Section: 12 | Polarizabilities of Atoms and Ions in Solids |
Help Manual

Page of 1
Type a page number and hit Enter.
/1
Back to Search Results
Type a page number and hit Enter.
Summary of table differences
No records found.
How to Cite this Reference
 The recommended form of citation is: John R. Rumble, ed., CRC Handbook of Chemistry and Physics, 103rd Edition (Internet Version 2022), CRC Press/Taylor & Francis, Boca Raton, FL. If a specific table is cited, use the format: "Physical Constants of Organic Compounds," in CRC Handbook of Chemistry and Physics, 103rd Edition (Internet Version 2022), John R. Rumble, ed., CRC Press/Taylor & Francis, Boca Raton, FL.

# POLARIZABILITIES OF ATOMS AND IONS IN SOLIDS

H. P. R. Frederikse

The polarization of a solid dielectric medium, P, is defined as the dipole moment per unit volume averaged over the volume of a crystal cell. A component of P can be expanded as a function of the electric field E :

${P}_{i}=\sum _{j}{a}_{j}{E}_{j}+\sum _{jk}{b}_{jk}{E}_{j}{E}_{k}$

For relatively small electric fields in isotropic substances P = χeE , where χe is the electric susceptibility. If the medium is made up of N atoms (or ions) per unit volume, the polarization is P = Npm where pm is the average dipole moment per atom. The polarizability α can be defined as pm = αE0 , where E0 is the local field at the position of the atom. Using the Lorentz method to calculate the local field one finds:

P = (E + 4πP) = χeE

Together with the definition of the dielectric constant (relative permittivity), ε = 1 + 4πχe, this leads to the Clausius-Mossotti equation:

α = (3/4πN)(ε - 1)/(ε + 2)

The total polarization associated with atoms, ions, or molecules is due to three different sources:

1. Electronic polarization arises because the center of the local electronic charge cloud around the nucleus is displaced under the action of the field: Pe = eE0 where αe is the electronic polarizability.
2. Ionic polarization occurs in ionic materials because the electric field displaces cations and anions in opposite directions: Pi = iE0, where αi is the ionic polarizability.
3. Orientational polarization can occur in substances composed of molecules that have permanent electric dipoles. The alignment of these dipoles depends on temperature and leads to an orientational polarizability per molecule: αor = p2/3kT, where p is the permanent dipole moment per molecule, k is the Boltzmann constant, and T is the temperature.

Because of the different nature of these three polarization processes the response of a dielectric solid to an applied electric field will strongly depend on the frequency of the field. The resonance of the electronic excitation in insulators (dielectrics) takes place in the ultraviolet part of the spectrum; the characteristic frequency of the lattice vibrations is located in the infrared, while the orientation of dipoles requires fields of much lower frequencies (below 1010 Hz). This response to electric fields of different frequencies is shown in Figure 1.

Values of the electronic polarizabilities αe for selected atomic elements and ions are given in the table. Additional data for other atomic elemnts and molecules are found in “Polarizabilties of Atoms and Molecules” in Section 10 of this CRC Handbook.

# References

1. Kittel, C., Introduction to Solid State Physics, Fourth Edition, John Wiley & Sons, New York, 1971.
2. Lerner, R.G., and Trigg, G.L., Eds., Encyclopedia of Physics, Second Edition, VCH Publishers, New York, 1990.
3. Ralls, K.M., Courtney, T.H., and Wulff, J., An Introduction to Materials Science and Engineering, John Wiley & Sons, New York, 1976.

Figure 1. Schematic graph of the frequency dependence of the different contributions to polarizability.

## Electronic Polarizabilities of Atomic Elements and Ions

 αe﻿(I)/10-24 cm 3 αe﻿(II)/10-24 cm 3 αe﻿(III)/10-24 cm 3 αe﻿(IV)/10-24 cm 3 αe﻿(VI)/10-24 cm 3 αe﻿(VII)/10-24 cm 3 αe﻿(VIII)/10-24 cm 3 He0.205 Li+0.029 Be2+0.008 B3+0.003 C4+0.0013 O2–3.88 F–1.04 Ne0.394 Na+0.179 Mg2+0.094 Al3+0.052 Si4+0.0165 S2–10.2 Cl–3.66 Ar1.64 K+0.83 Ca2+0.47 Sc3+0.286 Ti4+0.185 Se2–10.5 Br–4.77 Kr2.48 Rb+1.40 Sr2+0.86 Y3+0.55 Zr4+0.37 Te2–14.0 I–7.1 Xe4.04 Cs+2.42 Ba2+1.55 La3+1.04 Ce4+0.73
 Data from Pauling, L., Proc. R. Soc. London, A114, 181, 1927. See also Jaswal, S.S. and Sharma, T.P., J. Phys. Chem. Solids, 34, 509, 1973. Values are appropriate for cgs units. To convert to SI, use the relation α(SI)/C m2 V–1 = 1.11265.10–16 α(cgs)/cm3.

Page 1 of 1
1/1

Entry Display
This is where the entry will be displayed

#### Other ChemNetBase Products

 You are not within the network of a subscribing institution.Please sign in with an Individual User account to continue.Note that Workspace accounts are not valid.

Confirm Log Out
Are you sure?
Your personal workspace allows you to save and access your searches and bookmarks.

Are you sure?

