How (111) plane of FCC and (0001) plane of HCP is similar?

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(111) planes of fcc have the same arrangement as (0001) plane of hcp crystal

(111) planes of fcc have the same arrangement as (0001) plane of hcp crystal

See lessFor a plane to be similar first and foremost criteria is to have equal packing efficiency of planes(arrangements of atoms may be different) i.e. Planar Density. Formula for calculating Planar density = Number of atoms lying on that plane/ Area of that plane First take (111) plane of FCC Number of atRead more

For a plane to be similar first and foremost criteria is to have equal packing efficiency of planes(arrangements of atoms may be different) i.e. Planar Density.

Formula for calculating Planar density = Number of atoms lying on that plane/ Area of that plane

First take (111) plane of FCC

Number of atom = 1/6×3+ 1/2×3 = 2

Area of plane= 4✓3 r^2

Upon calculation you will get Planar density= 1/2✓3r^2

Now take (0001) plane of HCP

Number of atom = 1/3×6 + 1= 3

Area of plane = 6✓3r^2

Upon calculating you will get Planar density= 1/2✓3r^2

As you can see we got equal Planar density of planes (111) and (0001) that’s the reason why both planes are considered similar.

See lessHCP crystal structure is the mathematical gimmick of FCC crystal with following similarities: same atomic sequence (ABC,ABC...); same packing efficiency 0.74; same coordination number 12. Ref. Principles of Physical Metallurgy by Robert Reedhill. Now atomic density of (111) in FCC is 3x(1/3)+(1/2)×3Read more

HCP crystal structure is the mathematical gimmick of FCC crystal with following similarities: same atomic sequence (ABC,ABC…); same packing efficiency 0.74; same coordination number 12. Ref. Principles of Physical Metallurgy by Robert Reedhill. Now atomic density of (111) in FCC is 3x(1/3)+(1/2)×3=2(1/2); in (0001) of HCP is (1/2)x1+6×(1/3)=2(1/2). Therefore both are similar. Got it?

See lessAtomic configuration is same in both planes (1 1 1) in fcc and {0 0 0 1} in hcp.

Atomic configuration is same in both planes (1 1 1) in fcc and {0 0 0 1} in hcp.

See less