Pub Date : 2022-10-03DOI: 10.1080/09500839.2022.2123113
J. Maity
ABSTRACT An analytical model is developed to explain the kinetics of grain growth in steel that takes into account all feasible prime phenomena; namely, surface energy reduction, precipitate pinning effect and solute drag effect. The shapes of matrix grains and the precipitates are assumed to be tetrakeidecahedron and spherical, respectively. A single solute and a single type of precipitate are further assumed to be responsible for the solute drag and the precipitate pinning, respectively. An explanation of drag energy is provided in terms of Gibbs free energy change for solute segregation that eventually merges to the well-known Langmuir–McLean relationship. The developed model is validated in view of the existing database in available literature. A new methodology of grain growth analysis is accordingly proposed on the basis of the conceptualised ‘effective migration coefficient’ of the system.
{"title":"An analytical model of grain growth considering the conjoint effects of precipitate pinning and solute drag in steel","authors":"J. Maity","doi":"10.1080/09500839.2022.2123113","DOIUrl":"https://doi.org/10.1080/09500839.2022.2123113","url":null,"abstract":"ABSTRACT An analytical model is developed to explain the kinetics of grain growth in steel that takes into account all feasible prime phenomena; namely, surface energy reduction, precipitate pinning effect and solute drag effect. The shapes of matrix grains and the precipitates are assumed to be tetrakeidecahedron and spherical, respectively. A single solute and a single type of precipitate are further assumed to be responsible for the solute drag and the precipitate pinning, respectively. An explanation of drag energy is provided in terms of Gibbs free energy change for solute segregation that eventually merges to the well-known Langmuir–McLean relationship. The developed model is validated in view of the existing database in available literature. A new methodology of grain growth analysis is accordingly proposed on the basis of the conceptualised ‘effective migration coefficient’ of the system.","PeriodicalId":19860,"journal":{"name":"Philosophical Magazine Letters","volume":"102 1","pages":"307 - 323"},"PeriodicalIF":1.2,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46317395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-03DOI: 10.1080/09500839.2022.2129109
Jianlin Li, Jinke Han, Fance Song, Haoyu Zhang, Ge Zhou, Lijia Chen, Xue Cao
ABSTRACT High-entropy alloys (HEAs) were studied via hot compression experiments using a Gleeble-3800 thermal simulation tester. The hot deformation behaviour of an AlFeCoNiMo0.2 HEA and the physical significance of the associated parameters were analyzed according to the Prasad, Gegel, Malas, and Murty instability criteria. Processing maps of different instability criteria under different conditions were constructed. The domain corresponding to a temperature range of 1070°C–1150°C with a strain rate range of 0.001–0.1 s−1 and average power dissipation rates of >40% did not feature flow instability; thus, this domain is appropriate for the AlFeCoNiMo0.2 HEA deformation process. Through microstructure analysis, it was determined that the deformation mechanism in the optimal forming region is dynamic recrystallization.
