Open Software as a service (SaaS). Ex-ample just below, change "Put your text" and you will see:
Online Services headline animator, feedBurner
Thursday, December 29, 2016
Wednesday, November 23, 2016
Google Trips et Google Cultural Institute
En sept 2016, google présente une nouvelle application qui devrait intéresser tous les voyageurs : Google Trips.
En effet, cette appli pour iOS et Android souhaite vous gérer votre temps, et vous permettre d’accéder plus rapidement aux informations dont vous avez besoin lorsque vous vous êtes en déplacement, en voyage, en ballade touristique, en excursion.
Google Trips vous permet d’organiser votre voyage dans les moindres détails. Vous pouvez y conserver toutes les informations importantes au même endroit sur votre smartphone. Et vous pourrez y accéder à tout le contenu de Trips même sans connexion internet.
A conditions de l’y autoriser lors de l’installation, l’appli peut aussi analyser le contenu des vos mails, si vous utilisez Gmail. Elle peut alors en extraire les informations relatives à vos horaires de trains ou d’avion, les réservations de votre hôtel, les locations de véhicules et toutes les données en relation avec les activités prévues lors de votre séjour qui auront été trouvées dans votre messagerie ou dans votre agenda, si vous utilisez Google Agenda.
Trips propose également de conserver l’historique de vos déplacements dans Google Maps. Cela permettra à Trips d’analyser vos gouts et vos centres d’intérêts. L’appli pourra alors vous recommander des activités que vous aimerez sans doute. Google Trips peut également vous proposer des lieux plébiscités par les internautes, très pratique lorsque vous ne savez pas quoi faire dans un endroit que vous ne connaissez pas, ou même autour de chez vous.
Trips est aussi la "gentille organisatrice" de vos visites. Google Trips peut en effet vous aider à planifier vos déplacements dans la ville. Elle vous aide d’ailleurs à organiser vos visites de la manière la plus logique, en calculant les meilleurs trajets pour vous rendre d’un point d’intérêt à un autre, par rapport à ceux que vous avez choisi parmi les endroits marquants ou les suggestions faites par l’application.
Enfin, Google Trip peut aussi être votre guide en proposant des photos et des informations sur tous les lieux marquants que vous souhaitez découvrir. Les informations sont piochées dans Google Maps et bénéficient ainsi de la riche base de données de Google, mais aussi des avis des internautes.
Pour vos prochains weekend ou vos vacances, Google Trips pourra donc vous rendre de fiers services. L’appli est gratuite et disponible sur iOS et Android.
https://blog.google/topics/travel/see-more-plan-less-try-google-trips/
https://get.google.com/trips/
------------
Si vous n’avez pas encore eu la chance de visiter les Châteaux de la Loire, le Google Cultural Institute vous propose désormais une incroyable visite virtuelle depuis votre ordinateur, votre smartphone, ou votre tablette.
Les Châteaux de la Loire en visite virtuelle
Avec Google Street View, vous pouvez donc visiter l’Abbaye Royale de Fontevraud, la Cité Royale de Loches, le Domaine national de Chambord, les Châteaux d’Angers, d’Azay-le-Rideau, de Chateaudun, de Chenonceaux, du Clos Lucé, de Fougères-sur-Bièvre, de Meung-sur-Loire, de Montpoupon, du Moulin, du Rivau, de Sully-sur-Loire, de Talcy, de Villandry, ainsi que le Château et le Jardin de Bouges, et la Forteresse royale de Chinon.
Sur ces 18 sites historiques de la Vallée de la Loire, il est désormais possible de visiter châteaux et jardins de manière classique dans Google Street View, avec notamment 7 lieux qui peuvent être survolés. Mais le Google Cultural Institute nous permet aussi de faire des visites virtuelles en 360° de ces lieux, dont certains ne sont même pas ouverts au public !
Google Art Camera : des clichés en 1 000 Megapixels
Depuis le site dédié, 46 expositions virtuelles sont proposées. Elle permettent d’admirer plus de 2000 objets historiques. Google a notamment utilisé une caméra spéciale, la Art Caméra, qui permet de réaliser des clichés avec une très haute résolution de 1000 Megapixels. Ils permettent ainsi d’en apprécier les détails les plus infimes avec un zoom presque à infini dans 56 œuvres en particulier.
