О теpмодинамике пеpеохлажденных жидкостей и стекол

Термодинамика стеклообразующих жидкостей и стекол рассматривается с учетом вклада
 гетерофазных флуктуации в свободную энергию. Гетерофазными флуктуациями в жидкости
 являются зародыши некристаллического твердого тела, а в стекле - зародыши жидкой фазы.
 Твердотельное кристал...

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Збережено в:
Бібліографічні деталі
Опубліковано в: :Физика низких температур
Дата:1998
Автор: Бакай, А.С.
Формат: Стаття
Мова:Російська
Опубліковано: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 1998
Теми:
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/176357
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:О теpмодинамике пеpеохлажденных жидкостей и стекол / А.С. Бакай // Физика низких температур. — 1998. — Т. 24, № 1. — С. 27-46. — Бібліогр.: 40 назв. — рос.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
_version_ 1860253406080270336
author Бакай, А.С.
author_facet Бакай, А.С.
citation_txt О теpмодинамике пеpеохлажденных жидкостей и стекол / А.С. Бакай // Физика низких температур. — 1998. — Т. 24, № 1. — С. 27-46. — Бібліогр.: 40 назв. — рос.
collection DSpace DC
container_title Физика низких температур
description Термодинамика стеклообразующих жидкостей и стекол рассматривается с учетом вклада
 гетерофазных флуктуации в свободную энергию. Гетерофазными флуктуациями в жидкости
 являются зародыши некристаллического твердого тела, а в стекле - зародыши жидкой фазы.
 Твердотельное кристаллическое состояние исключается из рассмотрения. Описание свободной
 энергии основано на использовании капельной модели и модели смешанного состояния. Показано,
 что на плоскости (P, T) существуют три области стабильности различных структурных состояний
 рассматриваемой системы. Две из них — области стабильности капельных структурных состоянии, в
 которых гетерофазные флуктуации имеют форму изолированных капель. В третьей области
 стабильным является смешанное состояние, в нем сосуществуют два бесконечных взаимно
 протекающих кластера, жидкий и некристаллический твердотельный. Ширина температурного
 интервала, [Tt1, Tt2], в котором смешанное состояние стабильно, увеличивается с ростом
 конфигурационной энтропии (сложности) некристаллической твердотельной фракции. В
 использованном подходе обнаружены слабые фазовые переходы первого рода при Т = Tt1 и Т = Тt2.
 Показано, что в смешанном состоянии возможны фазовые переходы первого или второго рода.
 Приведены критерии наличия этих фазовых переходов. Получены уравнения состояния и выражения
 для термодинамических величин (энтропии, теплоемкости, сжимаемости и коэффициента теплового
 расширения) для капельных и смешанного состояний. Термодинаміка стеклоутворюючих р.дин х стекол розглядається з урахуванням внеску
 гетерофазних флуктуацій в вільну енергію. Гетерофазними флуктуаціями в рідині є зародки
 некристалічного твердого тіла, а в склі - зародки рідкої фази. Твердотільнии кристалічний стан
 виключено з розгляду. Опис вільної енергії грунтується на застосуванні краплинної моделі і моделі
 змішаного стану. Показано, що на площині (P, T) існують три області стабільності різних
 структурних станів системи, що розглядається. Дві з них - області стабільності краплинних
 структурних станів, в яких гетерофазні флуктуації мають форму ізольованих крапель. В третій
 області стабільним є змішаний стан, в ньому співіснують два нескінченних взаємно протікаючих
 кластери, рідкий і некристалічнии твердотільнии. Ширина температурного інтервалу, [Tt1, Tt2], в
 якому змішаний стан є стабільним, збільшується з ростом конфігураційної ентропії (складності)
 некристалічної твердотільної фракції. В межах застосованого підходу знайдено слабкі фазові
 переходи першого роду при Т = Tt1 і при Т = Тt2. Показано, що в змішаному стані можливі фазові
 переходи першого або другого роду. Знайдено критерії наявності цих фазових переходів. Одержано
 рівняння стану і вирази для термодинамічних величин (ентропії, теплоємності, стисливості і
 коефіцієнта теплового розширення) для краплинних і змішаного станів. Theomodynamics of glass-forming liquids and
 glasses is considered taking into account the contributions of heterophase fluctuations to tree energy.