{"title":"A comparative study of flow instability criteria in the processing map of AlFeCoNiMo0.2 high-entropy alloys","authors":"Jianlin Li, Jinke Han, Fance Song, Haoyu Zhang, Ge Zhou, Lijia Chen, Xue Cao","doi":"10.1080/09500839.2022.2129109","DOIUrl":"https://doi.org/10.1080/09500839.2022.2129109","url":null,"abstract":"ABSTRACT High-entropy alloys (HEAs) were studied via hot compression experiments using a Gleeble-3800 thermal simulation tester. The hot deformation behaviour of an AlFeCoNiMo0.2 HEA and the physical significance of the associated parameters were analyzed according to the Prasad, Gegel, Malas, and Murty instability criteria. Processing maps of different instability criteria under different conditions were constructed. The domain corresponding to a temperature range of 1070°C–1150°C with a strain rate range of 0.001–0.1 s−1 and average power dissipation rates of >40% did not feature flow instability; thus, this domain is appropriate for the AlFeCoNiMo0.2 HEA deformation process. Through microstructure analysis, it was determined that the deformation mechanism in the optimal forming region is dynamic recrystallization.","PeriodicalId":19860,"journal":{"name":"Philosophical Magazine Letters","volume":"102 1","pages":"348 - 358"},"PeriodicalIF":1.2,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44660630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-29DOI: 10.1080/09500839.2022.2126535
Katsutoshi Takashima, R. Han, K. Yokoyama, Y. Funakawa
ABSTRACT The continuousness of the interactions between hydrogen and plastic deformation of an ultra-high strength steel sheet consisting of ferrite and nanometer-sized precipitates has been investigated by tensile tests after or during cathodic hydrogen charging. In the tensile test in the air after hydrogen pre-charging, a hydrogen thermal desorption analysis shows that the amount of hydrogen desorbed decreases with increasing applied tensile strain from room temperature to 50 °C, but increases in the high temperature region. Upon tensile straining to 0.06, no hydrogen is desorbed in the low temperature region, and the change in desorption behaviour when strain exceeds 0.06 is negligible. This suggests that substantial interactions between hydrogen and plastic deformation in the test with hydrogen pre-charging occur only in the early stages of deformation. In contrast, in the tensile test during hydrogen charging, the hydrogen desorption which begins from room temperature continues even upon tensile straining to 0.06, suggesting continuous interactions, and a unique dislocation structure resembling sub-grain boundaries is observed. Upon aging at room temperature after tensile straining to 0.06 during hydrogen charging, all hydrogen desorption lower than 100 °C shifts to the high temperature region, but the recovery of elongation is not necessarily complete. When tensile strain is applied during hydrogen charging, continuous interactions presumably induce anomalous damage, thereby enhancing the degradation of ductility. The results of the present study strongly support the conclusion that the continuousness of the dynamic interactions between hydrogen and plastic deformation plays essential roles in hydrogen embrittlement of ferritic steel.
{"title":"Continuousness of interactions between hydrogen and plastic deformation of ultra-high strength steel sheet consisting of ferrite and nanometer-sized precipitates","authors":"Katsutoshi Takashima, R. Han, K. Yokoyama, Y. Funakawa","doi":"10.1080/09500839.2022.2126535","DOIUrl":"https://doi.org/10.1080/09500839.2022.2126535","url":null,"abstract":"ABSTRACT The continuousness of the interactions between hydrogen and plastic deformation of an ultra-high strength steel sheet consisting of ferrite and nanometer-sized precipitates has been investigated by tensile tests after or during cathodic hydrogen charging. In the tensile test in the air after hydrogen pre-charging, a hydrogen thermal desorption analysis shows that the amount of hydrogen desorbed decreases with increasing applied tensile strain from room temperature to 50 °C, but increases in the high temperature region. Upon tensile straining to 0.06, no hydrogen is desorbed in the low temperature region, and the change in desorption behaviour when strain exceeds 0.06 is negligible. This suggests that substantial interactions between hydrogen and plastic deformation in the test with hydrogen pre-charging occur only in the early stages of deformation. In contrast, in the tensile test during hydrogen charging, the hydrogen desorption which