Avec cette technologie inédite, on peut par exemple découvrir ou redécouvrir la célèbre Tenture de l’Apocalypse d’Angers ou les fresques de la salle capitulaire de l’Abbaye de Fontevraud, datant du XVIe siècle.
En plus des 18 millions de visiteurs qui parcourent chaque année la Vallée de la Loire, la numérisation des monuments et des oeuvres permet donc au plus grand nombre de les apprécier dans Google Street View dans un rendu proche de la réalité et jamais vu auparavant. Ces visites sont entièrement gratuites et accessibles depuis un ordinateur, un smartphone ou une tablette, mais aussi un casque de réalité virtuelle comme le Google Cardboard.
En effet, cette appli pour iOS et Android souhaite vous gérer votre temps, et vous permettre d’accéder plus rapidement aux informations dont vous avez besoin lorsque vous vous êtes en déplacement, en voyage, en ballade touristique, en excursion.
Google Trips vous permet d’organiser votre voyage dans les moindres détails. Vous pouvez y conserver toutes les informations importantes au même endroit sur votre smartphone. Et vous pourrez y accéder à tout le contenu de Trips même sans connexion internet.
A conditions de l’y autoriser lors de l’installation, l’appli peut aussi analyser le contenu des vos mails, si vous utilisez Gmail. Elle peut alors en extraire les informations relatives à vos horaires de trains ou d’avion, les réservations de votre hôtel, les locations de véhicules et toutes les données en relation avec les activités prévues lors de votre séjour qui auront été trouvées dans votre messagerie ou dans votre agenda, si vous utilisez Google Agenda.
Trips propose également de conserver l’historique de vos déplacements dans Google Maps. Cela permettra à Trips d’analyser vos gouts et vos centres d’intérêts. L’appli pourra alors vous recommander des activités que vous aimerez sans doute. Google Trips peut également vous proposer des lieux plébiscités par les internautes, très pratique lorsque vous ne savez pas quoi faire dans un endroit que vous ne connaissez pas, ou même autour de chez vous.
Trips est aussi la "gentille organisatrice" de vos visites. Google Trips peut en effet vous aider à planifier vos déplacements dans la ville. Elle vous aide d’ailleurs à organiser vos visites de la manière la plus logique, en calculant les meilleurs trajets pour vous rendre d’un point d’intérêt à un autre, par rapport à ceux que vous avez choisi parmi les endroits marquants ou les suggestions faites par l’application.
Enfin, Google Trip peut aussi être votre guide en proposant des photos et des informations sur tous les lieux marquants que vous souhaitez découvrir. Les informations sont piochées dans Google Maps et bénéficient ainsi de la riche base de données de Google, mais aussi des avis des internautes.
Pour vos prochains weekend ou vos vacances, Google Trips pourra donc vous rendre de fiers services. L’appli est gratuite et disponible sur iOS et Android.
https://blog.google/topics/travel/see-more-plan-less-try-google-trips/
https://get.google.com/trips/
------------
Google Cultural Institute
https://www.google.com/culturalinstitute/beta/Si vous n’avez pas encore eu la chance de visiter les Châteaux de la Loire, le Google Cultural Institute vous propose désormais une incroyable visite virtuelle depuis votre ordinateur, votre smartphone, ou votre tablette.
Les Châteaux de la Loire en visite virtuelle
Avec Google Street View, vous pouvez donc visiter l’Abbaye Royale de Fontevraud, la Cité Royale de Loches, le Domaine national de Chambord, les Châteaux d’Angers, d’Azay-le-Rideau, de Chateaudun, de Chenonceaux, du Clos Lucé, de Fougères-sur-Bièvre, de Meung-sur-Loire, de Montpoupon, du Moulin, du Rivau, de Sully-sur-Loire, de Talcy, de Villandry, ainsi que le Château et le Jardin de Bouges, et la Forteresse royale de Chinon.
Sur ces 18 sites historiques de la Vallée de la Loire, il est désormais possible de visiter châteaux et jardins de manière classique dans Google Street View, avec notamment 7 lieux qui peuvent être survolés. Mais le Google Cultural Institute nous permet aussi de faire des visites virtuelles en 360° de ces lieux, dont certains ne sont même pas ouverts au public !
