铝的晶格常数

1、铝的晶格常数-体弹模量及弹性常数分子模拟Calculation of material lattice constant and bulkCC2012modulusCalculati on of material lattice con sta ntand 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 th

2、e aluminum consequently make betteruse ofaluminum. In virtue of molecular dynamics simulation software, wecan solve the lattice constant . By the derivative of the lattice con stant, the bulk modulus can be obtained. The elastic constants of a material display the elasticity and we can use the softw

3、are material studio to simulate and get them. The simulation results match the experimental values.Key words:Aluminum, lattice constant, bulk modulus, elastic constant simulation.Calculation of material lattice constant and bulkCC2012modulusIn troductio n:In materials science, in order tofacilitate

4、analysis about theway in which the crystal particlesare arranged,the basic unit canbe removedfrom the crystallattice asa representative(usually thesmallest parallelhexahedron)as a compositionFigure Aunit of dot matrix, called a cellLattice constantis a basic(i.e. solid State Physics original cell co

5、ncept); lattice constant (or so-called lattice constant) refers to the side length of the unit cell, in other words, the sidelengthof eachparallelhexahedralcells. Latticeconstantis an important basicparameters of crystal structure. Figure A is the basic form of thestructural parameter , which hasa d

6、irectrelationshipwiththebondingsbetween theatomsof thecrystalsubstance.Itreflectsthe changesintheinternalcompositionofthecrystalof the latticeconstant,force state changes, etc.The bulk modulus ( K or B ) oflattice constant.a substancemeasurestheCalculation of material lattice constant and bulkCC2012

7、modulusK =dPdVvolume, anddP/d denotes thesubstancesresistance touniform compression. It is defined asthe ratioof theinfinitesimal 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 modulus11

8、canbe formally defined by the equation: where ； is pressure, is 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 a

9、luminum alloy are considered the most economic and applicable in many application fields as a consequence of their excellent properties.What smore , increased usage of aluminum will result from designers increased familiarity with the metal and solution to manufacturing problems that limit some appl

10、ications.constant and bulk modulus areboComput ing theory and methods:Our simulation is on the basisthat 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 constan

11、t for energy E , we obtain bulk modulus.To start with , compile a script for the use of operation and simulation in lammps. We setundary 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 ene

12、rgy , 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 thelinux system produced by lammps to continue the computation by means of matlab , from which we can get the lattice constant through several t

13、imes of matching.Calculation of material lattice constant and bulkCC2012modulusthe visualization of aluminu sFigure CFigure Cthe curveshows 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 cor

14、responding 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.crystal structure. Figure D is what we get through the visualization.Figure DThe bulk modulus is definedas :dPAs for cubic cell ,

15、 the formula can be transformed into the9陽 daSince we have obtained thelattice constant , we simulatedfollowing patternThe bulk modulus can be calculated with the formula above combined with the latticesimulation .Figure EFigure FIt comes to the CASTEP step after the geometry optimization. We manage

16、d to make Ecut =350eV and2012Calculation of material lattice constant and bulkCCmodulusconstant. 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 elas

17、tic 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 theKpoints =16*16*16, both ofwhich are ext

18、remely importantCalculation of material lattice constant and bulkCC2012modulusand also sensitive to the calculation of elastic constant after several trials. Figure G is the primitive cell that has beenthrough the geometryoptimization.Figure Gelastic constants are listed below :Cn=108112GpaC12=61.36

19、6GpaC44=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.The calculated results are as follows:C11 =106.2GpaCi2=60.5GpaC44=28.7GpaCorrespondingly , theCon clusi onOur group has calculated thelattice co

20、nstant and bulkmodulus of aluminum , both of which coincide with the experimental value , by means of lammps and matlab. Moreover we have found out that bulkexperimental range of the threemodulus has a close relationshipwith temperature. As lattice constant haven t made any change under small change

21、 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

22、 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 ofBesides , the most valuable thing we have learned is that we must seek the solutions and never

23、give up in face of difficulties.Refere nces1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 C

24、ohen, Marvin (1985).Calculation of material lattice constant and bulkCC2012modulusthe simulation.Calculation of material lattice constant and bulkCC2012modulusElectronics. Metallurgy. Oct2011.Calculation of bulk modulus of diamond and zinc-blende solids. Phys. Rev. B 32: 7988 -7991.4 Watson, I G; Le

25、e, 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. Ashley, Steven. Aluminum vehicle breaks new ground. Engineering-Mechanical Eng

26、ineering. Feb 1994.7 Sanders, Robert E, Jr;Farnsworth, David M. Trends inAluminum Materials Usage forCalculation of material lattice constant and bulkCC2012modulus附文：lammps 脚本unitsmetalboun daryP P Patom_styleatomicvariable iloop 20variablex equal 4.0+0.01*$ilatticefcc $xregi onboxblock 0 3 0 3 0 3create_box1 boxcreate_atoms1 boxpair_styleadppair_coeff* * AlCu.adp Almass1 27n eighbor1 binn eigh_modifyevery 1 delay 5 check yesvariablep equal pe/108variabl