5.3. INTERNAL PARAMETERS FOR ATOMS, LATTICES

next, previous Section / Table of Contents / Index For clusters and general lattices (codes 10,-10) values of atomic radii may be determined as renormalized default radii according to respective nuclear charges such that maximum packing without overlapping spheres is achieved, see Secs. 6.2.1, 6.3.2. The internal table of default atomic radii (given in Angstroms) is shown in the following. charge radius charge radius charge radius charge radius ----------------- ----------------- ----------------- ----------------- 1 (H ) 0.4350 25 (Mn) 1.3500 48 (Cd) 1.4894 71 (Lu) 1.7515 2 (He) 1.4000 26 (Fe) 1.2411 49 (In) 1.6662 72 (Hf) 1.5973 3 (Li) 1.5199 27 (Co) 1.2535 50 (Sn) 1.5375 73 (Ta) 1.4280 4 (Be) 1.1430 28 (Ni) 1.2460 51 (Sb) 1.4000 74 (W ) 1.3705 5 (B ) 0.9750 29 (Cu) 1.2780 52 (Te) 1.3600 75 (Re) 1.3800 6 (C ) 0.6550 30 (Zn) 1.3325 53 (I ) 1.3300 76 (Os) 1.3676 7 (N ) 0.7500 31 (Ga) 1.3501 54 (Xe) 2.2000 77 (Ir) 1.3573 8 (O ) 0.7300 32 (Ge) 1.2248 55 (Cs) 2.6325 78 (Pt) 1.3873 9 (F ) 0.7200 33 (As) 1.2000 56 (Ba) 2.1705 79 (Au) 1.4419 10 (Ne) 1.6000 34 (Se) 1.1600 57 (La) 1.8725 80 (Hg) 1.5025 11 (Na) 1.8579 35 (Br) 1.1400 58 (Ce) 1.8243 81 (Tl) 1.7283 12 (Mg) 1.6047 36 (Kr) 2.0000 59 (Pr) 1.8362 82 (Pb) 1.7501 13 (Al) 1.4318 37 (Rb) 2.4700 60 (Nd) 1.8295 83 (Bi) 1.4600 14 (Si) 1.1758 38 (Sr) 2.1513 61 (Pm) 1.8090 84 (Po) 1.4600 15 (P ) 1.0600 39 (Y ) 1.8237 62 (Sm) 1.8040 85 (At) 1.4500 16 (S ) 1.0200 40 (Zr) 1.6156 63 (Eu) 1.9840 86 (Rn) 1.4300 17 (Cl) 0.9900 41 (Nb) 1.4318 64 (Gd) 1.8180 87 (Fr) 2.5000 18 (Ar) 1.9000 42 (Mo) 1.3626 65 (Tb) 1.8005 88 (Ra) 2.1400 19 (K ) 2.2620 43 (Tc) 1.3675 66 (Dy) 1.7951 89 (Ac) 1.8775 20 (Ca) 1.9758 44 (Ru) 1.3529 67 (Ho) 1.7886 90 (Th) 1.7975 21 (Sc) 1.6545 45 (Rh) 1.3450 68 (Er) 1.7794 91 (Pa) 1.6086 22 (Ti) 1.4755 46 (Pd) 1.3755 69 (Tm) 1.7687 92 (U ) 1.5683 23 (V ) 1.3090 47 (Ag) 1.4447 70 (Yb) 1.9396 93-100 1.0000 24 (Cr) 1.2490 In addition to a free definition of lattices (lattice codes 10, -10), structure parameters for 9 different standard lattices as well as for all 14 Bravais lattices are defined internally and can be selected by respective lattice code numbers inside a LATTICE session. The following tables list all internal parameters. A) Lattice types ----------------------------------------------------------- code (NTYP) internal title lattice type ----------------------------------------------------------- 1 sc simple cubic 2, -2 fcc face centered cubic 3, -3 bcc body centered cubic 4, -4 hcp (hex+2) hexagonal closed packed 5, -5 diamond(fcc+2) diamond 6, -6 NaCl (fcc+2) sodium chloride 7 CsCl (sc+2) cesium chloride 8, -8 Znblnde(fcc+2) cubic Zincblende 9, -9 Graphite Graphite 10, -10 free lattice 10 Bravais # 1 