Google Art Camera : des clichés en 1 000 Megapixels
Depuis le site dédié, 46 expositions virtuelles sont proposées. Elle permettent d’admirer plus de 2000 objets historiques. Google a notamment utilisé une caméra spéciale, la Art Caméra, qui permet de réaliser des clichés avec une très haute résolution de 1000 Megapixels. Ils permettent ainsi d’en apprécier les détails les plus infimes avec un zoom presque à infini dans 56 œuvres en particulier.
Avec cette technologie inédite, on peut par exemple découvrir ou redécouvrir la célèbre Tenture de l’Apocalypse d’Angers ou les fresques de la salle capitulaire de l’Abbaye de Fontevraud, datant du XVIe siècle.
En plus des 18 millions de visiteurs qui parcourent chaque année la Vallée de la Loire, la numérisation des monuments et des oeuvres permet donc au plus grand nombre de les apprécier dans Google Street View dans un rendu proche de la réalité et jamais vu auparavant. Ces visites sont entièrement gratuites et accessibles depuis un ordinateur, un smartphone ou une tablette, mais aussi un casque de réalité virtuelle comme le Google Cardboard.
Labels:
google,
grandes images,
map,
pic,
recalage d'image,
traitement d'image
Du fait de la diversité des outils google pour y mettre des images, difficile de s'y retrouver...
your google+ profile, et aussi image valable pour tous les produits google
https://plus.google.com/u/0/photos/113300494682639557816/albums/profile(c'est le dossier profile)
if you select
https://plus.google.com/u/0/photos/113300494682639557816/albums
you will get :
https://photos.google.com/u/0/?+info qui disparait pour
https://photos.google.com/u/0/
qui est votre homepage google photos.
albumarchive
Si vous regardez votre albumarchivehttps://get.google.com/albumarchive/113300494682639557816
Profile photos you’ve chosen for any Google services you use, including Google+, Gmail, Hangouts & others. Changes you make here apply across all of Google, including when you communicate or share content.
dans "Auto Backup"
on a les photos/video des anciens "picasa album", des dossiers synchronisés avec google photos ou téléchargé avec photos
Photos and videos backed up from your devices and browser.
dans Photos from drive
on a les Photos & videos sauvées dans et avec Google Drive.
Les Changements réalisés ici sont appliqués dans drive.
Bref utiliser les albums Google archivés:
Vous pouvez consulter, supprimer ou télécharger les photos que vous avez importées dans d'autres produits Google, dont :
- Picasa Albums Web
- Google+
- Blogger
- Hangouts
- Google Photos
- Google Drive
Blogspot/blogger
vos images de blog, visible dans drive (en ordre temporelle) et album archive (apparaissent alors dans un dossier et par blog.On a des options comme:
Show your Google Drive photos & videos in your album archive
google drive et google photos
permet de faire des albums, de la recherche poussée, du stockage synchronisé (avec l'appli)
mais sur le fond comme fichier et stockage final
avec google drive, peu de différence :Wednesday, November 2, 2016
Javascript blog CMS : blogger
To build any webpage on internet there are three most important languages viz. HTML, JavaScript and CSS. JavaScript is one of the most commonly used client-side programming language that may communicate asynchronously (i.e. independently of other processes) to web browser.
If you are using BlogSpot.com blogger blog then you have lots of option to include JavaScript codes. It will depends on where you want to render it and for which purpose you are using that JavaScript files or codes.
See this present "ex-ample" blog.
http://www.superwebtricks.com/add-javascript-codes-to-blogger-template/
Wednesday, May 20, 2015
introduction to NVE, NVT, NpT ensembles
The first term with which to get acquainted is “ensemble”. In the context of
statistical mechanics, an ensemble is a collection of configurations of a system.
These configurations will have a set of common constraints such as temperature,
volume and pressure, but will differ in the positions and velocities of the individual
components (atom/molecule/fragment) across the different configurations. So,
even though these configurations differ microscopically, they possess the same
common macroscopic properties (based on the ensemble they belong to). This
means that ensemble averages for these properties can be computed.
