Translational-rotational interaction in dynamics and thermodynamics of 2D atomic crystal with molecular impurity

The interaction between the rotational degrees of freedom of a diatomic molecular impurity and the phonon excitations of a two-dimensional atomic matrix commensurate with a substrate is investigated theoretically. It is shown, that the translational-rotational interaction changes the form of the rot...

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Date:	2003
Main Authors:	Antsygina, T.N., Poltavskaya, M.I., Chishko, K.A.
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Language:	English
Published:	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2003
Series:	Физика низких температур
Subjects:	Physics in Quantum Crystals
Online Access:	http://dspace.nbuv.gov.ua/handle/123456789/128916
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Cite this:	Translational-rotational interaction in dynamics and thermodynamics of 2D atomic crystal with molecular impurity / T.N. Antsygina, M.I. Poltavskaya, K.A. Chishko // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 961-966. — Бібліогр.: 12 назв. — англ.

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spelling	irk-123456789-1289162018-01-15T03:04:01Z Translational-rotational interaction in dynamics and thermodynamics of 2D atomic crystal with molecular impurity Antsygina, T.N. Poltavskaya, M.I. Chishko, K.A. Physics in Quantum Crystals The interaction between the rotational degrees of freedom of a diatomic molecular impurity and the phonon excitations of a two-dimensional atomic matrix commensurate with a substrate is investigated theoretically. It is shown, that the translational-rotational interaction changes the form of the rotational kinetic energy operator as compared to the corresponding expression for a free rotator, and also renormalizes the parameters of the crystal field without change in its initial form. The contribution of the impurity rotational degrees of freedom to the low-temperature heat capacity for a dilute solution of diatomic molecules in an atomic two-dimensional matrix is calculated. The possibility of experimental observation of the effects obtained is discussed. 2003 Article Translational-rotational interaction in dynamics and thermodynamics of 2D atomic crystal with molecular impurity / T.N. Antsygina, M.I. Poltavskaya, K.A. Chishko // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 961-966. — Бібліогр.: 12 назв. — англ. 0132-6414 PACS: 68.35.Dv, 68.35.Ja, 68.65.+g http://dspace.nbuv.gov.ua/handle/123456789/128916 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	Physics in Quantum Crystals Physics in Quantum Crystals
spellingShingle	Physics in Quantum Crystals Physics in Quantum Crystals Antsygina, T.N. Poltavskaya, M.I. Chishko, K.A. Translational-rotational interaction in dynamics and thermodynamics of 2D atomic crystal with molecular impurity Физика низких температур
description	The interaction between the rotational degrees of freedom of a diatomic molecular impurity and the phonon excitations of a two-dimensional atomic matrix commensurate with a substrate is investigated theoretically. It is shown, that the translational-rotational interaction changes the form of the rotational kinetic energy operator as compared to the corresponding expression for a free rotator, and also renormalizes the parameters of the crystal field without change in its initial form. The contribution of the impurity rotational degrees of freedom to the low-temperature heat capacity for a dilute solution of diatomic molecules in an atomic two-dimensional matrix is calculated. The possibility of experimental observation of the effects obtained is discussed.
format	Article
author	Antsygina, T.N. Poltavskaya, M.I. Chishko, K.A.
author_facet	Antsygina, T.N. Poltavskaya, M.I. Chishko, K.A.
author_sort	Antsygina, T.N.
title	Translational-rotational interaction in dynamics and thermodynamics of 2D atomic crystal with molecular impurity
title_short	Translational-rotational interaction in dynamics and thermodynamics of 2D atomic crystal with molecular impurity
title_full	Translational-rotational interaction in dynamics and thermodynamics of 2D atomic crystal with molecular impurity
title_fullStr	Translational-rotational interaction in dynamics and thermodynamics of 2D atomic crystal with molecular impurity
title_full_unstemmed	Translational-rotational interaction in dynamics and thermodynamics of 2D atomic crystal with molecular impurity
title_sort	translational-rotational interaction in dynamics and thermodynamics of 2d atomic crystal with molecular impurity
publisher	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate	2003
topic_facet	Physics in Quantum Crystals
url	http://dspace.nbuv.gov.ua/handle/123456789/128916
citation_txt	Translational-rotational interaction in dynamics and thermodynamics of 2D atomic crystal with molecular impurity / T.N. Antsygina, M.I. Poltavskaya, K.A. Chishko // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 961-966. — Бібліогр.: 12 назв. — англ.
