Quest for Zero Point Energy Engineering Principles for Free Energy Getting Yours: The Complete Guide to Government Money (Getting Yours, 3rd Ed) The Free-Energy Device Handbook: A Compilation of Patents & Reports (Lost Science Series) Nikola Tesla: Free Energy and the White Dove Tapping the Zero Point Energy: Free Energy in Today's Physics Free Energy Relationships in Organic and Bioorganic Chemistry The Coming Energy Revolution: The Search for Free Energy Thermal Physics: Entropy and Free Energies The First Practical Pyramid Book: Free Energy for Beauty, Health, Gardening, Food Dehydration, and Meditation

• Interactive Calendar of Events! Feel Free to post your gig, event, workshop, seminar, performance, etc. ...
•   Divine Energy fuels us.

• Introduction to free energy .
• Free energy is perhaps the most important thermodynamic quantity. Many, if not almost all of the physical properties a chemist or a biochemist can be interested in depend directly or indirectly on the free energy of the system. For example, binding constants, association and dis-association constant and conformational preferences are all directly related to the difference in free energy between alternate states. ...
• Free energy is a statistical property, it can be seen as a measure of the probability of finding a system in a given state. ... To get a good estimate of the absolute free energy you would theoretically need to sample the whole phase space, which is not possible. ...
• What can be calculated is the difference in free energy between two related states of a system, which corresponds to the relative probability of finding a system in one state as opposed to the other. ...
• The free energy is usually expressed as the Helmholtz function, F, or the Gibbs function, G. The Helmholtz function is appropriate for a system with a constant number of particles, temperature and volume (constant NVT; the corresponding ensemble is also referred to as the canonical ensemble) whereas the Gibbs free energy is appropriate for constant number of particles, pressure and temperature (NPT ensemble).
• Free energy calculation methods: principal methods used to estimate free energy .
• example 1: direct determination of the hydration free energy of toluene .
• example 2: determination of the relative hydration free energy of p-cresol with respect to toluene .

• Free Energy Devices.
• Free Energy in thermodynamics is energylike property or state function of a system in thermodynamic equilibrium--it has the dimensions of energy and its value is determined by the state of the system and not by its history--expressed in two forms: the Helmholtz free energy, A, sometimes called work function, and the Gibbs free energy, G, sometimes F. If E is the internal energy of the system, PV the pressure-volume product, and TS the temperature-entropy product, then A = E - TS and G = E + PV - TS. Free energy is an extensive property; i. ...
• The changes in free energy, A or G, are useful in evaluating certain thermodynamic processes. In a reversible process, the work under constant temperature and constant volume is equal to the change in the Helmholtz free energy, A, and the work under constant temperature and constant pressure is equal to the change in the Gibbs free energy, G. ...
• Changes in free energy can be used to judge whether certain transformations of state can occur spontaneously. Under certain conditions of constant temperature and volume, the transformation of state will occur spontaneously, slowly or rapidly, if the Helmholtz free energy of the final state is smaller than that of the initial state; that is, if the difference A between the final and the initial state is negative. Under conditions of constant temperature and pressure, the transformation of state will occur if the change in the Gibbs free energy, G, is negative. ...
• The term "Free energy device" has a number of meanings: .
• - A device which collects energy from a source that's not recognized by modern science .
• - A device which collects energy at zero cost .

• A method for the computer simulation of the free energy difference in conformational changes of polyelectrolytes. ...
• A method for calculating the free energy difference between two dissimilar conformational states of a nucleic acid is proposed. ... The calculation of the free energy of each conformer is split into two steps; the first one consists in the buildup of the uncharged conformers while the other one ---which leads to the more important contribution--- corresponds to the charging process of such structures. We report preliminary results on the application of the method to evaluate the free energy difference for the the salt induced conformational change between the B and Z forms of DNA. This is the first rigorous evaluation of the dependence of the free energy difference on the added salt concentration. ...

