Quantum effects in cryocrystals in a wide temperature range
Due to the ever-increasing interest in cryocrystals in scientific and applied problems, a thorough study of their various properties and characteristics is necessary. The analysis of experimental anomalies in a number of physical properties of quantum cryocrystals (helium, hydrogen and methane) is...
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irk-123456789-1759512021-02-04T01:28:07Z Quantum effects in cryocrystals in a wide temperature range Leont’eva, A. Prokhorov, A. Romanusha, V. Efimov, V. Спеціальний випуск. “Proceedings of 12th International Conference on Cryocrystals and Quantum Crystals (CC-2018)” (Wrocław, Poland, August 26–31, 2018) Due to the ever-increasing interest in cryocrystals in scientific and applied problems, a thorough study of their various properties and characteristics is necessary. The analysis of experimental anomalies in a number of physical properties of quantum cryocrystals (helium, hydrogen and methane) is presented in the low-temperature region. In this temperature region thermal fluctuations decrease sharply, whereas the role of quantum fluctuations stays dominant. This is manifested not only in the translational motion of atoms or defects in such crystals (as helium, neon), but also in the rotational degrees of freedom, for example, in the properties of solid methane and hydrogen. У зв’язку з постійно зростаючим інтересом до кріокристалів у наукових та прикладних задачах необхідно ретельне вивчення їх різних властивостей і характеристик. Наведено аналіз експериментальних аномалій ряду фізичних властивостей квантових кріокристалів (гелій, водень, метан) в області низьких температур, де термічні флуктуації різко зменшуються, а роль квантових флуктуацій стає домінуючою. Це проявляється не тільки в поступальному русі атомів або дефектів в таких кріокристалах, як гелій і неон, але й в обертальних ступенях свободи, наприклад, твердого метану та водню. В связи с постоянно растущим интересом к криокристаллам в научных и прикладных задачах необходимо тщательное изучение их различных свойств и характеристик. Представлен анализ экспериментальных аномалий ряда физических свойств квантовых криокристаллов (гелий, водород, метан) в области низких температур, где термические флуктуации резко уменьшаются, а роль квантовых флуктуаций становится доминирующей. Это проявляется не только в поступательном движении атомов или дефектов в таких криокристаллах, как гелий и неон, но и во вращательных степенях свободы, например, твердого метана и водорода. 2019 Article Quantum effects in cryocrystals in a wide temperature range / A. Leont’eva, A. Prokhorov, V. Romanusha, V. Efimov // Физика низких температур. — 2019. — Т. 45, № 3. — С. 301-309. — Бібліогр.: 40 назв. — англ. 0132-6414 http://dspace.nbuv.gov.ua/handle/123456789/175951 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Спеціальний випуск. “Proceedings of 12th International Conference on Cryocrystals and Quantum Crystals (CC-2018)” (Wrocław, Poland, August 26–31, 2018) Спеціальний випуск. “Proceedings of 12th International Conference on Cryocrystals and Quantum Crystals (CC-2018)” (Wrocław, Poland, August 26–31, 2018) |
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Спеціальний випуск. “Proceedings of 12th International Conference on Cryocrystals and Quantum Crystals (CC-2018)” (Wrocław, Poland, August 26–31, 2018) Спеціальний випуск. “Proceedings of 12th International Conference on Cryocrystals and Quantum Crystals (CC-2018)” (Wrocław, Poland, August 26–31, 2018) Leont’eva, A. Prokhorov, A. Romanusha, V. Efimov, V. Quantum effects in cryocrystals in a wide temperature range Физика низких температур |
| description |
Due to the ever-increasing interest in cryocrystals in scientific and applied problems, a thorough study of their
various properties and characteristics is necessary. The analysis of experimental anomalies in a number of physical properties of quantum cryocrystals (helium, hydrogen and methane) is presented in the low-temperature region. In this temperature region thermal fluctuations decrease sharply, whereas the role of quantum fluctuations
stays dominant. This is manifested not only in the translational motion of atoms or defects in such crystals (as
helium, neon), but also in the rotational degrees of freedom, for example, in the properties of solid methane and
hydrogen. |
| format |
Article |
| author |
Leont’eva, A. Prokhorov, A. Romanusha, V. Efimov, V. |
| author_facet |
Leont’eva, A. Prokhorov, A. Romanusha, V. Efimov, V. |
| author_sort |
Leont’eva, A. |
| title |
Quantum effects in cryocrystals in a wide temperature range |
| title_short |
Quantum effects in cryocrystals in a wide temperature range |
