Question

Name: MCEG-2023 Engineering Materlals June 14 2019 QUIZ Take home quiz, due on Monday, June 17 Q1. Calculate the number of vacancies per cubic meter in gold (Au) at 900 C. The energy for vacancy formation is 0.98 ev/atom. Furthermore, the density and atomic weight for Au are 18.63 g/cm3 (at 900 C) and 196.9 g/mol, respectively. Q2. Atomic radius, crystal structure, electronegativity, and the most common valence are given in the following table for several elements; for those that are nonmetals, only atomic radi are indicated. Atemic Radie Electre- argativity Valence Crystal Structare Which of these elements would you expect to Element (am) +2 form the following with nickel 18 0.1246 FCC Ni (a) a substitutional solid solution having 0.071 C 0046 complete solubility 0.060 (b) a substitutional solid solution of +1 1,9 FOC 0.1445 incomplete solubility (c) an interstitial solid solution Ag +3 15 FCC Al 0.1431 +2 18 01253 НСР Co +3 16 BCC 0.1249 Cr +2 18 0.1241 BCC Fe +2 22 0.1387 FCC PI +2 16 НСР 0.1332 ZI Page 1 of 2

Answer 1

${\displaystyle N_{\rm {v}}=N\exp(-Q_{\rm {v}}/k_{\rm {B}}T)}$

N_v is the vacancy concentration

Q_v is the energy required for vacancy formation 0.98 eV/atom

k_B is the Boltzmann constant = 8.62 x 10^-5 eV/atom-K

T is the absolute temperature = 1173K

N is the concentration of atomic sites

${\displaystyle N=\rho N_{\rm {A}}/A}$

ρ is density = 18.63 g/cm3

N_A Avogadro constant = 6.022x10²³

A the atomic mass = 196.9 g/mol

Nv = (18.63x6.022x10²³/196.9)*exp (0.98 eV/atom/( 8.62 x 10^-5 eV/atom-K*1173K))

Nv = 3.52 x 10¹⁸ cm^-3 = 3.52 x 10²⁴ m^-3

(b)

                In this question, we are asked to choose which of the elements listed form with Ni the three possible solid solution types. For complete substitutional solubility the following criteria need to be met:

1) the difference in atomic radii between Ni and the other element (DR%) must be less than ±15%

2) the crystal structures must be the same

3) the electronegativities must be similar

4) the valencies should be the same or nearly the same.

                                                  Crystal

                          Element          DR%                   Structure Electronegativity   Valence

                          Ni                                                     FCC                                                         2+

                          C                        –43

                          H                       –63

                          O                       –52

                          Ag                     +16                        FCC                        +0.1                          1+

                          Al                      +15                        FCC                        -0.3                          3+

                          Co                     +0.6                        HCP                           0                            2+

                          Cr                      +0.2                        BCC                        -0.2                          3+

                          Fe                      -0.4                        BCC                          0                            2+

                          Pt                       +11                        FCC                        +0.4                          2+

                          Zn                       +7                         HCP                        -0.2                          2+

(a) Pt is the only element that meets all of the criteria and thus forms a substitutional solid solution having complete solubility. At high temperatures Co and Fe experience allotropic transformations to the FCC crystal structure, and thus display complete solid solubility at these temperatures.

(b) Ag, Al, Co, Cr, Fe, and Zn form substitutional solid solutions of incomplete solubility. All these metals have either BCC or HCP crystal structures, and/or the difference between their atomic radii and that for Ni is greater than ±15%, and/or have a valency other than 2+.

(c) C, H, and O form interstitial solid solutions. These elements have atomic radii that are significantly smaller than the atomic radius of Ni.

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