Q. 254.0( 2 Votes )

Which of the following statement is not true about the hexagonal close packing?
A. The coordination number is 12.

B. It has 74% packing efficiency.

C. Tetrahedral voids of the second layer are covered by the spheres of the third layer.

D. In this arrangement spheres of the fourth layer are exactly aligned with those of the first layer.

Answer :

Hexagonal close-packed crystal structure forms only when the centres of spheres in the 3rd layer are vertically above the centres of first layer (A) as the 2nd layer is placed in only one type of depressions of the 1st layer( at each junction of spheres ).


This depression gives rise to voids which by placing new layer of spheres i.e. the 3rd one (also A) can be covered well.


This third layer has to resemble the first layer because layer 1 and layer must be in the same alignment and thus the pattern of spheres is repeated in alternate layers. That is why, this pattern is often written as ABAB .......pattern.



Unlike in ccp which is the actual case for (iv).


The coordination number is 12 – it is true as in hcp each sphere in a layer is surrounded by 6 spheres in the same plane , 3 spheres above it and 3 spheres below it – therefore making a total 12 which is the coordination number for this arrangement.


(iii) It has 74% packing efficiency – also true as it resembles with ccp in efficiency it can be calculated in accordance with ccp structure ;


hex2.png


If the unit cell edge length= a and face diagonal AC=b


Then in right angled triangle ∆ ABC , AC2 or b2 =BC2+AB2= (a2+a2)=2a2


Or , b=√2a


if r is the radius of the sphere, then b=r +2r+r=4r=√2a


or, a=4r/√2=2√2r (i.e. r=a/2√2)


it is known that each unit cell in ccp/hcp arrangement has effectively four spheres.


Hence , the total volume occupied by four sphere is = to 4×(4/3)πr3 and


Therefore, volume of the cube = a3 = (2√2r)3.


Therefore, packing efficiency= (volume occupied by 4 spheres in unit cell/ total volume of the unit cell )×100℅


= 4×(4/3)πr3/(2√2r)3 ×100%=74%


Tetrahedral voids of the second layer are covered by the spheres of the third layer –


this is also a true fact for hcp , because When a sphere of the second layer(B) is placed above the void of the first layer (A) always tetrahedral void is formed this is because a tetrahedron forms when the centres of four spheres are joined and this tetrahedral voids can be totally covered by the placement of a 3rd layer (A) above them.


hhh.jpg

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