Scientific principles of the prediction and creation of film-forming materialsfor interference optics
V. F. Zinchenko
A. V. Bogatski� Physico-Chemical Institute, National Academy of Sciences of Ukraine, Odessa, Ukraine�Submitted October 26, 2005�Opticheski� Zhurnal 73, 72–77 �December 2006�
Film-forming materials �FFMs� are substances that arecapable of being evaporated and of forming rather strongcoatings on a substrate with definite optical and operationalcharacteristics. The most important optical parameters of thecoatings are the region of optical transparency, the refractiveindex, the absorption and scattering coefficients, and the ra-diation strength; the operating characteristics include adhe-sion of the coating to the substrate, mechanical strength,chemical and kinematic stability, stability against thermalshock, etc.
Not only individual elements �metals, germanium, sili-con� but also certain compounds are used as FFMs for inter-ference optics that operate in the UV, visible, and IR regions.The latter include oxides, fluorides, and chalcogenides.1–3
The fluorides �LaF3, MgF2, CaF2, LiF, and PbF2�, as well asSiO2, are the most widely used in the UV region. The oxides�SiO2, TiO2, and ZrO2� are the most widely used compoundsin the visible and near-IR regions, while the chalcogenides�ZnS, ZnSe, PbTe, and Sb2S3� are traditional FFMs for themid- and far-IR regions. The group of fluoride FFMs is dis-tinguished by low refractive index and high transparency ofthe coatings, which, however, are inadequately strong me-chanically. Oxide FFMs have higher refractive indices incoatings and possess high mechanical strength but are distin-guished by lower stability and inadequate reproducibility ofthe optical parameters. Finally, chalcogenide FFMs, whichare the only materials that are transparent in the far-IR regionand possess extremely high refractive indices, have ex-tremely poor parameters of the mechanical strength and ad-hesion to the substrate and to a layer of another FFM. Someof the indicated drawbacks are due to the very nature of thematerial, while others are caused by the presence of definiteimpurities because of imperfections in the FFM-synthesisprocess.
One of the most important characteristics of FFMs is theregion of optical transparency. Its short-wavelength edge�� � is determined by electronic transitions across the band
1
887 J. Opt. Technol. 73 �12�, December 2006 1070-9762/2006/
gap, while the long-wavelength limit ��2� is determined byvalence vibrations of the bonds. The position of the short-wavelength limit is determined by the band gap ��Eopt�,which in turn is determined by the strength �energy� of themetal-nonmetal bonds �W0�M–A��, since the electronic tran-sitions are associated with their complete or partial break-down. Consequently, to estimate the �1 value of compoundsof the same type, it is possible to use the energies of themetal-nonmetal bonds, which can be calculated �with a cor-rection for their ionicity� using the Born-Haber cycle.4 Itfollows from this that the �1 values must increase in theseries fluoride-oxide-sulfide. The binding energy and conse-quently �1 in complex FFMs acquires intermediate valuesbetween the corresponding values in binary compounds ac-cording to Vegard’s rule:
1/�1,ad = 1/�1,ad�1�g1 + 1/�1�2��1 − g1� , �1�
where �1�1� and �1�2� are the �1 values of each of the com-ponents, and g1 is the molar fraction equivalent to the first ofthem.
The value of �2 can be estimated from the position of thefirst principal absorption maximum �A1
. The approach basedon the simplest model of a harmonic oscillator for the metal-nonmetal bond is extremely useful for an approximate quali-tative estimate. We have obtained a fairly simple correlationrelation for compounds of the same type:
�2 � �A1= Bl0�M-A���M–A
* /W0�M-A� , �2�
where B is a constant, and l0�M–A�, and �M-A* are, respec-
tively, the length and reduced mass of the metal �M�-nonmetal �A� bond. It follows from this relation that �2 mustshift appreciably toward longer wavelengths when there is atransition from oxides to sulfides, since in this case the val-ues of l0�M-A� and �M-A
* increase, and there is simulta-neously an appreciable decrease of the value of W0�M–A�.The same is characteristic of chalcogenide FFMs when thereis an anion replacement of sulfur with selenium or tellurium.
An estimate shows that the �2 values of oxide FFMs liewithin the limits 7–12 �m �i.e., in the mid-IR region� and donot exceed 10–11 �m for most of them. However, the �2
values of the sulfide FFMs have a lower limit of 15 �m. Asfar as fluorides are concerned, their �2 has about the samevalues as do the oxides.
The second important optical characteristic of FFMs isthe refractive index n, which is closely connected with theshort-wavelength limit of the region of transparency by thewell-known Moss relation:
n4�Eopt = const, or n4/�1 = const. �3�
A qualitative fulfillment of this rule is illustrated in the dataof Table I for the oxides of the d metals of type MO2. Cationreplacement by a heavier analog has the opposite effect onthe value of n.5 Such a replacement causes the refractiveindex to increase in the series of p metals, whereas it isobserved to decrease in the oxides of the d metals �Table II�.The refractive index changes in a similar way, depending onthe change of the valence state of the metal. Thus, the refrac-tive index decreases as the valence of the same p metal in-creases �Table III�, whereas it increases for oxides of the dmetals. The regularities of the variation of n can be under-stood starting from the well-known Lorentz–Lorenz law, ac-cording to which, after the necessary transformations, we get
n = ��1 + 2a�/VM�/�1 − 2a�/VM� , �4�
where a is a constant, VM is the molar volume, and � is thepolarizability of the bond.
