Heat capacity of p-H₂–p-D₂–Ne solid solution: Effect of (p-D₂)Ne clusters
The heat capacity of a solid solution of 1% p-D₂ and 0.25% Ne in p-H₂ has been investigated in the interval ΔT = 0.5–4 K. An excess heat capacity ΔCNe of this solution exceeding the heat capacity of the 1% p-D₂ in p-H₂ solution has been detected and analyzed. It is found that below 2 K the domina...
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| Цитувати: | Heat capacity of p-H₂–p-D₂–Ne solid solution: Effect of (p-D₂)Ne clusters / M.I. Bagatskii, I.Ya. Minchina, V.M. Bagatskii // Физика низких температур. — 2005. — Т. 31, № 6. — С. 620-623. — Бібліогр.: 15 назв. — англ. |
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irk-123456789-1214802017-06-15T03:05:40Z Heat capacity of p-H₂–p-D₂–Ne solid solution: Effect of (p-D₂)Ne clusters Bagatskii, M.I. Minchina, I.Ya. Bagatskii, V.M. Квантовые жидкости и квантовые кpисталлы The heat capacity of a solid solution of 1% p-D₂ and 0.25% Ne in p-H₂ has been investigated in the interval ΔT = 0.5–4 K. An excess heat capacity ΔCNe of this solution exceeding the heat capacity of the 1% p-D₂ in p-H₂ solution has been detected and analyzed. It is found that below 2 K the dominant contribution to the heat capacity ΔCNe is made by the rotation of the p-D₂ molecules in the (p-D₂)Ne type clusters. The number of (p-D₂)Ne clusters in the solid sample is strongly dependent on the conditions of preparation. The splitting of the J = 1 level of the p-D₂ molecules in the (p-D₂)Ne clusters Δ = 3.2 K is consistent with the theoretical estimate. 2005 Article Heat capacity of p-H₂–p-D₂–Ne solid solution: Effect of (p-D₂)Ne clusters / M.I. Bagatskii, I.Ya. Minchina, V.M. Bagatskii // Физика низких температур. — 2005. — Т. 31, № 6. — С. 620-623. — Бібліогр.: 15 назв. — англ. 0132-6414 PACS: 65.40.+g http://dspace.nbuv.gov.ua/handle/123456789/121480 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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Квантовые жидкости и квантовые кpисталлы Квантовые жидкости и квантовые кpисталлы |
| spellingShingle |
Квантовые жидкости и квантовые кpисталлы Квантовые жидкости и квантовые кpисталлы Bagatskii, M.I. Minchina, I.Ya. Bagatskii, V.M. Heat capacity of p-H₂–p-D₂–Ne solid solution: Effect of (p-D₂)Ne clusters Физика низких температур |
| description |
The heat capacity of a solid solution of 1% p-D₂ and 0.25% Ne in p-H₂ has been investigated in
the interval ΔT = 0.5–4 K. An excess heat capacity ΔCNe of this solution exceeding the heat capacity
of the 1% p-D₂ in p-H₂ solution has been detected and analyzed. It is found that below 2 K the
dominant contribution to the heat capacity ΔCNe is made by the rotation of the p-D₂ molecules in
the (p-D₂)Ne type clusters. The number of (p-D₂)Ne clusters in the solid sample is strongly dependent
on the conditions of preparation. The splitting of the J = 1 level of the p-D₂ molecules in
the (p-D₂)Ne clusters Δ = 3.2 K is consistent with the theoretical estimate. |
| format |
Article |
| author |
Bagatskii, M.I. Minchina, I.Ya. Bagatskii, V.M. |
| author_facet |
Bagatskii, M.I. Minchina, I.Ya. Bagatskii, V.M. |
| author_sort |
Bagatskii, M.I. |
| title |
Heat capacity of p-H₂–p-D₂–Ne solid solution: Effect of (p-D₂)Ne clusters |
| title_short |
Heat capacity of p-H₂–p-D₂–Ne solid solution: Effect of (p-D₂)Ne clusters |
| title_full |
Heat capacity of p-H₂–p-D₂–Ne solid solution: Effect of (p-D₂)Ne clusters |
| title_fullStr |
Heat capacity of p-H₂–p-D₂–Ne solid solution: Effect of (p-D₂)Ne clusters |
| title_full_unstemmed |
Heat capacity of p-H₂–p-D₂–Ne solid solution: Effect of (p-D₂)Ne clusters |
| title_sort |
