3.3: Notation Quagmire

This text attempts to use notation consistent with the literature. However, consistency is a challenge because every author seems to have a different name for the same physical phenomena. Furthermore, the same term used by different authors may have completely different meanings. For example, as described by Equation 2.3.6, in some materials, a mechanical stress induces a material polarization proportional to the square of that stress. This text calls this phenomenon piezoelectricity, or to be more specific, quadratic piezoelectricity. However, references [3] and [6] call this phenomenon electrostriction. To make matters worse, reference [33] calls this effect ferroelectricity. Some authors make different assumptions when using terms too. For example, when reference [26] uses the term ferroelectricity, it assumes crystalline materials, but it makes no assumptions about whether the effect is linear or not.

Table \(\PageIndex{1}\) summarizes the notation used in this text to describe energy conversion processes involving material polarization. The first column lists the name used here to describe the effect. The second column lists what effect causes a material polarization. The third column describes whether the effect occurs in crystals only. The fourth column describes whether the material polarization varies linearly or not with the parameter described in the second column. The next column lists references which call this effect ferroelectricity. The last column gives names used by other references to describe this particular phenomenon. The last two columns are quite incomplete because a thorough literature survey was not done. However, these columns show quite a variety to the terminology even for the small fraction of the literature reviewed.

Table \(\PageIndex{1}\): Terminology related to processes involving material polarization.

Notation in this text	\(\overrightarrow{P}\) induced by ...	Crystalline? Amorphous? Polycrystalline?	Linear?	Who calls this ferro- electricity?	What others call this quantity
(Linear) Piezoelectricity	Mechanical stress, \(\overrightarrow{\varsigma}\)	Crystalline	Linear
(Quadratic) Piezoelectricity	Mechanical stress, \(\overrightarrow{\varsigma}\)	Crystalline	Quadratic	[33]	Electrostriction [3, p. 327] [6], photoelasticity [31]
Ferroelectric Piezoelectricity	Mechanical stress, \(\overrightarrow{\varsigma}\)	All	Nonlinear	[25, p. 408]
(Linear) Pyroelectricity	Temperature differential, \(\Delta T\)	Crystalline	Linear	[26, p. 556], [42, p. 50], [43]	Thermal nonlinear optical effects [42]
(Quadratic) Pyroelectricity	Temperature differential, \(\Delta T\)	Crystalline	Quadratic	[26, p. 556], [43]	Thermal nonlinear optical effects [42]
Ferroelectric Pyroelectricity	Temperature differential, \(\Delta T\)	All	Nonlinear	[3, p. 366], [26, p. 556], [43]	Thermal nonlinear optical effects [42]
Linear (Pockels) Electro-optic Effect	Optical Electromag. radiation \(\overrightarrow{E}\)	Crystalline	Linear		Electronic polarizablility [25, p. 390]
Quadratic (Kerr) Electro-optic Effect	Optical Electromag. radiation \(\overrightarrow{E}\)	Crystalline	Quadratic
Ferroelectric Electro-optic Effect	Optical Electromag. radiation \(\overrightarrow{E}\)	All	Nonlinear		Photoinduced anisotropy, photodarkening [44] [45], intimate valence alternation pair state [44

You might think that you can avoid confusion of terminology by looking for Greek or Latin roots. While many of the terms introduced in the preceding chapters do have etymological roots, looking at the roots of the words does not help and sometimes makes matters worse. As discussed above, the prefix ferro- means iron. However, the ferroelectric effect has nothing to do with iron, and ferroelectric materials rarely contain iron. This name is an analogy to ferromagnetics. Some forms of iron are ferromagnetic. In ferromagnetics, an external magnetic field changes the permeability of a material. In ferroelectrics, an external electric field influences the permittivity. To make matters worse, iron has the periodic table symbol \(\text{Fe}\) while iridium has the symbol \(\text{Ir}\). In this text, the term pyroelectric effect follows Roentengen's terminology which dates 1914 [3]. The root pyro-, showing up in pyroelectricity, also shows up in pyrite and pyrrhotite which are iron containing compounds.

Sometimes the terms phase change and photodarkening are applied to the electro-optic effect in amorphous materials, but not crystalline materials. More specifically, sulfides, selenides, and tellurides, referred to as chalcogenides, are sometimes called phase change materials. Examples include \(\text{GeAsS, GeInSe,}\) and so on. The word chalcogenide is itself a misnomer. The prefix chalc- comes from the Greek root meaning copper [24]. They are named in analogy to \(\text{CuS}\), chalcosulfide. The name phase change material was popularized by a company that made CDs and battery components. While crystalline materials can also be electro-optic, the name phase change is not typically applied to crystals.

Sometimes the terminology used in the literature can be quite different from the terminology of this text. For example, reference [44] describes material polarization in chalcogenide glasses by saying that when exposed to external optical electric fields, a material stores energy by "a transient exciton which can be visualized as a transient intimate valence alternation defect pair." ... "This means essentially that macroscopic anisotropies result from geminate recombination of electron-hole pairs, which do not diffuse out of the microscopic entity in which they were created by absorbed photons." An exciton is a bound electron-hole pair. In other words, the material polarizes. When an external optical electric field is applied, electric dipoles form throughout the material. When reading the literature related to piezoelectricity, pyroelectricity, and electro-optics, be aware that there is not much consistency in the terminology used.