triclinic-P 10 Bravais # 2 monoclinic-P 10 Bravais # 3 monoclinic-C 10 Bravais # 4 orthorhombic-P 10 Bravais # 5 orthorhombic-C 10 Bravais # 6 orthorhombic-I 10 Bravais # 7 orthorhombic-F 10 Bravais # 8 tetragonal-P 10 Bravais # 9 tetragonal-I 10 Bravais # 10 hexagonal-P 10 Bravais # 11 trigonal-R 10 Bravais # 12 cubic-P 10 Bravais # 13 cubic-I 10 Bravais # 14 cubic-F ----------------------------------------------------------- B) Lattice parameters B1) Standard lattices The following tables give, for each of the 9 standard lattices, cartesian coordinates of all lattice vectors of the real and reciprocal lattice and coordinates of all lattice basis vectors of non-primitive lattices. Also shown are default nuclear charges and atom/ion radii. The radii are calculated for touching spheres of maximum space filling and are used to determine the packing ratio (defined as the relative amount of space filled by the spheres). The point symmetry elements of the lattices reflect the point symmetry groups the cubic group for sc, fcc,bcc, NaCl, CsCl lattices, the tetrahedral group for diamond, cubic ZnS lattices, the reduced hexagonal group for hcp, graphite lattices. The symmetry labels and vectors (vx,vy,vz) are defined as "1" for identity operation with (vx,vy,vz) denoting the lattice origin, "I" for inversion operation with (vx,vy,vz) denoting the lattice origin, "Cn" for n-fold rotational axes with (vx,vy,vz) pointing along the axis (only n = 1, 2, 3, 4, 6 are meaningful), "Mn" for n-fold mirror planes with (vx,vy,vz) pointing along the mirror plane normal. Here n = 2 denotes standard mirror planes while n = 3, 4, 6 refer to n-fold rotations combined with inversions. In the following all coordinates in real space are given as multiples of the lattice constant A, those of the reciprocal space as multiples of 1/A. The numerical values are taken from BALSAC output (all parameters are defined internally with full REAL*8 accuracy). a) simple cubic lattice (lattice code = 1). lattice vectors reciprocal lattice vectors x y z x y z R1 1.00000 0.00000 0.00000 G1 6.28319 0.00000 0.00000 R2 0.00000 1.00000 0.00000 G2 0.00000 6.28319 0.00000 R3 0.00000 0.00000 1.00000 G3 0.00000 0.00000 6.28319 1 lattice basis vector x y z atom/ion radius nuclear charge r1 0.00000 0.00000 0.00000 0.5000 1 (H) packing ratio = 0.52360 48 symmetry operations : 1x1, 9xC2, 8xC3, 6xC4, 1xI, 9xM2, 8xM3, 6xM4 type(s) vector (x, y, z) 1 , I .000000 .000000 .000000 C2,C4,M2,M4 1.000000 .000000 .000000 C2,C4,M2,M4 .000000 1.000000 .000000 C2,C4,M2,M4 .000000 .000000 1.000000 C2, M2 .707107 .707107 .000000 C2, M2 .707107 -.707107 .000000 C2, M2 .707107 .000000 .707107 C2, M2 .707107 .000000 -.707107 C2, M2 .000000 .707107 .707107 C2, M2 .000000 .707107 -.707107 C3, M3 .577350 .577350 .577350 C3, M3 .577350 .577350 -.577350 C3, M3 .577350 -.577350 .577350 C3, M3 .577350 -.577350 -.577350 b) face centered cubic lattice (lattice code = 2, -2). lattice vectors reciprocal lattice vectors x y z x y z R1 0.00000 0.50000 0.50000 G1 -6.28319 6.28319 6.28319 R2 0.50000 0.00000 0.50000 G2 6.28319 -6.28319 6.28319 R3 0.50000 0.50000 0.00000 G3 6.28319 6.28319 -6.28319 1 lattice basis vector x y z atom/ion radius nuclear charge r1 0.00000 0.00000 0.00000 0.3536 13 (Al) packing ratio = 0.74048 48 symmetry operations : see simple cubic lattice c) body centered cubic lattice (lattice code = 3, -3). lattice vectors reciprocal lattice vectors x y z x y z R1 -0.50000 0.50000 0.50000 G1 0.00000 6.28319 6.28319 R2 0.50000 -0.50000 0.50000 G2 6.28319 0.00000 6.28319 R3 0.50000 0.50000 -0.50000 G3 6.28319 6.28319 0.00000 1 lattice basis vector x y z atom/ion radius nuclear charge r1 0.00000 0.00000 0.00000 0.4330 26 (Fe) packing ratio = 0.68017 48 symmetry operations : see simple cubic lattice d) hexagonal closed packed lattice (lattice code = 4, -4) defined as hexagonal with 2 atoms per unit cell. lattice vectors reciprocal lattice vectors x y z x y z R1 1.00000 0.00000 0.00000 G1 6.28319 -3.62760 0.00000 R2 0.50000 0.86603 0.00000 G2 0.00000 7.25520 0.00000 R3 0.00000 0.00000 1.63299 G3 0.00000 0.00000 3.84765 2 lattice basis vectors x y z atom/ion radius nuclear charge r1 0.00000 0.00000 0.00000 0.5000 27 (Co) r2 0.50000 0.28870 0.81650 0.5000 27 (Co) packing ratio = 0.74048 12 symmetry operations : 1x1, 3xC2, 2xC3, 4xM2, 2xM6 type(s) vector (x, y, z) 1 .000000 .000000 .000000 C2 .866025 .500000 .000000 C2 .866025 -.500000 .000000 C2 .000000 1.000000 .000000 C3,M2,M6 .000000 .000000 1.000000 M2 1.000000 .000000 .000000 M2 .500000 .866025 .000000 M2 .500000 -.866025 .000000 e) diamond lattice (lattice code = 5, -5) defined as face centered cubic with 2 atoms per unit cell. lattice vectors reciprocal lattice vectors x y z x y z R1 0.00000 0.50000 0.50000 G1 -6.28319 6.28319 6.28319 R2 0.50000 0.00000 0.50000 G2 6.28319 -6.28319 6.28319 R3 0.50000 0.50000 0.00000 G3 6.28319 6.28319 -6.28319 2 lattice basis vectors x y z atom/ion radius nuclear charge r1 0.00000 0.00000 0.00000 0.2165 6 (C) r2 0.25000 0.25000 0.25000 0.2165 6 (C) packing ratio = 0.34009 24 symmetry operations : 1x1, 3xC2, 8xC3, 6xM2, 6xM4 type(s) vector (x, y, z) 1 .000000 .000000 .000000 C2, M4 1.000000 .000000 .000000 C2, M4 .000000 1.000000 .000000 C2, M4 .000000 .000000 1.000000 C3 .577350 .577350 .577350 C3 .577350 .577350 -.577350 C3 .577350 -.577350 .577350 C3 .577350 -.577350 -.577350 M2 .707107 .707107 .000000 M2 .707107 -.707107 .000000 M2 .707107 .000000 .707107 M2 .707107 .000000 -.707107 M2 .000000 .707107 .707107 M2 .000000 .707107 -.707107 f) sodium chloride lattice (lattice code = 6, -6) defined as face centered cubic with 2 atoms per unit cell. The radii ratio r(Na)/r(Cl) = 0.525 is taken from Coulson's tables of ionic radii. lattice vectors reciprocal lattice vectors x y z x y z R1 0.00000 0.50000 0.50000 G1 -6.28319 6.28319 6.28319 R2 0.50000 0.00000 0.50000 G2 6.28319 -6.28319 6.28319 R3 0.50000 0.50000 0.00000 G3 6.28319 6.28319 -6.28319 2 lattice basis vectors x y z atom/ion radius nuclear charge r1 0.00000 0.00000 0.00000 0.1721 11 (Na) r2 0.00000 0.00000 0.50000 0.3279 17 (Cl) packing ratio = 0.67599 48 symmetry operations : see simple cubic lattice g) cesium chloride lattice (lattice code = 7) defined as simple cubic with 2 atoms per unit cell. Ratio of radii r(Cs)/r(Cl) = 0.934 is taken from Coulson's tables of ionic radii. lattice vectors reciprocal lattice vectors x y z x y z R1 1.00000 0.00000 0.00000 G1 6.28319 0.00000 0.00000 R2 0.00000 1.00000 0.00000 G2 0.00000 6.28319 0.00000 R3 0.00000 0.00000 1.00000 G3 0.00000 0.00000 6.28319 2 lattice basis vectors x y z atom/ion radius nuclear charge r1 0.00000 0.00000 0.00000 0.4182 55 (Cs) r2 0.50000 0.50000 0.50000 0.4478 17 (Cl) packing ratio = 0.68255 48 symmetry operations : see simple cubic lattice h) cubic Zincblende lattice (lattice code = 8, -8) defined as face centered cubic with 2 atoms per unit cell. Ratio of radii r(Zn)/r(S) = 0.476 is taken from Coulson's tables of ionic radii. lattice vectors reciprocal lattice vectors x y z x y z R1 0.00000 0.50000 0.50000 G1 -6.28319 6.28319 6.28319 R2 0.50000 0.00000 0.50000 G2 6.28319 -6.28319 6.28319 R3 0.50000 0.50000 0.00000 G3 6.28319 6.28319 -6.28319 2 lattice basis vectors x y z atom/ion radius nuclear charge r1 0.00000 0.00000 0.00000 0.1396 30 (Zn) r2 0.25000 0.25000 0.25000 0.2934 16 (S) packing ratio = 0.46868 24 symmetry operations : see diamond lattice i) Graphite lattice (lattice code = 9, -9) defined as hexagonal with 4 atoms per unit cell. A lattice constant ratio c/a = 2.72 is used as default. lattice vectors reciprocal lattice vectors x y z x y z R1 1.00000 0.00000 0.00000 G1 6.28319 -3.62760 0.00000 R2 0.50000 0.86603 0.00000 G2 0.00000 7.25520 0.00000 R3 0.00000 0.00000 2.72000 G3 0.00000 0.00000 2.30999 4 lattice basis vectors x y z atom/ion radius nuclear charge r1 0.00000 0.00000 0.00000 0.2887 6 (C) r2 0.50000 0.28870 0.00000 0.2887 6 (C) r3 0.00000 0.00000 1.36000 0.2887 6 (C) r4 1.00000 0.57740 1.36000 0.2887 6 (C) packing ratio = 0.17111 12 symmetry operations : see hexagonal closed packed lattice B1) Bravais lattices The following table gives, for each of the 14 Bravais lattices, all parameters necessary to define the lattice and cartesian coordinates of all lattice vectors R1, R2, R3 with lengths |R1| = a, |R2| = b, |R3| = c, and angles <(R1,R2) = v12, <(R1,R3) = v13, <(R2,R3) = v23. Further, we define cij = cos(vij) , sij = sin(vij) , i,j = 1, 2, 3. a) Triclinic-P lattice Lattice without symmetry (apart from inversion). Parameters a, b, c, v12, v13, v23 required. R1 = a ( 1, 0, 0 ) R2 = b ( c12, s12, 0 ) R3 = c ( c13, (c23-c13*c12)/s12, sqrt(1-c12**2-c13**2-c23**2+c12*c13*c23)/s12 ) 2 symmetry operations : 1x1, 1xI type(s) vector (x, y, z) 1 , I .000000 .000000 .000000 b) Monoclinic-P lattice Three different angular cases: Case 1: v23, v13 = v12 = 90, vector R1 perpendicular to R2, R3. Parameters a, b, c, v23 required (all tree angles must be given). R1 = a ( 1, 0, 0 ) R2 = b ( 0, 1, 0 ) R3 = c ( 0, c23, s23 ) 4 symmetry operations : 1x1, 1xC2, 1xI, 1xM2 type(s) vector (x, y, z) 1 , I .000000 .000000 .000000 C2,M2 1.000000 .000000 .000000 Case 2: v13, v23 = v12 = 90, vector R2 perpendicular to R1, R3. Parameters a, b, c, v13 required (all tree angles must be given). R1 = a ( 1, 0, 0 ) R2 = b ( 0, 1, 0 ) R3 = c ( c13, 0, s13 ) 4 symmetry operations : 1x1, 1xC2, 1xI, 1xM2 type(s) vector (x, y, z) 1 , I .000000 .000000 .000000 C2,M2 .000000 1.000000 .000000 Case 3: v12, v13 = v23 = 90, vector R3 perpendicular to R1, R2. Parameters a, b, c, v12 required (all tree angles must be given). R1 = a ( 1, 0, 0 ) R2 = b ( c12, s12, 0 ) R3 = c ( 0, 0, 1 ) 4 symmetry operations : 1x1, 1xC2, 1xI, 1xM2 type(s) vector (x, y, z) 1 , I .000000 .000000 .000000 C2,M2 .000000 .000000 1.000000 c) Monoclinic-C lattice Three different angular cases: Case 1: v23, v13 = v12 = 90, R1/R3 plane centered. Parameters a, b, c, v23 required (all tree angles must be given). R1 = a ( 1/2, -c23/2, -s23/2 ) R2 = b ( 0, 1, 0 ) R3 = c ( 1/2, c23/2, s23/2 ) 4 symmetry operations : see monoclinic-P lattice Case 2: v13, v23 = v12 = 90, R1/R2 plane centered. Parameters a, b, c, v13 required (all tree angles must be given). R1 = a ( .5, .5, 0 ) R2 = b ( -.5, .5, 0 ) R3 = c ( c13, 0, s13 ) 4 symmetry operations : see monoclinic-P lattice Case 3: v12, v13 = v23 = 90, vector R3 perpendicular to R1, R2. Parameters a, b, c, v12 required (all tree angles must be given). R1 = a ( 1, 0, 0 ) R2 = b ( c12/2, s12/2, 1/2 ) R3 = c ( -c12/2, -s12/2, 1/2 ) 4 symmetry operations : see monoclinic-P lattice d) Orthorhombic-P lattice Vectors R1, R2, R3 perpendicular to each other. Parameters a, b, c required. R1 = ( a, 0, 0 ) R2 = ( 0, b, 0 ) R3 = ( 0, 0, c ) 8 symmetry operations : 1x1, 3xC2, 1xI, 3xM2 type(s) vector (x, y, z) 1 , I .000000 .000000 .000000 C2,M2 1.000000 .000000 .000000 C2,M2 .000000 1.000000 .000000 C2,M2 .000000 .000000 1.000000 e) Orthorhombic-C lattice Vectors R1, R2, R3 perpendicular to each other. Plane R1/R2 is centered rectangular. Parameters