| title_full |
Quantum effects in cryocrystals in a wide temperature range |
| title_fullStr |
Quantum effects in cryocrystals in a wide temperature range |
| title_full_unstemmed |
Quantum effects in cryocrystals in a wide temperature range |
| title_sort |
quantum effects in cryocrystals in a wide temperature range |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2019 |
| topic_facet |
Спеціальний випуск. “Proceedings of 12th International Conference on Cryocrystals and Quantum Crystals (CC-2018)” (Wrocław, Poland, August 26–31, 2018) |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/175951 |
| citation_txt |
Quantum effects in cryocrystals in a wide temperature range / A. Leont’eva, A. Prokhorov, V. Romanusha, V. Efimov // Физика низких температур. — 2019. — Т. 45, № 3. — С. 301-309. — Бібліогр.: 40 назв. — англ. |
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Физика низких температур |
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2025-07-15T13:33:40Z |
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2025-07-15T13:33:40Z |
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| fulltext |
Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 3, pp. 301–309
Quantum effects in cryocrystals
in a wide temperature range
A. Leont’eva
O.O. Galkin Donetsk Physics-Technology Institute of the National Academy of Sciences of Ukraine
46 Nauki Ave., Kyiv, Ukraine
E-mail: tonya.leont@gmail.com
A. Prokhorov
Yaroslav-the-Wise Novgorod State University, 41 Bolshaya St. Petersburg Str., Veliky Novgorod 173003, Russia
V. Romanusha
Ukrainian Engineering Pedagogical Academy, 16 Universytetska Str., Kharkiv 61003, Ukraine
V. Efimov
Institute of Solid State Physics RAS, 2 Academician Ossipyan Str., Chernogolovka 142432, Russia
Received October 24, 2018
Due to the ever-increasing interest in cryocrystals in scientific and applied problems, a thorough study of their
various properties and characteristics is necessary. The analysis of experimental anomalies in a number of phy-
sical properties of quantum cryocrystals (helium, hydrogen and methane) is presented in the low-temperature re-
gion. In this temperature region thermal fluctuations decrease sharply, whereas the role of quantum fluctuations
stays dominant. This is manifested not only in the translational motion of atoms or defects in such crystals (as
helium, neon), but also in the rotational degrees of freedom, for example, in the properties of solid methane and
hydrogen.
Keywords: helium, hydrogen, methane, argon, quantum effects, quantum parameters, rotational heat capacity.
1. Introduction
An interest in studying various properties and features
of cryocrystals has recently increased taking into account
the possibility of its scientific and applied problems. The
development of models for computer calculations and ex-
perimental technique at low temperature has recently renew-
ed an interest in manifestations of the quantum properties
of crystals. First of all, this concerns quantum cryocrystals
in which the amplitude of quantum oscillations of atoms is
of the same order of magnitude as the interatomic dis-
tances. Due to large zero-point vibrations, the wave func-
tions of atoms are overlapped sufficiently. This leads to
subbarrier tunneling of atoms, for example, the motion of
a 3He atom in a 4He matrix or the helium atom exchange
with a vacancy or defect. The de Boer parameter is an indi-
cator of the manifestation of quantum effects in the system
of atoms and molecules. It is defined as the ratio of the
corresponding de Broglie wave of an atom or molecule in
the equilibrium position to the distance between particles
in a crystal.
Traditionally, a crystal is reckoned to quantum crystals
in the case when the de Boer parameter Λ· is comparable
with crystal distances and has the value ~ 0.1. For example,
3He, 4He, H2 have Λ*·> 0.3 [1]. However, the manifestation
of quantum properties is also observed for elements and
compounds in which the quantum kinetic energy of part-
icles at low temperatures is much greater than the energy
of thermal vibrations kBT. For instance, crystal methane
CH4 (“quantum rotator”) can also be assigned to quantum
crystals, if one takes into account not only the de Boer lon-
gitudinal parameter. As in the case of solid hydrogen, the ro-
tating quantum parameter λrot for methane [2] (Tables 1 and
2) is large enough. Unfortunately, in the recent review [1],
the rotational quantum oscillations in cryocrystals are not
even mentioned.
© A. Leont’eva, A. Prokhorov, V. Romanusha, and V. Efimov, 2019
A. Leont’eva, A. Prokhorov, V. Romanusha, and V. Efimov
The rest cryocrystals, like CO2, are characterized by ex-
tremely low values of the rotational quantum parameter.
