Study of First Principles of Mg-Si Binary Systems as Precipitates from T6 Heat Treatment of AL-MG-SI ALLOYS

One of the purposes adding the two main alloying elements Si and Mg in small quantities (≈ 1%) on Aluminum is to form strengthening precipitates in aluminium alloy, which typically contribute with a fivefold strength increase from pure aluminum. In the last decades, the investigation has begun to understand the structure and formation of the different phases during heat treatment. An important precipitate in Al-Mg-Si Alloy is β" and β. when the Precipitate β is created after β" is that the strength suddenly drops and the alloy is said to be overaged. By means of a first-principles supercell approach and density functional theory calculations, this research studied precipitate energy and interface energy of precipitate β" and β. Results show that precipitate β have precipitate energy higher then β" but have interface energy lowers then β". And each low energy interface was found possesses interface with the Al matrix is fully incoherent. The final result of calculation and simulation values for the interfacial energies, precipitate energies and strain energies that can be used in future predictions of the characteristic precipitate.


INTRODUCTION
Aluminium is the third most abundant element in the Earth's crust, after oxygen and silicon and the second most used metal in the world after Steel [1] . Alumunium has several advantages in many cases: light weight (and high strength-to-weight ratio), good formability and machinability, excellent corrosion resistance, high thermal and electrical conductivity and Recycling of aluminium products needs only 5% of the energy needed for primary aluminium production and infinite recyclability. Of special interest are Al-Mg-Si alloys, being the alloys of choice for medium-strength architectural and transportation applications, most prominently in the automotive industry [2,3] .The purpose of adding the two main alloying elements Mg and Si in small amounts (≈ 1%) is to form hardening precipitates, which typically contribute with a fivefold strength increase from pure aluminium. Understanding the process of precipitation and how it affects mechanical properties have been important subjects of research for hundred years [4] . Only in the last decades we begun to understand the structure and formation of the different phases during heat treatment. There is a handful of discovered metastable phases in the Al-Mg-Si system alone. precipitates forming during aging at medium high temperatures (around 150 ℃) after Soluton Heat treatments (around between 400 and 500 o C ). And then Rapid cooling ensures a supersaturated solid solution (SSSS), after which the solutes start clustering in the face centred cubic Al lattice. The strength is caused by a high number density of nano-sized, needle-shaped β" precipitates, usually together with Guinier-Preston (GP) zones. With increasing temperature and aging time, the number density decreases, while the precipitates coarsen and are replaced by more stable types. The precipitation sequence in Al-Mg-Si alloys is [3,4] .
One of the key factors that control the mechanical properties of precipitate-hardened alloys is the precipitate morphology,i.e. the size and shape of precipitates. In order to predict [5,6] the precipitate microstructural evolution and thus mechanical properties, it is critical that the thermodynamicdriving forces and kinetic mechanisms that lead to various precipitate shapes be understood. The morphology of a precipitate is primarily determined by two competing energetic contributions, i.e. the interfacial energy between the precipitate and the matrix and the coherency elastic strain energy generated due to the lattice mismatch between the precipitate and the matrix. Obtaining these quantities directly from experiments can be difficult due to the metastable nature of many precipitates. The main objective of this paper is to search for low energy interfaces between the precipitate and the -Al matrix from a firstprinciples approach. [7] DFT has been used to support the experimental results and better explain the observed features in each alloy. Precipitate energies and Strain energy have been calculated for solute additions and structural variants of the β" and β phase [8] . We will do calculations on equillibrium structure of the different precipitate plus interfaces using Density Functional Theory (DFT) with the Quantum Espresso computer code. The simulation models for calculations, we create using Visualization For Electronic and Structural Analysis (VESTA).

METHOD
Density functional theory (DFT) has been shown to provide reliable energetics for aluminum and its alloys . We have used self-consistent DFT as implemented in the Quantum ESPRESSO package [4] . Quantum ESPRESSO is open-Source Package for Research in Electronic Structure, Simulation, and Optimization, is an integrated software suite for first-principle simulations, using density-functional theory (DFT), a plane waves (PW) basis set and pseudopotentials (PP) Computational Details. quantum ESPRESSO is distributed under the GNU (Gnu's Not Unix) General Public License (GPL), probably the most common freesoftware license. used a gradient corrected exchange and correlation energy functional (PBE), together with a plane-waves expansion of Kohn-Sham orbitals and electronic density, using ultra-soft pseudopotentials for all the elements involved. The plane-wave cut-off energy was chosen to be 35 (280) Ry for the wavefunction when evaluating the energetics of defects.