a, b, c required. R1 = 1/2 ( a, -b, 0 ) R2 = 1/2 ( a, b, 0 ) R3 = ( 0, 0, c ) 8 symmetry operations : see orthorhombic-P lattice f) Orthorhombic-I lattice Vectors R1, R2, R3 perpendicular to each other. One additional atom in cell center. Parameters a, b, c required. R1 = 1/2 ( a, -b, c ) R2 = 1/2 ( a, b, -c ) R3 = 1/2 ( -a, b, c ) 8 symmetry operations : see orthorhombic-P lattice g) Orthorhombic-F lattice Vectors R1, R2, R3 perpendicular to each other. Planes R1/R2, R1/R3, R2/R3 are centered rectangular. Parameters a, b, c required. R1 = 1/2 ( a, 0, c ) R2 = 1/2 ( a, b, 0 ) R3 = 1/2 ( 0, b, c ) 8 symmetry operations : see orthorhombic-P lattice h) Tetragonal-P lattice Vectors R1, R2, R3 perpendicular to each other with |R1| = |R2| = a. Parameters a, c required. R1 = ( a, 0, 0 ) R2 = ( 0, a, 0 ) R3 = ( 0, 0, c ) 16 symmetry operations : 1x1, 5xC2, 2xC4, 1xI, 5xM2, 2xM4 type(s) vector (x, y, z) 1 , I .000000 .000000 .000000 C2,M2 1.000000 .000000 .000000 C2,M2 .000000 1.000000 .000000 C2,C4,M2,M4 .000000 .000000 1.000000 C2,M2 .707107 .707107 .000000 C2,M2 .707107 -.707107 .000000 i) Tetragonal-I lattice Vectors R1, R2, R3 perpendicular to each other with |R1| = |R2| = a. One additional atom in cell center. Parameters a, c required. R1 = 1/2 ( a, -a, c ) R2 = 1/2 ( a, a, -c ) R3 = 1/2 ( -a, a, c ) 16 symmetry operations : see tetragonal-P lattice j) Hexagonal-P lattice Vectors R3 perpendicular R1, R2 with |R1| = |R2| = a and v12 = 120. Parameters a, c required. R1 = a ( q, -1/2, 0 ) R2 = a ( 0, 1, 0 ) q = sqrt(3/4) R3 = c ( 0, 0, 1 ) 24 symmetry operations : 1x1, 7xC2, 2xC3, 2xC6, 1xI, 7xM2, 2xM3, 2xM6 type(s) vector (x, y, z) 1 , I .000000 .000000 .000000 C2,C3,C6,M2,M3,M6 .000000 .000000 1.000000 C2, M2 1.000000 .000000 .000000 C2, M2 .866025 .500000 .000000 C2, M2 .866025 -.500000 .000000 C2, M2 .500000 .866025 .000000 C2, M2 .500000 -.866025 .000000 C2, M2 .000000 1.000000 .000000 k) Trigonal-R lattice Vectors R1, R2, R3 form an equilateral rhombohedron where |R1| = |R2| = |R3| = a and v12 = v13 = v23 . Parameters a, v12 < 120 required. R1 = a ( p12, 0, q12 ) p12 = sqrt( (1-c12)*2/3 ) R2 = a ( -p12/2, p12*q, q12 ) q = sqrt(3/4) R3 = a ( -p12/2, -p12*q, q12 ) q12 = sqrt( 1- p12**2 ) 12 symmetry operations : 1x1, 3xC2, 2xC3, 1xI, 3xM2, 2xM3 type(s) vector (x, y, z) 1 , I .000000 .000000 .000000 C3, M3 .000000 .000000 1.000000 C2, M2 .000000 1.000000 .000000 C2, M2 .866025 .500000 .000000 C2, M2 .866025 -.500000 .000000 l) Cubic-P lattice Vectors R1, R2, R3 perpendicular to each other with |R1| = |R2| = |R3| = a. Parameter a required. R1 = a ( 1, 0, 0 ) R2 = a ( 0, 1, 0 ) R3 = a ( 0, 0, 1 ) 48 symmetry operations : 1x1, 9xC2, 8xC3, 6xC4, 1xI, 9xM2, 8xM3, 6xM4 type(s) vector (x, y, z) 1 , I .000000 .000000 .000000 