In this article we summarize a number of experimental
manifestations of quantum effects for various kinds of mo-
tions in crystals, which can be regarded as quantum ones. It
should be noted that recent articles do not provide an ex-
perimental evidence of the quantum nature of such crystals.
2. Experimental manifestations of the quantum nature
of cryocrystals–solid helium, hydrogen, and methane
2.1. Helium
The de Boer parameter has the greatest value for crys-
talline helium. So, the de Boer parameter is Λ*·= 3.07 for
3He and is equal 2.7 for 4He. The history of manifestation
of the quantum behavior of defects in quantum crystals
began with the work of Andreev and Lifshitz [3,4], in
which they theoretically predicted the nonclassical nature
of the mobility of atoms in crystals with large de Boer para-
meter and the possibility of existence of quantum defects,
for example, “vacancions”, “defectons”, “impuritons”. The
most pronounced quantum manifestations are observed in
the motion of defects in helium crystals. In particular, the
following facts were experimentally found:
1. The mobility of 3He impurities ceases to depend on
temperature with cooling below 1 K [5]. This behavior is
explained as a transition to the sub-barrier motion of 3He
atoms.
2. Melting waves were observed on the surface of he-
lium crystals — the effect of a weakly dissipative displace-
ment of atoms at the first-order phase transition from a su-
perfluid liquid to a crystalline phase and vice versa [6]. It is
assumed that the surface point defects are delocalized,
quantum defects appear and their superfluidity arises with
the increasing tunnel effects [3,4]. Apparently, the obser-
vation of anomalously high crystallization rates for some
crystalline planes of pure 4He can be referred to the same
quantum manifestations [7].
3. Along with magnetic impurity 3He injected charges
can be used as probe particles whose motion is fairly easy
to detect in 4He crystals. The motion of charges in the he-
lium lattice is determined by their exchange with vacancies.
The influence of quantum oscillations in the samples of so-
lid 4He grown at a pressure of 30–32 atm is most clearly
manifested for positive charges movement, the motion of
which is determined by the concentration and mobility of
vacancies. A feature of the positive charges in solid helium
is the existence of a region of compressed helium around
the charge, which is formed due to the van der Waals at-
traction of neutral helium atoms to a positive ion +He. In a
liquid, this polarization attraction leads to the formation of
a charged cluster consisting of a charge covered by several
layers of solid helium [8]. The motion of such a complex in
solid helium is defined by a consecutive exchange with
vacancies. At high temperatures (T ~ 1–2 K), the mobility
of charges µ+ (and their velocity v+) is explicitly described
by the thermal activation exponential dependence v+ ~ µ+ ~
~ exp (–ε+/T). The exponent of the charge diffusion coef-
ficient, estimated from the Einstein relation D+ = µ+kT/e,
turned out to be close to the exponent of the diffusion coef-
ficient of 3He impurity in the 4He matrix.
The absolute values of D+ and D3, as well as the cha-
racteristic activation energies of ε+, ε3 and vacancies εv [9]
are the cause of a basis for the development of vacancy
mechanisms of charge motion. In this model the rate of
charge transfer is determined by the interaction of an ion
with vacancies, i.e., by the relation v+~ nvDvσv, where nv is
the concentration of vacancies, Dv is the diffusion coef-
ficient of vacancies, σv is the effective cross section for
vacancy or “vacancion” scattering on a charge or the pro-
bability of their exchange of the places. If we assume that
the inflections of ions velocities at T < 0.7 K in Fig. 1 are re-
lated to the change in a transport mechanism, for example,
the transition from thermally activated (TA) diffusion to
quantum tunneling. We may write D+ = DTA + DQ, where
DTA ~ exp (–ε+/T) [10], at the additivity of these two me-
chanisms — quantum and thermal activate. The depend-
ence of DQ on temperature, calculated from the data for
different crystals at different pressures, is shown in Fig. 2.
An increase in the mobility of defects with cooling of
the crystal is explained by a decrease in the scattering of
quasiparticles (quantum defects — “defectons”) on pho-
nons [3]. A further decrease in ion (“defecton”) mobility
Table 1. Values of the quantum de Boer parameter for He, H2,
CH4, Ne, Ar cryocrystals [1]. Here λ(ε) is the de-Broglie wave
length, r0 and ε are the Lennard-Jones potential parameters
Cryocrystals Helium Hydrogen
Para-
hydrogen
Methane Neon Argon
Quantum de Boer
parameter
*
0 0
( ) .
r r m
λ ε
Λ = =
ε
2.7 1.79
1.78
1.48 0.55 0.16
Notes : here we show argon for comparison, it’s quantum para-
meter Λ*·is by order of magnitude smaller than the parameter
for helium, hydrogen or methane. In this case argon crystal may
be considered as a “classical” one.