series	Физика низких температур
work_keys_str_mv	AT antsyginatn translationalrotationalinteractionindynamicsandthermodynamicsof2datomiccrystalwithmolecularimpurity AT poltavskayami translationalrotationalinteractionindynamicsandthermodynamicsof2datomiccrystalwithmolecularimpurity AT chishkoka translationalrotationalinteractionindynamicsandthermodynamicsof2datomiccrystalwithmolecularimpurity
first_indexed	2025-07-09T10:13:35Z
last_indexed	2025-07-09T10:13:35Z
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fulltext	Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10, p. 961–966 Translational-rotational interaction in dynamics and thermodynamics of 2D atomic crystal with molecular impurity T.N. Antsygina, M.I. Poltavskaya, and K.A. Chishko B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkov 61103, Ukraine E-mail: chishko@ilt.kharkov.ua The interaction between the rotational degrees of freedom of a diatomic molecular impurity and the phonon excitations of a two-dimensional atomic matrix commensurate with a substrate is in- vestigated theoretically. It is shown, that the translational-rotational interaction changes the form of the rotational kinetic energy operator as compared to the corresponding expression for a free ro- tator, and also renormalizes the parameters of the crystal field without change in its initial form. The contribution of the impurity rotational degrees of freedom to the low-temperature heat capac- ity for a dilute solution of diatomic molecules in an atomic two-dimensional matrix is calculated. The possibility of experimental observation of the effects obtained is discussed. PACS: 68.35.Dv, 68.35.Ja, 68.65.+g 1. Introduction Two-dimensional (2D) cryocrystals on substrates of different kind are of great theoretical and experi- mental interest due to the wide variety of physical phenomena (in thermodynamics, excitation spectra, and magnetism) they demonstrate. For 2D mono- atomic crystals containing molecular impurities the interaction between rotational degrees of freedom and matrix phonon excitations, so-called translational-ro- tational interaction (TRI) [1], is an important factor controlling the dynamics of the impurity molecules. Since an impurity in a 2D solution moves in the low symmetry potential, its dynamics appears to be sub- stantially more complex than that in a 3D system [2]. This can appreciably affect all physical characteris- tics, in particular, low-temperature heat capacity, and also can lead to some effects not found in the 3D case. Theoretically, the problem of TRI in the 2D cryosolutions has not been sufficiently studied. The aim of the present paper is to investigate theo- retically the effect of the phonon excitations on rota- tional dynamics of a diatomic impurity in a 2D close-packed atomic matrix and the impurity heat ca- pacity at low temperatures. 2. Hamiltonian Let us consider a diatomic homonuclear substi- tutional impurity with mass M and internuclear dis- tance 2d in the two-dimensional close-packed mo- noatomic matrix (the coordination number in the layer z1 6� ), placed on a rigid substrate. The matrix and the substrate structures are supposed to be com- mensurate, so that a monolayer atom has z2 nearest neighbors in the substrate. The substrate forms either triangular (z2 3� ) or honeycomb (z2 6� ) lattice. For definiteness we assume, that the impurity is located at the origin, the OZ axis is chosen normal to the layer and is directed from the substrate, and theOX andOY axes are oriented in the matrix plane. We restrict our consideration to the case of the isotopic impurity. Assuming that the displacement u f of the impurity center of inertia from its equilibrium position is small in comparison with the distances to the nearest neigh- bors both in the layer, R1, and in the substrate, R2, and taking into account