Question

The atomic weights of Si and Al are very similar (28.09 and 26.98 g/mole, respectively), yet the densities of SiO, and Al,O, are quite different (2.65 and 3.98 g/cm2, respectively). Explain this difference in terms of crystal structure and Pauling's rules.

Answer 1

element At. Wt.Compounts Str. Name |Crystal Occupancy Densitygcm low 2.69 high 3.98 System Si 28.09 SiO2 quartzRhombohedral High or trigonal occupancy Al26.98Al203 Corundum Octahedral or Less terahedral occupancy SiO2 exibits crystal syastem having low occupacy while that of Al203 exibits crystal system having high occupancy therefore SiO2 having low density than Al203.

Rule 1: The ra dius ratio rule In case ionic solids, the cations are smaller than the anions, andeachcationis surrounded by coordinated arions which fom a polyhedron. The sum ofthe ionic radii detemines the cation-anion distance, while the cation-anionradius ratio detemines the coordinationnumbe (CN.)of the cation, as well as the shape ofthe coordinated polyhedronofanions. Forthe coordinationnumbers and corespondingpolyhedra in the table below Paulingmathematically derivedthe minimumradius ratio for which the cation is in contact with the givennumber ofanions (consideringthe ions asrigid spheres). If the cation is smaller, it will not be in contact with the anions whichresults in instability lea dingtolower coordinationnumber CN. Crystal System Radius ratio 3 triangular 0.155 4 tetrahedron 0.225 6 octahedron 0.414 8 cube 0.732 se in radius ofratio with mcrea mcreases coordination nurnber. That mcrease m 3% radius ratio increases coordination number from 4 to 6 and a gam 390 mcrease in radius ratio increases coordination number from 6 to Rule2: The electrostatic Valance rule: Accordingin a stable ionic structure the valence ofeach anion, with changed sign, e quals the sum ofthestrengths ofits electrostatic bonds to the adjacent cations.

Third 3: sharing of corners, edges and faces The sharing of edges and particularly faces by two anion decreases the stability of an ionic structure. The sharing of comers decrease stability small in amount. As by shairiın edge and faces cations come closer and there if cation- cation repulsive interactions. The effedt is lage for cations having high charge and low coordinationnumber Fourth 4: crystals containing different cations Ioniccontains compound containg various cations (those high valency and low C.N.) doesn't shair anions. By which cation increases distance between cation and get stability Fifth 5: the rule ofparsimon;y The repeating units will tend to be identical because each atom in the structure is most stable in a specific polyhedra, such as tetrahedra or octahedra, but there will