• Free Energy Changes.
• The free energy change of a chemical process under standard state conditions, Go, can be determined four different ways:.
• From Free Energies of Formation .
• Using Free Energies of Formation to Determine Standard State Free Energy Changes.
• If we know the standard free energy changes of formation, Gof, of each species in a change we can determine the standard state free energy change, Go, for the change using the following equation:.
• Using Enthalpy Changes and Entropy Changes to Determine Standard State Free Energy Changes.
• If we know the enthalpy change, Ho, and the entropy change, So, for a chemical process, we can determine the standard state free energy change, Go, for the process using the following equation:.
• Using Equilibrium Constants to Determine Standard State Free Energy Changes.
• If we know the equilibrium constant, Keq, for a chemical change (or if we can determine the equilibrium constant), we can calculate the standard state free energy change, Go, for the reaction using the equation:.
• Using Cell Potentials to Determine Standard State Free Energy Changes.
• If we know the standard state cell potential, Eo, for an electrochemical cell (or if we can determine the standard state cell potential), we can calculate the standard state free energy change, Go, for the cell reaction using the equation:.

• FREE ENERGY refers to energy that you can get without going through some utility meter.
• (The machines you build to collect and use the free energy still cost money to build and maintain).
• ELECTRICAL Free Energy refers to energy that we either save,gather or convert, ending up with more useable power for free.   We catagoize electrical Free Energy 3 ways:   1 NegaWatts, which refers to electrical energy saving technology, thus allowing more work to be done with the same energy.   2 Ambient, which refers to gathering electrical energy directly from environmental energy flows. ...
• 3 MegaWatts, refers to converting other forms of energy to electricity.
• saving energy.
• Negawatts is a word coined by Amory Lovins of the Rocky Mountain Institute; meaning electrical energy saved. ...
• Using proper techniques, we could double the amount of work done with the electrical energy we generate today, thus 'creating' free energy. This would be energy 'created' without building any more power plants, no upgrading of utility lines, no additional generating expense whatsoever. This created free energy would mostly be the product of innovative efficiency thinking and engineering.
• gathering energy.
• In this case we are actually gathering direct electrical free energy from the environment. We see two distinct types of electrical energy that we are designing machines to gather; electromagnetic waves, and free ions.
• converting energy.
• This is the largest conventional way of making electrical free energy. Usually there is some readily available source of environmental (or 'dirty') free energy which can be converted to electrical energy. This electrical energy is 'Free' to whoever converted it, except for the costs and responsibility of the equipment.

• Energy 4 Free.
• The objective of this site is to provide information, links and resources regarding the free energy project. ...
• What is the free energy project?.
• The free energy project is any technical, scientific, social or political effort related to the creation, use or proliferation of free energy. ...
• What is free energy?.
• Free energy is energy that can be harnessed to do work. ...
• Links To Free Energy Related Websites .
• Yahoo Free Energy Group.
• Group of scientists, skeptics and techies that discuss free energy and engineering issues. ...
• Something For Nothing An areticle about how Free Energy really works The Lifter Maximus II--> .
• Primordial Energy .
• Cool Free Energy Site .

• Is there free energy in magnets?.
• Every once in a while I come across a paper or article while surfing the web which claims that it is possible to tap into the free energy which is available from the earth's magnetism, or from some other magnet.
• This all sounds great, but there is the problem that energy is never free but always comes with a price. ...
• Sure, in order to magnetize a magnet, energy needs to be put into it. ...   The result of this pulse of current, which contains a certain amount of energy that can be measured, is to enlarge the magnetic domains which are parallel with the magnetic field within the material being magnetized. ...
• Each of these, as you can see, requires that energy be spent (heat, magnetic field, motion). ...   (Adiabatic cooling does capture some of the decrease in the overall magnetic domains, but it requires energy to be put into the matierial first. ) Also, there are always energy losses in every circuit (in various forms of heat energy, sound energy, mechanical energy, chemical energy, electrical energy, etc).
• A keyword often used by those who think they have found the secret to free energy is:   over-unity.   What they mean by this is that the ratio of the energy output to the energy input is greater than 1 (more energy comes out than goes in). ...   When making energy measurements, there are a number of errors that can be made, often unwittingly, that falsly indicate over-unity is possible. ...
• Here's a great site which explains what is often neglected by those proposing free energy devices:.
• In summary, there is no way to obtain free energy with any kind of combination of wires or magnets or switches (commutators, diodes, etc). ...

