Biomedical Engineering Reference
In-Depth Information
susceptibility for the strain). Ferroelastic materials are dei ned by having
switchable domains, or twins, which may be switched on application of an
external i eld: stress. Such domain microstructures ot en result from phase
transitions.
Ferroelasticity is most easily dei ned by its close analogy to ferroelectric-
ity, where one has to replace the polarization by the strain and the electric
i eld by the mechanical stress. h e main dif erence is that in the ferro-
elastic phase a spontaneous tensorial quantity, the strain, arises instead of
the polarization vector in the case of a ferroelectric. A ferroelastic crystal
exhibits strain-stress hysteresis and in the absence of an external stress has
two or more energetically equal orientational states (domains) of dif erent
spontaneous strain tensor. By a suitably chosen external stress the strain
orientation may be shit ed from one state to another.
13.1.2.4 Ferrotoroidic
A phase transition to spontaneous long-range order of microscopic mag-
netic toroidal moments has been termed “ferrotoroidicity.” It is expected
to i ll the symmetry schemes of primary ferroics (phase transitions with
spontaneous point symmetry breaking) with a space-odd, time-odd mac-
roscopic order parameter. A ferrotoroidic material would exhibit domains
which could be switched by an appropriate i eld, e.g., a magnetic i eld curl.
h e existence of ferrotoroidicity is still under debate and clear-cut evidence
has not been presented yet—mostly due to the dii culty in distinguishing
ferrotoroidicity from antiferromagnetic order, as both have no net magne-
tization and the order parameter symmetry is the same.
13.1.3 Multiferroics
Multiferroic materials are a class of materials that yield simultaneous
ef ects of ferroelectricity, ferromagnetism, and antiferromagnetism in the
same material. A general diagram of multiferroics is shown in Figure 13.4.
h ere is signii cant scientii c and technological interest in these materials
due to their unusual responses including very large magneto-electric sus-
ceptibility, giant magnetostriction and energy coupling coei cients.
Typical multiferroics belong to the group of the perovskite transition
metal oxides including rare-earth manganites and ferrites (e.g., TbMnO
3
,
HoMn
2
O
5
, LuFe
2
O
4
). Other examples of the bismuth-based compounds
are BiFeO
3
, BiMnO
3
and non-oxides such as BaNiF
4
as well as spinel chal-
cogenides, e.g., ZnCr
2
Se
4
, etc. h ese alloys show rich phase diagrams com-
bining dif erent ferroic orders in separate phases. Apart from single-phase