The simplest such ensemble is the microcanonical ensemble, in which the constraints
are number of particles, volume and total energy, i.e., these quantities
are constrained to be the same across all the configurations belonging to the
microcanonical ensemble, and hence this ensemble is also known as the “NVE” ensemble. The common nomenclature of the ensemble provides information about
the constraints in that ensemble. Hence, the NVE ensemble contains all possible
combinations of positions and velocities for the particles which satisfy an energy
constraint, provided all these configurations have the same particle density. The
total number of configurations for an ensemble is given by its “partition function”,
and for the microcanonical ensemble, the microcanonical partition function
(also called density of states) is represented as Ω(N,V,E).
The fundamental importance of the density of states is based on the relationship
S(N,V,E) = kB ln Ω(N,V,E) (2.2)
where S is the entropy and kB is Boltzmann’s constant. Eq. 2.2 shows how a macroscopic property like entropy is directly related to the density of states for a system at constant density. A more convenient and commonly used ensemble is the canonical (NVT) ensemble, where the density and temperature are constrained across the configuration.
Similar to the microcanonical ensemble, a thermodynamic quantity can be related to the partition function. In this case, it is the Helmholtz free energy A = −kBT ln Q(N,V,T) (2.6) A commonly used ensemble in MC is the grand canonical ensemble, in which the chemical potential, volume and temperature are constrained. This means that the number of particles is allowed to fluctuate to satisfy the chemical potential constraint. The NpT ensemble, also called the isothermal-isobaric ensemble is also a commonly used ensemble. Here, the number of particles, temperature and pressure are constrained.
The fundamental relationship for the NpT ensemble is the expression relating the Gibbs free energy to the partition function: G = −kBT ln ∆(N,P,T) (2.8) where G is the Gibbs free energy, a thermodynamic quantity of fundamental importance to the problem of phase equilibrium. In all the ensembles listed above, the partition function integrals grow rapidly with increasing complexity and system sizes. Hence, trying to solve these integrals analytically is impractical. Molecular simulations aid in sampling the configuration space for these ensembles subject to the probability distribution for a given ensemble, and ensemble averages can be obtained using expressions similar to Eq. 2.5.
Ref: http://etd.nd.edu/ETD-db/theses/available/etd-08182009-110710/unrestricted/JayaramanS082009D.pdf
The fundamental importance of the density of states is based on the relationship
S(N,V,E) = kB ln Ω(N,V,E) (2.2)
where S is the entropy and kB is Boltzmann’s constant. Eq. 2.2 shows how a macroscopic property like entropy is directly related to the density of states for a system at constant density. A more convenient and commonly used ensemble is the canonical (NVT) ensemble, where the density and temperature are constrained across the configuration.
Similar to the microcanonical ensemble, a thermodynamic quantity can be related to the partition function. In this case, it is the Helmholtz free energy A = −kBT ln Q(N,V,T) (2.6) A commonly used ensemble in MC is the grand canonical ensemble, in which the chemical potential, volume and temperature are constrained. This means that the number of particles is allowed to fluctuate to satisfy the chemical potential constraint. The NpT ensemble, also called the isothermal-isobaric ensemble is also a commonly used ensemble. Here, the number of particles, temperature and pressure are constrained.
The fundamental relationship for the NpT ensemble is the expression relating the Gibbs free energy to the partition function: G = −kBT ln ∆(N,P,T) (2.8) where G is the Gibbs free energy, a thermodynamic quantity of fundamental importance to the problem of phase equilibrium. In all the ensembles listed above, the partition function integrals grow rapidly with increasing complexity and system sizes. Hence, trying to solve these integrals analytically is impractical. Molecular simulations aid in sampling the configuration space for these ensembles subject to the probability distribution for a given ensemble, and ensemble averages can be obtained using expressions similar to Eq. 2.5.
Ref: http://etd.nd.edu/ETD-db/theses/available/etd-08182009-110710/unrestricted/JayaramanS082009D.pdf
Labels:
molecular dynamics
Monday, May 18, 2015
Molecular Dynamic simulation of heating of gold nanorod in water (nature 2015)
Molecular Dynamic simulation of heating of gold nanorod in water
Potential Model for Gold
Molecular dynamics (MD) simulations of the gold nano rods in presence of water were
performed using embedded atom method (EAM)
[7. Daw, M. & Baskes, M. Semiempirical, Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals. Phys. Rev. Lett. 50, 1285–1288 (1983).
8. Daw, M. & Baskes, M. Embedded-atom method: Derivation and application to impurities, surfaces,and other defects in metals. Phys. Rev. B 29, 6443–6453 (1984). ] .