• Welcome to Free Energy. ...
• For many people, "free energy" is a "buzz word" that has no clear meaning. ... This website is dedicated to clarifying exactly what free energy is, how it works and how it can be applied in your everyday life. ...
• In the simplest terms, free energy is any energy that is provided by the natural world. In science, energy is defined as "the ability to do work". Free energy is called by many names, such as renewable energy, alternative energy, or non-conventional energy, to list a few. Examples of free energy technologies include a wind generator on a remote homestead, or a solar panel on the International Space Station. ... Free energy also includes amazing technologies like a car powered by a water fuel cell, a battery charger powered by the earth, or a home furnace powered by permanent magnets. ... The best free energy systems deliver energy at no on-going cost to the user, without detrimental effects to the environment, and at extremely low costs for the maintenance of the equipment.
• On the PRODUCTS page of this website, you will find our very exciting information products about real free energy systems. First and foremost, we have the book and video titled The Free Energy Secrets of Cold Electricity, by Dr. ... Lindemann also reveals that Nikola Tesla discovered the same effect, back in 1889, and named it "Radiant Energy. ... And finally, The World of Free Energy, a two-hour videotaped lecture and slideshow, also by Dr. Lindemann, featuring information on about seven different free energy technologies.
• In our TECHNOLOGIES section, you will find many documents to assist you in learning more about real free energy technologies and the difference they could make in your life. ... Please feel free to download any of this material.

• Welcome to Free Energy Principles.
• This website is dedicated to the popularization of free energy technology by .
• discovering and explaining real free energy principles.
• disproving false free energy ideas.
• If you are new in this field, you can find a basic definition of free energy (FE) here.
• We will lay emphasis on principles, since that is the key for the successful utilization of free energy. If someone understands the working principle of a free energy converter, then he has good chance to successfully develop a working model even if he has got no ready design. But if he has obtained a draft of a free energy machine and does not understands its working principle then with great probability he will not be able to build a working model. If such a machine does not yield any excess of energy as it have been promised, then without knowing the basic principle he has no chance to find the cause for the failure, and even less to further improve the device. ...
• The main structure of the site will follow the natural flow of developing free energy ideas. ... So the free energy principles can be classified into the following categories: .
• The starting package of information is a good example for such a process, since this research has been initiated by weird measurement results which contradicted the law of energy preservation. ...
• Free energy.
• Free energy from wave-fields (Introduction).
• Simplified explanation how to gain free energy from wave-fields (Confirmed by SA & M).
• * Janos Vajda: VIOLATION OF THE ENERGY THESIS IN WAVE-FIELDS (Confirmed by SA & M).

• Free energy in an ideal Gas .
• The free energy in an ideal gas depends on the pressure and the temperature of the gas. The fee energy of a gas at atm pressure is given by: .
• Where is the free energy of the gas at a 1 atm pressure, T is the temperature, and R is the gas constant. ...
• A function to compute the free energy in an ideal gas would take in as arguments the pressure, the free energy of the gas at a 1 atm pressure, the temperature, and the gas constant and return the free energy. ...
• float FreeEnergyIdealGas( float pres, float G_o, float temp, float R) { /* This function calculates the free energy in an ideal gas. Its formal arguments are: pres the pressure, G_o the free energy of the gas at a 1 atm pressure, temp the temperature, and R the gas constant The local variables are: G the free energy of the ideal gas The function returns the variable G. */ float G; /* the Free energy G = G_0 + R * temp * log( pres ); return G; } .
• h" int main() { float P; /* The pressure */ float Go; /* the free energy of the gas at a 1 atm */ float T; /* the temperature */ float R; /* the gas constant */ float G; /* The free energy of the gas */ cout << "Please enter the pressure" << P << endl; cin >> P ; cout << "Please enter the temperature" << T << endl; cin >> T ; cout << "Please enter the gas constant" << R << endl; cin >> R ; cout << "Please enter the free energy of the gas at a 1 atm" << Go << endl; cin >> Go ; G = FreeEnergyIdealGas( P, Go, T, R); cout << "The free energy of the gas is = " << G << endl; return 0; } .