begins from room temperature continues even upon tensile straining to 0.06, suggesting continuous interactions, and a unique dislocation structure resembling sub-grain boundaries is observed. Upon aging at room temperature after tensile straining to 0.06 during hydrogen charging, all hydrogen desorption lower than 100 °C shifts to the high temperature region, but the recovery of elongation is not necessarily complete. When tensile strain is applied during hydrogen charging, continuous interactions presumably induce anomalous damage, thereby enhancing the degradation of ductility. The results of the present study strongly support the conclusion that the continuousness of the dynamic interactions between hydrogen and plastic deformation plays essential roles in hydrogen embrittlement of ferritic steel.","PeriodicalId":19860,"journal":{"name":"Philosophical Magazine Letters","volume":"102 1","pages":"324 - 334"},"PeriodicalIF":1.2,"publicationDate":"2022-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42138427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-02DOI: 10.1080/09500839.2022.2120644
Bejjipurapu Akhil, A. Bajpai, K. Biswas
ABSTRACT In the present study, the intelligent addition of Re and Al to TiZrHf equiatomic ternary alloy resulted in a new single-phase Ti30Zr30Hf30Re5Al5 HCP high entropy alloy. The XRD analyses show that the TiZrHfRex alloys have a single-phase HCP structure until x = 5 at.%. Subsequently, the TiZrHfRe5 retains its single-phase HCP microstructure with the addition of Al upto 5 at.%, leading to a new quinary TiZrHfRe5Al5 HCP HEA. Microstructural investigations using SEM revealed the formation of compositionally homogeneous single-phase HCP solid solution for TiZrHf, TiZrHfRe5 and TiZrHfRe5Al5 alloys. Vicker's microindentation measurements revealed that adding Re, followed by Al, increases the hardness of the TiZrHf ternary alloy from 7.85 0.37–8.35 0.42 GPa. In a nutshell, a novel quinary HCP alloy was developed based on transition metals, allowing HCP HEA compositional space to expand beyond rare-earth (RE) based HEAs.
{"title":"Microstructure and mechanical properties of the new TiZrHfReAl HCP high entropy alloy","authors":"Bejjipurapu Akhil, A. Bajpai, K. Biswas","doi":"10.1080/09500839.2022.2120644","DOIUrl":"https://doi.org/10.1080/09500839.2022.2120644","url":null,"abstract":"ABSTRACT In the present study, the intelligent addition of Re and Al to TiZrHf equiatomic ternary alloy resulted in a new single-phase Ti30Zr30Hf30Re5Al5 HCP high entropy alloy. The XRD analyses show that the TiZrHfRex alloys have a single-phase HCP structure until x = 5 at.%. Subsequently, the TiZrHfRe5 retains its single-phase HCP microstructure with the addition of Al upto 5 at.%, leading to a new quinary TiZrHfRe5Al5 HCP HEA. Microstructural investigations using SEM revealed the formation of compositionally homogeneous single-phase HCP solid solution for TiZrHf, TiZrHfRe5 and TiZrHfRe5Al5 alloys. Vicker's microindentation measurements revealed that adding Re, followed by Al, increases the hardness of the TiZrHf ternary alloy from 7.85 0.37–8.35 0.42 GPa. In a nutshell, a novel quinary HCP alloy was developed based on transition metals, allowing HCP HEA compositional space to expand beyond rare-earth (RE) based HEAs.","PeriodicalId":19860,"journal":{"name":"Philosophical Magazine Letters","volume":"102 1","pages":"287 - 298"},"PeriodicalIF":1.2,"publicationDate":"2022-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41333070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-02DOI: 10.1080/09500839.2022.2118386
Y. Mei
ABSTRACT This paper gives for the first time a complete equation to analyze the temperature dependence (or thermal variation) of spin-Hamiltonian parameter from low to high temperatures for transition metal and rare-earth ions in crystals. This equation includes not only the dynamic effect (only considered in previous papers) caused by electron–phonon interaction but also the static effect owing to lattice thermal expansion. Based on the complete equation, the thermal variations of zero-field splitting b4 0 from low to high temperatures for cubic Eu2+ and Gd3+ centers in CdF2 crystal are studied. The contributions due to static effect are estimated from the pressure dependence of zero-field splitting b4 0. The static parameters B (charactering the static effect) and the electron–phonon coupling parameters K (charactering the dynamic effect) for both systems are determined and the coefficients (B + K) in the complete equation are obtained. The results are discussed.