heat capacity of p-h₂–p-d₂–ne solid solution: effect of (p-d₂)ne clusters |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2005 |
| topic_facet |
Квантовые жидкости и квантовые кpисталлы |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/121480 |
| citation_txt |
Heat capacity of p-H₂–p-D₂–Ne solid solution: Effect of (p-D₂)Ne clusters
/ M.I. Bagatskii, I.Ya. Minchina, V.M. Bagatskii // Физика низких температур. — 2005. — Т. 31, № 6. — С. 620-623. — Бібліогр.: 15 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT bagatskiimi heatcapacityofph2pd2nesolidsolutioneffectofpd2neclusters AT minchinaiya heatcapacityofph2pd2nesolidsolutioneffectofpd2neclusters AT bagatskiivm heatcapacityofph2pd2nesolidsolutioneffectofpd2neclusters |
| first_indexed |
2025-07-08T19:58:33Z |
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2025-07-08T19:58:33Z |
| _version_ |
1837110094972583936 |
| fulltext |
Fizika Nizkikh Temperatur, 2005, v. 31, No. 6, p. 620–623
Heat capacity of p-H2–p-D2–Ne solid solution: Effect of
(p-D2)Ne clusters
M.I. Bagatskii, I.Ya. Minchina, and V.M. Bagatskii
B. Verkin Institute for Low Temperature Physics and Engineering
of the National Academy of Sciences of Ukraine, 47, Lenin Ave., Kharkov 61103, Ukraine
Å-mail: bagatskii@ilt.kharkov.ua
Received October 26, 2004
The heat capacity of a solid solution of 1% p-D2 and 0.25% Ne in p-H2 has been investigated in
the interval �T = 0.5–4 K. An excess heat capacity �CNe of this solution exceeding the heat capac-
ity of the 1% p-D2 in p-H2 solution has been detected and analyzed. It is found that below 2 K the
dominant contribution to the heat capacity �CNe is made by the rotation of the p-D2 molecules in
the (p-D2)Ne type clusters. The number of (p-D2)Ne clusters in the solid sample is strongly de-
pendent on the conditions of preparation. The splitting of the J = 1 level of the p-D2 molecules in
the (p-D2)Ne clusters � = 3.2 K is consistent with the theoretical estimate.
PACS: 65.40.+g
Introduction
Heavy impurities in quantum crystals of hydrogen
isotopes affect the phonon spectrum of the crystal and
disturb zero (quantum) vibrations of the lattice and
rotation of the molecules. Local changes in the lattice
structure and the formation of new quantum objects
(molecular clusters and complexes [1–8]) are also pos-
sible in the vicinity of heavy impurities, which can
produce considerable changes in the physical proper-
ties of crystals. These phenomena have recently a fo-
cus of intensive investigations [8,9].
The excess heat capacity �CNe of the solution of
2.5% o-H2 and xNe (x = 0.5%, 2%) in solid p-H2
caused by the heavy quasi-isotopic Ne impurity intro-
duced into the solid 2.5 % o-H2–p-H2 solution was
first observed in [1] at T = 2–6 K. Near T = 2 K �CNe
is an order of magnitude over the results calculated in
the harmonic approximation for �CL,Ne caused by the
heavy quasi-isotopic Ne impurity changing the phonon
spectrum of the crystal.
A theory was put forward in [2] to explain this
anomaly. Along with the anomalous heat capacity of
solid H2–Ne solutions attendant upon the change in
the phonon spectrum of crystal, there is an anomaly in
the rotational component of CR,Ne which is due to the
contribution from the rotational degrees of freedom of
the H2 molecules in the lowest state with the rota-
tional quantum number J = 1 (o-H2). The strong per-
turbation of zero (quantum) lattice vibrations by the
Ne atoms in the (o-H2)Ne – type clusters disturbs the
local symmetry of the crystal field [2] causing the J = 1
level of o-H2 molecules to split into two levels with
the degeneracies g0 = 1 and g1 = 2 (see Fig. 1). When
the (o-H2)Ne cluster is formed, the energy of the sub-
system decreases by 2�/3 (� is the splitting value).
