## Highlights

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The translucency of 3Y-TZP has been examined using the Rayleigh scattering model.

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The in-line transmission of 3Y-TZP increased with decreasing grain size and thickness.

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To achieve a translucency similar to porcelains, a nanostructured 3Y-TZP was needed.

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At 1.3 mm thickness, the mean grain size of a translucent 3Y-TZP should be 82 nm.

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At 1.5 mm and 2 mm thicknesses, the mean grain size needed to be 77 nm and 70 nm, respectively.

## Abstract

## Objective

The aim of this study was to provide a design guideline for developing tetragonal yttria-stabilized zirconia with improved translucency.

## Methods

The translucency, the in-line transmission in particular, of 3 mol.% yttria-stabilized tetragonal zirconia (3Y-TZP) has been examined using the Rayleigh scattering model. The theory predicts that the in-line transmission of 3Y-TZP can be related to its thickness with grain size and birefringence the governing parameters. To achieve a threshold value of translucency, the critical grain size of 3Y-TZP was predicted for various thicknesses (0.3–2.0 mm). The threshold value was defined by a measured average in-line transmission value of a suite of dental porcelains with a common thickness of 1 mm. Our theoretical predictions were calibrated with one of the very few experimental data available in the literature.

## Results

For a dense, high-purity zirconia, its in-line transmission increased with decreasing grain size and thickness. To achieve a translucency similar to that of dental porcelains, a nanocyrstalline 3Y-TZP structure was necessitated, due primarily to its large birefringence and high refractive index. Such a grain size dependence became more pronounced as the 3Y-TZP thickness increased. For example, at a thickness of 1.3 mm, the mean grain size of a translucent 3Y-TZP should be 82 nm. At 1.5 mm and 2 mm thicknesses, the mean grain size needed to be 77 nm and 70 nm, respectively.

## Significance

A promising future for zirconia restorations, with combined translucency and mechanical properties, can be realized by reducing its grain size.

## 1

## Introduction

Yttria-stabilized tetragonal zirconia polycrystal (Y-TZP) has been used as a dental restorative material for over a decade . While it is still the strongest and toughest ceramic ever used in dentistry, its esthetics—in particular, its translucency—remains as a major drawback. The opacity of zirconia becomes a problem especially when placing an anterior crown or shortspan fixed dental prosthesis in the presence of other anterior natural teeth. In this case, the reflectance and light scattering do not always appear natural. In order to create space for a porcelain veneer thick enough to cover the opaque zirconia core and to match the optical properties of the adjacent natural dentition, a substantial reduction of tooth structure is required. In addition, in an effort to prevent veneer chipping and delamination , monolithic zirconia is often used in full arch restorations, posterior crowns and fixed dental prostheses . In these cases, the opacity of zirconia can pose a problem.

After a decade of research and development, some progress has been made in improving the translucency of Y-TZP (e.g. increase the density of zirconia and eliminate the alumina sintering aid). However, close examinations have revealed that unless it is thin (<0.5 mm), the so-called commercial translucent Y-TZP restorative materials remain predominantly opaque. Beyond such phenomenon lies a critical question: how do we improve the translucency of Y-TZP? To answer this question, we must begin with the interactions of light and solids.

Light, X-rays, and heat are all part of electromagnetic waves; each is characterized by a specific range of wavelengths. X-rays have a wavelength typically in the range of 0.01–10 nm, while visible light lies between 400 nm (violet) and 700 nm (red). Under daylight conditions, the normal human eye is most sensitive to a wavelength of 555 nm, leading to a perception that green light, at this wavelength, is far “brighter” than the light at other wavelengths.

When light proceeds from air into a solid, part is reflected, part is absorbed, but part may be transmitted. Reflection occurs at the interfaces between the solid and air. Absorption happens when a photon of light transfers its energy and momentum to a valence band electron, excites the electron, across the band gap, into the conduction band. Naturally, these excitations with the accompanying absorption can take place only if the photon energy is greater than that of the band gap. The band gap of Y-TZP is around 5.2 eV and 6.0 eV according to the theoretical calculation and experimental determination, respectively . Both values are much greater than the maximum energy 3.1 eV associated with the minimum wavelength 400 nm of visible light, suggesting that no significant adsorptions occur over the visible region of the spectrum. The question then arises: what makes an inherently transparent Y-TZP material opaque? In the following section, we examine the light transmission properties of Y-TZP.

Light that transmitted into the interior of Y-TZP may experience interior reflection and refraction; the phenomenon is termed as scattering. This internal light scattering may result from several sources, including pores, impurities, defects, and grain boundaries ( Fig. 1 ).