C2,C4,M2,M4 1.000000 .000000 .000000 C2,C4,M2,M4 .000000 1.000000 .000000 C2,C4,M2,M4 .000000 .000000 1.000000 C2, M2 .707107 .707107 .000000 C2, M2 .707107 -.707107 .000000 C2, M2 .707107 .000000 .707107 C2, M2 .707107 .000000 -.707107 C2, M2 .000000 .707107 .707107 C2, M2 .000000 .707107 -.707107 C3, M3 .577350 .577350 .577350 C3, M3 .577350 .577350 -.577350 C3, M3 .577350 -.577350 .577350 C3, M3 .577350 -.577350 -.577350 m) Cubic-I (bcc) lattice Vectors R1, R2, R3 perpendicular to each other with |R1| = |R2| = |R3| = a. One additional atom in cell center. Parameter a required. R1 = a/2 ( 1, -1, 1 ) R2 = a/2 ( 1, 1, -1 ) R3 = a/2 ( -1, 1, 1 ) 48 symmetry operations : see cubic-P lattice n) Cubic-f (fcc) lattice Vectors R1, R2, R3 perpendicular to each other with |R1| = |R2| = |R3| = a. Planes R1/R2, R1/R3, R2/R3 are centered square. Parameter a required. R1 = a/2 ( 1, 0, 1 ) R2 = a/2 ( 1, 1, 0 ) R3 = a/2 ( 0, 1, 1 ) 48 symmetry operations : see cubic-P lattice The following table lists lattices and lattice constants a (in Angstroms) for the most common elements as taken from R. W. G. Wyckoff, "Crystal Structures", Interscience, New York 1963. Nearly closed packed hexagonal lattices are denoted by hcp and the two lattice constants a/c of the hexagonal lattice are given. charge lattice a (a/c) charge lattice a (a/c) ------------------------------ ------------------------------ 2 (He) hcp 3.57/5.83 47 (Ag) fcc 4.09 3 (Li) bcc 3.49 48 (Cd) hcp 2.98/5.62 4 (Be) hcp 2.29/3.58 50 (Sn) diamond 6.49 6 (C ) diamond 3.57 54 (Xe) fcc 6.20 10 (Ne) fcc 4.43 55 (Cs) bcc 6.05 11 (Na) bcc 4.23 56 (Ba) bcc 5.02 12 (Mg) hcp 3.21/5.21 57 (La) fcc 5.30 13 (Al) fcc 4.05 57 (La) hcp 3.75/6.07 14 (Si) diamond 5.43 58 (Ce) fcc 5.16 18 (Ar) fcc 5.26 58 (Ce) hcp 3.65/5.96 19 (K ) bcc 5.23 59 (Pr) fcc 5.16 20 (Ca) fcc 5.58 59 (Pr) hcp 3.67/5.92 21 (Sc) fcc 4.54 60 (Nd) hcp 3.66/5.90 21 (Sc) hcp 3.31/5.27 64 (Gd) hcp 3.64/5.78 22 (Ti) hcp 2.95/4.69 65 (Tb) hcp 3.60/5.69 23 (V ) bcc 3.02 66 (Dy) hcp 3.59/5.65 24 (Cr) bcc 2.88 67 (Ho) hcp 3.58/5.62 26 (Fe) bcc 2.87 68 (Er) hcp 3.56/5.59 27 (Co) hcp 2.51/4.07 69 (Tm) hcp 3.54/5.55 27 (Co) fcc 3.55 70 (Yb) fcc 5.49 28 (Ni) fcc 3.52 71 (Lu) hcp 3.50/5.55 29 (Cu) fcc 3.61 72 (Hf) hcp 3.20/5.06 30 (Zn) hcp 2.66/4.95 73 (Ta) bcc 3.31 32 (Ge) diamond 5.66 74 (W ) bcc 3.16 36 (Kr) fcc 5.72 75 (Re) hcp 2.76/4.46 37 (Rb) bcc 5.59 76 (Os) hcp 2.74/4.32 38 (Sr) fcc 6.08 77 (Ir) fcc 3.84 39 (Y ) hcp 3.65/5.73 78 (Pt) fcc 3.92 40 (Zr) bcc 3.61 79 (Au) fcc 4.08 40 (Zr) hcp 3.23/5.15 81 (Tl) bcc 3.88 41 (Nb) bcc 3.30 81 (Tl) hcp 3.46/5.53 42 (Mo) bcc 3.15 82 (Pb) fcc 4.95 44 (Ru) hcp 2.70/4.28 90 (Th) fcc 5.08 45 (Rh) fcc 3.80 94 (Pu) fcc 4.64 46 (Pd) fcc 3.89 next, previous Section / Table of Contents / Index