CR,Ne(T) exhibits a Schottky type anomaly. The equi-
librium contents of o-H2–o-H2 and (o-H2)Ne clusters
in this system depends on temperature. As the temper-
ature changes due to quantum diffusion of the angular
momentum of the o-H2 molecules, the number of clus-
ters varies with time (configurational relaxation). The
value of heat capacity is therefore dependent on the
time tm of the (single) heat capacity measurement and
the temperature prehistory. In [1] the heat capacity
was measured above the temperature of the CR,Ne(T)
maximum in the Schottky curve. The splitting 2.5 K <
< � < 5 K of the J = 1 level of the o-H2 molecules in the
neighborhood of the Ne impurity was roughly esti-
mated [2] from the analysis the results obtained in [1].
This study is concentrated on the contribution of
the rotational motion of the p-D2 molecules to the
heat capacity of the solid 1% p-D2 – p-H2 solution
doped with 0.25% Ne in the interval �T = 0.5–4 K.
The choice of impurity concentration and the tempera-
ture interval was dictated by the following conside-
© M.I. Bagatskii, I.Ya. Minchina, and V.M. Bagatskii, 2005
rations. Firstly, quantum diffusion of the p-D2 mole-
cules is impossible in the p-H2 lattice [10] and conver-
sion of the p-D2 molecules during the experiment is
negligible. Secondly, with the splitting � > 2 K of the
J = 1 level of the p-D2 molecules in the neighborhood
of the Ne impurity the temperature of the maximum in
the Schottky curves enters the temperature region of
this investigation [2]. Thirdly, earlier we investigated
the heat capacity of the solution of 1%p-D2 in solid
p-H2 using the same calorimeter [10]. This permits us
to separate accurately the excess heat capacity �CNe
caused by 0.25% Ne introduced into the solid 1% p-D2
– p-H2 solution.
Experiment
The heat capacity of the solid solution of 0.94 mole %
p-D2 and 0.06 mole % o-D2 in parahydrogen (below
referred to as 1% p-D2 in p-H2) doped with 0.25% Ne
has been measured using an adiabatic calorimeter [11]
in the interval �T = 0.5 – 4 K. The gas compositions
were H2 – 99.99% (the isotope – 99.985%, HD –
0.015%); D2 – 99.99% (the isotope – 99.9%, HD –
0.1%); Ne- 99.99%. The starting orto-para composi-
tion of hydrogen � 1�10–2 % o-H2 was obtained by
keeping hydrogen in catalytic Fe(OH)3 for 24 h at a
constant temperature (the triple point of H2). p-D2
was obtained in an adsorption column by the technique
described in [12]. The p-D2 concentration (94%) in
deuterium was estimated from the thermal conductivi-
ty of D2 gas at nitrogen temperatures using an
analyzer which we made and calibrated following the
configuration in [13]. Four measurement series were
performed. Series 1 was made on a sample prepared in
the calorimetric vessel by condensing the gas mixture
to the solid phase at T � 9.5 K. The other series were
made on solid samples prepared by crystallization
from the liquid phase. After each series of measure-
ment, the sample was melted, kept in the liquid state
during a period of ti at temperature Ti, crystallized
and cooled. Then the next run of measurement was
performed.
Table 1. Time ti during which the sample was kept in the
liquid phase near Ti before its crystallization and the subse-
quent series of heat capacity measurement.
Series t
i
, min T
i
, K
2 40 14.5
3 90 16
4 120 18
The heat capacities measured at T � 4 K are inde-
pendent of the temperature prehistory of the sample.
The measurement error was � 6% at 0.5 K, � 2% at 1K
and � 1% at T > 2 K.
Results and descussion
The experimental results on heat capacity per mole
of the solution 1%p-D2 and 0.25%Ne in solid p-H2 can
be written as
Ñ = Ñ1 + �ÑNe = Ñ1 + �Ñ
L,Ne + ÑR,Ne. (1)
Here C1 is the heat capacity of the solid 1%p-D2– p-H2
solution [9], �CNe is the excess heat capacity of the
solution 1%p-D2 and 0.25%Ne in solid p-H2 over the
heat capacity of the solution 1%p-D2 in solid p-H2.