 The heterophase fluctuations in liquids are nuclei of
 non-crystalline solids. In glass the heterophase fluctuations are nuclei of liquid. The crystalline solid
 state is not considered. The droplet approach and
 the mixed state model are applied to describe free
 energy. It is shown that there exist three regions of
 stability of different structure states of the system in
 the plane (P, T). Two of them are the stability regions of the droplet structure states. In the third one
 the mixed state is stable. In the droplet states the
 heterophase fluctuations exist as isolated droplets.
 In the mixed state two infinite percolating clusters
 (solid and liquid) are coexisting. The widths of the
 temperature interval, [Tt1, Tt2], where the mixed
 state is stable increase with the growth of the configurational entropy (complexity) of the non-crystalline solid fraction. In the frame of the approach used
 weak 1st order phase transitions are revealed at
 Т = Tt1 and Т = Тt2. It is shown that in the mixed
 state the 1st order or 2nd order phase transitions are
 possible. The criteria of these phase, transitions are
 obtained. Equations of state and expressions of thermodynamic quantities (entropy, specific heat capacity, compressibility and thermal expansion coefficient) in the droplet and mixed states are derived.
first_indexed 2025-12-07T18:46:07Z
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A H :�$'/�F;1�+ $'L�+"< @�8.A H = H � a%0�S�$�SH>g/'C�$B]6-�+"+ 1 Co/'1;/'021V3"+�A.A @"8�1�A�/2I.1;D"A�0 NZ-'P21 >;<Q7 @ $�8 $2I.1;Ds>�0�1�8 1 M�1 8 1 D"-!S _H-;F >;A D.+ 1^a � A M'8�-'$20 8 1 &"(s@.-�8�-'C�$20�8�- @!1�8�3�D�F!-!S f <%8�-4JO$�+.A $ � 5Q5 � 1 @"8 $'D�$'& 3�$20 $2M�1 0'$'CT@�$B8�-40�G"8�+�G"* P�-�>;A!/BA C�1V/20�( @!8�A CT-'&.<%IrP�+�-4L;$�+"AV3�I �XS ! 8�A.>�$'D $2C >;<%8.-'JZ$B+.AV3 D &�3 � ( H ) a9/�@"8!-�>�$'D�&)A!>;<�$Y> :;1 &�$'$ ]KA.8 1�FV1�7 1;: &"-�/'02A P�+.-'L�$�+�A.7 �XS _%1 M�D"-r>V<%@�1V&)+ $�+!1 G /'&"1 >;A!$ � 5Q8 � acD�&!3 � ( H ) A�P � 5Q% � a � 5�' � >V<%0�$�F�-'$'0 /'&�$2D!G�*Z5Z$'$ @.8�A�:V&)A�JK$B+!+�1V$ >;<%8.-'JZ$B+.A $!a @!1;&.G L $B+�+!1;$d@!G�0'$'C 8.-'P2&�1 JZ$�+"A�7 @�1 � > 1�F 8�$'/20'+�1V/20�A � = ��E% > � = % + ' δ + 0 δ 0 a � 8 � � M�D $ δ = � � ( H � − H ) H � �10 � − ¼ 6�� H − % � ( 6 � )∆µ� � a � 8 � � � = ∂   µ 0� − µ ¼�   M ∂ H   â = â�� S � 8Q% � !K8�A >V<%@�1V&)+ $�+.A�A G�/'&�1�>;AV3 � 5QB � /'G�56$'/202>4G"*%06D">;- G /20'1�7 L�A�>;<nI 8.-�>;+�1�>4$2/�+�<nI /'1 /20�1V3"+�A�3 /�A /20'$'CT< > 0'$2CX@ $�8�-�0�G"8�+ 1 C A.+ 0'$B8!>;-'&.