Table 2. Values of the rotational quantum de Boer parameter
for H2, CH4, CD4, and CО2 [2]
Cryocrystals Hydrogen Methane Deuterated
methane
Carbon
dioxide
Rotational quantum
de Boer parameter
rot
0
2
IU
π
λ =
4.78 0.627 0.318 0.0431
Notes : here I is the moment of inertia, U0 is the potential barrier.
302 Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 3
Quantum effects in cryocrystals in a wide temperature range
occurs due to the static failure of quantum subbarrier tun-
neling levels, taking into account different nature of the ex-
changing particles (charges and vacancies) and the addi-
tional energy of the electric field for moving the charges.
The cooling of a quantum crystal reduces the dynamic
probability of coincidence of the levels for the quantum
motion of defects and their interaction with charges [11].
The temperature range of the anomalous charge mobility
behavior in weak fields and the diffusion of the magnetic
impurity 3He in 4He matrix coincide (T < 0.7 K). This in-
dicates that the mechanism of anomalous motion of such
energetically different particles (isotope 3He and cluster —
positive charge with surrounding deformations), apparently,
have the same nature, the vacancy mechanism of motion.
The features of the interaction of quantum vacancies (”va-
cancions”) with isotopes, whose concentration is sufficiently
high, or with microscopic distortions of the lattice density
around the positive charge, determine different temperature
dependencies at temperatures below the thermoactivation
region. Estimation of the quantum mechanical band of the
motion of charged particles gives a value of ∆+ ~ 10–6 K,
while the band width for the “impurity” has appreciably
larger value ∆3 ~ 10–4 K [12].
2.2. Hydrogen
The influence of quantum effects is particularly great in
case of solid helium and hydrogen because of the small
mass of helium atoms and hydrogen molecules and the com-
paratively weak interparticle interaction and the quantum
demonstration is noticeable throughout the entire region of
existence of the crystalline state of both crystals. For solid
hydrogen, the manifestation of quantum behavior could be
observed at the motion of such lattice defects as disloca-
tions when studying deformation of the samples.
2.2.1. Creep of solid hydrogen
The plasticity of normal hydrogen n-H2, containing
75% of ortho-hydrogen and 25% of para-hydrogen p-H2,
was studied by the creep method in a wide range of tem-
peratures and stresses. The measurements were carried out
on fully transparent polycrystalline samples with grain size
of 0.5–1.0 mm [13]. The experiments focused on the study
of the steady-state creep ε = ∆l/l. Its duration ε(t) increased
with decreasing temperature or with decreasing value of
the applied load σ. At this stage, the strain rate dε/dt was
calculated.
It was found that, above 10 K, the strain rate of n-H2 is
extremely sensitive to small changes of temperature. At T
below 10 K, the fall inέdecreases with reducing tempera-
ture, and at helium temperatures the strain rate is practical-
ly independent from temperature (Fig. 3). Solid hydrogen
exhibits nonzero strain rates at a steady stage even at very
low loads. This sharply distinguishes hydrogen among other
cryocrystals by the influence of quantum properties, which
comes out through its plasticity and dislocation motion.
There is some appearance of the quantum phenomena
in solid hydrogen associated with the pining of dislocations
in the regions of short-range orientational order arising in
Fig. 1. Temperature dependence of positive ions velocity in two
samples of solid helium, grown at P = 31.2 atm (open circles) and
31.0 atm (closed circles) at different electric field stresses.
Fig. 2. Temperature dependence of DQ, calculated from positive
ion velocity for helium crystals growth at different pressures
(open circles — P = 28.8 bar, closes circles — 31.3, open trian-
gles — 33.0 and closed triangles — 35.9 bar). Applied electric
field U = 300 V.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 3 303
A. Leont’eva, A. Prokhorov, V. Romanusha, and V. Efimov
an orientationally disordered crystal as a result of quadru-
pole-quadrupole interaction of neighboring ortho-molecules.
Indeed, the formation of crystals from hydrogen vapor
molecules (i.e., para-hydrogen, p-H2) leads to an increase
in the strain rate by a factor of 50 (!) compared to normal
hydrogen containing an ortho-impurity (Fig. 4). Thus, dis-
ordered systems consisting of the ortho-para hydrogen mo-
lecules substantially reduce the creep rate of solid hyd-
rogen [14].