smallness of d/R ii, ( , )� 1 2 , the total Hamiltonian of the system can be written as H B H H Hc� � � � �� , ph int , (1) where the first term is the kinetic energy of the impu- rity molecule, B / I� � 2 2( ) is the rotational constant of the molecule, I Md� 2 is its moment of inertia, © T.N. Antsygina, M.I. Poltavskaya, and K.A. Chishko, 2003 � � �, is the angular part of the Laplacian, � and � are azimuth and polar angle specifying the molecule axis orientation. The Hamiltonian of the phonon subsystem Hph has the form H m m MN ph � � � � � � � � � � � 1 2 2 2 2 2\| \| \| \| ( , , � � � � � � � � � � � � e e ) ,� �� where e� and �� are the unit polarization vectors and frequencies of a pure monolayer phonon excitations, respectively, � �� ( , )k , k is a two-dimensional wave vector, � � l t z, , ; l t, specify the longitudinal and transverse modes polarized in the layer plane (in-plane modes), and z is the index for the mode po- larized normally to the layer (out-of-plane mode), �� are coefficients in a series expansion of u f in the unit polarization vectors e�, � �� i /� , m is the mass of a matrix atom, � � �( )m M /m is the mass defect, N is the number of sites in the layer. For a pure crys- tal in the commensurate regime all the phonon spec- trum branches have gaps: equal � for the in-plane modes and � z for the out-of-plane mode with � �z � . As a rule, the z-mode is practically dispersionless [3]. Explicit forms of �� for the system under consider- ation can be found in [3,4]. With an accuracy to ( )d/Ri 4 the crystal field Hc has the form H G w G w G w w w wc z z z y z y x� � � � �0 2 1 4 3 2 2 2 2 1 2 3 2 [ ( )] .� (2) Here w � (sin cos ,sin sin ,cos )� � � � � , � ij is the Kro- necker symbol, G d z z b d bi i i0 2 12 2 2 2 2 2 21 3 5 2� � � � � � � � �� , ( )[ ( ) ]M M P � , G d z z b b G d i i i1 4 12 2 2 2 2 2 2 5 3 1 1 7 4 � � � � � � ! " # # � � , ( )( ) ,P P 4 2 3 2 23 1z b b� P , M P i i i i i i i i i i i A d R d dR R dA dR R d dR R d dR � � � � � �� 2 3 8 1 1 8 , i i i A R4 � � � � � , A R d dR R dV dRi i i i i i � � � � �� 1 , parameter b is equal to R / R1 23( ) and R / R1 23( ) for the substrates with triangular and honeycomb lattices respectively; Vi are atom-atom potentials describing interactions between the impurity and matrix atoms ( )i � 1 and between the impurity and substrate atoms (i � 2). The first two terms in (2) are determined by both the matrix and the substrate, whereas the last term with a lower symmetry (of group S6) is associated only with the crystal field of the substrate. The analy- sis ofG01, shows that the substrate field makes the im- purity lie down in the layer, while the matrix field tends to orientate it perpendicular to the substrate. Thus, the equilibrium position of the impurity is de- termined by a competition between the two factors. Interaction between the phonon subsystem and the rotational degrees of freedom of the impurity is de- scribed by the following Hamiltonian [5,6]: H d N f f Q Cint c. c.� � � � � 2 2 ( ), . � � � � � �$ �$ �� % (3) Here Q w w /�$ � $ �$� � � 3 is the dimensionless quadrupole moment of the impurity molecule, %� �$ �$& � & � � $ � ��& & � & � � � � s h C s h ( ) ( ) , [ ( ) ( )] k k k k e e e 2 1 3 5 , s i R�$& � ' $ & � $ &' ' ' '( ) exp ( ) ,k k� � K K1 1 2 � � � � � � � (4) h i R R d dR A R i i i i i � � ' �( ' ' ( ( (k k) exp ( ) , , � � � 1 1 2 2 2 � � � � � K i i i A R � , � ', � � are unit vectors directed to the nearest neigh- bours in the layer and in the substrate. 