We assume that �CNe = �CL,Ne + CR,Ne, where
�CL,Ne is the increment in the heat capacity of the
lattice produced by the quasi-local frequencies in the
phonon spectrum of hydrogen, which appear when the
heavy quasi-isotopic Ne impurity is introduced into the
lattice of p-H2; CR,Ne is the rotational heat capacity of
the p-D2 molecules caused by the 0.25% Ne impurity
introduced into the p-H2–1% p-D2 solution. �CL,Ne
was calculated in the harmonic approximation using
the technique developed by Peresada et al [14].
The temperature dependences of the excess heat ca-
pacities �CNe(T) = C–C1 taken in series 1–4 are
shown in Fig. 2. The figure also shows the tempera-
ture dependences of the excess heat capacity of solid
solution of 1% p-D2, 0.25% Ne in p-H2 in comparison
with the heat capacity of pure p-H2 (Series 1), the
Heat capacity of p-H2–p-D2-Ne solid solution: Effect of (p-D2)Ne clusters
Fizika Nizkikh Temperatur, 2005, v. 31, No. 6 621
J=1 J=0 Ne
a b dc
(3)
(4)
(2)
–4�
(2)
(2)
(1)
(1)
6�
�
0
�
0
.0
0
7
K
�
�
/3
Fig. 1. Schematical arrangement of lower energy levels of
î-Í2 (p-D2) (J = 1) molecules as a function of molecular
surroundings (level degeneracy is indicated in brackets):
(a) free molecule; (b) twelve p-H2 molecules (J = 0) of
the first coordination sphere of an hcp lattice (only six
molecules are shown) [15]; (c) two nearest neighboring
o-H2 molecules (cluster o-Í2–o-Í2, � = 0.83 Ê), p-D2
(cluster p-D2–p-D2, � = 0.95 Ê) surrounded by the nearest
neighboring p-H2 molecules of the hcp lattice (eight mole-
cules are shown) [15]; (d) the nearest neighboring Ne
atom and p-D2 molecule ((p-D2)Ne cluster) surrounded by
the nearest neighboring p-H2 molecules of the hcp lattice
(eight molecules are shown) [2].
excess heat capacity �Cp-D2
(T) of the solid 1%
p-D2–p-H2 solution in comparison with the heat ca-
pacity of pure p-H2 and the increment in the lattice
heat capacity — �CL,Ne. Note that at T < 2 K the con-
tribution of �CL,Ne to �CNe is negligible (see Fig. 2).
Therefore, the excess heat capacity �CNe is practically
determined by the rotational motion of the p-D2 mole-
cules in the (p-D2)Ne type clusters. The temperature
dependences CR,Ne(T) and CR,p-D2
(T) [10] (CR,p-D2
is
the heat capacity of the rotational subsystem of the 1%
p-D2–p-H2 solution) are shown in Fig. 3.
The excess heat capacity CR,Ne was analyzed within
the theoretical model of [2]. A number of new phenom-
ena have been observed, which are induced by doping
the solid 1% p-D2 in p-H2 solution with 0.25% Ne.
1. An anomalously high excess heat capacity �CNe
has been observed after addition of 0.25% Ne to the
solid 1% p-D2–p-H2 solution. It is found that below
2 K the dominant contribution (CR,Ne) to the heat ca-
pacity �CNe is made by the rotation of the p-D2 mole-
cules in the (p-D2)Ne clusters (Fig. 2).
2. The heat capacity �CNe is strongly dependent on
the method of preparation of a solid sample. Note that
the excess heat capacity of the solid p-H2 – 1% p-D2
solution over that of pure ð-Í2 is independent of the
method of solid sample preparation.
