deviations from the expected cubic behavior for crystals at the lowest temperatures are more easily observed and analyzed. Nevertheless, data appear noisier than in other representations due to the T 3 factor in the Fig. 4 Longitudinal and transverse sound velocities. Sound velocity as a denominator. function of temperature for the differently prepared glasses, as indicated in The TPD crystal shows the expected Cp ∼ T3 Debye law, at the legend: a longitudinal sound velocity vL; b transverse sound velocity vT. least below 2 K, with a shallow hump at 4 K, usually ascribed to a In the case of the conventional glass the darker symbols represent a cooling van-Hove singularity for transverse acoustic phonons in crystals. run and the less dark ones represent a heating run. In the case of the Strikingly, the rather anisotropic and most ultrastable glass anisotropic ultrastable glasses (USG), both symbols (darker and less dark (deposited at 0.85 Tg) exhibits a very similar behavior in Cp, ones) represent two different cooling runs. It is to be stressed that data in although with a ≈30% higher magnitude, which is attributable to anisotropic glasses refers only to the sound velocity measured in the the lower elastic constants in the glass state. In particular, the direction of the acoustic vector (see the Sound velocity subsection for more depletion of the TLS density (i.e., the absence of an upturn in Cp/ details). Errors associated with the data points are calculated from the T 3 at very low temperatures) confirms the previous observation frequency error values obtained from the non-linear fits to the peaks in the in ultrastable glasses of IMC27. Oppositely, the isotropic and Brillouin spectra and are below 1% for vL and about 2.5% for vT, making ordinary glass (deposited at Tg) shows the typical glassy behavior, them smaller than the symbols in the plot. with a clear upturn in Cp/T 3 below 1 K featuring the presence of TLS and a significant boson peak below 3 K, even better defined to triplicate the sample mass and improve the sensitivity of the than for the conventional glass of IMC27. In addition, we have measurement. As a useful reference, the material in crystalline measured the glass film deposited at 0.9 Tg, which corresponds to state, in powder as received, was measured too. Additionally, a highly stable glass (albeit somewhat less stable than the 0.85 Tg another crystal sample and another ultrastable glass grown at one, see Fig. 1) but fully isotropic. This intermediate glass exhibits 0.85 Tg had been previously measured in a higher temperature a temperature dependence below 1 K near to cubic, that is, the range, employing a standard 4He cryostat (see all raw data, after TLS contribution is almost negligible, while above 1 K its specific subtracting the corresponding addenda, in Supplementary Fig. 3). heat is very similar to that of the conventional glass. Therefore, As can be seen, the overlap between the net data from the two the degree of stability appears to control the density of TLS, different setups under so many different conditions is good, whereas the more-or-less anisotropic structure of the molecular further supporting the accuracy of these measurements. Cp data network seems to influence the elastic constants (see Fig. 4), and shown in Figs. 5−7 are therefore the result of statistically aver- hence the lattice dynamics and the Cp/T 3 vibrational background aging many experimental data points, from different experi- (see Fig. 5). mental runs. The final precision, that can be envisaged from the The previous analysis referred to Fig. 5 can be complemented data scatter in the most demanding Cp/T 3 representation used in by means of the also usual Cp/T vs T 2 plot for the data at the Fig. 5, can be estimated to be better than 5%. Of course, the real lowest temperatures, as done in Fig. 6. By employing this accuracy in absolute value of the specific heat data, which is representation, the linear-term coefficients, if any, can be directly influenced by the subtracted, significant contribution of the determined from linear or quadratic least-squares fits57,58. addenda, could be above that value, but it is a systematic error Besides the numerical fits, whose obtained coefficients are that hardly affects the comparison among the different samples presented in the central column of Table 1, the linear coefficient measured. Cp is visualized as the intercept of Cp/T curves with the ordinate COMMUNICATIONS PHYSICS | (2023)6:274 | https://doi.org/10.1038/s42005-023-01398-4 | www.nature.com/commsphys 5 ARTICLE COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-023-01398-4 a good agreement with the previous ones (central column) using a different approach. Conclusions In summary, we have thoroughly studied several key properties of a glass-forming substance, TPD, where both its degree of ther- modynamic and kinetic stability, and its degree of structural/ optical anisotropy can be dramatically varied. Specifically, we have performed calorimetric experiments, both around the glass transition and at low temperatures, as well as elastoacoustic and structural characterization measurements. In particular, three representative and clearly different glass states of TPD have been studied, depending on the deposition temperature of the PVD films. The glass deposited at 285 K (0.85 Tg) is anisotropic, where the molecules are preferentially oriented parallel to the substrate, and exhibits the strongest stabilization as indicated by a large +30 K shift in the devitrification temperature Ton, compared to the conventional glass. It also shows some layering, though less Fig. 6 Linear contributions to the specific heat. Specific-heat data below than the other stable glass, and of the same magnitude that the 2 K for the three different glasses and the reference crystal of TPD (see the conventional glass, which implies at least that the existence of symbols in the legend) in a Cp/T vs T 2 plot. Dashed lines show the layering is not the only reason for the different properties of the corresponding least-squares fits: quadratic, below 2 K for the glasses; linear, ultrastable glass. Brillouin measurements of longitudinal and below 1 K for the crystal. Error associated with the data points was transverse sound velocities at low temperatures show that the calculated using one standard deviation and is of the size of the data points. most stable glass (deposited at 0.85 Tg) has the highest values among the studied TPD glasses, and hence the lowest Debye level, in agreement with Cp/T 3 data at low temperature. Furthermore, this 0.85 Tg ultrastable glass lacks TLS within experimental error, Table 1 Linear coefficients of the specific heat from the fits. as it was also observed in the ultrastable glass of IMC27. On the contrary, the ordinary or conventional glass (grown at Tg) Sample CTLS (μJ/g·K2) exhibited the expected glassy features, namely a linear term in the TOTAL FIT (i) EXCESS FIT (ii) specific heat due to the presence of TLS and a boson peak Cp/T 3 slightly below 3 K. Conventional glass (Tg) 8.0 ± 1.0 6.2 ± 0.5 However, the most novel finding in this work has been Isotropic stable glass 1.5 ± 0.8 1.4 ± 0.3 (0.90 Tg) obtained from preparing and studying an intermediate glass state Anisotropic stable glass 0.5 ± 0.7 −0.3 ± 0.3 (the glass deposited at 0.9 Tg), which is almost as stable as the (0.85 Tg) 0.85 Tg one, but almost as isotropic as the conventional glass. Crystal 0 0 Interestingly, it shows a linear term in Cp much smaller than that of the conventional glass, although not strictly zero within Linear coefficients of the specific-heat determined from: (i) least-squares quadratic fits of the experimental error, what we attribute to the slightly lesser stabi- total curves below 2 K for the three different glasses (see dashed lines in Fig. 6); (ii) coefficients obtained from linear fits of the “glassy excess” ΔCp (T) below 1.4 K (see dashed lines in Fig. 7b). lity than the 0.85 Tg glass. In short, the density of TLS appears to inversely correlate with the degree of stability and is independent of the anisotropy. However, the vibrational Debye-like back- axis in Fig. 6. Only the isotropic, conventional glass has a ground of Cp dominating above 1 K of this isotropic/stable glass, significant linear coefficient, ascribed to a typical density of TLS, is very similar to that of the conventional glass, but clearly higher whereas the stable glasses show a clear depletion of TLS, than that of the anisotropic glass of 0.85 Tg. Hence this vibra- especially the most stable glass deposited at 0.85 Tg, for which tional background around the boson peak seems to be governed its presence is null within experimental error, as in the crystal by the molecular ordering influencing the network structure, state. rather than by the degree of stability, oppositely to the TLS In order to enhance and better visualize the glassy features of contribution. the specific heat, we have subtracted the reference crystal value Finally, it can be remarked that our better understanding of the from the total