3. Impurity dynamics Let us consider the effect of interaction between the rotational degrees of freedom of the impurity and the matrix phonon excitations on the character of the molecule motion. To do this we use the functional in- tegration method [7]. Within an insignificant normal- izing factor the partition function Z of the system un- der study has the following form Z D D S/� ) [ ( )] [ ( )] exp ( )� * w � , (5) 962 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 T.N. Antsygina, M.I. Poltavskaya, and K.A. Chishko where S is the total action S d L L L L L L /T c� � � � �) 0 � ( ), ph rot int , L m Nph � � � � � � ! "� � � 2 2 2 2\| � \| \| \| ( , )� � � � � � �� e e # # � , L I I L L Hc rot int i � � � � � � � � � � � � � � 2 2 2 2 2 2w * � � �(� � sin ), ( nt � Hc) , * is the imaginary time, the Botzmann constant kB � 1. The dots denote differentiation with respect to *. After integration over the phonon variables, the partition function (5) takes the form of the product Z Z Z� ph 1. The factor Zph is the phonon partition function of the 2D crystal, and Z1 corresponds to the rotational motion of the molecule with regard to influ- ence on it of the phonon subsystem. For real systems rotational levels of a molecular impurity are, as a rule, low-energetic, and, hence, specific effects caused by rotational excitations make themselves evident at ex- tremely low temperatures. Besides, due to the pres- ence of an isotopic impurity there appear local +loc and quasi-local frequencies in the phonon spectrum [8]. For the light impurity (� � 0) the local levels lay above the top edge of the continuous spectrum, whereas for the heavy impurity (� < 0) these levels are situated below its bottom edge, i.e. in the gap. Our in- terest here is in the temperature range T , � ��, +loc. Within the present approximation TRI gives rise to additional terms of the order ( )d/Ri 4 in the crystal field H H H H H d mN f c c c c c - � � � � ~ , \| \| , � � � 4 2 22 � �� (6) and also in the kinetic energy operator H H H Hrot rot rot rot- � �~ � , � � � H d m N f N f rot � � . . . . . . � � � �� 4 2 4 2 2 2 1 1\| � \| � � �� e � � �� . (7) To analyze Eqs. (6), (7) it is necessary to calculate sums (4) over the nearest neighbors in the layer. For lattices with the coordination number large enough an effective way of the calculation is to replace the sum- mation by integration over a circle of unit radius [3,4]. Such a replacement is quite justified since the corrections (6), (7) are integral characteristics (ob- tained by the summation over k in the Brillouin zone). The interaction between the impurity rotational de- grees of freedom and phonons does not modify the general form of the crystal field (2), but renormalizes its coefficients: G G G G G G G ii i i i i i L i S- � � � � �~ , , , , ,� � � � 0 1 2 where the indices L and S specify contributions caused mainly by the impurity interaction with the matrix atoms and substrate atoms, respectively: / 0�G z d m L 0 1 2 4 1 1 16 3� � � �A B C , / 0�G z d m L 1 1 2 4 1 14 � � �A B , � �G z d m K K s K K sS z z0 2 2 4 0 2 2 2 3 1 0 1 1 2 2 2 � � �1[( ) ], ( ) ( ) , � � � G z d m K K s K s G S z z S 1 2 2 4 0 2 2 2 3 1 1 2 1 2 4 4 2 � � � � � 1[( ) ] ,, ( ) ( ) z d m K K s2 2 4 0 2 1 1 ( ) . Here A B m l m m l m t m N N � � � � �� 1 1 8 1 2 2 2 3 2 2 2 3 2 2 � � � � � � � � k , ( ) ( ) ! " # # k , C Km l mN J kR� � � � 1 3 21 2 1 2 1 1 1 1 1 � � � � ( ( ) , ( ) ( ) , �k � ( � ( 2 1 1 1 1 3 1 3 1 0 2 2 2 2 4 1 2 � � � � � � ( ) ( ) , ( ), ( ) , K K K J kR J kR K b b K b b K b 1 2 2 2 2 2 3 21 3 2 4 2 � � � � �[( ) ] ,K K( , s N s N m m l t z m z m1 � � � ( ) , , ( ), 1 2 1 1 1 2 2� ��k k . where J xn ( ) is the Bessel function. By symmetry rea- soning the impurity interaction with the neighbors in the layer results only in the renormalization of the co- efficients G0 and G1 in (2). It can be shown, that for short-range potentials the values �GL 0 and �GL 1 are negative, whereas �GS 0 is positive. The contributions to the crystal field both from the monolayer and from the substrate decrease in ampli- Translational-rotational interaction in dynamics and thermodynamics of 2D atomic