•  Free Energy!.
•  Why is it that the semi conductor industry has gone exponential in the last 30 years while Solar energy technology (very closely related) has almost been forgotten? It could have something to do with the monolithic oil empires buying up all of the patents and sitting on them. Luckily energy is all around us and all we have to do is tap into it.
• I've definitely got my own ideas of how the universe fits together but here are some links to some incredible people who've spent their life trying to break our self-imposed chains of limited energy.

• Entropy and Gibbs free energy, DG = DH - TDS.
• P: Sure, but q is the transfer of thermal energy (that we often, too loosely, call "heat"). So isn’t DH really a "q", a thermal energy transfer? Also, DG/T has the form of an energy transfer/T just as that DH/T does. ...
• There can be thermal energy transferred ("heat") from the system to its surroundings or vice versa. ...
•         Now, if chemicals are mixed in the system (at constant T and, normally, constant P) and a reaction occurs, some thermal energy transfer ("heat"), q, takes place in the reaction. ...
• However, from the viewpoint of the surroundings, the sign of DH changes when thermal energy is transferred from the system and becomes absorbed by the surroundings, i. ...
• To put it in the most general terms, the energy change that occurred in the reaction in the system -- and which entropy measures by DS = q/T -- has been spread out, some remaining in the system as DS and some being transferred to the surroundings and identifiable as the DH/T(surroundings). (It can be used for work, but right now we're looking at it either as though it was all dissipated as unavailable thermal energy or as though the work itself had resulted in the same amount of waste energy, i. ...
• But exactly what was the original energy change that came out of the reaction in our system? We don't know, but let's give it a symbol of DG(system). OK, since that was the only event that occurred in the universe, and because energy flow (thermal energy transfer, "heat") divided by T is entropy, DG/T(system) is equal to the total entropy change in the entire universe due to this reaction! DS(universe) = DG/T(system).
• Oops! Watch it! We have to switch algebraic signs when looking at this energy/T change from a universe's viewpoint rather than from the system's. ...
• What kind of fast shuffle are you dealing me when you to start with all entropy and end up with enthalpy and DG that’s called "free energy"? Is entropy enthalpy? Is entropy free energy? I’m REALLY confused now. ...
•         Entropy is never enthalpy, nor free energy. ... Gibbs free energy change, DG, is only considered entropy change(after being divided by T) when no useful work of any kind is done by the heat transfer in the system or in the surroundings.
• Even when we focus on a little chemical system in our lab on earth by means of the Gibbs equation, we see the driving force -- the tendency of energy formerly bound in reactants to be spread out in the products. From information in other areas of chemistry than thermodynamics, we now know that the DH of Gibbs primarily comes from the difference in electronic binding energy between products and reactants. Usually in exothermic reactions, the products have stronger bonds and so some of the greater binding energy in the less strongly bound reactants is released as heat. From the energetics of molecules (again, outside of macrothermodynamics) we know that this increased thermal energy is due to molecules moving more rapidly and colliding more forcefully with one another. ...

• Free Energy.
• What is free energy?.
• Example of Free Energy Machines.
• What is free energy? The portion of the energy of a system which is the maximum available for doing work (The Macquarie Dictionary, 1981, Australia) Other dictionaries to look at.
• Examples of Free Energy Machines .
• A free energy machine is a simple device having the ability to harness or produce Free Energy.