For the EAM, the total energy (Etot) for a system of N atoms can be written as equa S14.
To model the interactions of water molecules, we have employed flexible SPC/Fw water
model to conduct simulations at various temperatures9
. The potential interaction in the flexible
SPC/Fw, as shown in equation (S15), is a sum of pair-wise interactions for bonded and nonbonded
terms.
Potential model and parameters for gold-water interaction
We used the Lorentz-Berthelot rule to estimate the interaction between water and gold
that is modeled using standard 6-12 potential.
Melting temperatures as a function of nanorod aspect ratios:
We have further calculated the bulk melting point as well as the melting of nanorods with
different aspect ratios. The melting point of bulk gold predicted by the EAM potential used in this work is 1281 K. The experimental value is 1337 K and thus the prediction of our potential model is very good.
The melting points for nanorods with different aspect ratios (AR) are summarized below. It can be seen that nanorods with higher aspect ratios have lower melting points compared to bulk. This is not surprising since the surface area (Table S3) increases with increasing AR.
Ref: http://www.nature.com/srep/2015/150130/srep08146/extref/srep08146-s1.pdf
Potential Model for Gold
Molecular dynamics (MD) simulations of the gold nano rods in presence of water were
performed using embedded atom method (EAM)
[7. Daw, M. & Baskes, M. Semiempirical, Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals. Phys. Rev. Lett. 50, 1285–1288 (1983).
8. Daw, M. & Baskes, M. Embedded-atom method: Derivation and application to impurities, surfaces,and other defects in metals. Phys. Rev. B 29, 6443–6453 (1984). ] .
For the EAM, the total energy (Etot) for a system of N atoms can be written as equa S14.
To model the interactions of water molecules, we have employed flexible SPC/Fw water
model to conduct simulations at various temperatures9
. The potential interaction in the flexible
SPC/Fw, as shown in equation (S15), is a sum of pair-wise interactions for bonded and nonbonded
terms.
Potential model and parameters for gold-water interaction
We used the Lorentz-Berthelot rule to estimate the interaction between water and gold
that is modeled using standard 6-12 potential.
Melting temperatures as a function of nanorod aspect ratios:
We have further calculated the bulk melting point as well as the melting of nanorods with
different aspect ratios. The melting point of bulk gold predicted by the EAM potential used in this work is 1281 K. The experimental value is 1337 K and thus the prediction of our potential model is very good.
The melting points for nanorods with different aspect ratios (AR) are summarized below. It can be seen that nanorods with higher aspect ratios have lower melting points compared to bulk. This is not surprising since the surface area (Table S3) increases with increasing AR.
Ref: http://www.nature.com/srep/2015/150130/srep08146/extref/srep08146-s1.pdf
Labels:
0-potentiel,
gold,
molecular dynamics,
nanoparticles
Wednesday, May 13, 2015
Gold and Lennard-Jones potential
Gold
e/k=5123°K
sigma=2.637 Angström
[T. HALICIOGLU and G. M. POUND: Calculation of Potential Energy Parameters ; phys. stat. sol. (a) 30, 619 (1975) ]
---------------------------------
Lennard-Jones potential:
Using the continuous approach, where the atoms at discrete locations on the mol- ecule are averaged over a surface, the molecular interatomic energy is obtained by calculating integrals over the surfaces of each molecule, given by
where η1 and η2 represent the mean surface density of atoms on each molecule. Further, we may define the integral In in the form of
Ref: http://link.springer.com/article/10.1007%2Fs10910-010-9796-x
e/k=5123°K
sigma=2.637 Angström
[T. HALICIOGLU and G. M. POUND: Calculation of Potential Energy Parameters ; phys. stat. sol. (a) 30, 619 (1975) ]
---------------------------------
Lennard-Jones potential:
A = 4εσ6 and B = 4εσ12
Using the continuous approach, where the atoms at discrete locations on the mol- ecule are averaged over a surface, the molecular interatomic energy is obtained by calculating integrals over the surfaces of each molecule, given by
where η1 and η2 represent the mean surface density of atoms on each molecule. Further, we may define the integral In in the form of
and therefore, E = η1η2(−AI3 + BI6).
