铝的晶格常数,体弹模量及弹性常数分子模拟.docx

Calculation of material lattice constant and bulk modulus2012CCCalculation of material lattice constant and bulk modulusSummary：Aluminum is one of the worlds most used metals, the calculated aluminum lattice constant and bulk modulus can be used to improve the performance of the aluminum consequently make better use of aluminum. In virtue of molecular dynamics simulation software，we can solve the lattice constant . By the derivative of the lattice constant, the bulk modulus can be obtained. The elastic constants of a material display the elasticity and we can use the software material studio to simulate and get them. The simulation results match the experimental values.Key words:Aluminum, lattice constant, bulk modulus, elastic constant , simulation.Introduction:In materials science, in order to facilitate analysis about the way in which the crystal particles are arranged, the basic unit can be removed from the crystal lattice as a representative (usually the smallest parallel hexahedron) as a composition unit of dot matrix, called a cell (i.e. solid State Physics original cell concept); lattice constant (or so-called lattice constant) refers to the side length of the unit cell, in other words, the side length of each parallel hexahedral cells. Lattice constant is an important basic parameters of crystal structure. Figure A is the basic form of the lattice constant.Figure ALattice constant is a basic structural parameter，which has a direct relationship with the bondings between the atoms ，of the crystal substance. It reflects the changes in the internal composition of the crystal of the lattice constant, force state changes, etc.The bulk modulus (K or B) of a substance measures the substances resistance to uniform compression. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume. Its base unit is the pascal. Figure B describes the effect of bulk modulus.Figure BThe bulk modulus can be formally defined by the equation:where is pressure, is volume, and denotes the derivative of pressure with respect to volume.Our research object is aluminum，whose atomic number is 13 and relative mass is 27.The reserves of aluminum ranks only second to ferrum compared with other metallic elements. Aluminum and aluminum alloy are considered the most economic and applicable in many application fields as a consequence of their excellent properties. Whats more，increased usage of aluminum will result from designers increased familiarity with the metal and solution to manufacturing problems that limit some applications. The crystal structure of aluminum is face-centered cubic. The experimental value of lattice constant and bulk modulus are 0.0.40491nm and 79.2Gpa.Computing theory and methods：Our simulation is on the basis that aluminum is of face-centered cubic crystal structure. We can get the exact value of lattice constant in virtue of molecular dynamics simulation software. Then by the derivation of lattice constant for energy E，we obtain bulk modulus.To start with ，compile a script for the use of operation and simulation in lammps. We set periodic boundary conditions in the script and create an analog box，whose x ,y ,z coordinate values are all confined to 0,3.Run the script in lammps, calculating the potential energy，kinetic energy as well as the nearest neighbor atoms for each atom. Finally put out the potential energy function of aluminum.Extract the datas under the linux system produced by lammps to continue the computation by means of matlab，from which we can get the lattice constant through several times of matching.Figure CFigure Cthe curve shows the relationship between cohesive energy and lattice constant，which is what we get in the process of computing in matlab，points out the lattice constant corresponding with the least cohesive energy. The horizontal ordinate of the rock bottom stand for the lattice constant of aluminum which can be clearly located as 0.40500nm.Since we have obtained the lattice constant，we simulated the visualization of aluminus crystal structure. Figure D is what we get through the visualization.Figure DThe bulk modulus is defined as：As for cubic cell，the formula can be transformed into the following pattern：The bulk modulus can be calculated with the formula above combined with the lattice constant. Finally，the bulk modulus is 78.1Gpa.Besides，to enrich our research, we have calculated the elastic constants of aluminum. Because of the symmetry of face-centered cubic，aluminum only has three elastic constants. To reach the target ，we have to establish a cell of aluminum in the software material studio in the first place and then transform it into a primitive cell. Figure E and figure F are the cell and the primitive cell we have established during the simulation . Figure E Figure FIt comes to the CASTEP step after the geometry optimization. We managed to make Ecut=350eV andKpoints=16*16*16 ，both of which are extremely important and also sensitive to the calculation of elastic constant， after several trials. Figure G is the primitive cell that has been through the geometry optimization.Figure G The calculated results are as follows:C11=106.2GpaC12=60.5GpaC44=28.7GpaCorrespondingly ，the experimental range of the three elastic constants are listed below：C11=108112GpaC12=61.366GpaC44=27.928.5GpaAs we can see，although a little outside of the value range of the experimental standards, our results are right within the error range.Conclusion：Our group has calculated the lattice constant and bulk modulus of aluminum，both of which coincide with the experimental value，by means of lammps and matlab. Moreover ，we have found out that bulk modulus has a close relationship with temperature. As lattice constant havent made any change under small change of temperature while the energy of the material have changed，so we concluded that temperature change can influence bulk modulus as a consequence of the change of cohesive energy change resulting from temperature change.There are still problems in our research as you can see that the three elastic constants are a little out of the value range. But this group is the one closest to the experimental value. Our group have concluded that the errors result from the script which can affect the accuracy of the simulation. Besides，the most valuable thing we have learned is that we must seek the solutions and never give up in face of difficulties.References：1材料科学基础（胡赓祥、蔡珣、戎咏华 上海交通大学出版社） 2 Ayton, Gary; Smondyrev, Alexander M; Bardenhagen, Scott G; McMurtry, Patrick; Voth, Gregory A. “Calculating the bulk modulus for a lipid bilayer with none quilibrium molecular dynamics simulation. Biophysical Society. 2002.3 Cohen, Marvin (1985).Calculation of bulk modulus of diamond and zinc-blende solids. Phys. Rev. B 32: 79887991.4 Watson, I G; Lee, P D; Dashwood, R J; Young, P. Simulation of the Mechanical Properties of an Aluminum Matrix Composite using X-ray Microtomography: Physical Metallurgical and Materials Science. Springer Science & Business Media. 2006.6 Ashley, Steven. Aluminum vehicle breaks new ground. Engineering-Mechanical Engineering. Feb 1994.7 Sanders, Robert E, Jr; Farnsworth, David M. Trends in Aluminum Materials Usage for Electronics. Metallurgy. Oct 2011. 附文：lammps脚本units metalboundary p p patom_style atomicvariable i loop 20variable x equal 4.0+0.01*$ilattice fcc $xregion box block 0 3 0 3 0 3 create_box 1 boxcreate_atoms 1 boxpair_style adppair_coeff * * AlCu.adp Almass 1 27neighbor 1 binneigh_modify every