The Einstein Nanocrystal

Autores
Bertoldi, Dalía Surena; Fernandez Guillermet, Armando Jorge; Miranda, Enrique Nestor
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the simplest possible model of nanocrystal consisting in a simple cubic lattice with a small number of atoms (NA ~ 10-10^3), where each atom is linked to its nearest neighbor by a quantum harmonic potential. Some properties (entropy, temperature, specific heat) of the nanocrystal are calculated numerically but exactly within the framework of the microcanonical ensemble. We find that the presence of a surface in the nanocrystal modifies the thermostatistic properties to a greater extent than the small number of atoms in the system. The specific heat Cv behaves similarly to the Einstein solid, with an asymptotic value for high temperatures that differs from that of the Dulong-Petit law by a term of the order of NA^(-1/3) and that can be explained easily in terms of the surface. The entropy is non-additive, but this is due to the presence of the surface and we show that the additivity is recovered in the thermodynamic limit. Finally, we find that, when calculations follow the canonical ensemble, results differ little for small systems (NA = 27) and are inexistent for larger systems (NA = 1000).
Fil: Bertoldi, Dalía Surena. Universidad Nacional de Cuyo. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Fernandez Guillermet, Armando Jorge. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina
Fil: Miranda, Enrique Nestor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Provincia de Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Universidad Nacional de Cuyo. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales; Argentina
Materia
FEW PARTICLE SYSTEMS
MICROCANONICAL ENSEMBLE
NANOCRYSTAL
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/62773
Acceder
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network_name_str CONICET Digital (CONICET)
spelling The Einstein NanocrystalBertoldi, Dalía SurenaFernandez Guillermet, Armando JorgeMiranda, Enrique NestorFEW PARTICLE SYSTEMSMICROCANONICAL ENSEMBLENANOCRYSTALhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We study the simplest possible model of nanocrystal consisting in a simple cubic lattice with a small number of atoms (NA ~ 10-10^3), where each atom is linked to its nearest neighbor by a quantum harmonic potential. Some properties (entropy, temperature, specific heat) of the nanocrystal are calculated numerically but exactly within the framework of the microcanonical ensemble. We find that the presence of a surface in the nanocrystal modifies the thermostatistic properties to a greater extent than the small number of atoms in the system. The specific heat Cv behaves similarly to the Einstein solid, with an asymptotic value for high temperatures that differs from that of the Dulong-Petit law by a term of the order of NA^(-1/3) and that can be explained easily in terms of the surface. The entropy is non-additive, but this is due to the presence of the surface and we show that the additivity is recovered in the thermodynamic limit. Finally, we find that, when calculations follow the canonical ensemble, results differ little for small systems (NA = 27) and are inexistent for larger systems (NA = 1000).Fil: Bertoldi, Dalía Surena. Universidad Nacional de Cuyo. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Fernandez Guillermet, Armando Jorge. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; ArgentinaFil: Miranda, Enrique Nestor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Provincia de Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Universidad Nacional de Cuyo. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales; ArgentinaSociedad Mexicana de Física2016-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/62773Bertoldi, Dalía Surena; Fernandez Guillermet, Armando Jorge; Miranda, Enrique Nestor; The Einstein Nanocrystal; Sociedad Mexicana de Física; Revista Mexicana de Física E; 62; 1; 1-2016; 60-651870-35420035-001XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://rmf.smf.mx/pdf/rmf-e/62/1/62_1_60.pdfinfo:eu-repo/semantics/altIdentifier/url/https://rmf.smf.mx/page/rmf-e_anteriores?volume=62&issue=1info:eu-repo/semantics/altIdentifier/url/http://www.redalyc.org/articulo.oa?id=57048165009info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:10:04Zoai:ri.conicet.gov.ar:11336/62773instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:10:04.792CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The Einstein Nanocrystal
title The Einstein Nanocrystal
spellingShingle The Einstein Nanocrystal
