P d A d R d T d 4 OPTICAL AND PHYSICAL PROPERTIES OF MATERIALS CHAPTER 33 PROPERTIES OF CRYSTALS AND GLASSES William J . Tropf , Michael E . Thomas , and Terry J . Harris Applied Physics Laboratory Johns Hopkins Uniy ersity Laurel , Maryland 33 . 1 GLOSSARY A i , B , C , D , E , G constants a , b , c crystal axes B inverse dielectric constant B bulk modulus C heat capacity c speed of light c elastic stif fness D electric displacement d piezoelectric coef ficient (2) d ij nonlinear optical coef ficient E Young’s modulus E energy E electric field e strain G shear modulus g degeneracy Hi Hilbert transform h heat flow k extinction coef ficient k B Boltzmann constant , phonon mean free path MW molecular weight m integer N ( ) occupation density 33 .3 33 .4 OPTICAL AND PHYSICAL PROPERTIES OF MATERIALS n refractive index n ˜ complex refractive index 5 n 1 ik P electric polarization P x , y relative partial dispersion p elasto-optic tensor p elasto-optic compliance p pyroelectric constant q piezo-optic tensor r electro-optic coef ficient r amplitude reflection coef ficient r i j electro-optic coef ficient S ( ) line strength s elastic compliance T temperature t amplitude transmission coef ficient U enthalpy u atomic mass unit V volume v velocity of sound x displacement x variable of integration Z formulas per unit a linear expansion coef ficient a intensity absorption a thermal expansion a m macroscopic polarizability a , b , g crystal angles b power absorption coef ficient g ( ) line width g Gruneisen parameter e dielectric constant , permittivity e emittance θ D Debye temperature k thermal conductivity L ( ) complex function m permeability … wave number ( v / 2 π c ) r density r intensity reflectivity s stress τ intensity transmission τ power transmittance PROPERTIES OF CRYSTALS AND GLASSES 33 .5 χ susceptibility χ ( 2 ) second-order susceptibility Ω solid angle v radian frequency Subscripts ABS absorptance bb blackbody c 656 . 3 nm d 587 . 6 nm EXT extinctance F 486 . 1 nm i integers 0 vacuum , T 5 0 , or constant terms P constant pressure p , s polarization component r relative SCA scatterance V constant volume 33 . 2 INTRODUCTION Nearly every nonmetallic crystalline and glassy material has a potential use in optics . If a nonmetal is suf ficiently dense and homogeneous , it will have good optical properties . Generally , a combination of desirable optical properties , good thermal and mechanical properties , and cost and ease of manufacture dictate the number of readily available materials for any application . In practice , glasses dominate the available optical materials for several important reasons . Glasses are easily made of inexpensive materials , and glass manufacturing technology is mature and well-established . The resultant glass products can have very high optical quality and meet most optical needs . Crystalline solids are used for a wide variety of specialized applications . Common glasses are composed of low-atomic-weight oxides and therefore will not transmit beyond about 2 . 5 m m . Some crystalline materials transmit at wavelengths longer (e . g ., heavy-metal halides and chalcogenides) or shorter (e . g ., fluorides) than common glasses . Crystalline materials may also be used for situations that require the material to have very low scatter , high thermal conductivity , or high hardness and strength , especially at high temperature . Other applications of crystalline optical materials make use of their directional properties , particularly those of noncubic (i . e ., uni- or biaxial) crystals . Phasematching (e . g ., in wave mixing) and polarization (e . g ., in wave plates) are example applications . This chapter gives the physical , mechanical , thermal , and optical properties of selected crystalline and glassy materials . Crystals are chosen based on availability of property data and usefulness of the material . Unfortunately , for many materials , property data are imprecise , incomplete , or not applicable to optical-quality material . Glasses are more accurately and uniformly characterized , but their optical property data are usually limited to wavelengths below 1 . 06 m m . Owing to the preponderance of glasses , only a representative 33 .6 OPTICAL AND PHYSICAL PROPERTIES OF MATERIALS small fraction of available glasses are included below . SI derived units , as commonly applied in material characterization , are used . Property data are accompanied with brief explanations and useful functional relation- ships . We have extracted property data from past compilations 1 – 1 1 as well as recent literature . Unfortunately , property data are somewhat sparse . For example , index data may be available for only a portion of the transparent region or the temperature dependence of the index may not be known . Strength of many materials is poorly characterized . Thermal conductivity is frequently unavailable and other thermal properties are usually sketchy . 