Saturday, December 26, 2015

What does formation energy mean?

I had read some theoretical paper about defect in GaN. They analysis the defect using formation energies as a function of Fermi level. If the formation energy is too big, this defect is very unlikely to be seen. So what does this “formation energy” mean?
The formation energy is the energy required to produce a defect (a vacancy) into the perfect crystal structure.In the case of GaN, the formation energy of each defect is a function of the Fermi energy and the difference of the chemical potentials between Ga and N.
The formation energy is the cost of creating a defect into an otherwise perfect solid. For a vacancy it is calculated as the energy needed to remove an atom from the bulk and take it to infinity. Formation energies are very important because the concentration of defects in a solid in thermodynamic equilibrium depends exponentially on it.

What's the differences among the concepts: binding energy, cohesive energy and formation energy?

  • Formation energy is the change in energy when a material is formed from it's constituent elements in their reference states. For example, the formation energy of alumina (Al2O3) is the change in energy when fcc aluminum and O2 gas combine to make Al2O3.
  • Cohesive energy is the amount of energy it takes to break something up into isolated atoms. This is also called the atomization energy.
  • Binding energy in general means the amount of energy to split something up, and can mean different things depending on the context. For example, if you're talking about a molecule, it can refer to atomization energy.
Something to keep in mind regarding sign conventions is that formation energies are typically given as negative values, whereas cohesive energies and binding energies are typically positive values.

Standard enthalpy of formation

The standard enthalpy of formation or standard heat of formation of a compound is the change of enthalpy during the formation of 1 mole of the compound from its constituent elements, with all substances in their standard states at 1 atmosphere (1 atm or 101.3 kPa). Its symbol is ΔHfO or ΔfHO. The superscript theta (zero) on this symbol indicates that the process has occurred under standard conditions at the specified temperature (usually 25 degrees Celsius or 298.15 K). Standard states are as follows:
  1. For a gas: the standard state is a pressure of exactly 1 atm
  2. For a solute present in an ideal solution: a concentration of exactly one mole/liter (M) at a pressure of 1 atm
  3. For a pure substance or a solvent in a condensed state (a liquid or a solid): the standard state is the pure liquid or solid under a pressure of 1 atm
  4. For an element: the form in which the element is most stable under 1 atm of pressure. One exception is phosphorus, for which the most stable form at 1 atm is black phosphorus, but white phosphorus is chosen as the standard reference state for zero enthalpy of formation.[1]
For example, the standard enthalpy of formation of carbon dioxide would be the enthalpy of the following reaction under the conditions above:
C(s,graphite) + O2(g) → CO2(g)
All elements are written in their standard states, and one mole of product is formed. This is true for all enthalpies of formation.
The standard enthalpy of formation is measured in units of energy per amount of substance, usually stated in kilojoule per mole (kJ mol−1), but also in calorie per mole, joule per mole or kilocalorie per gram (any combination of these units conforming to the energy per mass or amount guideline). In physics the energy per particle is often expressed inelectronvolts which corresponds to about 100 kJ mol−1.
All elements in their standard states (oxygen gas, solid carbon in the form of graphite, etc.) have a standard enthalpy of formation of zero, as there is no change involved in their formation.
The formation reaction is a constant pressure and constant temperature process. Since the pressure of the standard formation reaction is fixed at 1 atm, the standard formation enthalpy or reaction heat is a function of temperature. For tabulation purposes, standard formation enthalpies are all given at a single temperature: 298 K, represented by the symbol ΔHf298O .
The standard enthalpy of formation is equivalent to the sum of many separate processes included in the Born-Haber cycle of synthesis reactions. For example, to calculate the standard enthalpy of formation of sodium chloride, we use the following reaction:
Na(s) + (1/2)Cl2(g) → NaCl(s)
This process is made of many separate sub-processes, each with its own enthalpy. Therefore, we must take into account:

  1. The standard enthalpy of atomization of solid sodium
  2. The first ionization energy of gaseous sodium
  3. The standard enthalpy of atomization of chlorine gas
  4. The electron affinity of chlorine atoms
  5. The lattice enthalpy of sodium chloride
The sum of all these values will give the standard enthalpy of formation of sodium chloride.
Additionally, applying Hess's Law shows that the sum of the individual reactions corresponding to the enthalpy change of formation for each substance in the reaction is equal to the enthalpy change of the overall reaction, regardless of the number of steps or intermediate reactions involved. This is because enthalpy is a state function. In the example above the standard enthalpy change of formation for sodium chloride is equal to the sum of the standard enthalpy change of formation for each of the steps involved in the process. This is especially useful for very long reactions with many intermediate steps and compounds.
Chemists may use standard enthalpies of formation for a reaction that is hypothetical. For instance carbon and hydrogen will not directly react to form methane, yet the standard enthalpy of formation for methane is determined to be −74.8 kJ mol−1 from using other known standard enthalpies of reaction with Hess's law. That it is negative shows that the reaction, if it were to proceed, would be exothermic; that is, it is enthalpically more stable than hydrogen gas and carbon.
It is possible to predict heat of formations for simple unstrained organic compounds with the Heat of formation group additivity method.
(State: g = gaseous; l = liquid; s = solid; aq = aqueous)

Standard Enthalpies of Formation (at 25°C, 298 K)


Chemical CompoundPhase (matter)Chemical formulaΔ Hf0 in kJ/mol
AcetonelC3H6O−248.4
AcetylenegC2H2+227.4
AmmoniagNH3−46.1
Ammonia (Ammonium Hydroxide)aqNH3 (NH4OH)−80.8
Ammonium nitratesNH4NO3−365.6
BenzenelC6H6+49.1
BrominelBr20
BrominegBr2+31
BrominegBr+111.9
CalciumsCa0
Calcium carbonatesCaCO3−1207.6
Calcium oxidesCaO−634.9
CarbonsC (graphite)0
CarbonsC (diamond)+1.88
Carbon dioxidegCO2−393.5
Carbon monoxidegCO−110.5
ChlorinegCl20
ChlorinegCl+121.3
Copper(II) sulfateaqCuSO4−769.98
EthanegC2H6−84.68
EthanollC2H5OH−277.6
EthylenegC2H4+52.4
FluorinegF20
FluorinegF+79.38
GlucosesC6H12O6−1273.3
HydrogengH20
Hydrogen bromidegHBr−36.3
Hydrogen chloridegHCl−92.3
Hydrogen fluoridegHF−273.3
IodinesI20
IodinegI2+62
IsopropanolgC3H7OH−318.1
MethanegCH4−74.87
MethanollCH3OH−238.6
Nitric oxidegNO+91.3
NitrogengN20
Nitrogen dioxidegNO2+33.2
OxygengO20
OzonegO3+142.7
PropanegC3H8−103.85
SilicasSiO2−911
SilversAg0
Silver chloridesAgCl−127.0
SodiumsNa0
SodiumgNa+107.5
Sodium bicarbonatesNaHCO3−950.8
Sodium carbonatesNa2CO3−1131
Sodium chloride (table salt)aqNaCl−407
Sodium chloride (table salt)sNaCl−411.12
Sodium chloride (table salt)lNaCl−385.92
Sodium chloride (table salt)gNaCl−181.42
Sodium hydroxideaqNaOH−470.1
Sodium hydroxidesNaOH−426.7
Sodium nitrateaqNaNO3−446.2
Sodium nitratesNaNO3−424.8
SucrosesC12H22O11−2226.1
Sulfur (monoclinic)sS80.3
Sulfur (rhombic)sS80
Sulfur dioxidegSO2−296.8
Sulfur trioxidegSO3−395.7
Sulfuric acidlH2SO4−814
WaterlH2O−285.8
Water vaporgH2O−241.82
Zinc sulfatesZnSO4−980.14