A sharp increase of mobility of dislocation and the tem-
perature independence of their velocity for hydrogen with-
out the orientational disordering indicate the quantum me-
chanical mechanism of their motion. The possibility of the
existence of two-dimensional superfluidity on the surface
of hydrogen crystals was pointed out in [15]. Similar con-
ditions can also arise for the diffusion of hydrogen mo-
lecules during the motion of dislocations in a force field.
2.2.2. Low-frequency internal friction of solid hydrogen
The effect of quantum phenomena on creep and plas-
ticity is also observed in the experiments on low-frequency
internal friction (LFIF) of solid hydrogen, when the damp-
ing decrement of the system for torsional vibrations with
small amplitude has been measured. The investigations of
the temperature dependence of LFIF and shear modulus
G~ f 2 (Fig. 4) in the temperature range of 2–12.5 K were
carried out on free (separated from the container walls)
samples of solid hydrogen n-H2 by the inverse torsional
pendulum [16] using the methods described in [33].
For comparison, Fig. 4 also shows the experimental re-
sults of LFIF for solid argon, the quantum de Boer para-
meter of which is smaller by orders of magnitude than that
for hydrogen (Table 1). This allowed us to consider argon
in a series of cryocrystals as a “classical” object convenient
for comparisons. First of all, it is worth paying attention
to the tendency of increasing the absorption of energy at
the LFIF in n-H2 as the temperature decreases. Thus, Q–1
increases from 4·10–3 at 7 K to 1.5·10–2 at 2 K, whereas the
tendency of the temperature dependence of internal friction
for argon practically does not change and remains at a rela-
tively low level (lower than 10–3). Such an anomalous rise
in the LFIF of solid hydrogen with decreasing temperature,
may be explained by the effect of quantum properties of
motion of dislocations. The same anomalous behavior is
observed for the shear modulus G(T) ~ f 2 for n-hydrogen
in the interval 0.15–0.95 of reduced temperatures.
The hardness of hydrogen samples practically does not
change throughout almost the entire temperature range
of their existence, remaining at a constant level close to
G(T = 0 K), while argon samples become harder. The ab-
solute values of f 2 in hydrogen are lower by an order of
magnitude than those in argon in scale T/Tm at cooling.
Fig. 3. Dependence of the steady-state creep rate of solid hydro-
gen on temperature. The curve corresponds to a sample of normal
hydrogen (75% of ortho-modification and 25% of para-hydro-
gen). The creep rate at helium temperatures is different from zero.
The dashed line corresponds to pure para-hydrogen, έ is 50 times
higher than that for normal hydrogen and absolute temperature
independent [14].
Fig. 4. Dependencies of energy absorption for free torsional oscillations for hydrogen and argon samples (a) and the shear modulus
for the same samples (b) on reduced temperature.
304 Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 3
Quantum effects in cryocrystals in a wide temperature range
The indicated features of LFIF in solid hydrogen the fol-
lowing: an anomalous increase in the background of inter-
nal friction with a decrease in temperature in the region
T/Tm < 0.5, the relative constancy of the shear modulus and
its low values throughout the studied temperature range are
apparently related to the behavior of temperature-inde-
pendent quantum phenomena.
2.3. Methane
For simple atoms, such as helium or argon ones, occu-
pying lattice sites in crystals, only quantum-mechanical
exchange is possible at very low temperature. All the above
examples of the macroscopic manifestation of quantum pro-
perties were associated with the delocalization of defects in
crystals with the high de Boer parameter.
Crystals formatted from molecules have the possibility
for quantum rotational motion of the molecules as well as
thermomechanical mechanisms and quantum mechanisms
of translational displacement.
At sufficiently low temperature, when the quantum fluc-
tuations stay dominant, two types of disordering quantum
rotational phenomena take place: first, at λrot ~ 10–5,
the system goes over into a radially ordered but orientation-
ally disordered state when different atoms in molecules are
rotated on the lattice position. For much larger λrot ~ 0.1,
a transition to a disordered state takes place [17].
In this sense the quantum manifestations of rotational
displacements can be found in crystals with simple mole-
cules such as hydrogen and methane, for which the quan-
tum rotational parameter λrot has the values > 0.1.
2.3.1. Creep of solid methane
The creep of solid methane (Ttr = 90.4 K) was studied
in the most interesting low-temperature region (4–23 K), in
which quantum features of methane plasticity were observed.
