Hard water
Water's hardness is determined by the concentration of multivalent cations in the water. Multivalent cations are positively charged metal complexes with a charge greater than 1+. Usually, the cations have the charge of 2+. Common cations found in hard water include Ca and Mg. These ions enter a water supply by leaching from minerals within an aquifer. Common calcium-containing minerals are calcite and gypsum. A common magnesium mineral is dolomite (which also contains calcium). Rainwater and distilled water are soft, because they contain few ions.
Fracture toughness
In materials science, fracture toughness is a property which describes the ability of a material to resist fracture, and is one of the most important properties of any material for many design applications. The linear-elastic fracture toughness of a material is determined from the stress intensity factor (formula_1) at which a thin crack in the material begins to grow. It is denoted K and has the units of formula_2 or formula_3. Plastic-elastic fracture toughness is denoted by J, with the unit of J/cm or lbf-in/in, and is a measurement of the energy required to grow a thin crack.