• Free energy calculations.
•   The Helmholtz free energy , and other thermal quantities, such as entropy and the Gibbs free energy, cannot be directly obtained from the simulations as averages over functions of the phase space coordinates of the system. However, the internal energy E is a mechanical quantity that can be easily determined from the simulation as the average on the potential energy function. The free energy can then in principle be obtained through an integration of the thermodynamic relation, .
• By simulating the system at different temperatures T, and obtaining data for energy as a function of temperature, E(T), we can calculate the integral, .
• where is the free energy at a reference temperature. The following coupling-constant integration method  40, 39, 41, 42 can be used to find , provided one has a reference system for which the free energy is known, either exactly or numerically. ...
• Then the free energy difference between these two systems is, .

• Free-energy-top10. ...
• Top 10 is a neutral information resource for the free energy field. After researching through 20 000 - 30 000 pages on Internet and other information sources and printing 5 000 pages for further research our team made a decision: this has to become easier for all the friends of free energy.
• You can take part in discussions and also rate different free energy web sites.
• info@free-energy-top10. ...

• Next: The Empirical Potential Energy Up: Simulating Biomolecules: The Three Previous: II. ...
• An Empirical Energy Function: Free Energy vs. Potential Energy .
• Finally, given a defined system and its initial atomic coordinates, we need a function describing the energy of the system for any configuration, , of the atomic coordinates. A functional form must be chosen for the energy as well as the associated numerical constants. ... The energy function and its associated constants are contained in the Parameter File (. ...
• Free Energy vs. Potential Energy .
• For a system held at constant , the Helmholtz free energy, , is a minimum at equilibrium, where is the average total energy of the system (kinetic energy plus potential energy), T is the absolute temperature, S is the entropy, and Z is the partition function (eq 3). ... In this case, the Gibbs free energy, , is minimized at equilibrium. ...
• Some empirical energy functions are designed to approximate the Gibbs free energy G. For example, in Monte Carlo studies of protein structure prediction, the energy function may be based simply on the likelihood of residues of type i and j being within a certain distance of each other. ... Because the p's are derived from structures at constant T and P determined experimentally, these energy functions account for entropic contributions to the Gibbs free energy in an approximate way. ...
• In most molecular dynamics software packages, however, the empirical energy function, (not to be confused with the volume ), is developed to approximate the potential energy of the system. ... Many simulations have been performed at constant energy, E. That is, E is fixed and T fluctuates about an average value as energy is exchanged between the kinetic energy and the potential energy. ... Constant E simulations have the advantage that they allow energy conservation to be checked. ...

• Free energy profiles .
• In fact, if we were to plot the potential energy between atoms A and B, that is the curve we would expect a minimum at , as illustrated below. ...
• Because the surrounding solution is always in motion at a given temperature and pressure (or volume), we cannot speak of one single energy at a given distance between A and B, since it will actually depend on the particular configuration of the host solvent. ... If represents this averaged probability at different values of , then a free energy function of , can be computed from using .
• This will actually be the Gibbs free energy at different values of. If it were at constant volume instead of constant pressure, we would obtain the Helmholtz free energy, alluded to earlier. Such functions are called free energy profiles. ... Different solvent will lead to different free energy profiles, as will different experimental conditions, such as temperature and pressure. ...
• If we measure the Gibbs free energy as a function of , we might expect there to be two minima near each of the oxygens, with a maximum in the middle, indicating that some energy is needed to push the proton from one oxygen to the other. This energy can come from interactions with the solvent. Thus, the free energy profile might appear as shown below: .
• The hill in the middle is referred to as a free energy barrier since is resembles a barrier or obstacle that must be crossed in order to get to the other side. If represents the energy difference from the bottom of the well to the top of the barrier, then the probability that the barrier will be crossed at a temperature can be estimated from .
• In general, free energy profiles are useful for knowing the thermodynamics of a reaction on a point-by-point basis as the reaction occurs. An important application of free energy profiles is in drug design, where it is important to know the thermodynamics of how a certain drugs binds to an active site. If one has an appropriate reaction coordinate, then the free energy profile of that reaction coordinate can be computed, giving an indication of how many barriers need to be crossed in order for the drug to take hold. ...