The influence of pore size and pore population on light scattering in zirconia has been examined by a number of authors . It was found that pore sizes in the range of 200–400 nm (typical of the current dental zirconia) and pore populations as low as 0.05% can significantly relegate the translucency of Y-TZP. The dental community is well-aware the deleterious effect of porosity on zirconia translucency. Measures, such as high sintering temperatures (1510–1550 °C) coupled with prolonged dwell time (up to 6 h) (BruxZir, Glidewell, Newport Beach, CA), have been taken to ensure a respectable density.

Impurities that have different refractive index than zirconia (e.g. alumina sintering additives) can dampen the translucency of Y-TZP . (The index of refraction for alumina and zirconia, at 600 nm wave length, is *n *= 1.76 and *n *= 2.21, respectively.) In this case, scattering of light occurs when a light beam travels across the two phase boundaries. To achieve a better translucency, some dental manufacturers have eliminated the light-scattering alumina sintering aids (e.g. Glidewell, Newport Beach, CA and 3M ESPE AG, Seefeld, Germany).

Point defects, such as oxygen vacancies, can form in the Y-TZP lattice, thus, absorbing light . This is especially the case for Y-TZPs sintered in reduced atmosphere or a controlled environment. Post-sintering heat treatment in air is, therefore, necessary to diffuse oxygen back into crystal lattice, eliminating the oxygen vacancies .

Finally, tetragonal zirconia crystal is birefringent, meaning that the index of refraction is anisotropic in different crystallographic directions . In polycrystalline Y-TZPs, birefringence results in the discontinuity of the refractive index at the grain boundaries if the adjacent grains do not have the same crystallographic orientation. This causes both reflection and refraction at grain boundaries, leading to diversions in the incident beam and thus reductions in light transmittance.

There has been a large volume of literature concerning the transparency/translucency of yttria-stabilized zirconia (YSZ); most of which has been focusing on the development of transparent cubic YSZ (fully stabilized with 8 mol.% or more yttria), due primarily to its isotropic refractive index property and thus the absence of scattering from birefringent grain boundaries . The problem is that the strength of fully stabilized cubic zirconia can only attain one-half to two-thirds of that of partially stabilized tetragonal zirconia . Few studies have investigated the translucency/transparency properties of 3 mol.% Y-TZP . The findings suggest that nanocrystalline 3Y-TZP may potentially exhibit both desirable translucency and mechanical properties . The challenge, however, lies in the fabrication of such high-quality nanocrystalline structures with little to no porosity and defects.

Several authors went on to predict the desirable grain size of 3Y-TZP for obtaining a good translucency/transparency using light-scattering models . Following a pioneering theoretical treatment on the transparent property of alumina , Krell et al. used the Rayleigh–Gans–Debye (RGD) scattering model to predict the dependence of translucency on the grain size of 3Y-TZP. However, these authors later discovered that the RGD approximation works perfectly for alumina (example see Ref. ) but not 3Y-TZP, due to a large birefringence of 3Y-TZP relative to alumina . Klimke et al. used the Mie scattering model—a solution of Maxwell’s equations for electromagnetic waves—to elucidate the translucency of 3Y-TZP . However, only limited cases—two ceramic thicknesses (0.5 mm and 1.0 mm) at two wavelengths of the incident light (500 nm and 640 nm)—were examined. In addition, the Mie solution involves infinite series, which requires numerical simulation using computer codes, and thereby is not preferred over its approximations—the RGD or the Rayleigh scattering model.

In this study, we used a more straight forward Rayleigh scattering model—an approximation of the more general Mie scattering model—to systematically examine the effects of grain size, refractive index, birefringence, and layer thickness on the in-line transmission of 3Y-TZP. The transmittance of electromagnetic waves in the visible light range was investigated. The design philosophy in producing translucent 3Y-TZP restorative ceramics with excellent mechanical properties and phase stability through microstructural tailoring has been proposed.

## 2

## Theory

## 2.1

## Rayleigh approximation

The main factors that limit the translucency of a solid—apart from reflection and absorption—are scatting from pores, impurities, defects, and grain boundaries. For a dense, high purity and nonabsorbing 3Y-TZP, the Rayleigh approximation can be used to estimate its translucency (in-line transmission, *T *_{IT }) based on light scattering at grain boundaries due to the birefringence :

T IT = ( 1 − R ) exp − 128 π 4 r 3 18 λ 4 Δ n ave ( 2 n + Δ n ave ) 2 2 t

where Δ *n *_{ave }is the average birefringence, *n *is the refractive index, 2 *r *is the grain diameter, *t *is the thickness of 3Y-TZP, *λ *is the wavelength of the incident light, and *R *is the loss due to reflection at the solid surfaces. *Note *: Klimke et al., in Eq. (2) of their original paper, had left out a negative sign in the exponents of the natural base. The first term of the exponential function (Eq. (1) ) signifies the dominance of ceramic grain size, while the second term emphases the importance of birefringence in anisotropic crystals.