As shown by the estimate, � makes the main contribu-tion to the refractive index. It is well known that the polar-izability of the bond is greater, the smaller is the rigidity andionicity of the metal-nonmetal bonds, as well as the stabilityof the valence state of the metal. As the order number of a pmetal increases, the ionicity of the bond and its rigidity falloff �as does the stability of the highest valence state�, andthis causes n to increase. The ionicity of the bonds and thestability of the valence state of the metal in oxides of the d
TABLE I. Correlation between the short-wavelength limit of the transpar-ency region and the refractive index for oxides of the same type.
TABLE II. Dependence of the refractive index n of oxide FFMs �o
888 J. Opt. Technol. 73 �12�, December 2006
metals, on the contrary, increase with increasing order num-ber, and this causes the refractive index to decrease.
The character of the process of evaporating FFMs can beestimated from the ratio of the metal-nonmetal bonding en-ergies. Starting from the data that we obtained �Table IV�,the vacuum condensate is enriched in the component withthe smaller energy of the metal-nonmetal bond. The degreeof enrichment in this case is greater, the greater the differ-ence in the W0�M–A� values of the components. However, ifone starts only from the energy principle, a significantlylarger spread of the components during evaporation shouldbe expected.
Actually, a second factor that affects the FFM-evaporation process is the chemical interaction between thecomponents, with the formation of complex compounds. It iswell known that, because of donor-acceptor interaction, it ispossible to stabilize a definite valence state �degree of oxi-dation� of a complex-forming atom. When two binary com-pounds �for example, oxides� interact, an atom of one of themetals will occupy the inner coordination position, whereasan atom of the other metal will lie outside the coordinationsphere. The higher valence state of the former of them and ofthe lower valence state of the latter will stabilize in this case.Their properties will equalize and the system of chemicalbonds will be redistributed as a result of the donor-acceptorinteraction between the components. This in turn stabilizesthe properties of the evaporated FFMs and of the opticalcoatings based on them. The capability of such interactioncan be estimated by analyzing the properties of the startingcomponents �the diffuse reflection spectra, state diagrams,high-temperature electrical conductivity, thermal stability,enthalpy of formation, effective and equalized electronega-tivities, etc.�.
It is a rather complex problem to estimate the thermalstability of complex compounds, especially in the high-temperature region and still more in the molten state. Dataare given in Table V on the thermal stability of certain com-plex oxides of the rare-earth metals �REMs�, estimated fromthe thermodynamic functions under standard conditions.6 Asfollows from these data, the greatest thermal stability is in-herent to the phosphates and tungstates of the REMs,whereas the zirconates of the REMs are the least stable com-pounds. However, such data are available for a limited num-ber of compounds, mainly oxides, and therefore indirectmethods are often used to estimate the thermal stability. Onesuch method is to do a thermodynamic analysis of the state
formula/n value� on the position of the metal in the periodic table.
xide
888V. F. Zinchenko
diagrams of quasi-binary systems. In this method, the shapeof the liquidus curve is analyzed, which is adjacent to thedystectic point �the compound�. When the thermal dissocia-tion of the complex compound is comparatively insignificant���50% �, it is possible to use a modified Schröder equa-tion:
ln xL = �SL0�ln TL
0 − ln TL�/R , �5�
where xL and TL are the coordinates of a point of the liquidusline, �SL
0 is the entropy of melting, and TL0 is the hypothetical
dystectic temperature of the undissociating compound. Thethermal stability parameters of certain dititanates and nio-bates of the REMs at their melting points, calculated fromthis equation �Table VI�, are evidence that the indicated com-plex compounds are maintained in the molten state.
One more indirect way to estimate the stability of a com-plex compound is the method based on using the variationsof the optical properties of binary FFMs that result fromchemical interaction. Thus, when �black� EuS interacts with�dark red� In2S3, dark yellow EuIn2S4 is formed. Even morestriking is the color change when dark orange EuIn2Se4 isformed from black EuSe and In2Se3. This is evidence thatthere are negative deviations of �1 because of donor-acceptorinteraction. These deviations are associated with thestrengthening of the system of metal-nonmetal bonds mainlybecause of the increase of the ionicity of the metal-nonmetalbond �in this case, europium-chalcogen� outside the coordi-nation sphere. The band gap by comparison with the additivevalues must increase in this case; i.e.,
TABLE III. Dependence of the refractive index n of oxide FFMs
TABLE IV. Composition of thin-film condensates �coatings�.
