Quiz 2.2 (Imperfections in Solids) PDF

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QUIZ – IMPERFECTIONS IN SOLIDS NAME KRISTINA MAJA SALINAS I.

II.

DATE MAY 29, 2021

Identify the following: Self-Interstitial _________________1. An atom from the crystal that is crowded into a small void space that under ordinary circumstances in not occupied. Electroneutrality _________________2. It is the state that exists when there are equal numbers of positive and negative charges from the ions. Schotty Defect _________________3. Structure defect wherein there are cation vacancy – anion vacancy pair. Dislocation _________________4. It is a linear or one-dimensional defect around which some of the atoms are misaligned. Screw Dislocation _________________5. It is thought of as being formed by a shear stress that is applied to produce distortion as a result of the shift of the upper front region of the crystal one atomic distance to the right relative to the bottom portion. Grain boundary _________________6. The boundary separating two small grains or crystals having different crystallographic orientations in polycrystalline materials. Edge Dislocation _________________7. It is a linear defect that centers around the line that is defined along the end of the extra half-plane of atoms. Twin _________________8. It is a special type of grain boundary across which there is specific mirror lattice symmetry. Frenkel Defect _________________9. Structure defect with a cation-vacancy and a cationinterstitial pair. _________________10. Boundaries that have two dimensions and normally Interfacial Defects separate regions of the materials that have different crystal structures and/or crystallographic orientations. Solve the following: 1. Calculate the energy for vacancy formation in silver, given that the equilibrium number of vacancies at 800oC is 3.6 x 1023 atoms/m3. The atomic weight and density for silver are107.9 g/mol and 9.5 g/cm3, respectively. Given : T =800 °C +273=1073 K N D =3.6 x 10 23 m 3 eV −5 k =8.62 x 10 atm∙ K Solution : −Q D ND =exp N kT

( )

ρ Ag ∙ N A A Ag atm 6.023 x 1023 mol N=

g 9.5 ( c m )( N= 3

(

)

)

x

(

100 cm 1m

)

3

g mol 28 3 N=5.30 x 10 atm /m −Q D 3.6 x 1023 m 3 =exp 28 3 eV 5.30 x 10 atm /m −5 8.62 x 10 ( 1073 k ) atm ∙ K 107.87

((

Q D =1.10

)

)

eV atm

2. What is the composition in weight percent of an alloy that consists of 30 atom% Zn (atomic weight = 65.38 g/mol) and 70 atom% Cu (atomic weight = 63.54 g/mol)? C ' Zn A Zn % wt Zn = x 100 C 'Zn A Zn +C ' Cu A Cu g ( 30 ) 65.38 mol x 100 % wt Zn = g g +( 70 ) 64.54 ( 30) 65.38 mol mol % wt Zn =30.6 % Zn C ' Cu A Cu % wt Cu= x 100 C ' Zn A Zn + C ' Cu ACu g ( 70 ) 63.54 mol x 100 % wt Cu= g g +( 70 ) 64.54 ( 30) 65.38 mol mol % wt Cu=69.4 %Cu

(

(

)

) (

(

(

)

)

) (

)

Composition∈weight percent of an alloy :30.6 % Zn∧69.4 % Cu

3. What is the composition, in atom percent, of an alloy that contains 98 g Sn (AW = 118.70 g/mol) and 65 g Pb (AW = 207.21 g/mol)? m Sn 98 g =0.83mol = nSn= A sn 118.70 g /mol m 65 g =0.31 mol n Pb= Pb = A Pb 207.21 g /mol 0.83 mol %atomSn = x 100 0.83 mol+ 0.31 mol

%atomSn =72.8 %Sn 0.31 mol %atom Pb = x 100 0.83 mol+ 0.31 mol %atom Pb=27.2 % Pb Composition∈atom percent of an alloy :72.86 %Sn ∧69.4 % Pb 4. Germanium forms a substitutional solid solution with silicon. Compute the number of germanium atoms per cubic centimeter for a germanium-silicon ally that contains 15 wt% Ge and 85 wt% Si. The densities of pure germanium and silicon are 5.32 g/cm3and 2.33 g/cm3, respectively. The atomic weight of germanium is 72.60 g/mol. N A C¿ C¿ A ¿ A ¿ ( 100−C ¿ ) + ρ¿ ρ Si 23 atm ( 15 wt % ) 6.023 x 10 mol

N ¿=

N ¿=

(

)

(

( 15 wt % ) 72.64 3

5.32 g /c m

) + 72.64 molg ( 100−15 wt %)

g mol

2.33 g /c m 3

21

3

N ¿ =3.16 x 10 atoms/c m...