Question

1. Listed below are the atomic weight, density, and atomic radius for three hypothetical alloys. For each determine its crystal structure and then justify your determination.

Alloy // Atomic weight (g/mol) // Density (g/ cm^3) // Atomic Radius (nm)

A // 43.1 // 6.4 // 0.122

B   // 184.4 // 12.3 // 0.146

C // 91.6 // 9.6 // 0.137

Answer 1

Solution to this problem is based on the trial and error method. There are three basic crystal structures, SC, BCC and FCC. (simple cubic, body centered cubic and face centered cubic).

density of unit cell = n*Aw/a³*N_A ; Aw atomic weight, n = no.of atoms in unit cell (1-SC, 2-BCC and 4-FCC), NA Avagadro's number, a-lattice parameter. a = 2R, 4/3^1/2 R and 2*2^1/2 R for SC, BCC and FCC respectively.

Calculated the unit cell density using the values given in the question for all the three structures and compare the density with the atomic density given for the alloy. The one that matches closely suggests the crystal structure of the alloy. The calculated values are listed below

Awt.	A.radius	SC	FCC	BCC
4.31	0.122	0.492601	0.696642	0.639907
184.4	0.146	12.29701	17.3906	15.97428
91.6	0.137	7.393174	10.45553	9.604015

Alloy A and C, has BCC structure (Note: the density of alloy A may be typed wrongly in the question)

Alloy B has SC structure.