Building initial configuration. Ideal crystals (I)

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1 Building initil configurtion. Idel crstls (I) An crstlline solid cn be defined in terms of Brvis lttice which specifies the periodic rr in which the repeted units of the crstl re rrnged. Brvis lttice is defined b three primitive vectors b c. Rel crstl structure consists of identicl copies of the sme phsicl unit (group of toms) clled bsis locted t ll the points of Brvis lttice. Rel crstlline structure = Brvis lttice with bsis. The crstl structure is often discussed in terms of its unit cell bsic building block of the crstl the spce limited b the prllelepiped defined b vectors b c Emple: D honecomb net is tringulr Brvis lttice with two point bsis. Universit of Virgini MSE 70/670: Introduction to Atomistic Simultions Leonid Zhigilei

2 Building initil configurtion. Idel crstls (II) One cn lso describe Brvis lttice s lttice with bsis b choosing nonprimitive conventionl unit cell. For emple lthough BCC nd FCC re Brvis lttices (but not HCP D nlog of honecomb) we cn describe them s simple cubic Brvis lttices with primitive vectors ˆŷẑ nd two-point bsis for BCC: 0 ˆ ŷ ẑ or four-point bsis for FCC: 0 ˆ ŷ ŷ ẑ ˆ ẑ These descriptions re implemented in MSE67-CG code. Universit of Virgini MSE 70/670: Introduction to Atomistic Simultions Leonid Zhigilei

3 Universit of Virgini MSE 70/670: Introduction to Atomistic Simultions Leonid Zhigilei Building initil configurtion. Idel crstls (III) Dimond lttice cn be considered s two interpenetrting FCC Brvis lttices. Dimond lttice is not Brvis lttice nd cn be described s FCC Brvis lttice with the two-point bsis: ẑ ŷ ˆ 0 0 Dimond structure (C-d Si Ge α-sn) But it is lso possible to consider dimond lttice s simple cubic Brvis lttice with 8-point bsis This ltter description is implemented in MSE67-CG code.

4 Building initil configurtion. Idel crstls (IV) Hegonl close-pcked (HCP) structure is lso not Brvis lttice nd cn be considered s two interpenetrting simple hegonl Brvis lttices. Multi-component structures Another clss of crstlline structures for which we hve to use bsis consisting of more thn one tom re multi-component structures even if the toms re locted t the points of Brvis lttice. Sodium chloride structure (NCl KCl MgO CO) consists of equl number of sodium nd chlorine ions plced t n lternte points of simple cubic lttice. Cn be described s FCC Brvis lttice with bsis consisting of two toms. NCl structure fcc with toms in the bse: t (0 0 0) nd (½ 0 0) N + ions filling octhedrl holes in the fcc structure KCl AgBr KBr PbS MgO FeO Universit of Virgini MSE 70/670: Introduction to Atomistic Simultions Leonid Zhigilei

5 Building initil configurtion. Idel crstls (V) Cesium chloride structure (CsCl CsBr) consists of equl number of cesium nd chlorine ions plced t n lternte points of BCC lttice. Cn be described s simple cubic Brvis lttice with bsis consisting of two toms. Implemented in MSE67- CG code. CsCl structure simple cubic with two toms in the bse t (000) nd (½ ½ ½) CsCl TlI TlCl AlNi CuZn - intermetllic comp. Universit of Virgini MSE 70/670: Introduction to Atomistic Simultions Leonid Zhigilei

6 Building initil configurtion. Idel crstls (VI) Intermetllic llos (Ni Al Cu Au Ni Mn ) Intermetllics re llos composed of two or more elements in which the unlike toms hve strong ffinit for ech other. Intertomic bonding in intermetllics is still metllic in nture but hs n dditionl ionic chrcter tht is influenced b the difference in electronegtivities between the constitutive elements. This ttrction between dissimilr toms forces the crstl to dopt structure tht ccommodtes these tomic bonding preferences. The hve FCC structure which however is not Brvis lttice. The cn be described b simple cubic Brvis lttice with four-point bsis. This description is implemented in MSE67-CG code. Universit of Virgini MSE 70/670: Introduction to Atomistic Simultions Leonid Zhigilei

7 Building initil configurtion. Idel crstls (VII) Two-component sstems with dimond structure (inc blende structure) ZnS CuF CuCl - ionic crstls; GAs GP InP- semiconductors in ionic crstls tetrhedrl sites re preferred becuse of the reltive sies of the positive nd negtive ions but not ll of them re filled to mintin stoichiometr These mterils hve their two components distributed on dimond lttice so tht ech hs four of the opposite tpe s nerest neighbors. This structure cn be described s FCC Brvis lttice with the twopoint bsis. fcc with two toms in the bse t (000) nd (¼ ¼ ¼) Alterntivel this structure cn be described s simple cubic Brvis lttice with 8-point bsis. The description is implemented in MSE67-CG code. Universit of Virgini MSE 70/670: Introduction to Atomistic Simultions Leonid Zhigilei