Ductility
Ductility can be quantified by the fracture strain formula_1, which is the engineering strain at which a test specimen fractures during a uniaxial tensile test. Another commonly used measure is the reduction of area at fracture formula_2. The ductility of steel varies depending on the alloying constituents. Increasing the levels of carbon decreases ductility. Many plastics and amorphous solids, such as Play-Doh, are also malleable.
The most ductile metal is platinum and the most malleable metal is gold.
Lanthanide
Gschneider and Daane (1988) attribute the trend in melting point which increases across the series, (lanthanum (920 °C) – lutetium (1622 °C)) to the extent of hybridization of the 6s, 5d, and 4f orbitals. The hybridization is believed to be at its greatest for cerium, which has the lowest melting point of all, 795 °C.
The lanthanide metals are soft; their hardness increases across the series. Europium stands out, as it has the lowest density in the series at 5.24 g/cm and the largest metallic radius in the series at 208.4 pm. It can be compared to barium, which has a metallic radius of 222 pm. It is believed that the metal contains the larger Eu ion and that there are only two electrons in the conduction band. Ytterbium also has a large metallic radius, and a similar explanation is suggested.
The resistivities of the lanthanide metals are relatively high, ranging from 29 to 134 μΩ·cm. These values can be compared to a good conductor such as aluminium, which has a resistivity of 2.655 μΩ·cm.
With the exceptions of La, Yb, and Lu (which have no unpaired f electrons), the lanthanides are strongly paramagnetic, and this is reflected in their magnetic susceptibilities. Gadolinium becomes ferromagnetic at below 16 °C (Curie point). The other heavier lanthanides – terbium, dysprosium, holmium, erbium, thulium, and ytterbium – become ferromagnetic at much lower temperatures.