Bertoldi, Dalía Surena
FEW PARTICLE SYSTEMS
MICROCANONICAL ENSEMBLE
NANOCRYSTAL
title_short The Einstein Nanocrystal
title_full The Einstein Nanocrystal
title_fullStr The Einstein Nanocrystal
title_full_unstemmed The Einstein Nanocrystal
title_sort The Einstein Nanocrystal
dc.creator.none.fl_str_mv Bertoldi, Dalía Surena
Fernandez Guillermet, Armando Jorge
Miranda, Enrique Nestor
author Bertoldi, Dalía Surena
author_facet Bertoldi, Dalía Surena
Fernandez Guillermet, Armando Jorge
Miranda, Enrique Nestor
author_role author
author2 Fernandez Guillermet, Armando Jorge
Miranda, Enrique Nestor
author2_role author
author
dc.subject.none.fl_str_mv FEW PARTICLE SYSTEMS
MICROCANONICAL ENSEMBLE
NANOCRYSTAL
topic FEW PARTICLE SYSTEMS
MICROCANONICAL ENSEMBLE
NANOCRYSTAL
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study the simplest possible model of nanocrystal consisting in a simple cubic lattice with a small number of atoms (NA ~ 10-10^3), where each atom is linked to its nearest neighbor by a quantum harmonic potential. Some properties (entropy, temperature, specific heat) of the nanocrystal are calculated numerically but exactly within the framework of the microcanonical ensemble. We find that the presence of a surface in the nanocrystal modifies the thermostatistic properties to a greater extent than the small number of atoms in the system. The specific heat Cv behaves similarly to the Einstein solid, with an asymptotic value for high temperatures that differs from that of the Dulong-Petit law by a term of the order of NA^(-1/3) and that can be explained easily in terms of the surface. The entropy is non-additive, but this is due to the presence of the surface and we show that the additivity is recovered in the thermodynamic limit. Finally, we find that, when calculations follow the canonical ensemble, results differ little for small systems (NA = 27) and are inexistent for larger systems (NA = 1000).
Fil: Bertoldi, Dalía Surena. Universidad Nacional de Cuyo. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Fernandez Guillermet, Armando Jorge. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina
Fil: Miranda, Enrique Nestor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Provincia de Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Universidad Nacional de Cuyo. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales; Argentina
description We study the simplest possible model of nanocrystal consisting in a simple cubic lattice with a small number of atoms (NA ~ 10-10^3), where each atom is linked to its nearest neighbor by a quantum harmonic potential. Some properties (entropy, temperature, specific heat) of the nanocrystal are calculated numerically but exactly within the framework of the microcanonical ensemble. We find that the presence of a surface in the nanocrystal modifies the thermostatistic properties to a greater extent than the small number of atoms in the system. The specific heat Cv behaves similarly to the Einstein solid, with an asymptotic value for high temperatures that differs from that of the Dulong-Petit law by a term of the order of NA^(-1/3) and that can be explained easily in terms of the surface. The entropy is non-additive, but this is due to the presence of the surface and we show that the additivity is recovered in the thermodynamic limit. Finally, we find that, when calculations follow the canonical ensemble, results differ little for small systems (NA = 27) and are inexistent for larger systems (NA = 1000).
publishDate 2016
dc.date.none.fl_str_mv 2016-01
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/62773
Bertoldi, Dalía Surena; Fernandez Guillermet, Armando Jorge; Miranda, Enrique Nestor; The Einstein Nanocrystal; Sociedad Mexicana de Física; Revista Mexicana de Física E; 62; 1; 1-2016; 60-65
1870-3542
0035-001X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/62773
identifier_str_mv Bertoldi, Dalía Surena; Fernandez Guillermet, Armando Jorge; Miranda, Enrique Nestor; The Einstein Nanocrystal; Sociedad Mexicana de Física; Revista Mexicana de Física E; 62; 1; 1-2016; 60-65
1870-3542
0035-001X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://rmf.smf.mx/pdf/rmf-e/62/1/62_1_60.pdf
info:eu-repo/semantics/altIdentifier/url/https://rmf.smf.mx/page/rmf-e_anteriores?volume=62&issue=1
info:eu-repo/semantics/altIdentifier/url/http://www.redalyc.org/articulo.oa?id=57048165009
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Sociedad Mexicana de Física
publisher.none.fl_str_mv Sociedad Mexicana de Física
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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