Atomistic Modelling
Supercell files are made with a Visualization For Electronic and Structural Analysis called VESTA. This package lets us build a supercell atom by atom.

a. Supercell From β" and β
The phase β (fluorite Mg2Si) is the terminal equilibrium structure of the precipitation sequence. It has a fcc primitive unit cell (space group Fm-3m (225)), with an experimental lattice parameter a = 6.39 °A [4] . It forms precipitates of a plate-like or cubic shape up to 20 μm in diameter. Its interface with the Al matrix is fully incoherent [8,10] . The β"-Phasehas a base-centred-monoclinic conventional unit cell (space group C2m) with experimental lattice parameters a = 15.16 Å, b = 6.74 Å, c = 4.05 Å, and ab=105.3 o [8,11] b. Structural Relationship between β"-Mg5Si6 , β-Mg2Si and -Al  For bulk fcc Al, we computed the lattice parameter to be 4.057 Å, in excellent agreement with the experimental value and with previous modelling using the same functional [5] . These lattice parameters are used through out our study to build supercells representing the Al matrix. All of the β" and β phases we consider can be described by Interfacial orientations below.
To obtain higher quantitative accuracy for the interfacial energies, we use larger supercells, as shown in figure

Bulk Properties Of Matrix And Precipitate Phases
Bulk properties (lattice structure, lattice constants, elastic constants) of Al and the various β" and β -precipitates studied here have been previously computed in the literature. Here, we present our results as a means of.

a. The Solute Energies Element Precipitate
In order to define a reference state for the thermodynamics of the precipitates we define the solid solution energies asbenchmarking our methods, verifying literature results, and most importantly obtaining reference values that are fully consistent with our computational details -which is crucial to evaluate the energy diferences that determine interface and Precipitate energies.

b. Precipitae Energy
To be consistent with the denition of Precipiate energies used above, we define the precipitation energy using the SSSS as reference, where nAl is the number of Atoms Al in the matrix for give simulation supercell, and n(Mg, Si) and ( , ) indicate the β" compsition and the solid-solution energy for Al, Si dan Mg. NFU is the number of formula units in the precipitate cross-section.

c. Interfece Energy
It is common practice to talk of interfacial energy. In reality, however, what is usually meant and measured by experiment is the interfacial free energy, γ. The free energy of a system containing an interface of area A and free energy γ per unit area is given by Where Λ is the cross section of the simulation supercell corresponding to the orentation of the interface, nAl is the number of Al atoms in the Matrix, and nβ" is the number of β " formula units inside the supercell and  is Interface Energy.

d. Strain Energy
The Precipitate energy as defined in Eq. (1) thus contains both contributions from the interfacial energy, as well as the elastic strain energy from the lattice mismatch between Matrix and Precipitate. Specifically, the energy of formation of Eq. (1) can be expressed as Where  is Strain energy and NFU is the number of formula units in the precipitate [9] .

RESULTS AND DISCUSSIONS a. Calulations Precipitate Energy
The precipitate energy is the energy required to produce a defect (a vacancy) into the perfect crystal structure. In order to find the energetically most stable composition of β". we compared the total energy of an Al supercell with an embedded precipitate to that of a solid solution containing the corresponding number of (noninteracting) solute atoms spread throughout the matrix. We quantified this by the precipitate energy, Energy of precipitate defined by Equation 3. .2726849805 eV respectively. The precipitate energy required to produce a defect (a vacancy) into the perfect crystal structure, and to compare the energy precipitate which is owned by precipitate β" and β, thatprecipitate β have higher energy than precipitate β". So precipitate β is more stable and stronger in its crystalline structure compared to precipitate β "which has a metastable structure.

b. Calulations Interface Energy
Interface energy comes from a mismatch in the bondings between phase 1 and phase 2. When the interface is between two different phases there are usally three contributions to the free energy. The chemical-bonding and lattice strain-energy, and the cohesive energy of the separate phases, Ec . To compute the interface energy,  we must compute the total energy of the slab and subtract the constituents from it until we are left with the excess strain energy from the misfit, and the chemical interface energy. Small variations in the interfacial energy can lead to large variations in the predicted precipitation behaviour of an alloying system  The interface precipitate β "and matrix aluminum are coherent, in contrast to the precipitate β interface that has an interface that is incoherent with the aluminum matrix. Interface energy has this important role because Precipitate holds the atomic dislocation so that its mechanical properties increase, The barriers that block the dislocation can be generated during the deformation process, where the load will focus around the interface, resulting in an energy strain around the interface between the precipitate and the matrix and the highest energy interface between precipitate β "and precipitate β is precipitate β" thus mechanical properties will increase.

c. Calculation Strain Energy
In the molecule, strain energy is the energy stored by a system undergoing deformation, strain energy is released when the constituent atoms are allowed to rearrange themselves in a chemical reaction. The external work done on an elastic member in causing it to distort from its unstressed state is transformed into strain energy which is a form of potential energy. The strain energy in the form of elastic deformation is mostly recoverable in the form of mechanical work.

CONCLUSIONS
The influence type of interfaces between precipitate and matrix aluminum, a coherent interface (Precipitate β") to the matrix has a higher energy interface compared to an incoherent interface (precipitate β). Influence Interface orientation to energy interfaces and strain energy, on the precipitate β" the highest interface energy is the Interface Alumunium  In the optimum aging state formed precipitate β" with the chemical formula Mg5Si6. Based on the results of calculations and simulations, precipitate β" has a lower precipitate energy in comparison with precipitate β (Mg2Si) which has a more stable energy precipitate. But precipitate β has a lower energy interface in comparison with precipitate β". The interface plays an important role in improving its mechanical properties. In the optimum aging state, the material will have the highest hardness value, because precipitate β" has a higher energy interface, so it can hold the rate of deformation of atoms larger than the precipitate β.