Surface energy is the sum of the energies of all surfaces and the preferred shape of...

Surface energy is the sum of the energies of all surfaces and the preferred shape of a crystal that is bounded by free surfaces is the one that minimizes its total interfacial energy.

a) In simple metal solids, the preferred shape is nearly spherical. Please explain why.

b) Ionic solids tend to have polygonal shapes with large, flat facets parallel to the low-energy planes. Please explain why.

c) Use the NaCl ionic structure to explain what you described in (b).

Expert Solution

Wulff construction:

This is a method to determine the equilibrium shape of a crystal. The shape of an equilibrium crystal is obtained by minimizing the total surface energy associated with the crystal.

If surface of the crystal is made up of facets, consider an n^th face having interfacial tension and area A_n. Then the energy is given by:

To minimise the energy we need to minimise interfacial tension or surface area according to the above equation.

a) When crystal is a simple metal, which have isotropic . So to minimise energy they need to minimise surface area. The optimum shape for minimizing the surface energy is sphere. This is why the preferred shape of simple metal solid is spherical.

b) To minimize the interfacial energy (thereby decreasing the surface energy), ionic solids tend to have polygonal shapes with large, falt facets parallel to the low energy plane. These have anisotropic .

c) The natural macroscopic shape is compound solids are polygonal (crystalline) due to their anisotropic . According to Wulff construction for crystalline solids depends on the orientation of (hkl) of the surafce. Then is a function of orientation of surface, n.

The shape of NaCl is cubic. This is because of the low energy of (100) surface in NaCl structure.

queen_honey_blossom answered 2 years ago

Show that the connected sum of two compact surfaces is a compact surface.

5. Surface energy (2 pts). Let’s use the concept of surface tension as surface energy per...

5. Surface energy (2 pts). Let’s use the concept of surface tension as surface energy per unit area to see if we can estimate, at least to the correct order of magnitude, the surface tension of water. a) Water has a molar mass of 18 g/mol and a density of 1000 kg/m3 (or 1 g/cm3). Based on this data, estimate the number of water molecules per unit surface area of water. b) The coordination number of water (i.e., the average...

Define electric potential energy, electric potential, and equipotential surfaces? Can equipotential surfaces touch or cross one...

Define electric potential energy, electric potential, and equipotential surfaces? Can equipotential surfaces touch or cross one another? If yes/no, why/how? Under what angle do the electric field lines cross equipotential surfaces? Explain why, if all charges are at rest, the surface of a conductor is an equipotential surface? What’s the relationship between the electric potential on the surface of and inside the conductor when all charges are at rest? Define electron volt. If you know electric potential V as a...

The surface energy of a single crystal depends on crystallographic orientation. Does this surface energy increase...

The surface energy of a single crystal depends on crystallographic orientation. Does this surface energy increase or decrease with an increase in planar density? Why? (Hint: Read “External Surface” part in S.4.6: Surface energy is proportional to the number of unsatisfied bonds of surface atoms) please clear hand writing, also plesae don't give me the book answer. Thank you.

Iron-56 has one of the highest binding energies of all nuclides. Calculate its nuclear binding energy...

Iron-56 has one of the highest binding energies of all nuclides. Calculate its nuclear binding energy in kJ per mol nucleon. 1 amu is equivalent to 1.492 ´ 10-10 J. mass of iron-56 nuclide 55.934994 amu (includes electrons) proton mass 1.00728 amu neutron mass 1.00866 amu electron mass 5.4858 ´ 10–4 amu speed of light 2.998 ´ 108 m/s

Tabulate the 20 lowest energies (as multiples of the lowest energy) and their degeneracies for the...

Tabulate the 20 lowest energies (as multiples of the lowest energy) and their degeneracies for the following cases: (a) the one dimensional infinite potential energy well, (b) the one dimensional simple harmonic oscillator, (c) the one dimensional half of the simple harmonic oscillator, (d) the two dimensional infinite potential energy well, (e) the three dimensional infinite potential energy well.

1) identify the processes that shape planetary surfaces and identify the most common planetary process 2)...

1) identify the processes that shape planetary surfaces and identify the most common planetary process 2) identify the processes that have taken place on the surface of Mars and Venus. 3) identify the surface processes that have taken place on the surface of Mercury the Moon and the moon's of Jupiter.

What are the reasons that electron energies in atoms have an energy quantum number?

(From 4.8) The bowl shaped surface of a satellite dish is typically in the shape of...

(From 4.8) The bowl shaped surface of a satellite dish is typically in the shape of a rotated elliptical paraboloid. The cross section of the surface is typically in the shape of a rotated parabola. Perform a rotation of axis to eliminate the xy term of this conic section and then sketch the graph of the conic: 9? ^2 + 24?? + 16?^2 + 90? − 130? = 0

A Gaussian surface in the shape of a right circular cylinder with end caps has a...

A Gaussian surface in the shape of a right circular cylinder with end caps has a radius of 16.4 cm and a length of 68.1 cm. Through one end there is an inward magnetic flux of 36.6 μWb. At the other end there is a uniform magnetic field of 1.40 mT, normal to the surface and directed outward. What are the (a) magnitude and (b) direction (inward or outward) of the net magnetic flux through the curved surface?

Question