889 J. Opt. Technol. 73 �12�, December 2006
���Eopt� = �Eopt − �Eopt ad. �6�
The stronger the interaction, the larger will be the value of���Eopt�, and consequently of the hypsochromic shift ���1�.As can be seen from the data shown in Table VII, the valueof ���Eopt� for complex oxides �orthotantalates of theREMs� is appreciably greater than for complex chalco-genides of the d metals �with the exception of the chal-cospinels of europium�. It follows from this that the ortho-tantalates of the REMs, like the chalcospinels of europium,can be extremely promising FFMs.
As far as the influence of the chemical interaction be-tween the binary components of FFMs on the position of �2
is concerned, this question has not been conclusively an-swered. Since �2 is determined by the valence vibrations ofthe “lightest” and most “rigid” of the bonds,7 namely thecation-nonmetal bond inside the coordination sphere, a sig-nificant broadening of the transparency region in the long-wavelength region should not be expected. It follows fromthe data in Table VIII that the position of �2 weakly dependson the nature of the metal outside the coordination sphere butstrongly shifts toward longer wavelengths when the intra-sphere metal is replaced by a heavier analog �for example, inthe series LnBO3–LnAlO3–LnInO3 or MGa2S4–MIn2S4�.The influence of anion replacement on �2 is discussed above.A more detailed correlation between the position of the firstprincipal absorption peak in the long-wavelength region andthe structural-energetic factor of the intrasphere metal-nonmetal bond can be tracked from the data of Table IX. The
e valence state of the metals.
on th
889V. F. Zinchenko
data shown there confirm that �2 can be predicted even forcomplex compounds.
It naturally becomes necessary to make an a priori esti-mate of the capability of binary compounds for donor-acceptor interaction. The simplest approach is to construct adefinite scale of values that is similar to the Pauling elec-tronegativities of the elements. We have developed a scale ofso-called effective electronegativities ��� of the oxides,based on the thermodynamic parameters of binary and cer-tain ternary oxides. It is based on the well-known Paulingrelation
− �Hf0 = ��2 − �1�2. �7�
If � of one of the oxides �for example BaO� is taken to beunity, it is possible to calculate � for the other oxides. Thevalue of � is in fact a measure of the donor capacity of theoxide. For an a priori estimate, we proposed the basicitycriterion:
� = − �Hf0rc
2/zc, �8�
where �Hf0 is the enthalpy of formation of the oxide, which
reflects the ionicity of the metal-oxygen bonds, zc is thecharge of the cation, and rc is the radius of the cation. As awhole, the capability of donor-acceptor interaction must cor-relate with the difference of the electronegativities ���� or
TABLE V. Thermodynamic parameter of thermal stability of complex ox-ides of the REMs.
TABLE VII. Optical factor of thermal stability of complex oxide
890 J. Opt. Technol. 73 �12�, December 2006
with the basicity factor ����. The basicity of the compoundssubstantially decreases as one goes from the oxides to thesulfides and then to the fluorides. This makes it possible topredict the possibility of creating FFMs on the basis of notonly heterocation compounds but also heteroanion com-pounds. However, it is necessary in this case to take intoaccount the different donor capability of the anions �F−, O2−,S2−�. It has been suggested that the width of the transparencyregions can be used as a criterion of basicity, i.e.,
�2/�1 = Al0�M–A��W0�M–A��M–A* . �9�
The indicated factors display a distinct correlation whenthere is cation replacement in the oxide, namely: the morebasic are the properties of the oxide, the wider the region ofoptical transparency �Table X�.
CONCLUSIONS
1. The values of �1 and n increase regularly in the seriesfluorides-oxides-sulfides of the same type of metals.
TABLE VI. Thermal characteristics of complex oxides of the REMs.
chalcogenides of the REMs.
s and
890V. F. Zinchenko
2. The �2 value is displaced toward longer wavelengths asone goes from oxides to sulfides, as well as when there isanion replacement of sulfur with selenium and tellurium.
3. When the cation is replaced by a heavier analog in theseries of p metals, the region of optical transparency ����is displaced toward longer wavelengths, whereas this pat-tern will be reversed for the oxides of the d metals. Simi-lar regularities are observed for the dependences of re-fractive index n on the valence state of the p and d metals.
TABLE VIII. Long-wavelength limit of the transparency region of com-plex oxides and chalcogenides of the REMs.
TABLE IX. Correlation of the optical and structural-energetic parametersof spinel-type compounds.
891 J. Opt. Technol. 73 �12�, December 2006
4. The character of the process of evaporating compositeFFMs can be estimated, starting from the ratio of themetal-anion �Me-A� bonding energies: A vacuum conden-sate is enriched in the component with lower Me-A bond-ing energies, with the degree of enrichment being larger,the greater the difference in the binding energies in eachof the components.
5. When two binary compounds interact, stabilization ofdefinite valence states of the metals is observed.
6. The electronegativity difference or the basicity factor canbe used a preliminary estimate of the capability of binarycompounds for donor-acceptor interaction. It has been es-tablished that the more basic the properties of the originalcompounds, the wider the optical transparency region ofthe FFMs based on them.
This prediction makes it possible to develop promisingFFMs with new functional properties.
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TABLE X. Donor-acceptor capability factors of binary oxides.