The Lennard-Jones parameters for gold nanoparticles are taken from the work
of Pu et al. [Q. Pu, Y. Leng, X. Zhao, P.T. Cummings, Molecular simulations of stretching gold nanowires in solvents. Nanotechnology 18, 424007 (2007)], who use
ε = 0.039kcal mol−1 and σ = 2.934Å
corresponding to A = 7.2465eV ×Å6 and B = 4,622.6273eV ×Å12.
From the fact that gold adopts a face-centred cubic (fcc) crystal structure, the triangular arrangement is employed to determine a mean surface density of gold nanoparticles. Assuming that each atom of gold is coordinated with six other atoms, the area of a unit cell is given by A⋆ = √3d2/2Å2 where d denotes the equilibrium spacing which can be obtained as d = 21/6σ = 3.2933Å. Consequently, the mean surface density η of the gold layers is taken to be 1/A⋆ = 0.1065Å−2.
The Lennard-Jones parameters for gold nanoparticles are taken from the work
of Pu et al. [Q. Pu, Y. Leng, X. Zhao, P.T. Cummings, Molecular simulations of stretching gold nanowires in solvents. Nanotechnology 18, 424007 (2007)], who use
ε = 0.039kcal mol−1 and σ = 2.934Å
corresponding to A = 7.2465eV ×Å6 and B = 4,622.6273eV ×Å12.
From the fact that gold adopts a face-centred cubic (fcc) crystal structure, the triangular arrangement is employed to determine a mean surface density of gold nanoparticles. Assuming that each atom of gold is coordinated with six other atoms, the area of a unit cell is given by A⋆ = √3d2/2Å2 where d denotes the equilibrium spacing which can be obtained as d = 21/6σ = 3.2933Å. Consequently, the mean surface density η of the gold layers is taken to be 1/A⋆ = 0.1065Å−2.
Ref: http://link.springer.com/article/10.1007%2Fs10910-010-9796-x
Labels:
0-potentiel,
gold
example of NVT equilibration in LAMMPS
All the simulation was carried out in the NVT ensemble.
The initial equilibration was done by heating the system from 20 K to 300 K with discrete steps of 20 K/50 ps.
After the equilibration, the systems were run at a temperature of 300 K for additional 5 ns.
Dynamics of transfer, and variance in distributions were analyzed by heating equilibrated systems from 300 K to 400 K followed by cooling from 400 K to 300 K in discrete steps of 10 K/ 200 ps.
For accurate analyses at each temperature, the last snapshot from the heating cycles were run for more than 2 ns and data collected in the equilibrated phase as seen through block averages of
total energy.
All simulations were carried out using the LAMMPS simulation package.
The equations of motion were integrated using the velocity-Verlet algorithm using a time step
of 1 fs. For NVT ensembles, a Nosé-Hoover thermostat with a damping time of 100 fs
was used to maintain the temperature of the system.
Ref: http://www.rsc.org/suppdata/nr/c3/c3nr05671f/c3nr05671f.pdf
The initial equilibration was done by heating the system from 20 K to 300 K with discrete steps of 20 K/50 ps.
After the equilibration, the systems were run at a temperature of 300 K for additional 5 ns.
Dynamics of transfer, and variance in distributions were analyzed by heating equilibrated systems from 300 K to 400 K followed by cooling from 400 K to 300 K in discrete steps of 10 K/ 200 ps.
For accurate analyses at each temperature, the last snapshot from the heating cycles were run for more than 2 ns and data collected in the equilibrated phase as seen through block averages of
total energy.
All simulations were carried out using the LAMMPS simulation package.
The equations of motion were integrated using the velocity-Verlet algorithm using a time step
of 1 fs. For NVT ensembles, a Nosé-Hoover thermostat with a damping time of 100 fs
was used to maintain the temperature of the system.
Ref: http://www.rsc.org/suppdata/nr/c3/c3nr05671f/c3nr05671f.pdf
Labels:
0-LAMMPS
Thursday, May 7, 2015
triple point: gold (Au) in both the solid and liquid phases; binodal, spinodal.
The Liquid-vapor critical point in a pressure–temperature phase diagram
is at the high-temperature extreme of the liquid–gas phase boundary
(the dotted green line shows the anomalous behavior of water).
The figure shows the schematic PT diagram of a pure substance (as opposed to mixtures, which have additional state variables and richer phase diagrams, discussed below). The commonly known phases solid, liquid and vapor are separated by phase boundaries, i.e. pressure-temperature combinations where two phases can coexist.