Methane samples with a working section 30mm in length
and 6 mm in diameter were crystallized from the liquid
phase and they were completely transparent without visible
defects. The purity of the feed gas was 99.99%. The sample
was detached from the container wall by pumping methane
vapor over the sample at a temperature close to the triple
point. At the same time, grain boundaries with linear dimen-
sions of 2–4 mm were identified. The method for studying
creep is described in [20]. Figure 5 shows an anomalous
increase in the rate of stationary creep ε as temperature
decreases in the interval of 10–4 K. The limiting value of ε
at T = 4.5 K and σ = 200 g/mm2 is ε = 1.2·10–7 s–1, which
exceeds ε at 9 K (0.3·10–7 s–1) by 4 times [18]. We com-
pare the results of creep measurement of methane with
the results of studies of crystalline argon as the standard
of classical behavior of creep.
The general form of the temperature dependence of
the creep rate έ of methane at different loads in the range
of 4–30 K is shown in Fig. 6. As in Fig. 5, the creep of
argon is practically brittle and with zero creep rate below
23 K [19]. An increase in the load σ leads only to a jump
in the instantaneous creep of argon, but at the steady-state
stage of creep is equal to zero ε = 0 within an experimental
error [20].
An increase in the rate of stationary creep of methane
with decreasing temperature (below 10 K), unlike argon, is
apparently associated with quantum effects in methane.
2.3.2. Thermodynamic indicators of the quantum nature
of crystalline methane
In 1953 Tomita [21] discovered an unexpected pheno-
menon in NMR studies of solid methane: methane mole-
cules in the solid state rotate in a wide range of tempera-
tures, up to 65 K, when (according to the NMR data) the
Fig. 5. Temperature dependence of the rate of stationary creep of
solid methane and argon in the temperature range of 4–10 K.
Solid argon in this temperature interval has the creep rate very
close to zero.
Fig. 6. Temperature dependence of ε (T) for crystalline methane
at various loads, g/mm2: 440 (1), 300 (2), 200 (3). The solid line
is practically zero velocity ε for argon. The vertical dashed line
corresponds to the temperature of the phase transition in solid
methane.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 3 305
A. Leont’eva, A. Prokhorov, V. Romanusha, and V. Efimov
character of rotation of CH4 molecules changes sharply,
like as upon melting. The rotation of molecules in the CH4
lattice allows suggesting that solid methane is a quantum
crystal throughout the entire range of existence of the solid
phase.
These experimental data of Tomita directed us to ana-
lyze the rotational heat capacity of this cryocrystal. Avail-
able literature sources showed that the entire rotational heat
capacity of methane and other gases has been calculated
only for an ideal quantum gas. One of the first proofs of
the quantum nature of rotational motion was paper [22] by
the example of gaseous deuterium. Figure 7 presents the cal-
culated and experimental results of the temperature depend-
ence of heat capacity for gaseous deuterium. The main fea-
ture of such dependences is the presence of a characteristic
maximum at T0, which is a purely quantum effect [34].
When analyzing the experimental works of other authors
on methane, it was unexpectedly found that the special tem-
perature of Tomita (65 K) manifests itself in a large num-
ber of physical properties of solid methane in the form
of anomalies in the temperature dependences of these pro-
perties [32]. These anomalies were especially pronounced
in the investigations of low-frequency internal friction [24],
nuclear magnetic resonance [21], adhesion [25], etc., in
which the anomalies at 60–70 K even significantly exceed-
ed the anomalies at α–β phase transition. It is seen (Fig. 8)
that near 65 K there is a peak of LFIF, which is much
greater than the anomaly at α–β transition. At these tem-
peratures, a sharp decrease in the shear modulus is also
observed, which is apparently due to the transition of solid
methane to a state close to a liquid [21]. We should also
note a significant increase in LFIF as the temperature de-
creases in the temperature region T below 20 K, which indi-
cates quantum effects, as in the case of the most quantum
manifestation of rotational motion in hydrogen crystal [16].
It should be noted that new reports have recently ap-
peared in which the anomalies described above are con-
firmed [26,27,35].