• ALTERNATIVE ENERGY.
• FREE ENERGY.
• PLASMA ENERGY AND HEALING DATABASE compiled by Dee Finney .
• Henry: The Radiant Energy Device.
• Moray built a device capable of producing 50,000 watts of energy, if rebuilt, will be capable of answering the world's needs with a non-polluting form of energy. ... The size of a Radiant-Energy unit will be capable of delivering 60 kilowatts and will be about 42 inch by 26 inch by 22 inch and weighing no more than 60 pounds.
• The main energy probably came from the sunlight possibly modulated by wing flapping. ...
• He spent over 5 million dollars exploring uses of the drug dilantin (diphynlhadantoin--DPH), which helped him get back to normal with more energy than usual. ...
• A Critical Review of the Available Information Regarding Claims of Zero-Point Energy, Free-Energy, and Over-Unity Experiments and Devices .
• Allan's Time Interval Metrology Enterprise - New Unified Field Theory shows relationship between gravity, mass, energy density, weak and strong nuclear force fields; evidence and discussion. ...
• Eric's History of Perpetual Motion and Free Energy Machines .
• Finsrud Free Energy - Mr. ...
• Free Energy and Perpetual Motion - An account of Johann Bessler and his perpetual motion machine. Includes new theory on free energy machine, plus description of secret code, containing full details of construction of his machine - so far not deciphered. ...
• Free Energy Flywheel - Creative Science & Research, We have discovered a new Free Energy device wheel that will supply free electricity for your home or car. ...
• Free Energy with wires and magnets - A sceptics page on various free energy electrical devices. ...

• Jonathan Yedidia - Generalized belief propagation and free energy minimization .

• Free Energy Projects.
• We've complied together the most up-to-date free energy plans and other details in this report, which is 225 pages in length and nearly 2 megabytes of information. ...
• Plans and diagrams for: a pollution-free fuel used by Caterpillar, a process to extract water from the air, a rotating electrostatic self-running machine secretly in use in Europe, an air-driven turbine inspired by Schauberger, a solar box cooker, a solid-state free energy converter using parts available at Radio Shack, a unique water pump, a Van de Graf generator, a solar water desalinization plant, a water electrostatic generator, a Tesla high-voltage generator, a wind generator, several designs for over-unity motor/generators, a crystal power generator, how to extract energy from the air, a simple battery made with salt, flying vehicles, anti-gravity and levitation secrets, free energy experiments, and much, much more. ...
• How to test your free energy machine and prepare it for commercialization .
• A detailed review of Free Energy experimenters and their machines. ...
• the energy industry -- a nearly $5 trillion a year business. ...
• A list of over 190 free-energy and other advanced energy patents!  Along with 8 foreign over-unity patents! .
• If for any reason you feel that the Free Energy Projects report cannot help you in constructing a working, advanced energy technology, after trying it for 90 days, simply return it for an immediate refund. ...
• ORDER NOW and get the complete Free Energy Projects report for just $24. ...
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• YOU ARE HERE: Home  > Sciences  > Alternative Science  > Free Energy .
• Free Energy and Perpetual Motion Machines - Learn about free energy devices, over-unity theory, and perpetual motion machines.
• 777 Energy Science fair on free energy systems refutes pollution and oil burning technology. ...
• allRefer Reference - Free Energy (Gibbs Free Energy), Chemistry Take a look at this concept and access related articles on enthalpy, entropy, and thermodynamics. ...
• Eric's History of Perpetual Motion and Free Energy Machines Try to describe in brief the history of perpetual motion and free energy machines development. ...
• Free Energy: FAQ Find some answers of typical questions about free energy devices and machines. ...
• Jim's Free Energy Page Dedicated to find a solution for a cleaner and more efficient fuel for tomorrow. Find patents, ideas, and some tests on free energy topic. ...
• KeelyNet Explore news about and descriptions of dubious technological advances for free energy, gravity control, and electronic health. ...
• Space Energy Access Systems Organization of scientists advocate plan to solve the energy crisis and save the environment. ...
• The Free Energy Page Find links to "free energy" devices, technical, cautionary and other sites, concerned to alternative energy. ...
•  Join the Zeal community and help build the "Free Energy and Perpetual Motion Machines" Directory Category. ...