{"title":"A complete study on the temperature dependences of zero-field splitting b4 0 for Eu2+ and Gd3+ ions in CdF2 crystal","authors":"Y. Mei","doi":"10.1080/09500839.2022.2118386","DOIUrl":"https://doi.org/10.1080/09500839.2022.2118386","url":null,"abstract":"ABSTRACT This paper gives for the first time a complete equation to analyze the temperature dependence (or thermal variation) of spin-Hamiltonian parameter from low to high temperatures for transition metal and rare-earth ions in crystals. This equation includes not only the dynamic effect (only considered in previous papers) caused by electron–phonon interaction but also the static effect owing to lattice thermal expansion. Based on the complete equation, the thermal variations of zero-field splitting b4 0 from low to high temperatures for cubic Eu2+ and Gd3+ centers in CdF2 crystal are studied. The contributions due to static effect are estimated from the pressure dependence of zero-field splitting b4 0. The static parameters B (charactering the static effect) and the electron–phonon coupling parameters K (charactering the dynamic effect) for both systems are determined and the coefficients (B + K) in the complete equation are obtained. The results are discussed.","PeriodicalId":19860,"journal":{"name":"Philosophical Magazine Letters","volume":"102 1","pages":"278 - 286"},"PeriodicalIF":1.2,"publicationDate":"2022-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48700283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-02DOI: 10.1080/09500839.2022.2121866
C. Singh, S. Singh, J. Jain
ABSTRACT The hydrogen evolution process in the as-cast Mg-0.6Ca alloy was investigated using real-time optical imaging of the corroding surface. It was revealed that hydrogen evolved as large stable bubbles and continuous streams of tiny bubbles because of high localised current density. To the best of the author’s knowledge, this is the first attempt to characterise the hydrogen evolution behaviour of Mg-Ca binary alloy employing a mechanistic model based on real-time imaging.
{"title":"Elucidating the role of micro-galvanic coupling between eutectic α-Mg lamellas and α-Mg matrix on the hydrogen evolution behaviour of Mg-0.6Ca binary alloy using real-time imaging","authors":"C. Singh, S. Singh, J. Jain","doi":"10.1080/09500839.2022.2121866","DOIUrl":"https://doi.org/10.1080/09500839.2022.2121866","url":null,"abstract":"ABSTRACT The hydrogen evolution process in the as-cast Mg-0.6Ca alloy was investigated using real-time optical imaging of the corroding surface. It was revealed that hydrogen evolved as large stable bubbles and continuous streams of tiny bubbles because of high localised current density. To the best of the author’s knowledge, this is the first attempt to characterise the hydrogen evolution behaviour of Mg-Ca binary alloy employing a mechanistic model based on real-time imaging.","PeriodicalId":19860,"journal":{"name":"Philosophical Magazine Letters","volume":"102 1","pages":"299 - 306"},"PeriodicalIF":1.2,"publicationDate":"2022-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42352419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ABSTRACT Ti–0.3Mo–0.8Ni alloy has excellent corrosion resistance and is widely used in making crystallizers, heaters and evaporators for salt production, as well as chemical reactors and heat exchangers. To study the distribution of Mo in the Ti–0.3Mo–0.8Ni alloy during electron beam cold hearth melting, the solidification process has been numerically modelled and the calculations compared with experimental data. A distribution law similar to the calculated results is obtained, which verifies the reliability of the numerical modelling and provides theoretical guidance for the industrial production of Ti–0.3Mo–0.8Ni alloy. In addition, the experimental data indicates that the deviation of the Mo content in each end face and cross-section is within ±0.05%.