crystal Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 963 tude due to TRI. Such a result is physically quite clear. The rotational motion is mainly affected by high-frequency phonons creating maximal deforma- tions in the first coordination sphere around the impu- rity. The considered situation is close to the known problem on the motion of a particle in a fast-oscillat- ing field where after averaging on oscillations the depth of the initial potential well effectively de- creases [9]. Rather different situation takes place for the ki- netic energy. The TRI results in essential change of Hrot form. After appropriate transformations the ef- fective kinetic energy (7) can be represented as a gen- eralized quadratic form of the angular velocity components �wi with coefficients dependent on the molecular orientation: � � � � �H I I w I w w w w z z z ij i j x rot � � � � 1 1 1 2 2 2 32 ( � � � � ) , � ( , ,w w y, ) .0 (8) The additives �I z1, to the impurity moment of inertia are � � � � � I I I I z d m w I z d m z z L z S L z L 1 1 1 1 1 � � � � , , , , ,1 2 4 2 2 1 2 4 2 B A wz 2 , � � � I z d m K w K w I z d m K S z z z S 1 1 1� � � 2 2 4 0 2 2 3 2 2 2 2 2 4 0 2 2 2 2 ( ) , [ , 1 � �( ) ] ,1 3 2 1 2 2w K wz z z2 where 2 �/1 1 1� �, , ( ) , ( ) )z z zs s2 1 2 . Besides, for the substrates with a triangular lattice ( )z2 3� there are also nondiagonal on � �w wi j terms in (8) with �I z d m K K w w w w w w w w w w w wij y z x z x y x z y z x y� � � �1 2 2 4 0 2 2 2 2 2 2 22 2 2 22 0w w w wx y x y� � � � � � �� . By virtue of positive definiteness of the form (8) the coefficients �I z1, > 0. As a result, TRI leads to an increase in impurity main moments of inertia, that is the molecule becomes effectively heavier. We have calculated the renormalized parameters for a number of atomic-molecular systems using for the impurity-matrix as well as for the impurity-sub- strate interactions the Lennard-Jones model with the parameters corresponding to the gaseous phase [10]. It has been found that at real values of d/Ri the maxi- mal relative change in moment of inertia is about 30%, and the renormalization of the crystal field amplitude may be as much as 50–60 %. Certainly, the estima- tions are quite rough because the Lennard-Jones po- tential is known to be extremely sensitive to a choice of its parameters. On the other hand, the real values of these parameters for a 2D system can differ signifi- cantly from those in the gaseous phase [3]. Neverthe- less, it is clear that the properties of the system under consideration can be substantially affected by TRI, so that the renormalization effects due to TRI should be properly taken into account when discussing the phys- ical phenomena in real systems. 4. Rotational heat capacity Now we consider the rotational heat capacity of the dilute solution of diatomic molecules in a 2D atomic matrix. We restrict ourselves to the case of strong binding, when the molecules make small librations near their equilibrium positions normal to the layer plane. The impurity contribution to the free energy (per one impurity molecule) from the rotational de- grees of freedom and the molecular in-plane translational motion has the form: �F � � � � � - 3 )� � � + + + ' +' lim ( , ) ( )0 0 2 d T P R coth arctan . Here P a ( , ) [ ( )( )] ( )[ ( ) ] , + ' +' �4 + + + 5 + �+ + + � � � � � � � 2 1 2 2 0 2 2 2 0 2 R a( ) ( )[ ( )] ( )+ + + �+ 4 + 4 +� � � �2 0 2 21 , 4 + 5 + + ' �� ( ) ( ) ( ) ), , � � � �� i N il t 1 2 1 2 2� (kk , +0 is the librational frequency of the rotator with nonrenormalized parameters (in the absence of TRI), a z d K B/ m� 2 2 2 4 0 2 2( )� is a parameter describing the TRI intensity. For most real systems the librational frequency +0 is small as compared to the top edge �max of the con- tinuous spectrum of the pure 2D crystal, so that +0 is either in