LOW-TEMPERATURE PROPERTIES OF GLASSES
AND DISORDERED SOLIDS
Prof. Miguel Angel Ramos
Dr. César Talón
Prof. Sebastián Vieira
Since 30 years ago, it is well known that glasses or amorphous solids exhibit universal
thermal properties at low temperatures, which are in turn very different from those of
crystalline solids. Below 1 K, the specific heat Cp of dielectric glasses is much larger and the
thermal conductivity  orders of magnitude lower than the corresponding values found in
their crystalline counterparts. Cp depends approximately linearly and  almost quadratically
on temperature. This is in clear contrast to the cubic dependences observed in crystals for both
properties, well understood in terms of Debye's theory of lattice vibrations. Above 1 K, Cp
still deviates strongly from the expected CDebye  T 3 dependence, exhibiting a hump in Cp/T 3
which is directly related to the so-called boson peak observed by neutron or Raman
vibrational spectroscopies. In the same temperature range the thermal conductivity exhibits an
ubiquitous plateau.
These “anomalous” thermal properties of amorphous solids (at least for T < 1 K), together
with other dielectric and acoustic universal properties, are well accounted for since in 1972
Phillips and Anderson, Halperin and Varma independently introduced the tunneling model
(TM), whose fundamental postulate was the general existence of atoms or small groups of
atoms in amorphous solids which can tunnel between two configurations of very similar
energy (two-level systems, TLS). The intrinsic structural disorder of noncrystalline solids
would produce a random distribution of these in terms of their assymmetry and tunneling
parameters which is able to explain phenomenologically most of low-temperature properties
of glasses. On the other hand, the also rich universal behavior of glasses at T > 1 K remains
more controversial and is not so well understood, altough the phenomenological soft-potential
model (SPM), which can be regarded as an extension of the TM, has been very succesfully
used to explain these low-temperature and low-frequency properties below and above 1 K. In
brief, the SPM postulates the coexistence of extended lattice vibrations (sound waves) with
quasilocalized low-frequency (soft) modes. In this model, the potential of these soft modes
has a uniform stabilizing fourth-order term. In addition, each mode has its individual firstorder asymmetry and second-order restoring force terms, which can be either positive or
negative. Similarly to the TM, a random distribution of potentials is assumed.
The research line on Low-temperature properties of glasses and disordered solids, being
carried out in the Laboratory of Low Temperatures within the Department of Condensed
Matter Physics, aims to deepen in our understanding of abovementioned properties
universally exhibited by non-crystalline solids at low temperatures. This subject remains a
matter of widely interest and vivid debate, in conjunction with the more general problem of
the very nature of the glass-transition phenomenon and the glassy state itself.
Following investigations on archetypical glasses such as boron oxide and how these
properties depend on the thermal history of the glass, more recently we have focused on
hydrogen-bonded molecular systems, namely simple alcohols, which present the peculiarity
of being liquid at room temperature and have been hence seldom studied at low temperatures.
Specifically, we have measured during last years the low-temperature specific heat of
different alcohols (normal and fully-deuterated ethanol, 1- and 2- propanol, and glycerol) in
their different -ordered or disordered- phases. Ethanol exhibits a very interesting
polymorphism presenting three different solid phases at low temperature: a fully-ordered
(monoclinic) crystal, an orientationally-disordered (cubic) crystal or “orientational glass”, and
the ordinary structural glass. By measuring and comparing the low-temperature specific heat
of the three phases, in the “boson peak” range (2-10 K) as well as in the tunneling-states range
below 1K, we were able to provide a quantitative confirmation that “glassy behavior” is not
an exclusive property of amorphous solids. On the other hand, propanol is the simplest
monoalcohol with two different stereoisomers (1- and 2-propanol), what has allowed us to
study directly the influence of the spatial rearrangement of atoms on the universal properties
of glasses. We have measured the specific heat of both isomers, finding a noteworthy
quantitative difference between them. Finally, low-temperature specific-heat data of glassy
and crystalline glycerol have also been obtained. In this case, the concurrent measurement of
the low-temperature thermal conductivity of glassy glycerol enabled us to test some SPM
predictions, which were found to be well fulfilled in this case.
Furthermore, several collaborations with research groups at University of Bayreuth and
University of Leipzig, in Germany, are being conducted. In particular, several experiments on
acoustic properties of metallic (including superconducting) glasses at very low temperatures
(down to 0.1 mK) and as a function of the applied strain have been performed. These studies
were done by using the vibrating-reed technique which, in contrast to other techniques, allows
measuring at very low strains only limited by experimental resolution. As a result, these
experiments have provided in our opinion the first direct evidence of the interaction between
tunneling states and have enabled us to assess the interaction strength between TLS in
amorphous solids which is found to be in quantitative agreement with the model of interacting
TLS proposed years ago by Yu and Leggett. Moreover, these findings provide a clue to
generally account for the overall observed experimental deviations of the acoustic properties
in glasses from the predictions of the Standard Tunneling Model.
In addition, light-scattering experiments on glasses are being carried out in joint projects with
Dr. Rafael Jiménez-Riobóo (Instituto de Ciencia de Materiales de Madrid, CSIC), and also
with Dr. Nikolay Surovtsev (Novosibirsk, Russia), as well as neutron scattering experiments
in collaboration with Prof. F. Javier Bermejo (Instituto de Estructura de la Materia , CSIC).