At the triple point, even all three phases coexist. However, the liquid-vapor boundary terminates in an endpoint at some critical temperature Tc and critical pressure pc. This is the critical point.
In water, the critical point occurs at around 647 K and 22.064 MPa.
- Gold 7250 K 510MPa.
At the critical point, only one phase exists. The heat of vaporization is zero.
----------------------
Van der Walls-like phase-diagram of gold
Temperature 0.5ev<->0.5ev/kB=5802°K->
kB=8.6173 10^-5eV/°K
DOI: 10.1016/j.apsusc.2005.03.019 ; [Vitiello,2005]
--------------------------------------------
GOLD
Electron configuration [Xe] 4f14 5d10 6s1
melting point: 1336.15°K
Heat of fusion (10^3 J/kg): 64.5
or 12.55 kJ·mol^−1
boiling point: 3243 °K
Heat of vaporization (10^3 J/kg): 1578
or 342 kJ·mol^−1
Density near r.t. 19.30 g·cm−3
when liquid, at m.p. 17.31 g·cm−3
Molar heat capacity 25.418 J·mol−1·K−1
---------------------------------------------
Problem:
1) Using the CRC thermodynamic data from the handout in class, make a plot of the Gibbs free energy (in [J/mole]) as a function of temperature for gold (Au) in both the solid and liquid phases over the temperature range of 1000-2000K. Both free energies must be on the same plot. Determine the equilibrium temperature between liquid and solid Au from your calculations.
2) Yet another approach to calculating the Gibbs free energy is using empirical polynomial fitting equations from thermodynamic databases. One such example is the CALPHAD database. As an example of the fitting equations I have listed the equations for solid Au in the FCC crystal structure below. Make a plot of the Gibbs free energy (in [J/mole]) as a function of temperature over the range of 1000-2000 [K] using both the CRC data from problem 1 and the CALPHAD data. Both calculations must be on the same plot. Comment as to the agreement or lack thereof between the two calculations.
3) Calculate the triple point (as T, P) for gold. (NOTE that all the thermodynamic information you need to do this calculation can be found from the CRC Handbook data. I'm not looking for the whole phase diagram, just the triple point. There are a variety of ways to approach this problem, but I'm looking for a pretty simple one.)
Solution
1) Using the CRC thermodynamic data from the handout in class, make a plot...
The CRC data for Au gives the following equations for the Gibbs free energy as a function of temperature:
Plugging into EXCEL and plotting between 1000-2000 [K] gives the following plot:
With this calculation, the crossing point is at about T = 1341 [K], which is the equilibrium melting temperature (a bit higher than the stated temperature of 1336.16 [K].)
NOTE: The CRC is pretty confusing by calling the function for Gibbs free energy "FT-H298." In fact, the enthalpy at 298 [K] is included in the equations and fitting parameters. What it means is that the thermodynamic functions are determined relative to a temperature of 298 [K].
2) Yet another approach to calculating the Gibbs free energy...
I used EXCEL again to make the calculation and the plot.
3) Calculate the triple point (as T, P) for gold.
The simple trick approach uses the fact that we discussed in class that the slope of the S-L equilibrium line on the P-T phase diagram is VERY STEEP (a nearly vertical line with pressure) so that the equilibrium melting temperature changes very little with pressure.
This means that, within a small error, the triple point temperature is given by the equilibrium melting temperature at 1 [atm], which for Au is found in the CRC handout as TM = 1336.16 [K]. The problem is half done!
To find the triple point pressure, we need to find the equilibrium pressure for the temperature of 1336.16 [K] for either the S-V or the L-V equilibrium. I decided to use the "shortcut" approach (see problem 2 on themidterm for F08 for more information.) The Clausius-Clapeyron equation gives:
In this equation, we can either use the enthalpy of vaporization for ∆H, and the vaporization temperature for T0 (which would give us the L-V equilibrium), or we could use the enthalpy and temperature of sublimation (which would give us the S-V equilibrium.) The CRC has the data for the vaporization, but not the sublimation information, so...
There's our answer for the triple point of Au: T = 1336 [K], P = 2.44 x 10-7 [atm].