• 3 Entropy, Helmholtz Free Energy and the Partition Function .
• Take-home message: Once we have the Helmholtz free energy we can calculate everything else we want. ...
• Here is the crucial equation which links the Helmholtz free energy and the partition function: The details of the derivation can be found here. ...
• For instance the energy levels of a particle in a box of side are proportional to. ...
• These relations are reminiscent of those we met in the case of an isolated system, but there the entropy was the key; here it is the Helmholtz free energy. ...
• It should not surprise us to find that the Helmholtz free energy is the key to a system at fixed temperature (in contrast to the entropy for an isolated system) as that is what we found classically (see here. ...

• Here You'll Find all the information we have on the Free Energy & Free Energy Products. ...
• Free Energy / Products:     Free Energy Bible: (Now Shipping !)     BE READY TO MAKE YOUR OWN ENERGY FOR THE NEXT BLACK OUT or POWER INCREASE !   A comprehensive guide to all the "Free Energy Hype". Learn the top free energy ideas including: Magnetism, induction motors, fuel cells, new age batteries able to regenerate power through chemical reaction and more. This guide explains some of the top internet scams related to free energy as well as worth while idea's concerning revolutionary breakthroughs in energy research. ...       ** Introductory Price !**   Free Energy Bible on CD-ROM:   Price - $ 30. ...

• Theoretical Semiconductor Physics Group - Free Energy.
• Theory of surface free energies of solids.
• By contrast, our ability to predict free energies of solids or solid surfaces as a function of temperature is much less advanced. In fact, the determination of free energies from microscopic theory is a daunting task, mainly because the free energy cannot be calculated as an ensemble average. Nevertheless, free energies are essential to understand or predict many physical phenomena, from the stability of crystal structures to crystal growth at elevated temperatures and to associated morphology changes and phase transitions. ...
• Approximate computational methods, mostly based on the harmonic vibrational properties of the system, are commonly used to estimate free energies. In the so-called quasiharmonic approach, the crystal potential energy is replaced by its quadratic expansion about the atomic equilibrium positions at zero temperature and the free energy is calculated for a collection of independent harmonic oscillators. An alternative and principally exact approach is the so-called thermodynamic integration which replaces the solid by a fictitious system in which the interparticle interaction potential is gradually switched on from a known reference potential (with known free energy). ...
• We have performed detailed theoretical studies of free energies of solid Al surfaces employing this exact thermodynamic inte­gration. ...
• 1: Calculated surface free energy of Al(100) as a function of temperature. ...
• 1, we compare the surface free energy for Al (100) calculated with the quasi-harmonic approach and with the exact method of thermodynamic integration, respectively. The former grossly underestimates the temperature dependence of the free energy and fails even qualitatively to predict the temperature variation of the surface free energy near and above the Debye temperature of Al (~ 400 K). ...
• At zero temperature, on the other hand, the equilibrium shape of a free crystal is determined by the minimum of the surface energy for given volume. This can be calculated by examining the surface energy as a function of its orientation and determining its minimum geometrically from a polar representation of this energy (known as Wulff construction). We have performed such calculations and depict two different views of the equilibrium shape of a free three-dimensional Al crystal in Figure 2. ...
• 2: Calculated zero temperature surface energy for Aluminium with surface orientations that lie in two high symmetry planes. ... Open circles mark energy of a particular surface orientation. ...

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