Cleavage of brittle single crystals is reviewed and the historical cri
teria for the phenomenon are critically examined. Previously proposed
criteria, including those based on crystal structure (crystal growth p
lanes, the planes bounding the unit cell, and planar atomic packing) a
nd crystal properties (ionic charge of possible cleavage planes, bond
density, elastic modulus, and surface free energy), are found to be ap
plicable only to particular crystals or to isostructural groups, but e
ach lacks universal application. It is concluded that the fracture tou
ghness (K(Ic)) of the crystallographic planes is the most appropriate
criterion. Measurements reveal that the 'cleavage toughnesses' of brit
tle single crystals are usually about 1 MPa m1/2 or less. Measurements
of the fracture toughnesses of brittle polycrystalline aggregates are
then compared to the single crystal cleavage values in those instance
s where reliable results are available for the same crystal structures
. Polycrystalline toughnesses are consistently higher, in part because
of the lack of continuity of cleavage cracks through the polycrystall
ine aggregates. However, the increment of toughness increase is only 1
-2 MPa m1/2. The role of grain texture or preferred crystal orientatio
n is also addressed. It is concluded that polycrystalline aggregate to
ughnesses are often highly anisotropic and that the values for intense
ly oriented microstructures may approach those for single crystal clea
vage.