$ � H − a I + � a)M�D�$ H ± ≅ � � ± � ( 6 � ) ∆µ� ∆ � � + JLK � ( ± )� ( � +− ) � a =   − %�6 D H � M 6 � � ( 6 � )∆µ�   ¼�� � a ∆ � � = � � M I � � � 8 ' � � D!$2/�(Z+�$Z@�8�A.>�1;D�3�0'/�3 -�+.-'&"A!0BA L $'/BF!A $O>V<%8�-�JZ$�+"AV3 D�& 3 @�-V8�-'C�$20�8�- @ 1�8V3�D"F - > G /'021�7 L�A�>V<%I 8�-V>;+ 1�>�$'/�+�<�Ir/'1 /20'1�3"+.AV3�I A!P2[ P�- A I M�8�1VCE1VP2D.F 1;/'0BAES *^$2CX@ $�8.-'02G�8�+.-�3 PB-�>VA�/�A C�1;/'0B(p@�-;8!-'CE$'0�8�-?@�1 8V3�D"F�- +!$2G /'021 7�L A">41;M�1 8"-�>V+ 1�>�$'/B+ 1 M�1 /21V/20'1�3"+.AV3 > 1�F 8�$'/20'+�1V/20�A 0'$'CT@�$B8.-'02G�8�< H � � @�8.A H + �#HA� H − � @.8�A : &"A!JO$�+.+ 1 1�@.A /B<%>V-�$'0�/�3 >V<%8"-'JZ$�+"A�3�CXA � 8 � a � 8Q% � S 9`$2028!G D"+ 1 G /20�-�+!1�>;A!02()a L 0'1 @.8�A H H H �/'0B-':�A &�(�+"<�C 3">�&!3�$'0'/�3 /21 /'0�1V3!+!A�$ /h@�-V8�-'C�$20�8 1;C � 1 ��E%)a - @!8�A H 1 H � /'0B-':�A &�(�+�1o/'1 /20�1V3"+�A!$�acG F 1V021�8 1VM�1 � H � % S !K8�A H = H � A�C�$'$20YC�$'/20'1 NZ-'P21 >;<Q7 @ $�8 $2I.1;Ds@ $B8!>�1 M�1 8!1;D"-!S _%1 M�D"- @.8 1�A!/2I!1�D.A 0 NH-�P�1�>V<%7 @!$B8�$2I�1 D >4021 8�1VM�1 8 1 D"- � G /2&�1�>VA $ � 5QO �Z� a > 1�F 8!$2/'02+!1;/'0BA H �/�@"8�-�>4$2D!&"A">41 /2&!$2D�G�*Z5Z$'$ >;<H8!-'JK$B+!A�$ D�& 3 @.-�8�-'C�$20�8�-d@ 1�8V3�D"F�-�> U�V�W]V'{|z Y�VXW�{ V]\�^ _�`4aX_�b'z ^CcZb ~'���2��� ~1^2v6T�d�~ eo� J'� � = %   + √ ' ( H � − H ) M H �   @�8.A H32#H � � 8R0 - � � = %   − √ ' ( H − I � ) M H �   @!8"A H ��H � S � 8 0�: � !O8!A">4$2D�$�+�+.<�$ >;<%]6$ >V<%8�-�JZ$�+"A�3 D�& 3 I)A CXA!L;$'/BF�1�M�1 @!1;0'$B+.R�A.-'&)- /�A /20'$'CT< > /2C�$�]K-�+"+�1�C /21 /'02143!+.A�A @.8 1V3�/B+�3!*Q0 � +�1 a F -;F : G D�$20`@�1 F�-'PB-�+!1�a + $ A�/'L $B8�@!<H>;-�*n0 � >41�@.8 1 / 1 /'G�5K$'/20'>�1�>;-�+.A�A NZ-'P21�>V<�I @�$�8 $'I"1VD�1�>=@�8.A H = H � S _H-�Fq>VA D"+ 1^a @!8�A W'0�1�7 02$'CX@ $B8.-'0'G�8�$ D $�7�/'0�>;A 0'$2&.(;+ 1 C�1�JZ$'0r/'G�5K$'/20'>�1�>;-'0�( NO-'P'1�>;<%7 @�$�8 $'I"1VD @�$B8.>�1VM�1,A &)A >�0'1�8!1;M�1j8�1�D�-)S fXCE$'/'02$ / 0�$'C � /2CQS 8!-�P�D�S#0 � > D 1�@ 1 &"+!$B+!A�$ F 1�@!A�/�-�+"+!<�C >;<%]Z$KNZ-'P21 >;<�C @ $�8 $'I"1VD"-'CgC 1 M�G�0ZA C�$20�( CE$'/'021 NZ-'P21 >;<n$ @!$B8�$2I.1;D"<6a /�>'3�P2-V+�+.<�$ / @"8 $�>;8!-;5Z$�+�A�3�CXA /20'$BF�&"- A J`A D"F 1V/20�A / A�P'1;&�A�8 1�>;-�+.+�<�CXA P�-�8 1 D�<H]K-'CXA +!1�>41�7 NZ-'P�< � A�P�1 &"A.8 1�>;-�+!+"<�CXA F -;@�&�3�CEA � > /2C�$�]K-�+"+�1�$ /21V/20'1�[ 3!+.A $!S <E-'/'/'CE1V0B8!A�Cs02$�@!$B8�( 02$�8 C�1 D�A.+�-4CEA.F Gd/2C^$B]`-�+�+!1;M�1 /21 /'02143!+.AV3 @�8�AjCT-'&.1�7j1�:Vm"$'CX+�1 7 D�1V&"$ JKA!D"FV1�7 NO8!-;F R"A.A�� ≡ � − � 2 2 S4; &!3dW20'1;M�1`>Z/21 1V0B>4$20'/20'>;A.A/21 /2D�$'&"-�+.