2.3.3. Topons
We will consider the rotational component of the ther-
modynamic functions of solid methane in the framework
of the ideal gas model consisting of topon quasiparticles
(tops). The thermodynamics of an ideal quantum gas with
rotational degrees of freedom of molecules was created in
the late 1920s [36]. The rotational component of the heat
capacity rotC of an ideal gas consisting of tops is a func-
tion of the dimensionless temperature
( )rot
rot
= , = .TC f
T
τ τ
2
rot =
2
T
Iκ
(1)
(k is the Boltzmann constant, I is moment of inertia of the
molecule-gyroscope). To calculate the temperature de-
pendence of the rotational heat capacity of methane, it is
required to calculate the corresponding partition function
=0
( 1)exp ,n
n
n nZ g
∞ + = − τ
∑ (2)
where ng is the multiplicity of degeneracy of the ith state
of the top, τ is the dimensionless temperature determined
by the relation (1).
All the specifics of thermodynamics of a particular ideal
quantum gas in terms of dimensionless temperature lies in
the nature of the dependence of the multiplicity of degener-
ation of the top on the number of its state. The dependence
of g on n is entirely determined by the symmetry properties
of the molecule-top. Unlike other degrees of freedom, the ro-
tational component of the heat capacity is a non-monotonic
function of temperature: before rushing to zero at 0T → ,
the rotational heat capacity increases to some maximum
value at 0=T T and then only rushes to zero. The value of
Fig. 7. Temperature dependence of rotational heat capacity for
gaseous deuterium [23] with a maximum near 90 K.
Fig. 8. Temperature dependence of LFIF Q–1and square of tor-
sion oscillation frequency f 2 of solid methane [32].
306 Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 3
Quantum effects in cryocrystals in a wide temperature range
the rotational heat capacity at the maximum point of
rot 0( )C T is greater than its classical value, achieved at high
temperatures. [37].
Using the concept of quasiparticles (or, what is the same
thing, elementary excitations) allows us to consider a sys-
tem of interacting particles as an ideal (or almost perfect)
gas of particles, whose parameters are usually determined
from experimental data. The quasiparticles include phonons,
electrons in crystals, polarons, etc.
It is a striking fact that, until now, the thermodynamic
approach to the properties of solid methane has been com-
pletely absents in literature. Since 1920, up to the present
time (Landau’s work [37]), the thermodynamics of methane
has been studied only for an ideal quantum gas. It led to
the need to create a model of the rotational heat capacity of
solid methane, where the rotational degrees of freedom are
described within the concept of the corresponding quasi-
particles called topons.
In particular, it was suggested in [28,29] that in solid
methane due to the intermolecular interaction the collective
excitations of the rotational degrees of freedom of CH4
molecules should be considered instead of the independent
rotation of individual molecules as for a gas. Such a con-
ception corresponds to the work of Pauling [30]. A topon is
characterized by a single parameter the effective moment
of inertia. A topon is a spherical top not because of its sym-
metry. Therefore, the degeneracy of the levels of a topon is
determined by the relation gn = (2n + 1)2, where n is the
level number [31].
The plot of the temperature dependence of rotational
heat capacity for solid methane has the form shown in
Fig. 9 [28]. The maximum corresponds to temperature T0 =
= 60 K.
We may identify the temperature of a sharp change in
the character of rotation of solid methane moleculeswith
the maximum of the rotational heat capacity T0 according
to the Tomita’s result. Then we find a rough estimate of
the rotational temperature, Trot = 100 K, i.e., rotational
temperature of topons is 13 times higher than Trot for an
ideal gas.
It should be noted that the thermodynamic properties of
methane at low temperatures (i.e., at temperatures below
the phase transition point of about 20 K) were studied in
[38–40]. In these works, it was shown that the characteris-
tic maximum of the rotational component of the heat ca-
pacity of solid methane occurs at temperatures of the order
of 1 K. This value is noticeably lower than the rotational
temperature of gaseous methane, which is about 5 K. The
difficulty of molecular rotations of methane leads to a de-
crease in the effective rotational temperature of solid me-
thane relative to gaseous methane. This conclusion is in-
terpretable within the framework of the topon concept.
In the high-temperature region of about 60 K, the situa-
tion is significantly different: the structure of methane cry-
stals is different from the low-temperature structure that
occurs
at T <20 K . Here there is a significant excess of the ef-
fective rotational temperature of solid methane over gase-
ous methane.
Based on the analysis of the thermodynamic character-
istics of methane crystals, it can be concluded that solid
methane retains quantum features up to high temperatures
of 60–65 K (0.7Ttr ). The temperature T0 above which, ac-
cording to NMR data, solid methane sharply converts to
a state close to the liquid one. This temperature can be con-
sidered as the temperature of the quantum-classical transi-
tion for solid methane [28,29].
3. Conclusions
1. Quantum manifestations in the physical properties of
crystalline helium, hydrogen and methane are demonstrat-
ed using numerous experimental data.
