How Good Is the Debye Model for Nanocrystals?

Autores
Miranda, Enrique Nestor; Mora Barzaga, Geraudys
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The question here is whether the Debye model is suited to evaluate the specific heat of nanocrystals. For this, the simplest possible nanocrystal is considered: a basic cubic structure made of atoms that interact through a harmonic potential. This simple model can be solved exactly. This allows the dispersion relation of the mechanical waves to be determined, so that calculating the exact specific heat turns out to be quite straightforward. Then, the same problem is solved using the Debye approximation. Our findings show that the specific heat of a nanocrystal evaluated exactly is higher than the value found in the thermodynamic limit, that is to say, the specific heat decreases as the nanocrystal size increases. In addition, it becomes clear that the Debye model is a poor approximation for calculating the specific heat of a nanocrystal. Naturally, the Einstein model yields an even worse result. The cause of the discrepancy is found in the role of the nanocrystal surface.
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. Universidad Nacional de Cuyo. Facultad de Ciencias Exactas y Naturales; Argentina
Fil: Mora Barzaga, Geraudys. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Nacional de Cuyo. Facultad de Ciencias Exactas y Naturales; Argentina
Materia
NANOCRISTALES
SISTEMAS CON POCAS PARTÍCULAS
MODELO DE DEBYE
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/126687
Acceder
id CONICETDig_40a665f49f336cf35308065b82a818f8
oai_identifier_str oai:ri.conicet.gov.ar:11336/126687
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling How Good Is the Debye Model for Nanocrystals?Miranda, Enrique NestorMora Barzaga, GeraudysNANOCRISTALESSISTEMAS CON POCAS PARTÍCULASMODELO DE DEBYEhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The question here is whether the Debye model is suited to evaluate the specific heat of nanocrystals. For this, the simplest possible nanocrystal is considered: a basic cubic structure made of atoms that interact through a harmonic potential. This simple model can be solved exactly. This allows the dispersion relation of the mechanical waves to be determined, so that calculating the exact specific heat turns out to be quite straightforward. Then, the same problem is solved using the Debye approximation. Our findings show that the specific heat of a nanocrystal evaluated exactly is higher than the value found in the thermodynamic limit, that is to say, the specific heat decreases as the nanocrystal size increases. In addition, it becomes clear that the Debye model is a poor approximation for calculating the specific heat of a nanocrystal. Naturally, the Einstein model yields an even worse result. The cause of the discrepancy is found in the role of the nanocrystal surface.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. Universidad Nacional de Cuyo. Facultad de Ciencias Exactas y Naturales; ArgentinaFil: Mora Barzaga, Geraudys. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Nacional de Cuyo. Facultad de Ciencias Exactas y Naturales; ArgentinaScientific Research2019-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/126687Miranda, Enrique Nestor; Mora Barzaga, Geraudys; How Good Is the Debye Model for Nanocrystals?; Scientific Research; Journal of Modern Physics; 10; 06; 5-2019; 601-6122153-1196CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.scirp.org/journal/doi.aspx?DOI=10.4236/jmp.2019.106042info:eu-repo/semantics/altIdentifier/doi/10.4236/jmp.2019.106042info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:22:54Zoai:ri.conicet.gov.ar:11336/126687instacron: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:34982025-10-22 11:22:54.467CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv How Good Is the Debye Model for Nanocrystals?
title How Good Is the Debye Model for Nanocrystals?
spellingShingle How Good Is the Debye Model for Nanocrystals?
Miranda, Enrique Nestor
NANOCRISTALES
SISTEMAS CON POCAS PARTÍCULAS
MODELO DE DEBYE
title_short How Good Is the Debye Model for Nanocrystals?
title_full How Good Is the Debye Model for Nanocrystals?
title_fullStr How Good Is the Debye Model for Nanocrystals?
title_full_unstemmed How Good Is the Debye Model for Nanocrystals?
title_sort How Good Is the Debye Model for Nanocrystals?
dc.creator.none.fl_str_mv Miranda, Enrique Nestor
Mora Barzaga, Geraudys
author Miranda, Enrique Nestor
author_facet Miranda, Enrique Nestor
Mora Barzaga, Geraudys
author_role author
author2 Mora Barzaga, Geraudys
author2_role author
dc.subject.none.fl_str_mv NANOCRISTALES
SISTEMAS CON POCAS PARTÍCULAS
MODELO DE DEBYE
topic NANOCRISTALES
SISTEMAS CON POCAS PARTÍCULAS
MODELO DE DEBYE
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The question here is whether the Debye model is suited to evaluate the specific heat of nanocrystals. For this, the simplest possible nanocrystal is considered: a basic cubic structure made of atoms that interact through a harmonic potential. This simple model can be solved exactly. This allows the dispersion relation of the mechanical waves to be determined, so that calculating the exact specific heat turns out to be quite straightforward. Then, the same problem is solved using the Debye approximation. Our findings show that the specific heat of a nanocrystal evaluated exactly is higher than the value found in the thermodynamic limit, that is to say, the specific heat decreases as the nanocrystal size increases. In addition, it becomes clear that the Debye model is a poor approximation for calculating the specific heat of a nanocrystal. Naturally, the Einstein model yields an even worse result. The cause of the discrepancy is found in the role of the nanocrystal surface.
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. Universidad Nacional de Cuyo. Facultad de Ciencias Exactas y Naturales; Argentina
Fil: Mora Barzaga, Geraudys. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Nacional de Cuyo. Facultad de Ciencias Exactas y Naturales; Argentina
description The question here is whether the Debye model is suited to evaluate the specific heat of nanocrystals. For this, the simplest possible nanocrystal is considered: a basic cubic structure made of atoms that interact through a harmonic potential. This simple model can be solved exactly. This allows the dispersion relation of the mechanical waves to be determined, so that calculating the exact specific heat turns out to be quite straightforward. Then, the same problem is solved using the Debye approximation. Our findings show that the specific heat of a nanocrystal evaluated exactly is higher than the value found in the thermodynamic limit, that is to say, the specific heat decreases as the nanocrystal size increases. In addition, it becomes clear that the Debye model is a poor approximation for calculating the specific heat of a nanocrystal. Naturally, the Einstein model yields an even worse result. The cause of the discrepancy is found in the role of the nanocrystal surface.
publishDate 2019
dc.date.none.fl_str_mv 2019-05
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/11336/126687
Miranda, Enrique Nestor; Mora Barzaga, Geraudys; How Good Is the Debye Model for Nanocrystals?; Scientific Research; Journal of Modern Physics; 10; 06; 5-2019; 601-612
2153-1196
CONICET Digital
CONICET
url http://hdl.handle.net/11336/126687
identifier_str_mv Miranda, Enrique Nestor; Mora Barzaga, Geraudys; How Good Is the Debye Model for Nanocrystals?; Scientific Research; Journal of Modern Physics; 10; 06; 5-2019; 601-612
2153-1196
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.scirp.org/journal/doi.aspx?DOI=10.4236/jmp.2019.106042
info:eu-repo/semantics/altIdentifier/doi/10.4236/jmp.2019.106042
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Scientific Research
publisher.none.fl_str_mv Scientific Research
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
_version_ 1846781751532191744
score 12.982451

Publicaciones similares