3. At T < 3 K the temperature dependence of the
excess heat capacity CR,Ne has the form of the
Schottky curve and is described be the theory [2]. The
splitting � = (3.2 � 0.1) K of the J = 1 level of the
p-D2 molecules in the (p-D2)Ne type clusters was ob-
tained from the analysis of CR, Ne(T) and is consistent
with the theoretical estimate [2]. The number of
(p-D2)Ne clusters in the samples measured in Series 1
and 4 is 2.8 times larger and 1.25 times smaller than
that in the case of randomly distributed p-D2 and Ne
impurities (see Fig. 3).
The effects observed evidence in favor of the exis-
tence of new condensable systems formed by the
Van-der-Waals complexes of the Ne(H2)n or Ne(D2)n
type [6,7]. It has been found [3–7] that mixtures of
quantum substances (e.g., helium and hydrogen) with
inert elements or simple molecular substances can
form Van der Waals complexes which make a basis for
a new type of solids. X-ray investigations of Ne – con-
taining H2 and D2 polycrystals samples prepared by
condensation of gas mixtures on to a substrate at T � 5 K
show that in addition to the hexagonal and cubic
phases based on the H2 and Ne lattices, the samples
contain hcp inclusion (even of the 0.25% Ne concen-
tration [6,7]) whose lattices have somewhat larger
(by 1.5%–0.7%) volumes than that of pure Ne. The
authors believe that the additional hcp phase in these
systems is formed on the basis of the Ne(H2)n or
Ne(D2)n types of Van der Waals complexes. We can
assume that in the 1% p-D2 and 0.25% Ne in ð-Í2 solu-
tion the solid p-D2 concentration produced by the
Ne(p-H2)n type complexes and the amount of this
phase are strongly dependent on the preparation con-
622 Fizika Nizkikh Temperatur, 2005, v. 31, No. 6
M.I. Bagatskii, I.Ya. Minchina, and V.M. Bagatskii
12
8
4
0
0.5 1.0 1.5 2.0 2.5 3.0 3.5
T, K
�
C
,m
J/
(m
o
l K
)
�
Fig. 2. Temperature dependences of excess heat capacities:
(�) is solution 1% p-D2 and 0.25% Ne in solid ð-Í2 over
that of pure ð-Í2 (series 1);(�), (+), (�), (�) are solu-
tions 1% p-D2 and 0.25% Ne in solid ð-Í2 over that of so-
lutions 1% p-D2 in solid ð-Í2 (series 1–4, respectively);
(�) is solutions 1% p-D2 in solid ð-Í2 over that of pure
ð-Í2 [9]; (�) is �ÑL,Ne induced by the change in the
phonon spectrum of the crystal due to introduction of
heavy quase-isotopic Ne impurity to the lattice of ð-Í2.
0.5 1.0 1.5 2.0 2.5 3.0 3.5
0
2
4
6
T, K
1
2
3
C
,m
J/
(m
o
l K
)
R
�
Fig. 3. Temperature dependences of heat capacities deter-
mined by rotation of p-D2 molecules. Experiment: (�),
(+), (�), (�) are in (p-D2)Ne clusters, solid solution
1% p-D2, 0.25% Ne in ð-Í2, series 1, 2, 3, 4, respectively;
(�) is in p-D2–p-D2 clusters, solid solution 1% p-D2 in
ð-Í2 [10]. The curves show calculated heat capacities
CR, Ne for different contents of (p-D2)Ne clusters: curve 2
is the number of clusters is NR at random distribution of
Ne and p-D2 impurities; curve 1 is the number of clusters
is 2.8 times larger than NR; curve 3 is the number of clus-
ters is 1.25 times smaller than NR.
ditions. This is because the formation of the (p-D2)Ne
clusters decreases the energy of the system by 2�/3
and, hence, the total (elastic) energy of dilatation. In
a liquid sample, the phase formed by the Ne(p-H2)n
complexes dissociates rather slowly, which reduces
the number of (p-D2)Ne clusters.
The authors are indebted to A.I. Prokhvatilov and
M.A. Strzhemechny for helpful discussions. The study
was supported by the Ukraine Minister of Education
and Science State Foundation of for Basic research
(Project ¹ 02.07/00391-2004).
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Heat capacity of p-H2–p-D2-Ne solid solution: Effect of (p-D2)Ne clusters
Fizika Nizkikh Temperatur, 2005, v. 31, No. 6 623
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