International Journal of Fracture 119/120: 441–448, 2003.
© 2003 Kluwer Academic Publishers. Printed in the Netherlands.
Measurement of the noibium/sapphire interface toughness via
and M.D. THOULESS
Department of Materials Science & Engineering,
Department of Nuclear Engineering
& Radiological Sciences,
Department of Mechanical Engineering and Applied Mechanics all at the University
of Michigan, Ann Arbor, MI 48109, U.S.A.
Abstract. Niobium ﬁlms were deposited on sapphire substrates using both physical vapor deposition (PVD) and
ion beam assisted deposition (IBAD) at an ion energy of 1000 eV and an ion-to-atom arrival rate ratio of 0.4.
The interface between the niobium ﬁlm and the sapphire substrate was doped with up to 7.6 monolayers of silver.
The ﬁlms were patterned into ﬁne lines using photolithography. During the photolithography process, curling and
buckling were observed. The curling indicated a stress gradient in which the top of the ﬁlm is tensile with respect
to the bottom of the ﬁlm, while buckling demonstrated that a portion of the ﬁlm thickness must have been in
compression. An analysis of the delamination showed that the critical energy release rate for the interface was on
the order of 1 J m
, and that the compressive stress is of the order 1 GPa. The higher energy release rate of the
IBAD samples conﬁrmed that the stronger interface is due either to the orientation relationship between the ion
beam textured niobium ﬁlm and the (0001) sapphire surface or the interface mixing caused by ion bombardment.
Key words: Buckling, delamination, IBAD, interface, niobium, toughness.
The mechanical quality of a metal-ceramic interface can be characterized by the critical energy
release rate (also referred to as the critical crack driving force, or toughness) G
, having units
of energy per unit area (J m
incorporates both the reversible thermodynamic work of
, and the energy, W
, associated with plastic deformation of the metal region
adjacent to the interface:
As suggested by Jokl et al. (1980), W
are interrelated. The dissipated work of
plastic deformation of the metal constituent depends, non-linearly, on the work of adhesion:
where the exponent, n, is an experimental quantity larger than unity and is dependent on
the material system. Although the thermodynamic work of adhesion contributes directly to
the toughness only minimally, its indirect contribution through the plastic dissipation term
can be much greater. Thus, controlling W
is an effective means of controlling the interface
The overall objective of this project was to control the toughness of the interface between
niobium ﬁlms and sapphire substrates by controlling the interface properties. Scratch tests
have shown (Ji et al., 1997b) that the interface toughness correlates with silver interlayer