Labels:
gold,
molecular dynamics,
spinodal
Monday, April 27, 2015
Comparison of time- and length-scales, accessible to different types of simulation techniques (quantum simulations (QM), molecular dynamics (MD), Brownian Dynamics (BD) and hydrodynamics/fluid dynamics (HD))
Computing every force on each atom is a demanding part of a MD simulation. In order to limit the number of force calculations, the smallest possible system – in terms of number of atoms – should be simulated. The minimum system size necessary to compute a given desired property is not always obvious and a common practice is to analyze how increasing system size influences obtained results. A number of algorithmic approaches exist that help minimize system size such as applying periodic boundary conditions.
In addition to how large a system must be, one must determine how long a simulation must be run to obtain reliable answers (i.e. with sufficient accuracy and precision). Related to this is that the MD simulation time step should be small compared to the period associated with the highest frequency atomic event. A typical time step for MD simulations of metals is of order 1 fs (i.e. 1 E-15 s). The very small time step is the main drawback of MD method compared to other commonly used numerical simulations. Processes with time scale of order microseconds and larger are outside the reasonable realm for even highly parallel, efficient MD codes. Conversely, MC techniques cannot probe dynamics but they can probe long time equilibrium properties.
Accessible length- and time- scales of microscopic simulation should be considered. Figure 2.1 shows a schematic representation for different types of simulations in a length-time-diagram. It is clear that the more detailed a simulation technique addresses, the smaller is the accessibility of times and length scales. Hence, quantum simulations (QS), where fast motion of electrons are considered, are located in the lower left corner of the diagram and typical length time scales are of order of Å (Å) and ps. MD method puts fixed partial charges on interaction sites or adds a dynamics model for polarization effects to simulate electronic distribution. Hence, the time scale of the system is determined by the time of collision between atoms and atomic vibration frequencies. Consequently, the accessible time scale is of order ns and corresponding accessible length scale becomes of order 10-10000 Å. Note Figure 2.1 was originally presented in 2002; accessible length scales for MD have increased dramatically. Brownian Dynamics (BD) can be applied to deal with particles in a solvent medium, where one is not interested in a detailed description of the solvent. In BD the effect of the solvent is hidden in average quantities. If one is not interested in a molecular picture but in macroscopic quantities, the concepts of hydrodynamics (HD) may be applied, where the system properties are hidden in effective numbers, like density and sound velocity.
In addition to how large a system must be, one must determine how long a simulation must be run to obtain reliable answers (i.e. with sufficient accuracy and precision). Related to this is that the MD simulation time step should be small compared to the period associated with the highest frequency atomic event. A typical time step for MD simulations of metals is of order 1 fs (i.e. 1 E-15 s). The very small time step is the main drawback of MD method compared to other commonly used numerical simulations. Processes with time scale of order microseconds and larger are outside the reasonable realm for even highly parallel, efficient MD codes. Conversely, MC techniques cannot probe dynamics but they can probe long time equilibrium properties.
Figure 2.1 Schematic comparison of time- and length-scales, accessible to different types of simulation techniques (quantum simulations (QM), molecular dynamics (MD), Brownian Dynamics (BD) and hydrodynamics/fluid dynamics (HD))
Accessible length- and time- scales of microscopic simulation should be considered. Figure 2.1 shows a schematic representation for different types of simulations in a length-time-diagram. It is clear that the more detailed a simulation technique addresses, the smaller is the accessibility of times and length scales. Hence, quantum simulations (QS), where fast motion of electrons are considered, are located in the lower left corner of the diagram and typical length time scales are of order of Å (Å) and ps. MD method puts fixed partial charges on interaction sites or adds a dynamics model for polarization effects to simulate electronic distribution. Hence, the time scale of the system is determined by the time of collision between atoms and atomic vibration frequencies. Consequently, the accessible time scale is of order ns and corresponding accessible length scale becomes of order 10-10000 Å. Note Figure 2.1 was originally presented in 2002; accessible length scales for MD have increased dramatically. Brownian Dynamics (BD) can be applied to deal with particles in a solvent medium, where one is not interested in a detailed description of the solvent. In BD the effect of the solvent is hidden in average quantities. If one is not interested in a molecular picture but in macroscopic quantities, the concepts of hydrodynamics (HD) may be applied, where the system properties are hidden in effective numbers, like density and sound velocity.
Labels:
molecular dynamics
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