 You have entered your Individual User account sign in credentials instead of Workspace credentials. While using this network, a personal workspace account can be created to save your bookmarks and search preferences for later use. Click the help icon for more information on the differences between Individual User accounts and Workspace accounts.
My Account

 Username Title [Select]DrProfMissMrsMsMrMx [Select]DrProfMissMrsMsMrMx First Name (Given) Last Name (Family) Email address

Searching for Chemicals and Properties

The CRC Handbook of Chemistry and Physics (HBCP) contains over 700 tables in over 450 documents which may be divided into several pages, all categorised into 17 major subject areas. The search on this page works by searching the content of each page individually, much like any web search. This provides a challenge if you want to search for multiple terms and those terms exist on different pages, or if you use a synonym/abbreviation that does not exist in the document.

We use metadata to avoid some of these issues by including certain keywords invisibly behind each table. Whilst this approach works well in many situations, like any web search it relies in the terms you have entered existing in the document with the same spelling, abbreviation etc.

Since chemical compounds and their properties are immutable, a single centralised database has been created from all chemical compounds throughout HBCP. This database contains every chemical compound and over 20 of the most common physical properties collated from each of the >700 tables. What's more, the properties can be searched numerically, including range searching, and you can even search by drawing a chemical structure. A complete list of every document table in which the compound occurs is listed, and are hyperlinked to the relevant document table.

The 'Search Chemicals' page can be found by clicking the flask icon in the navigation bar at the top of this page. For more detailed information on how to use the chemical search, including adding properties, saving searches, exporting search results and more, click the help icon in to top right of this page, next to the welcome login message.

Below is an example of a chemical entry, showing its structure, physical properties and document tables in which it appears.

We have developed this cookie policy (the “Cookie Policy”) in order to explain how we use cookies and similar technologies (together, “Cookies”) on this website (the “Website”) and to demonstrate our firm commitment to the privacy of your personal information.

The first time that you visit our Website, we notify you about our use of Cookies through a notification banner. By continuing to use the Website, you consent to our use of Cookies as described in this Cookie Policy. However, you can choose whether or not to continue accepting Cookies at any later time. Information on how to manage Cookies is set out later in this Cookie Policy.

Cookies are small text files containing user IDs that are automatically placed on your computer or other device by when you visit a website. The Cookies are stored by the internet browser. The browser sends the Cookies back to the website on each subsequent visit, allowing the website to recognise your computer or device. This recognition enables the website provider to observe your activity on the website, deliver a personalised, responsive service and improve the website.

## Cookies We Use and Their Purpose

‘Strictly Necessary’ Cookies enable you to move around the Website and use essential features. For example, if you log into the Website, we use a Cookie to keep you logged in and allow you to access restricted areas, without you having to repeatedly enter your login details. If you are registering for or purchasing a product or service, we will use Cookies to remember your information and selections, as you move through the registration or purchase process.

Strictly Necessary Cookies are necessary for our Website to provide you with a full service. If you disable them, certain essential features of the Website will not be available to you and the performance of the Website will be impeded.

‘Performance’ Cookies collect information about how you use our Website, for example which pages you visit and if you experience any errors. These Cookies don’t collect any information that could identify you – all the information collected is anonymous. We may use these Cookies to help us understand how you use the Website and assess how well the Website performs and how it could be improved.

‘Functionality’ Cookies enable a website to provide you with specific services or a customised experience. We may use these Cookies to provide you with services such as watching a video or adding user comments. We may also use such Cookies to remember changes you make to your settings or preferences (for example, changes to text size or your choice of language or region) or offer you time-saving or personalised features.

You can control whether or not Functionality Cookies are used, but disabling them may mean we are unable to provide you with some services or features of the Website.

## First and Third Party Cookies

The Cookies placed on your computer or device include ‘First Party’ Cookies, meaning Cookies that are placed there by us, or by third party service providers acting on our behalf. Where such Cookies are being managed by third parties, we only allow the third parties to use the Cookies for our purposes, as described in this Cookie Policy, and not for their own purposes.

You always have a choice over whether or not to accept Cookies. When you first visit the Website and we notify you about our use of Cookies, you can choose not to consent to such use. If you continue to use the Website, you are consenting to our use of Cookies for the time being. However, you can choose not to continue accepting Cookies at any later time. In this section, we describe ways to manage Cookies, including how to disable them.

You can manage Cookies through the settings of your internet browser. You can choose to block or restrict Cookies from being placed on your computer or device. You can also review periodically review the Cookies that have been placed there and disable some or all of them.

Please be aware that if you choose not to accept certain Cookies, it may mean we are unable to provide you with some services or features of the Website.

In order to keep up with changing legislation and best practice, we may revise this Cookie Policy at any time without notice by posting a revised version on this Website. Please check back periodically so that you are aware of any changes.

## Questions or Concerns

You can also contact the Privacy Officer for the Informa PLC group at [email protected].

Here is a list of cookies we have defined as 'Strictly Necessary':

### Taylor and Francis 'First Party' Cookies

JSESSIONID

Here is a list of the cookies we have defined as 'Performance'.

_ga

_gid

_gat

Accessibility

The Voluntary Product Accessibility Template (VPAT) is a self-assessment document which discloses how accessible Information and Communication Technology products are in accordance with global standards.

The VPAT disclosure templates do not guarantee product accessibility but provide transparency around the product(s) and enables direction when accessing accessibility requirements.

Taylor & Francis has chosen to complete the International version of VPAT which encompasses Section 508 (US), EN 301 549 (EU) and WCAG2.1 (Web Content Accessibility Guidelines) for its products.