Cp(T) of each glass sample, as depicted in Fig. 7. key variables that deplete the amount of TLS in amorphous solids The left panel (a) shows this glassy excess ΔCp,glassy over the is expected to be very useful in the field of superconducting cir- crystal curve in the Cp/T 3 plot, while the right panel (b) shows cuits and quantum technologies, which are currently much lim- the lowest-temperature data in a Cp/T vs T 2 plot. ited by the losses due to tunneling states present in the In Fig. 7a, we can observe the typical glassy behavior for the amorphous parts employed in those devices43–47. conventional glass, while the anisotropic, stable glass shows a flat excess ΔCp,glassy/T 3 signaling a mere difference in the cubic Methods Debye coefficient relative to the crystal one. In the intermediate Sample preparation. TPD (N,N—bis(3-methylphenyl)_N,N- case (the more isotropic but still stable glass at 0.9 Tg), a weak bis(phenyl)-benzidine, Tg = 333 K and Tm = 440 K) crystalline upturn in ΔCp,glassy/T 3 below 1 K is seen, together with a “boson powders with 99% purity were purchased from Sigma-Aldrich peak” very similar to that of the conventional glass, both in and used as received. The films were thermally evaporated and position and height. In Fig. 7b, the corresponding data are plotted deposited at three different substrate temperatures, 285 K as ΔCp,glassy/T vs T 2 to scrutinize more precisely the behavior at (0.85 Tg), 300 K (0.9 Tg), and 333 K (Tg), within a high vacuum the lowest temperatures. The linear fits performed below 1.4 K chamber with a base pressure of 1 × 10−8 Torr. An effusion cell (dashed lines) are also shown in Table 1 (right column) and show filled with TPD powder was heated to achieve a deposition rate of 6 COMMUNICATIONS PHYSICS | (2023)6:274 | https://doi.org/10.1038/s42005-023-01398-4 | www.nature.com/commsphys COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-023-01398-4 ARTICLE Fig. 7 Net glassy contribution to the specific heat. Glassy specific-heat excess (subtracting its value for the crystal state) for the three different glasses (see legend) in: a Cp/T 3 representation; b Cp/T vs T 2 representation at the lowest temperatures. Dashed lines show the least squares linear fits performed to determine the corresponding linear coefficients. 0.20 ± 0.05 nm/s, as measured by a quartz crystal microbalance. Measurements were carried out in an X-Pert diffractometer from Once the substrate temperature was stabilized and the desired Phillips in the Bragg–Brentano configuration with Cu Kα radia- growth rate attained, the shutter was removed to start depositing tion. The samples were scanned in Bragg–Brentano geometry onto several 1 × 1 cm2 sapphire substrates (Sigma Aldrich). Films from 2θ = 3° to 30° with an angular step of 0.05° and time per around 50 μm thick were produced to enhance the signal-to-noise point of 20 s for both samples. The average molecular orientation ratio in the low-temperature heat capacity measurements. After of the samples was inferred from the variation of the UV/Vis deposition the samples were stored in vacuum for few days at a spectra measured in thinner (100−200 nm thick) samples, temperature of 4 °C and shipped from Barcelona to Madrid for through the order parameter, Sz, calculated as reported the low-temperature measurements. Control samples were grown elsewhere56,59, see Fig. 3. The Sz value of the sample deposited simultaneously on aluminum substrates and checked by calori- directly at Tdep = 333 K (in the liquid state) and a conventional metry just before the low-T measurement for the determination glass obtained from the liquid (square and star black symbols in of the thermodynamic stability of the glass, on silicon wafers Fig. 3b, respectively) are both isotropic within the experimental (with native oxide) for the study of molecular layering with XRD uncertainty. This technique provides information about the and on quartz substrates (from Ossila) for UV/Vis analysis electronic transitions in the range of ultraviolet-visible wave- devoted to the determination of molecular orientation of the as- lengths. As each electronic transition has associated a transition grown glasses. Two of the selected deposition temperatures dipole moment, the molecular orientation of the glass may yield (285 K and 300 K) were determined with the intention to have variations on the intensity of the transition. samples of comparable stability but different molecular orienta- tion and layering according to previous reports17,26,35. The third Brillouin light