{"title":"Experimental verification of molybdenum segregation for large-scale slab ingots of Ti–0.3Mo–0.8Ni alloy during electron-beam cold-hearth melting","authors":"Zhenze Zhu, Zulai Li, Rongfeng Zhou, Hai-guang Huang, Wentao Xiong, Xiangming Li","doi":"10.1080/09500839.2022.2100935","DOIUrl":"https://doi.org/10.1080/09500839.2022.2100935","url":null,"abstract":"ABSTRACT Ti–0.3Mo–0.8Ni alloy has excellent corrosion resistance and is widely used in making crystallizers, heaters and evaporators for salt production, as well as chemical reactors and heat exchangers. To study the distribution of Mo in the Ti–0.3Mo–0.8Ni alloy during electron beam cold hearth melting, the solidification process has been numerically modelled and the calculations compared with experimental data. A distribution law similar to the calculated results is obtained, which verifies the reliability of the numerical modelling and provides theoretical guidance for the industrial production of Ti–0.3Mo–0.8Ni alloy. In addition, the experimental data indicates that the deviation of the Mo content in each end face and cross-section is within ±0.05%.","PeriodicalId":19860,"journal":{"name":"Philosophical Magazine Letters","volume":"102 1","pages":"270 - 277"},"PeriodicalIF":1.2,"publicationDate":"2022-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49230126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-13DOI: 10.1080/09500839.2022.2096267
I. M. Suslov
ABSTRACT
Resistance ρ of an one-dimensional disordered system of length L has the log-normal distribution in the limit of large L. Parameters of this distribution depend on the Fermi level position, but are independent on the boundary conditions. However, the boundary conditions essentially affect the distribution of phases entering the transfer matrix and generally change the parameters of the evolution equation for the distribution . This visible contradiction is resolved by the existence of the hidden symmetry, whose nature is revealed by the derivation of the equation for the stationary phase distribution and by analysis of its transformation properties.
{"title":"Hidden symmetry in 1D localisation","authors":"I. M. Suslov","doi":"10.1080/09500839.2022.2096267","DOIUrl":"https://doi.org/10.1080/09500839.2022.2096267","url":null,"abstract":"<p><b>ABSTRACT</b></p><p>Resistance <i>ρ</i> of an one-dimensional disordered system of length <i>L</i> has the log-normal distribution in the limit of large <i>L</i>. Parameters of this distribution depend on the Fermi level position, but are independent on the boundary conditions. However, the boundary conditions essentially affect the distribution of phases entering the transfer matrix and generally change the parameters of the evolution equation for the distribution <span><noscript><img alt=\"\" src=\"/na101/home/literatum/publisher/tandf/journals/content/tphl20/2022/tphl20.v102.i08-09/09500839.2022.2096267/20221101/images/tphl_a_2096267_ilm0001.gif\"/></noscript><img alt=\"\" data-formula-source='{\"type\" : \"image\", \"src\" : \"/na101/home/literatum/publisher/tandf/journals/content/tphl20/2022/tphl20.v102.i08-09/09500839.2022.2096267/20221101/images/tphl_a_2096267_ilm0001.gif\"}' src=\"//:0\"/><span></span></span><span><img alt=\"\" data-formula-source='{\"type\" : \"mathjax\"}' src=\"//:0\"/><math><mi>P</mi><mo>(</mo><mi>ρ</mi><mo>)</mo></math></span>. This visible contradiction is resolved by the existence of the hidden symmetry, whose nature is revealed by the derivation of the equation for the stationary phase distribution and by analysis of its transformation properties.</p>","PeriodicalId":19860,"journal":{"name":"Philosophical Magazine Letters","volume":"4 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ABSTRACT The hot compression of A-100 steel at 850–1150°C and strain rate of 0.01–10 s−1 was tested on a Gleeble-3800 thermal simulation machine to determine the corresponding true stress–strain curve. Based on theoretical calculation, the dislocation density factor was introduced into the Avrami equation and thereby a dynamic recovery physical constitutive relational model based on dislocation density theory was established. Then the hot deformation behaviour of A-100 steel was predicted (correlation coefficient R = 0.9964 with an average absolute relative error AARE = 4.0923%). The structures after hot compression were observed by electron backscattered diffraction and found to be lath-shaped martensite and austenite. With an increase of temperature and deceleration of strain rate, the proportions of large-angle boundaries and substructures increased and the softening mechanism became dominated by dynamic recovery.