the gap (+0 < �) or in the continuous spec- trum near its bottom. On the other hand, the less +0 and the lower temperature the easier to extract the ro- tational part from the total heat capacity containing also contributions from translational excitations (both from the continuous spectrum, and the local and 964 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 T.N. Antsygina, M.I. Poltavskaya, and K.A. Chishko quasi-local states). Hereafter we consider the case of small +0. We start with +0 6 �. For the light impurity ( )� � 0 the local and quasilocal translational levels are close to �max, and their influence on low-temperature thermodynamics is negligible. Thus, the main contri- bution to the thermodynamic functions is from the ro- tational degrees of freedom. The rotational free energy and the heat capacity (per one particle) have the form: �F rot 2 sinh� � � � �2 2 0T T ln ~�+ , �C T T � � � � ��2 2 2 0 1 0 2 � �~ ~+ + sinh , (9) ~ [ ] ( )+ + 20 2 0 2 11� � �1 1a as , where ~+0 is the librational frequency renormalized due to TRI. The result (9) corresponds to the heat ca- pacity of a two-dimensional Einstein oscillator with the frequency ~+0. As it should be, renormalization of the rotator motion parameters leads to an effective decrease of +0 and, hence, to an increase of a relative contribution from the rotational degrees of freedom to the low-temperature heat capacity. In the case of the heavy impurity (� 6 0) the local level falls within the gap (+loc< �), and a contribu- tion from +loc to thermodynamic functions can be comparable with that from the rotational degrees of freedom. Thus, the main contribution to the free en- ergy and heat capacity from the impurity subsystem consists of two terms of the form (9) with frequencies ~+0 and ~+loc, being determined as two least roots of the equation R( )+ � 0. Namely, ~ [ ( , )] ( )+ + + +0 2 0 2 0 11� � � 1af asloc , ~ [ ( , )] , ( , ) ( ) + + + + + + + loc loc loc loc loc 2 2 0 0 1 2 1� � � �1 af f s s1 � ( ) . 2 2 0 2+ +loc If the spacing between the frequencies +loc and +0 is large in comparison with the TRI intensity, a 66 �( )+ +loc 2 0 2 2, the considered excitations can be classified as librational and local ones with renormalized frequencies. In the opposite case, when a 7 �( )+ +loc 2 0 2 2, «mixing» of the frequencies occurs, and, as a result, molecular librations and local oscil- lations are no longer well determined eigenstates. The situation is more complicated, when the librational frequency is inside the continuous phonon spectrum near its bottom (+0 � �) [2,11]. Since for the heavy impurity +loc 6 �, the contribution to the thermodynamic functions from the local excitations prevails over the contribution from the rotational de- grees of freedom. Thus, the solutions with light impu- rities (� � 0) are of main interest here. In this case the rotational free energy can be written as � � � F � � � � � � �)2 2 2 0 0 2 0 2 T d T� + + & + + & max ln ( ~ ) sinh � , (10) where & 5 + +0 0 02� � a /(~ ) ( ~ ) is a Lorentz peak half- width and ~+0 is the same as in Eq. (9). It should be noted, that the validity of Eq. (10) is restricted to the condition + &0 0� � �� , (i.e. +0 is not too close to the bottom of the continuous spectrum). Taking into account smallness of &0, the rotational heat capacity can be approximately represented in the form (9). Thus, the rotational heat capacity at low tempera- tures has an exponential form �C T T � � � � � �� 2 0 2 0� �~ exp ~+ + , (11) unlike three-dimensional systems where the power- type dependence takes place [2]. Such a result is due to the gap in the phonon spectrum of the 2D mo- noatomic crystal commensurate with the substrate [3,12]. In this connection we remind that the matrix heat capacity also has an exponential form [3,12] C T Tph 8 �� exp , but its temperature dependence differs by preexpo- nential factor from Eq. (11). This circumstance can be useful when extracting the rotational part from a measured total heat capacity particularly if +0 and � are close in magnitude. 