scattering. Temperature dependent measure- deposition temperature (333 K) was chosen to prepare a con- ments of the longitudinal and transverse acoustic phonons have ventional glass, isotropic and much less stable than the others (see been performed by means of HRBS. Due to the sample geometry Fig. 3b), as a reference. The sample grown at Tdep =333 K is (film of about 5 μm on Si substrate) the scattering geometry equivalent, from the thermodynamic (onset and fictive tem- applied in these experiments was the 2αA scattering geometry. perature) and structural (XRD and Sz parameter) points of view Supplementary Fig. 1 shows the schematics of this scattering to a conventional (−10 K/min) liquid-cooled glass. Additionally, geometry. The most important point is that the reflecting sub- the low-temperature specific heat of the reference crystal state was strate acts as a virtual light source, introducing the 2αA scattering also measured. geometry that is confined in the sample/substrate plane60. This scattering geometry allows the observation of the longitudinal and Calorimetric characterization. DSC was carried out in a Perkin- transverse phonons, whereas in the pure Backscattering geometry Elmer 7 DSC with a heating rate of 10 K/min in samples of the transverse phonons in principle do not couple to the elec- thickness ≈15 μm and total mass around 8−12 mg deposited on tromagnetic field of the incoming light. Al foil. The first scan corresponds to the as-deposited state, while As it is shown in Supplementary Fig. 1, the acoustic wave the second upscan is characteristic of a sample that has been vector q2αA is related to the scattering angle (2α) as: heated up to the liquid state at 380 K and subsequently cooled 4π sinðαÞ down at −10 K/min. The strong variation of the onset of devi- q2αA ¼ ð2Þ λ0 trification (Ton) and the enthalpy overshoot between both vapor- deposited and liquid-cooled glasses (see Fig. 1) is related to the being α the angle of incidence and λ0 the laser wavelength. It is enhanced kinetic and thermodynamic stability of these ultrastable not dependent on the refractive index of the sample. Thus, the glasses. sound velocities are given by: 2πf L;T f L;T λ0 Structural characterization. The glassy nature of the sample and vL;T ¼ ¼ ð3Þ the presence of layering was investigated by WAXS. q 2 sinðαÞ COMMUNICATIONS PHYSICS | (2023)6:274 | https://doi.org/10.1038/s42005-023-01398-4 | www.nature.com/commsphys 7 ARTICLE COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-023-01398-4 where fL,T is the measured Brillouin frequency shift of the 13. Franz, S., Maimbourg, T., Parisi, G. & Scardicchio, A. Impact of jamming longitudinal (L) or transverse (T) phonons. criticality on low-temperature anomalies in structural glasses. Proc. Natl. Acad. Sci. USA 116, 13768 (2019). 14. Ramos, M. A. (ed.). Low-Temperature and Vibrational Properties of Low-temperature specific heat. Heat capacity of the different Disordered Solids: A Half-Century of “Anomalies” of Glasses (World Scientific, samples was measured in the temperature range 0.4−8 K Singapore, 2022). employing a 3He cryostat. Some complementary measurements 15. Goldstein, M. Viscous liquids and the glass transition: a potential energy for a crystal and an ultrastable glass of TPD were previously barrier picture. J. Chem. Phys. 51, 3728 (2003). 16. Stillinger, F. H. A topographic view of supercooled liquids and glass performed in a standard 4He cryostat between 2 and 20 K, formation. Science 267, 1935 (1995). showing good agreement with the others despite so many dif- 17. Rodríguez-Tinoco, C., González-Silveira, M., Ramos, M. A. & Rodríguez- ferent experimental conditions, as can be observed in Supple- Viejo, J. Ultrastable glasses: new perspectives for an old problem. Riv. Nuovo mentary Fig. 3, where all raw data are depicted together. In all Cim. 45, 325 (2022). cases the thermal relaxation method was used27,61, with the 18. Kauzmann, W. The nature of the glassy state and the behavior of liquids at low temperatures. Chem. Rev. 43, 219 (1948). samples placed on the sapphire substrate (1 inch diameter) of the 19. Ramos, M. A. Are universal “anomalous” properties of glasses at low calorimetric cell, with a small, carefully measured amount of temperatures truly universal? Low. Temp. Phys. 46, 104 (2020). Apiezon N grease. More details of our calorimetric methods at 20. Zink, B. L., Pietri, R. & Hellman, F. Thermal conductivity and specific heat of low temperatures can be found in refs. 62,63. For these experi- thin-film amorphous