Question

Q3. The surface energy of a new surface can be calculated based on the equation discussed in class: Where Nb is the number of bonds broken to create the surface, pa is the number of atoms per unit area of the new surface and ε is the bond strength. Considering an FCC structure with a lattice constant of a, using this equation the surface energy of different facets (or crystal planes) can be calculated For the (100) plane this was calculated in class as being: Show that for the (110) plane it will be: 5E Y1102a

Answer 1

In a cube all the edge length are equal AB = BC = CD = AE = a delta ABC is a right angle triangle where AB = a BC = a and CA is hypotenuse which is unknown Using Pythagoras theorem: In delta ABC (CA)^2 = (AB)^2 + (BC)^2 (CA)^2 = a^2 + a^2 (CA)^2 = 2a^2 CA = squareroot 2a According to the above figure plane 110 is ACDE surface area of rectangle ACDE = length times breadth \r\n = AE times CA implies a times squareroot 2a implies squareroot 2 a^2 so, surface area of plane 110 is squareroot 2a^2 implies To find Number of atoms in plane 110 According to the figure in surface ACDE implies atoms in the corner = 4 atoms at the face centre = 2 we know that a corner has 1/4 part of an atom is present at a face centre so, Total no of atoms at cornet is implies No of atoms at corner