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Surface energy of solids

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Inorganic and Physical Chemistry

Part of the book series: Topics in Current Chemistry ((TOPCURRCHEM,volume 77))

Abstract

At least five conclusions may be formulated after perusing this review.

  1. 1.

    No method so far suggested for measuring the surface energy or surface tension of solids is satisfactory.

  2. 2.

    This failure may be caused, above all, by the fact that solids, contrary to liquids, cannot alter their shape without changing the strain energy in their volumes. The changes in strain energy are so much greater than those in surface energy that the latter remain unrecognized.

  3. 3.

    Solids possess an energy unknown in typical liquids. This cuticular energy exists because the surface region of innumerable solids has a chemical composition, a frequency of lattice defects, and so on, different from those in the bulk.

  4. 4.

    Small solid particles obtained by cooling of vapors, by grinding, or many other methods, usually have a less perfect lattice and more impurity than have bigger crystals of nominally identical composition. Hence, the cuticular energy of the former exceeds that of the latter.

  5. 5.

    Cuticular energy implies no tendency of the surface to contract, i.e., no surface tension. The theoretical calculations of the difference in energy between a broken and an unbroken crystal, if correct, afford a quantity which is related to cuticular energy and, like this, causes no contractile tendency.

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Abbreviations

A:

Surface area; a constant

A m :

Area of surface or interface per molecule

A, As, Asl:

Areas of vapor-liquid, vapor-solid, and liquid-solid interfaces

A 1 :

Combined area of grain boundaries

A0, A1:

Surface areas of a large and a minute crystal

A1, A2, A3:

Areas of different crystal faces

a:

The longer half-axis of an ellipse; lattice parameter

B:

A constant

b:

The shorter half-axis of an ellipse

C, C1, C2:

Solubilities

C.E.:

Cuticular energy

c:

Depth or half-length of scratch

D:

Grain diameter; diffusion coefficient

E:

Modulus of elasticity; intensity of electrostatic field

E 0 :

Internal energy of a bar

E 1 :

Internal energy of a broken bar

e:

Charge of an electron

F:

Helmholtz free energy

F o :

Free osmotic energy

F s :

Free surface energy

f:

Force; number depending on crystal structure

G:

Shear modulus; arbitrary constant; temperature gradient

H:

Amount of heat evolved

h:

Planck's constant; half-thickness or thickness of a slice or a ribbon; depth of scratch

h 0 :

Initial depth of scratch

K:

Modulus of compressibility; proportionality constant

k:

Boltzmann's constant; coordination number of atoms in bulk; compressibility

ks, kv:

Number of atoms in two-dimensional and three-dimensional unit cells

Δk:

Number of broken bonds per atom

L:

Length; thickness of a crystal

Ll, Ls:

Heat of vaporization or sublimation

l:

Length; length of a “roof”; variable length of a filament

l 0 :

Initial length of a filament

l1, l2:

Edges of two cubes

M:

Molecular weight; atomic mass

MW:

Molecular weight

m:

Mass of an atom; mass of hydrogen atom; mass

N:

Number of atoms in unit cell; Avogadro number

n:

Number of grain boundaries in a wire; number of molecules in unit volume

n+, n−:

Number of cations or anions on unit area

P:

Gas pressure

P c :

Capillary pressure

P o :

Vapor pressure above a plane surface

P1, P2:

Pressure in gas, in liquid

Q:

Heat content

Qo, Qp, Q∞:

Heat of solution of large and powdered solids, and solids with zero surface

q:

Number depending on crystal structure; surface density of electric charge

q0, q1:

Heat of solution of unit mass

R:

Radius of curvature; gas constant

R1, R2:

The principal radii of curvature

R ∞ :

Distance at which deformation becomes negligible

R:

Radius of wires; distance from an atom or ion; cube root of molecular volume; radius of a void

r 0 :

Radius at the bottom of a groove; radius at zero time

r1, r2:

Radius of wire before and after elongation

S. E.:

Strain energy

T:

Absolute temperature

Tb, Tm:

Boiling and melting points

Tl :

Melting point of plate of thickness l.

T mr :

Melting point of drop of radius r

T t :

Temperature of treatment

t:

Time

U:

Interatomic potential

Ul, Us:

Total surface energy of a liquid, a solid

u:

Height of a ridge point

u1, u2:

Displacement of neighboring atoms

V:

Volume of unit cell; specific volume of a liquid; volume; molecular volume

V1, V2:

Gas and liquid volumes

W:

Load; breaking load

W 0 :

Equilibrium load on a filament

W w :

Breaking load of wires

W :

Work of extending a rod

W f :

Fracture energy

W m :

Work spent on macroscopic deformation

w:

Width; distance between two ridges

x:

Variable depth of crack

Y:

Plate thickness

Z:

Valency of an ion; effective number of electrons per ion

α:

Angle on a crystal surface; numerical constant; an angle

β:

Contact angle at the edge of a solid

γ:

Surface tension of a liquid

γc :

“Critical surface tension”

γ s :

Specific surface energy or surface tension of a solid

γ *s :

Specific free energy of an interface between UC and U vapor

γ sl :

Specific energy or tension of a liquid-solid interface

γ sv :

Surface tension of a solid in a foreign vapor

γ 1 :

Surface tension of a grain boundary

γ12, γ13, γ23:

Tensions along boundaries between fluids 1 and 2, 1 and 3, and 2 and 3

“γ”:

Specific fracture energy

Δ:

Thickness of a line on which facts

δ:

Thickness of surface layer; an angle

∈ 0 :

Maximum strain

η:

Viscosity

θ:

Contact angle

θ 0 :

The characteristic (Debye) temperature

λ:

Wave length of disturbances; heat of melting

λ1; λs:

Internal heat of vaporization, sublimation

ν:

Number of free valence electrons per atom; Poisson's ratio

ξ:

Cohesion of a solid

ρ1, ρ3:

Density of a solid

ρ1, ρ2:

Density of a gas, a liquid

σ 0 :

Average stress

σ m :

Local stress

τ:

Thickness of surface layer

ϕ:

Potential energy of a crystal

ϕ:

Work of removing an atom from its neighbor; work function; half the dihedral angle in a liquid medium; electric potential

ϕ 1 :

Energy of valency electrons at the Fermi level

ψ:

Half the dihedral angle in a gas

ψ * :

Dihedral angle in a foreign vapor

Ω:

Volume of a molecule or atom

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  1. Dept. of Chemical Engineering, Case Western Reserve University, 44106, Cleveland, Ohio, USA

    Jacob J. Bikerman

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© 1978 Springer-Verlag

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Bikerman, J.J. (1978). Surface energy of solids. In: Inorganic and Physical Chemistry. Topics in Current Chemistry, vol 77. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0048037

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  • DOI: https://doi.org/10.1007/BFb0048037

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