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| > Infrared Reflectance Spectrum   |                                   |
| > of CaTiO~3~                     |                                   |
| >                                 |                                   |
| > Calculated from First           |                                   |
| > Principles                      |                                   |
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| > *An important route to progress |                                   |
| > in wireless communications is   |                                   |
| > the development of microwave    |                                   |
| > dielectrics with improved       |                                   |
| > properties and lower costs.     |                                   |
| > Understanding the               |                                   |
| > structure-property              |                                   |
| > relationships of these          |                                   |
| > technologically important       |                                   |
| > materials will lead to the      |                                   |
| > rational design of new          |                                   |
| > materials with desired          |                                   |
| > properties. Infrared            |                                   |
| > reflectivity is an important    |                                   |
| > tool for characterizing such    |                                   |
| > materials, because the IR       |                                   |
| > reflectance spectrum is closely |                                   |
| > related both to the dielectric  |                                   |
| > properties and to the atomic    |                                   |
| > scale structure. Materials for  |                                   |
| > microwave dielectrics, such as  |                                   |
| > those based on CaTiO~3~, have   |                                   |
| > complicated crystal structures  |                                   |
| > and thus complicated infrared   |                                   |
| > spectra. This work shows that   |                                   |
| > the IR reflectance spectrum of  |                                   |
| > CaTiO~3~ can be computed from   |                                   |
| > first principles density        |                                   |
| > functional theory, and can be   |                                   |
| > interpreted in terms of the     |                                   |
| > structure and chemistry of      |                                   |
| > CaTiO~3~.*                      |                                   |
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|                                   |                                   |
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| > Microwave dielectrics are used  | > CaTiO~3~ (CT) (Figure 1) is an  |
| > as resonators and filters in    | > important material for          |
| > applications such as wireless   | > microwave dielectrics because   |
| > communications. Microwave       | > it has very high dielectric     |
| > dielectric materials must have  | > constant ε' (approximately 180  |
| > (1) high dielectric constant    | > at room temperature) and a      |
| > ε\', (2) low dielectric loss,   | > positive temperature            |
| > and (3) temperature stability.  | > coefficient. By combining CT in |
| > BaZn~1/3~Ta~2/3~O~3~ (BZT),     | > solid solutions with materials  |
| > currently in use, has excellent | > with negative temperature       |
| > properties, but contains the    | > coefficients, a large variety   |
| > expensive metal tantalum. The   | > of potentially useful, zero     |
| > development of lower-cost, next | > temperature coefficient,        |
| > generation, devices will        | > materials can be obtained.      |
| > require a replacement for BZT.  | >                                 |
| >                                 | > The dielectric constant of a    |
| > Fundamental knowledge of        | > material as a function of       |
| > structure-chemistry-property    | > frequency ν is given by         |
| > relationships in dielectric     | >                                 |
| > materials will help achieve     | > ε(ν) = ε~elec~ + Σ~μ~ S~μ~      |
| > this goal. Current empirical    | > ν~μ~^2^/(ν~μ~^2^-ν^2^+iγ~μ~ν),  |
| > knowledge of structure-property | > (1)                             |
| > relationships in dielectrics is | >                                 |
| > insufficient for the rational   | > where ε~elec~ is the electronic |
| > design of new materials.        | > contribution to ε, the sum is   |
| > First-principles (FP)           | > over phonon modes μ, S~μ~ are   |
| > calculations complement         | > the phonon oscillator           |
| > experiment and are ideally      | > strengths, ν~μ~ their           |
| > suited for studying the physics | > frequencies, and γ~μ~ their     |
| > of dielectric materials because | > damping coefficients. The       |
| > they allow the origin of their  | > oscillator strength of phonon   |
| > physical properties to be       | > μ, in turn, is proportional to  |
| > studied on an ion-by-ion basis. | > Z\*~μ~^2^/ν~μ~^2^, where Z\*~μ~ |
| >                                 | > is the phonon's effective       |
| > ![](media/image1.               | > charge. Note that the number of |
| png){width="2.8361111111111112in" | > phonon modes in Eq. (1) is      |
| > height="3.688888888888889in"}   | > determined from the crystal     |
| >                                 | > structure (25 in the case of    |
| > **Figure 1: Perovskite-type     | > CT), while Z\*~μ~ and ν~μ~ are  |
| > structure of CaTiO~3~. Ti ions  | > determined by the crystal       |
| > are at the centers of oxygen    | > chemistry.                      |
| > octahedra, which are joined at  | >                                 |
| > their corners. Ca ions (yellow) | > The dielectric constant as a    |
| > occupy special positions        | > function of frequency can be    |
| > between the octahedra**.        | > measured in many ways. Infrared |
|                                   | > reflectivity is a very useful,  |
|                                   | > though indirect, method.        |
|                                   | > Infrared reflectivity           |
|                                   | > measurements are commonly fit   |
|                                   | > using equation (1) to determine |
|                                   | > the phonon parameters. This     |
|                                   | > becomes difficult, however, for |
|                                   | > a system as complicated as CT.  |
|                                   | >                                 |
|                                   | > Alternatively, one can use FP   |
|                                   | > methods to *compute* the phonon |
|                                   | > and dielectric properties, and  |
|                                   | > thus the IR reflectance         |
|                                   | > spectrum. Advances in FP        |
|                                   | > methods have made it possible   |
|                                   | > to compute Z\*~μ~ and ν~μ~ of a |
|                                   | > crystal, given as input only    |
|                                   | > the experimental unit cell and  |
|                                   | > atomic positions. The ability   |
|                                   | > to correctly compute Z\*~μ~ is  |
|                                   | > a relatively recent development |
|                                   | > and has led to the discovery    |
|                                   | > that large Z\*~μ~ are common in |
|                                   | > perovskites, which enhances     |
|                                   | > their dielectric constants.     |
|                                   | >                                 |
|                                   | > Because of the technological    |
|                                   | > importance of CT, and its       |
|                                   | > strongly temperature-dependent  |
|                                   | > ε', collaborators at the Czech  |
|                                   | > Academy of Sciences used IR     |
|                                   | > reflectivity to explore the     |
|                                   | > temperature dependence of ε' in |
|                                   | > terms of the temperature        |
|                                   | > dependence of the phonon        |
|                                   | > properties. The experimental IR |
|                                   | > reflectance spectrum at T = 6 K |
|                                   | > is shown in Fig. 2. The IR      |
|                                   | > reflectance spectrum that we    |
|                                   | > calculated from FP is shown for |
|                                   | > comparison. (Although           |
|                                   | > calculation of the damping      |
|                                   | > parameters from FP is not yet   |
|                                   | > practical, simply setting all   |
|                                   | > γ~μ~ to the same value of 5     |
|                                   | > cm^-1^ leads to good agreement  |
|                                   | > with experiment in this case.)  |
|                                   | >                                 |
|                                   | > .                               |
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