33 . 3 OPTICAL MATERIALS Crystalline and amorphous (including glass) materials are dif ferentiated by their structural (crystallographic) order . The distinguishing structural characteristic of amorphous sub- stances is the absence of long-range order ; the distinguishing characteristics of crystals are the presence of long-range order . This order , in the form of a periodic structure , can cause directional-dependent (anisotropic) properties that require a more complex description than needed for isotropic , amorphous materials . The periodic features of crystals are used to classify them into six crystal systems , * and further arrange them into 14 (Bravais) space lattices , 32 point groups , and 230 space groups based on the characteristic symmetries found in a crystal . Glass is by far the most widely used optical material , accounting for more than 90 percent of all optical elements manufactured . Traditionally , glass has been the material of choice for optical systems designers , owing to its high transmittance in the visible- wavelength region , high degree of homogeneity , ease of molding , shaping , and machining , relatively low cost , and the wide variety of index and dispersion characteristics available . Under the proper conditions , glass can be formed from many dif ferent inorganic mixtures . Hundreds of dif ferent optical glasses are available commercially . Primary glass-forming compounds include oxides , halides , and chalcogenides with the most common mixtures being the oxides of silicon , boron , and phosphorous used for glasses transmitting in the visible spectrum . By varying the chemical composition of glasses (glasses are not fixed stoichiometrically) , the properties of the glass can be varied . Most notably for optical applications , glass compositions are altered to vary the refractive index , dispersion , and thermo-optic coef ficient . Early glass technologists found that adding BaO of fered a high-refractive-index glass with lower than normal dispersion , B 2 O 3 of fered low index and very low dispersion , and by replacing oxides with fluorides , glasses could be obtained with very low index and very low dispersion . Later , others developed very high index glasses with relatively low dispersions by introducing rare-earth elements , especially lanthanum , to glass compositions . Other compounds are added to silica-based glass mixtures to help with chemical stabilization , typically the alkaline earth oxides and in particular Al 2 O 3 to improve the resistance of glasses to attack by water . To extend the transmission range of glasses into the ultraviolet , a number of fluoride and fluorophosphate glasses have been developed . Nonoxide glasses are used for infrared applications requiring transmission beyond the transmission limit of typical optical glasses (2 . 4 to 2 . 7 m m for an absorption coef ficient of 1 cm 2 1 ) . These materials include chalcogen- ides such as As 2 S 3 glass and heavy-metal fluorides such as ZrF 4 -based glasses . Crystalline materials include naturally occurring minerals and manufactured crystals . Both single crystals and polycrystalline forms are available for many materials . Polycrys- talline optical materials are typically composed of many small (cf ., 50 m m) individual * Cubic (or isometric) , hexagonal (including rhombohedral) , tetragonal , orthorhombic , monoclinic , and triclinic are the crystallographic systems . PROPERTIES OF CRYSTALS AND GLASSES 33 .7 crystals with random orientations and grain boundaries between them . These grain boundaries are a form of material defect arising from the lattice mismatch between individual grains . Polycrystalline materials are made by diverse means such as pressing powders (usually with heat applied) , sintering , or chemical vapor deposition . Single crystals are typically grown from dissolved or molten material using a variety of techniques . Usually , polycrystalline materials of fer greater hardness and strength at the expense of increased scatter . Uniformity of the refractive index throughout an optical element is a prime considera- tion in selecting materials for high-performance lenses , elements for coherent optics , laser harmonic generation , and acousto-optical devices . In general , highly pure , single crystals achieve the best uniformity , followed by glasses (especially those selected by the manufacturer for homogeneity) , and lastly polycrystalline materials . Similarly , high-quality single crystals have very low scatter , typically one-tenth that of glasses . Applications requiring optical elements with direction-dependent properties , such