This preview shows pages 1–5. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Molecular Dynamics simulations Lecture 07: Interaction models for metals Dr. Olli Pakarinen Original lecture notes by Dr. Jani Kotakoski, 2010 University of Helsinki Fall 2011 M ETALS I By definition, a metal is a material which is kept together by metallic bonding I Metallic bonding is a result of nearlyfree electrons of a group of atoms which bind with the positively charged atomic cores I Of all elements, 80% are metals [image from A. Kuronen] C RYSTAL STRUCTURES FOR METALS I The most typical crystal structure for a metal is the hexagonal close packed (HCP) I The next most common is face centered cubic (FCC), whereas the third one is the body centered cubic (BCC) I With potentials describing these three lattices, already 60 % of all stable singleelement structures are covered I Both HCP and FCC have a packing density of 0.74 (filling of space with hard spheres) I No structure, regular or not, has a denser packing HCP I Hexagonal close packed lattice vectors are: a = ( a , , ) = = 90 b = ( a / 2 , 3 2 a , ) = 120 c = ( , , c ) I The two atoms in the primitive cell are located at: ( , , ) & ( 2 3 , 1 3 , 1 2 ) I Atom in the HCP structure has 12 nearest neighbors I If the binding energy would depend only on the nearestneighbor distance (i.e., a pair potential), there would be no difference in the energy of HCP and FCC I Examples of materials with HCP lattice: He, Be, Mg, Ti, Zn, Cd, Co, Y, Zr, Gd and Lu FCC I FCCs lattice vectors are, of course, cubic: a = ( a , , ) b = ( , a , ) c = ( , , a ) I The atoms are located at: ( , , ) , ( , 1 2 , ) ( 1 2 , 1 2 , ) , ( , 1 2 , 1 2 ) I Again, there are 12 nearest neighbors and a 0.74 packing I FCC metals tend to be soft and ductile over a wide temperature range I Examples include: Au, Ag, Cu, Al and Fe BCC I Also BCC has, by definition, a cubic lattice: a = ( 1 , , ) b = ( , 1 , ) c = ( , , 1 ) I The atoms are located at: ( , , ) ( 1 2 , 1 2 , 1 2 ) I Each atom has 8 nearest neighbors and 6 nextnearest neighbors I Packing density is 0.68 I BCC metals are typically strong and reasonably ductile I Examples include: W, Cr, Fe and K Effective Medium Theory I In the effective medium theory (EMT) the interactions between the particles are assumed to depend on an effective environment I In this case, the total energy is written as U tot = X i F [ n i ( R i )] + 1 2 X i , j ( R i R j ) (1) I Here, F is a functional of the local electron density, and is (typically) a purely repulsive pair potential for the atom cores I In principle, EMT obtained from ab initio calculations can be directly used as a potential I However, more typically, EMT is used as the starting point for developing a more flexible potential I Within EMT, the real material is modeled as jellium which consists of 1) a homogeneous electron gas, formed from the free electrons 2) a constant positive background density (ions) I Hence, both electrons and ions are smeared to a respective effective medium I Placing (i.e., Placing (i....
View Full
Document
 Winter '12
 Kotakoski
 The Land

Click to edit the document details