+�<%Cr>V<%]K$ @.8 $'D"@ 1 &�1 JZ$B+.A $'C @ 1 &�1 JKA�Cr> � 5 % � � ( � ) = a�@�1�/'&�$QL�$'M�1e>68 $2P'G &)('0�-'0'$O>;<�L�A /'&.$B+�A.7^a @�1VD�1 :�+.<�I >V<H@ 1 &"+!$�+�+"<�C @.8�A @!1;&.G�L $�+�A.A >;<H8!-'JK$B+!A"7 � 5Q2 � a � 5Q5 � a + $20�8 G D"+!1 +�-�7!0�AG> µ ��� ( . a H ) = µ � (� 1)H ) − 6 D H 6 �− ¼ � ( − � ) 1 � 8 2 � � ≅ � ���    − � � � µ ¼� − µ � + � ( 6 � )(µ� − µ ¼� ) �   S � 8 5 � � � �(� � # '���� ! 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id nasplib_isofts_kiev_ua-123456789-176357
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 0132-6414
language Russian
last_indexed 2025-12-07T18:46:07Z
publishDate 1998
publisher Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
record_format dspace
spelling Бакай, А.С.
2021-02-04T13:37:56Z
2021-02-04T13:37:56Z
1998
О теpмодинамике пеpеохлажденных жидкостей и стекол / А.С. Бакай // Физика низких температур. — 1998. — Т. 24, № 1. — С. 27-46. — Бібліогр.: 40 назв. — рос.
0132-6414
PACS: 64.70.Dv
https://nasplib.isofts.kiev.ua/handle/123456789/176357
Термодинамика стеклообразующих жидкостей и стекол рассматривается с учетом вклада&#xd; гетерофазных флуктуации в свободную энергию. Гетерофазными флуктуациями в жидкости&#xd; являются зародыши некристаллического твердого тела, а в стекле - зародыши жидкой фазы.&#xd; Твердотельное кристаллическое состояние исключается из рассмотрения. Описание свободной&#xd; энергии основано на использовании капельной модели и модели смешанного состояния. Показано,&#xd; что на плоскости (P, T) существуют три области стабильности различных структурных состояний&#xd; рассматриваемой системы. Две из них — области стабильности капельных структурных состоянии, в&#xd; которых гетерофазные флуктуации имеют форму изолированных капель. В третьей области&#xd; стабильным является смешанное состояние, в нем сосуществуют два бесконечных взаимно&#xd; протекающих кластера, жидкий и некристаллический твердотельный. Ширина температурного&#xd; интервала, [Tt1, Tt2], в котором смешанное состояние стабильно, увеличивается с ростом&#xd; конфигурационной энтропии (сложности) некристаллической твердотельной фракции. В&#xd; использованном подходе обнаружены слабые фазовые переходы первого рода при Т = Tt1 и Т = Тt2.&#xd; Показано, что в смешанном состоянии возможны фазовые переходы первого или второго рода.&#xd; Приведены критерии наличия этих фазовых переходов. Получены уравнения состояния и выражения&#xd; для термодинамических величин (энтропии, теплоемкости, сжимаемости и коэффициента теплового&#xd; расширения) для капельных и смешанного состояний.