SOME RECENT PUBLICATIONS:
* "Are the calorimetric and elastic Debye temperatures of glasses really different?",
M. A. Ramos,
Philos. Mag. 84, 1313-1321 (2004).
* "Acoustic Properties of Amorphous Solids at Very Low Temperatures: The Quest for
Interacting Tunneling States" .
P. Esquinazi, M. A. Ramos, and R. König,
J. Low Temp. Physics 135, 27 (2004).
* "Density of vibrational states and light-scattering coupling coefficient in the
structural glass and glassy crystal of ethanol",
N. V. Surovtsev, S. V. Adichtchev, E. A. Rössler, and M.A. Ramos,
J. Phys.: Condens. Matter 16, 223 (2004).
* “Low-temperature specific heat of structural and orientational glasses of simple
alcohols”,
M. A. Ramos, C. Talón, R. Jiménez-Riobóo, and S. Vieira,
J. Phys.: Condens. Matter 15, S1007 (2003).
* "Density of states and light-vibration coupling coefficient in B2O3 glasses with different
thermal history”,
N. V. Surovtsev, A. P. Shebanin, and M. A. Ramos,
Phys. Rev. B 67, 024203 (2003) .
* “Low-temperature specific heat and thermal conductivity of glycerol”,
C. Talón, Q. W. Zou, M. A. Ramos, R. Villar, and S. Vieira,
Phys. Rev. B 65, 012203 (2002).
* “The boson peak in structural and orientational glasses of simple alcohols: Specific heat
at low temperatures”,
M. A. Ramos, C. Talón, and S. Vieira,
J. Non-Cryst. Solids 307-310, 80 (2002).
* “Chemical isomerism as a key to explore free-energy landscapes in disordered matter”,
C. Talón, F. J. Bermejo, C. Cabrillo, G. J. Cuello, M. A. González, J. W. Richardson, Jr.,
A. Criado, M. A. Ramos, S. Vieira, F. L. Cumbrera, and L. M. González,
Phys. Rev. Lett. 88, 115506 (2002).
* “Strain dependence of the acoustic properties of amorphous metals below 1 K: Evidence
for the interaction between tunneling states”,
R. König, M. A. Ramos, I. Usherov-Marshak, J. Arcas-Guijarro, A. Hernando-Mañeru,
and P. Esquinazi,
Phys. Rev. B 65, 180201(R) (2002).
* “Low-temperature specific heat of amorphous, orientational glass, and crystal phases of
ethanol”,
C. Talón, M. A. Ramos, and S. Vieira,
Phys. Rev. B 66, 012201 (2002).
* “Thermodynamic and structural properties of the two isomers of solid propanol”,
C. Talón, M. A. Ramos, S. Vieira, I. Shmyt’ko, N. Afonikova, A. Criado, G. Madariaga,
and F. J. Bermejo,
J. Non-Cryst. Solids 287, 226 (2001).
* “Amorphous Materials: Two-level and Tunneling States”,
M. A. Ramos,
in “Encyclopedia of Materials: Science and Technology”, pp. 237-242,
edited by K. H. Jürgen Buschow, R. W. Cahn, M. C. Flemings, B. Ilschner, E. J. Kramer
and S. Mahajan,
(Elsevier Science, 2001).
ISBN: 0-08-0431526
* “Acoustic Properties of Amorphous Metals at Very Low Temperatures:
Applicability of the Tunneling Model“
M. A. Ramos, R. König, E. Gaganidze, and P. Esquinazi,
Phys. Rev. B 61, 1059 (2000).
* “Inelastic light scattering in B2O3 glasses with different thermal history”,
N. V. Surovtsev, J. Wiedersich, A. E. Batalov, V. N. Novikov, M. A. Ramos, and E.
Roessler,
J. Chem. Phys. 113, 5891 (2000).
* "Low-temperature specific heat and glassy dynamics of a polymorphic molecular solid",
C. Talón, M. A. Ramos, S. Vieira, G. J. Cuello, F. J. Bermejo, A. Criado, M. L. Senent,
S.M. Bennington, H. E. Fischer and H. Schober,
Phys. Rev. B 58, 745 (1998).
* "Comment on 'High Frequency Dynamics of Glass Forming Liquids at the Glass
Transition’ ",
F. J. Bermejo, G. J. Cuello, E. Courtens, R. Vacher, and M. A. Ramos,
Phys. Rev. Lett. 81, 3801 (1998).
* “Beyond the Standard Tunneling Model: The Soft-Potential Model”,
M. A. Ramos and U. Buchenau,
in “Tunneling Systems in Amorphous and Crystalline Solids”, Chapter 9, pp. 527-591,
edited by P. Esquinazi.
(Springer-Verlag, Berlin, Heidelberg, New York, 1998).
ISBN: 3-540-63960-8
* "Low-temperature thermal conductivity of glasses within the soft-potential model",
M. A. Ramos and U. Buchenau,
Phys. Rev. B55, 5749 (1997).
* "Low-temperature specific heat of different B2O3 glasses",
E. Pérez-Enciso, M. A. Ramos and S. Vieira,
Phys. Rev. B56, 32 (1997).
* "Quantitative Assessment of the Effects of Orientational and Positional Disorder on
Glassy Dynamics",
M. A. Ramos, S. Vieira, F. J. Bermejo, J. Dawidowski, H. E. Fischer, H. Schober, M. A.
González, C. K. Loong, and D. L. Price,
Phys. Rev. Lett. 78, 82 (1997).