2. It is shown that in order to estimate the size of quan-
tum effects in these cryocrystals, it is convenient to com-
pare their properties with the simplest cryocrystal argon,
which has an extremely low de Boer quantum parameter
and may be considered as a classical solid.
3. Quantum features of cryocrystals are manifested in
the form of anomalous temperature dependences different
from thermoactivation behavior and in the peculiarities of
motion of test particles and defectsas well. The quantum
features are manifested also in thermodynamic properties
as the presence of a maximum of the rotational heat ca-
pacity, for example, in the case of solid methane and deu-
terium.
The authors are grateful to A. Zakharov for essential
contribution and help in the work, and to O. Kirichek and
L. Alekseeva for support of this work.
Author A.Yu. Prokhorov is grateful to the Ministry of
Education and Science of the Russian Federation for finan-
Fig. 9. Temperature dependence of the rotational heat capacity C
of topons on the dimensionless temperature T/Trot.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 3 307
A. Leont’eva, A. Prokhorov, V. Romanusha, and V. Efimov
cial support of work within the framework of the project
part of the State Assignment (grant No. 3.3572.2017), and
author V.B. Efimov is grateful to the Ministry of Education
and Science of the Russian Federation for financial support
of the work within the framework of the State Assignment
of the ISSP.
_______
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___________________________
Квантові ефекти в кріокристалах у широкому
температурному діапазоні
А. Леонтьєва, А. Прохоров, В. Романуша,
В. Єфімов
У зв’язку з постійно зростаючим інтересом до кріокри-
сталів у наукових та прикладних задачах необхідно ретельне
вивчення їх різних властивостей і характеристик. Наведено
аналіз експериментальних аномалій ряду фізичних властиво-
стей квантових кріокристалів (гелій, водень, метан) в області
низьких температур, де термічні флуктуації різко зменшу-
ються, а роль квантових флуктуацій стає домінуючою. Це
проявляється не тільки в поступальному русі атомів або де-
фектів в таких кріокристалах, як гелій і неон, але й в обер-
тальних ступенях свободи, наприклад, твердого метану та
водню.
Ключові слова: гелій, водень, метан, аргон, квантові ефекти,
квантові параметри, обертальна теплоємність.
308 Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 3
https://doi.org/10.3367/UFNr.0118.197602c.0251
https://doi.org/10.3367/UFNr.0185.201511b.1163
https://doi.org/10.1103/PhysRev.116.1339
https://doi.org/10.1103/PhysRev.89.429
https://doi.org/10.1016/j.cryogenics.2017.10.017
https://doi.org/10.1088/1742-6596/969/1/012006
https://doi.org/10.1103/PhysRev.36.430
https://doi.org/10.1016/j.cryogenics.2016.06.002
https://doi.org/10.1007/978-3-642-52601-5
https://doi.org/10.1007/978-3-642-52601-5
https://doi.org/10.1143/PTP.43.1121
https://doi.org/10.1143/PTP.43.1121
https://doi.org/10.1143/PTPS.E68.436
https://doi.org/10.1103/PhysRevLett.20.1
Quantum effects in cryocrystals in a wide temperature range
Квантовые эффекты в криокристаллах в широком
температурном диапазоне
А. Леонтьева, А. Прохоров, В. Романуша,
В. Ефимов
В связи с постоянно растущим интересом к криокристал-
лам в научных и прикладных задачах необходимо тщательное
изучение их различных свойств и характеристик. Представ-
лен анализ экспериментальных аномалий ряда физических
свойств квантовых криокристаллов (гелий, водород, метан) в
области низких температур, где термические флуктуации
резко уменьшаются, а роль квантовых флуктуаций становит-
ся доминирующей. Это проявляется не только в поступа-
тельном движении атомов или дефектов в таких криокри-
сталлах, как гелий и неон, но и во вращательных степенях
свободы, например, твердого метана и водорода.
Ключевые слова: гелий, водород, метан, аргон, квантовые
эффекты, квантовые параметры, вращательная теплоемкость.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 3 309
1. Introduction
2. Experimental manifestations of the quantum nature of cryocrystals–solid helium, hydrogen, and methane
2.1. Helium
2.2. Hydrogen
2.2.1. Creep of solid hydrogen
2.2.2. Low-frequency internal friction of solid hydrogen
2.3. Methane
2.3.1. Creep of solid methane
2.3.2. Thermodynamic indicators of the quantum nature of crystalline methane
2.3.3. Topons
3. Conclusions
|