{"title":"Physical constitutive relational model and structure evolution during dynamic recovery of 23Co14Ni12Cr3MoE (A-100) high-strength steel","authors":"Jinke Han, Jianlin Li, Yifan Zhang, Haoyu Zhang, Ge Zhou, Lijia Chen","doi":"10.1080/09500839.2022.2084570","DOIUrl":"https://doi.org/10.1080/09500839.2022.2084570","url":null,"abstract":"ABSTRACT The hot compression of A-100 steel at 850–1150°C and strain rate of 0.01–10 s−1 was tested on a Gleeble-3800 thermal simulation machine to determine the corresponding true stress–strain curve. Based on theoretical calculation, the dislocation density factor was introduced into the Avrami equation and thereby a dynamic recovery physical constitutive relational model based on dislocation density theory was established. Then the hot deformation behaviour of A-100 steel was predicted (correlation coefficient R = 0.9964 with an average absolute relative error AARE = 4.0923%). The structures after hot compression were observed by electron backscattered diffraction and found to be lath-shaped martensite and austenite. With an increase of temperature and deceleration of strain rate, the proportions of large-angle boundaries and substructures increased and the softening mechanism became dominated by dynamic recovery.","PeriodicalId":19860,"journal":{"name":"Philosophical Magazine Letters","volume":"102 1","pages":"229 - 238"},"PeriodicalIF":1.2,"publicationDate":"2022-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47635382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-20DOI: 10.1080/09500839.2022.2084571
Lei Lu, Chongzheng Na
ABSTRACT Adsorption is a physicochemical phenomenon important in both natural and engineering processes. In the research and practice of adsorption equilibrium, a long-standing challenge is how to reconcile the classical models proposed by Gibbs, Langmuir, Freundlich, and Temkin for interpreting experimentally obtained adsorption isotherms. Here, we show that the Langmuir, Freundlich, and Temkin isotherms can be derived from the Gibbs equation under different conditions for the change of surface energy (a.k.a. surface tension) by adsorption. When the change of surface energy is predominantly controlled by the change of chemical potential with negligible contribution from the change of internal energy and entropy, the Gibbs equation can be integrated to give the Langmuir isotherm. When changes of internal energy and entropy are no longer negligible, the integration of the Gibbs equation gives the Freundlich and Temkin equations, according to a change of surface energy either independent or linearly dependent on the adsorption capacity. These results indicate that the classical models share the common mechanism of phase equilibrium described by the Gibbsian thermodynamics, thereby providing novel insights for their application.
{"title":"Gibbsian interpretation of Langmuir, Freundlich and Temkin isotherms for adsorption in solution","authors":"Lei Lu, Chongzheng Na","doi":"10.1080/09500839.2022.2084571","DOIUrl":"https://doi.org/10.1080/09500839.2022.2084571","url":null,"abstract":"ABSTRACT Adsorption is a physicochemical phenomenon important in both natural and engineering processes. In the research and practice of adsorption equilibrium, a long-standing challenge is how to reconcile the classical models proposed by Gibbs, Langmuir, Freundlich, and Temkin for interpreting experimentally obtained adsorption isotherms. Here, we show that the Langmuir, Freundlich, and Temkin isotherms can be derived from the Gibbs equation under different conditions for the change of surface energy (a.k.a. surface tension) by adsorption. When the change of surface energy is predominantly controlled by the change of chemical potential with negligible contribution from the change of internal energy and entropy, the Gibbs equation can be integrated to give the Langmuir isotherm. When changes of internal energy and entropy are no longer negligible, the integration of the Gibbs equation gives the Freundlich and Temkin equations, according to a change of surface energy either independent or linearly dependent on the adsorption capacity. These results indicate that the classical models share the common mechanism of phase equilibrium described by the Gibbsian thermodynamics, thereby providing novel insights for their application.","PeriodicalId":19860,"journal":{"name":"Philosophical Magazine Letters","volume":"102 1","pages":"239 - 253"},"PeriodicalIF":1.2,"publicationDate":"2022-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44181689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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