silicon. Phys. Rev. Lett. 96, 055902 (2006). ments, a 1 kΩ resistor chip (used as a heater) and a thermal 21. Queen, D. R., Liu, X., Karel, J., Metcalf, T. H. & Hellman, F. Excess specific heat in evaporated amorphous silicon. Phys. Rev. Lett. 110, 135901 (2013). sensor were also fixed on the sapphire support in very good 22. Liu, X., Queen, D. R., Metcalf, T. H., Karel, J. E. & Hellman, F. Hydrogen-free thermal contact with the samples. The calorimetric cell was amorphous silicon with no tunneling states. Phys. Rev. Lett. 113, 025503 (2014). connected to the controlled thermal sink through a thin PtW 23. Swallen, S. F. et al. Organic glasses with exceptional thermodynamic and wire, chosen to have relaxation times of tens of seconds. kinetic stability. Science 315, 353–356 (2007). For the lower temperature measurements in the 3He cryostat, a 24. Leon-Gutierrez, E., Sepúlveda, A., Garcia, G., Clavaguera-Mora, M. T. & Rodríguez-Viejo, J. Stability of thin film glasses of toluene and ethylbenzene RuO2 thermal sensor was selected to minimize its contribution to formed by vapor deposition: an in situ nanocalorimetric study. Phys. Chem. the total heat capacity. A radiation shield of polished metal was put Chem. Phys. 12, 14693–14698 (2010). surrounding the calorimetric setup to allow this to reach 25. Leon-Gutierrez, E., Sepúlveda, A., Garcia, G., Clavaguera-Mora, M. T. & temperatures around 0.3 K. The contribution of the addenda Rodríguez-Viejo, J. Correction: Stability of thin film glasses of toluene and (slightly below 50% of the total heat capacity at 2 K, though ethylbenzene formed by vapor deposition: an in situ nanocalorimetric study. Phys. Chem. Chem. Phys. 18, 8244–8245 (2016). gradually increasing below 1 K) was carefully measured and 26. Ediger, M. D. Perspective: Highly stable vapor-deposited glasses. J. Chem. subtracted to obtain the specific heat of the corresponding material. Phys. 147, 210901 (2017). To improve the sensitivity of the heat capacity measurements, three 27. Pérez-Castañeda, T., Rodríguez-Tinoco, C., Rodríguez-Viejo, J. & Ramos, M. samples grown simultaneously were measured together, so A. Suppression of tunneling two-level systems in ultrastable glasses of triplicating the sample mass, for each case. Additionally, many indomethacin. Proc. Natl. Acad. Sci. USA 111, 11275 (2014). 28. Khomenko, D., Scalliet, C., Berthier, L., Reichman, D. R. & Zamponi, F. different experimental runs were performed to improve data Depletion of two-level systems in ultrastable computer-generated glasses. statistics. Smoothed statistical-averaged data from the whole of Phys. Rev. Lett. 124, 225901 (2020). datasets shown in Supplementary Fig. 3 are presented in Fig. 5. 29. Mocanu, F. C. et al. Microscopic observation of two-level systems in a metallic glass model. J. Chem. Phys. 158, 014501 (2023). 30. Pérez-Castañeda, T., Jiménez-Riobóo, R. J. & Ramos, M. A. Low-temperature thermal properties of a hyperaged geological glass. J. Phys.: Cond. Matter 25, Data availability 295402 (2013). All data are available in the main text or the supplementary materials, as well as from the 31. 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M.M. and M.A.R. are grateful to J. G. Rodrigo and J. M. Castilla for unvaluable help with 43. Clarke, J. & Wilhelm, F. K. Superconducting quantum bits. Nature 453, the 3He cryostat. M.M. and M.A.R. acknowledge financial support from PID2021- 1031–1042 (2008). 127498NB-I00/AEI/FEDER/10.13039/501100011033, also from MCIN/AEI/10.13039/ 44. Devoret, M. H. & Schoelkopf, R. J. Superconducting circuits for quantum 501100011033 through the “María de Maeztu” Program for Units of Excellence in R&D information: an outlook. Science 339, 1169–1174 (2013). (CEX2018-000805-M), as well as from the Autonomous Community of Madrid through 45. Müller, C., Cole, J. H. & Lisenfeld, J. Towards understanding two-level- program S2018/NMT-4321 (NANOMAGCOST-CM). J.R.V., C.R.T. and M.R.L. acknowl- systems in amorphous solids: insights from quantum circuits. Rep. Prog. Phys. edge Grant PID2020-117409RB-I00, funded by MCIN/AEI/10.13039/ 501100011033. 82, 124501 (2019). C.R.T. is a Serra Hunter Fellow. 