Термодинаміка стеклоутворюючих р.дин х стекол розглядається з урахуванням внеску&#xd; гетерофазних флуктуацій в вільну енергію. Гетерофазними флуктуаціями в рідині є зародки&#xd; некристалічного твердого тіла, а в склі - зародки рідкої фази. Твердотільнии кристалічний стан&#xd; виключено з розгляду. Опис вільної енергії грунтується на застосуванні краплинної моделі і моделі&#xd; змішаного стану. Показано, що на площині (P, T) існують три області стабільності різних&#xd; структурних станів системи, що розглядається. Дві з них - області стабільності краплинних&#xd; структурних станів, в яких гетерофазні флуктуації мають форму ізольованих крапель. В третій&#xd; області стабільним є змішаний стан, в ньому співіснують два нескінченних взаємно протікаючих&#xd; кластери, рідкий і некристалічнии твердотільнии. Ширина температурного інтервалу, [Tt1, Tt2], в&#xd; якому змішаний стан є стабільним, збільшується з ростом конфігураційної ентропії (складності)&#xd; некристалічної твердотільної фракції. В межах застосованого підходу знайдено слабкі фазові&#xd; переходи першого роду при Т = Tt1 і при Т = Тt2. Показано, що в змішаному стані можливі фазові&#xd; переходи першого або другого роду. Знайдено критерії наявності цих фазових переходів. Одержано&#xd; рівняння стану і вирази для термодинамічних величин (ентропії, теплоємності, стисливості і&#xd; коефіцієнта теплового розширення) для краплинних і змішаного станів.
Theomodynamics of glass-forming liquids and&#xd; glasses is considered taking into account the contributions of heterophase fluctuations to tree energy.&#xd; The heterophase fluctuations in liquids are nuclei of&#xd; non-crystalline solids. In glass the heterophase fluctuations are nuclei of liquid. The crystalline solid&#xd; state is not considered. The droplet approach and&#xd; the mixed state model are applied to describe free&#xd; energy. It is shown that there exist three regions of&#xd; stability of different structure states of the system in&#xd; the plane (P, T). Two of them are the stability regions of the droplet structure states. In the third one&#xd; the mixed state is stable. In the droplet states the&#xd; heterophase fluctuations exist as isolated droplets.&#xd; In the mixed state two infinite percolating clusters&#xd; (solid and liquid) are coexisting. The widths of the&#xd; temperature interval, [Tt1, Tt2], where the mixed&#xd; state is stable increase with the growth of the configurational entropy (complexity) of the non-crystalline solid fraction. In the frame of the approach used&#xd; weak 1st order phase transitions are revealed at&#xd; Т = Tt1 and Т = Тt2. It is shown that in the mixed&#xd; state the 1st order or 2nd order phase transitions are&#xd; possible. The criteria of these phase, transitions are&#xd; obtained. Equations of state and expressions of thermodynamic quantities (entropy, specific heat capacity, compressibility and thermal expansion coefficient) in the droplet and mixed states are derived.
ru
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
Физика низких температур
Низкоразмерные и неупорядоченные системы
О теpмодинамике пеpеохлажденных жидкостей и стекол
On thermodynamics of supercooled liquids and glasses
Article
published earlier
spellingShingle О теpмодинамике пеpеохлажденных жидкостей и стекол
Бакай, А.С.
Низкоразмерные и неупорядоченные системы
title О теpмодинамике пеpеохлажденных жидкостей и стекол
title_alt On thermodynamics of supercooled liquids and glasses
title_full О теpмодинамике пеpеохлажденных жидкостей и стекол
title_fullStr О теpмодинамике пеpеохлажденных жидкостей и стекол
title_full_unstemmed О теpмодинамике пеpеохлажденных жидкостей и стекол
title_short О теpмодинамике пеpеохлажденных жидкостей и стекол
title_sort о теpмодинамике пеpеохлажденных жидкостей и стекол
topic Низкоразмерные и неупорядоченные системы
topic_facet Низкоразмерные и неупорядоченные системы
url https://nasplib.isofts.kiev.ua/handle/123456789/176357
work_keys_str_mv AT bakaias otepmodinamikepepeohlaždennyhžidkosteiistekol
AT bakaias onthermodynamicsofsupercooledliquidsandglasses