5. Conclusion The most pronounced effect resulting from the in- teraction between translational and rotational degrees of freedom consists in the radical change of the iner- tial properties of the impurity molecule. This mani- fests itself in the change in the form of the rotational kinetic energy operator as compared to the corre- sponding expression for the free rotator. The inertia tensor components become functions of molecular ori- entation, and the molecule, in terms of rotational mo- tion, transforms into a «parametric rotor» whose ef- fective kinetic energy is represented as a generalized quadratic form of the angular velocity components with a symmetry corresponding to the external crystal field. For example, if the substrate atoms form honey- comb structure, then within the present approxima- tion the tensor of inertia remains diagonal, while it Translational-rotational interaction in dynamics and thermodynamics of 2D atomic crystal Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 965 has also nondiagonal components for substrates with triangular lattices. The TRI also results in the renormalization of the crystal field parameters. However, although the corre- sponding corrections are sufficiently large, the poten- tial form determined by the symmetry of the system remains unchanged. We would like to note that the dynamics of a di- atomic impurity in a 2D monoatomic matrix on a sub- strate is more complicated than in a 3D matrix of cu- bic symmetry [2,5]. Indeed, due to the high symmetry of the surroundings in 3D systems, TRI leads only to an increase in the molecular momentum of inertia without changing the form of the kinetic energy oper- ator. In view of possible experiments on the rotational heat capacity of 2D solid solutions of diatomic mole- cules in monoatomic matrices on commensurate sub- strates, the 2D solutions with light impurities are ex- pected to be more preferable, because at low temperatures the contribution from the rotational de- grees of freedom dominates over the contribution from the local translational excitations. Being richer from the theoretical standpoint, the systems with heavy im- purities are more complicated for an experimental re- search due to the problem of correct separation of con- tributions from the local and rotational excitations. 1. R.M. Lynden-Bell and K.H. Michel, Rev. Mod. Phys. 66, 721 (1994). 2. T.N. Antsygina and V.A. Slusarev, Teor. Mat. Fiz. 77, 234 (1988) (in Russian). 3. T.N. Antsygina, I.I. Poltavsky, M.I. Poltavskaya, and K.A. Chishko, Fiz. Nizk. Temp. 28, 621 (2002) [Low Temp. Phys. 28, 442 (2002)]. 4. T.N. Antsygina, K.A. Chishko, and I.I. Poltavsky, J. Low Temp. Phys. 126, 15 (2002). 5. T.N. Antsygina, K.A. Chishko, and V.A. Slusarev, Phys. Rev. B55, 3548 (1997). 6. T.N. Antsygina, M.I. Poltavskaya, and K.A. Chishko, Phys. Solid State 44, 1268 (2002). 7. R.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York (1965). 8. I.M. Lifshits and A.M. Kosevich, Rep. Progr. Phys. 29, 217 (1966). 9. L.D. Landau and E.M. Lifshits, Mechanics, Nauka, Moscow (1965) (in Russian). 10. Physics of Cryocrystals, V.G. Manzhelii and Yu.A. Freiman (eds.), AIP Press, New York (1996). 11. Yu. Kagan and Ya. Iosilevsky, Zhurn. Eksp. Teor. Fiz. 45, 819 (1963) (in Russian). 12. J.G. Dash, Fiz. Nizk. Temp. 1, 839 (1975) [Sov. J. Low Temp. Phys. 1, 401 (1975)]. 966 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 T.N. Antsygina, M.I. Poltavskaya, and K.A. Chishko

Translational-rotational interaction in dynamics and thermodynamics of 2D atomic crystal with molecular impurity

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