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Vila-Costa, A., González-Silveira, M., Rodríguez-Tinoco, C., Rodríguez-López, the experimental setups for low-temperature calorimetry under the supervision of M. & Rodríguez-Viejo, J. Emergence of equilibrated liquid regions within the M.A.R., M.R.L. prepared the samples. M.R.L. and C.R.T. performed the calorimetric and glass. Nat. Phys. 19, 114–119 (2023). structural characterizations and their data analysis. R.J.J.R. conducted the Brillouin light 50. Gujral, A., O’Hara, K. A., Toney, M. F., Chabinyc, M. L. & Ediger, M. D. scattering measurements and obtained the sound velocity data. M.M. conducted the Structural characterization of vapor-deposited glasses of an organic hole specific-heat measurements at low temperature and their data analysis with the input of transport material with X-ray scattering. Chem. Mater. 27, 3341 (2015). M.A.R. M.A.R. and J.R.V. wrote the original manuscript draft. All authors contributed to 51. Vragović, I., Calzado, E. M. & Díaz García, M. A. The structure and energetics the writing and editing of the manuscript. of TPD ground and excited states. Chem. Phys. 332, 48 (2007). 52. Scholz, R. et al. Asymmetry between absorption and photoluminescence line shapes of TPD: spectroscopic fingerprint of the twisted biphenyl core. J. Phys. Competing interests Chem. A 113, 315 (2009). The authors declare no competing interests. 53. Ward, I. M. Structure and Properties of Oriented Polymers, 2nd edn, Ch. 1 (Springer, Berlin, 1997). 54. Yokoyama, D. Molecular orientation in small-molecule organic light-emitting Additional information diodes. J. Mater. Chem. 21, 19187 (2011). Supplementary information The online version contains supplementary material 55. Dalal, S. S., Walters, D. M., Lyubimov, I., de Pablo, J. J. & Ediger, M. D. available at https://doi.org/10.1038/s42005-023-01398-4. Tunable molecular orientation and elevated thermal stability of vapor- deposited organic semiconductors. Proc. Natl. Acad. Sci. USA. 112, 4227–4232 Correspondence and requests for materials should be addressed to Miguel A. Ramos. (2015). 56. Sakai, Y., Shibata, M. & Yokoyama, D. Simple model-free estimation of Peer review information Communications Physics thanks Xiao Liu, and the other, orientation order parameters of vacuum-deposited and spin-coated anonymous, reviewer(s) for their contribution to the peer review of this work. A peer amorphous films used in organic light-emitting diodes. Appl. Phys. Express 8, review file is available. 096601 (2015). 57. Ramos, M. A. Are the calorimetric and elastic Debye temperatures of glasses Reprints and permission information is available at http://www.nature.com/reprints really different? Philos. Mag. 84, 1313 (2004). Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in 58. Ramos, M. A. Low-temperature specific heat of glasses and disordered published maps and institutional affiliations. crystals. in Low-Temperature and Vibrational Properties of Disordered Solids: A Half-Century of “Anomalies” of Glasses (ed. Ramos, M. A.) Ch.2 (World Scientific, Singapore, 2022). 59. Walters, D. M., Antony, L., de Pablo, J. J. & Ediger, M. D. Influence of Open Access This article is licensed under a Creative Commons molecular shape on the thermal stability and molecular orientation of Attribution 4.0 International License, which permits use, sharing, vapor-deposited organic semiconductors. J. Phys. Chem. Lett. 8, 3380–3386 adaptation, distribution and reproduction in any medium or format, as long as you give (2017). appropriate credit to the original author(s) and the source, provide a link to the Creative 60. Krüger, J. K., Ems, J., Brierley, J. & Jiménez Riobóo, R. J. A new Brillouin Commons licence, and indicate if changes were made. The images or other third party scattering technique for the investigation of acoustic and opto-acoustic material in this article are included in the article’s Creative Commons licence, unless properties: application to polymers. J. Phys. D. 31, 1913 (1998). indicated otherwise in a credit line to the material. If material is not included in the 61. Bachmann, R. et al. Heat capacity measurements on small samples at low article’s Creative Commons licence and your intended use is not permitted by statutory temperatures. Rev. Sci. Instrum. 43, 205 (1972). regulation or exceeds the permitted use, you will need to obtain permission directly from 62. Pérez-Enciso, E. & Ramos, M. A. Low-temperature calorimetry on molecular the copyright holder. To view a copy of this licence, visit http://creativecommons.org/ glasses and crystals. Thermochim. Acta 461, 50 (2007). licenses/by/4.0/. 63. Pérez-Castañeda, T. et al. Low-temperature specific heat of graphite and CeSb2: validation of a quasi-adiabatic continuous method. J. Low. Temp. Phys. 173, 4 (2013). © The Author(s) 2023 COMMUNICATIONS PHYSICS | (2023)6:274 | https://doi.org/10.1038/s42005-023-01398-4 | www.nature.com/commsphys 9