Eq. (1) describes, in a very succinct way, the interrelation between the in-line translucency and ceramic thickness with grain size and birefringence the governing parameters. In design of highly translucent ceramics, it is crucial to keep their grain size small, especially for ceramics with a high refractive index and large birefringence such as 3Y-TZP.

## 2.2

## Applicable range for the Rayleigh scattering model

Any meaningful application of the Rayleigh scattering model requires knowledge of its range of validity. Strictly speaking, Rayleigh scattering describes the elastic scattering of light by insulating particles much smaller than the wavelength of the incident light. In the case of propagation of light through polycrystalline 3Y-TZP, the criterion for Rayleigh scattering is:

2 π r n λ < 1

where *r *is the radius of the 3Y-TZP grain, *n *is the refractive index, and *λ *is the wavelength of the light. Accordingly, the upper threshold of 3Y-TZP grain size, which satisfies the criterion for Rayleigh scattering, can be estimated using Eq. (2) . Consider the shortest (370 nm) and the longest (750 nm) wavelengths that the human eye recognizes, the maximum grain size for Rayleigh scattering ranges from 50 nm to 110 nm.

## 2.3

## Index of refraction

The refractive index is arguably the most important optical property of a material; it generally varies with the wavelength of light *n *( *λ *). We use one of the very few comprehensive refractive index data available for zirconia ( refractiveindex.info/ ), and plot it as a function of wavelength in Fig. 1 b (solid curve). The shaded area represents the visible light region ( *λ *= 400–700 nm). As one can see, the refractive index of zirconia, *n *, increases drastically as the wavelength approaches the UV regime (<400 nm), but gradually decreases as the wavelength enters the visible spectrum and beyond. The *n *– *λ *curve is then calibrated against experimental data from the literature. Individual data points of various symbols in Fig. 1 b are experimental data for 3Y-TZP (square ) and 4.5Y-TZP (circles ). The measured *n *values for 3Y-TZP sit on the *n *– *λ *curve, whereas those for 4.5Y-TZP lie just below the *n *– *λ *curve. It has been reported that, for a given wavelength, *n *decreases as the Y _{2 }O _{3 }content increases . This observation agrees with the fact that the *n *values for 4.5Y-TZP determined by French et al. are slightly lower than the *n *– *λ *curve for 3Y-TZP, which boosts the confidence on the *n *( *λ *) data utilized.

As alluded to in our Introduction, when light strikes a solid, some will be reflected. If the incident light is normal to the solid surfaces, the loss of reflection, *R *, at the front and back faces of a solid is given by <SPAN role=presentation tabIndex=0 id=MathJax-Element-3-Frame class=MathJax style="POSITION: relative" data-mathml='R=1−2nnair/(n2+nair2)’>R=1−2nnair/(n2+n2air)R=1−2nnair/(n2+nair2)

R = 1 − 2 n n air / ( n 2 + n air 2 )

, where *n *and *n *_{air }are the refractive indices of solid and air, respectively. Using the *n *( *λ *) data for 3Y-TZP from Fig. 1 b and *n *_{air }≈ 1 for air in the visible range, the loss due to reflection at both the front and back surfaces of Y-TZP can be predicted by <SPAN role=presentation tabIndex=0 id=MathJax-Element-4-Frame class=MathJax style="POSITION: relative" data-mathml='R=1−2n/(n2+1)’>R=1−2n/(n2+1)R=1−2n/(n2+1)

R = 1 − 2 n / ( n 2 + 1 )

, and results are plotted in Fig. 1 c. Assuming no scattering from the grain boundaries and pores and no absorption occurred, the maximum theoretical transmission, *T *, of 3Y-TZP can be estimated by <SPAN role=presentation tabIndex=0 id=MathJax-Element-5-Frame class=MathJax style="POSITION: relative" data-mathml='T=1−R=2n/(n2+1)’>T=1−R=2n/(n2+1)T=1−R=2n/(n2+1)

T = 1 − R = 2 n / ( n 2 + 1 )

( Fig. 1 c). In the visible spectrum (shaded area in Fig. 1 c), 3Y-TZP has a higher refractive index value relative to other dental ceramics. For instance: alumina ( *n *∼ 1.76) , lithium disilicate ( *n *∼ 1.55 ), leucite ( *n *∼ 1.51 ), and porcelain ( *n *∼ 1.50 ). As a result, 3Y-TZP exhibits a high surface reflection and a low light transmission relative to other dental ceramics, especially in the short wavelength region.

## 2.4

## Birefringence in zirconia

Y-TZP has an anisotropic crystal structure, which causes different refractive indices in different crystalline directions. This optical anisotropy, or birefringence, can create discontinuity of the refractive index (Δ *n *) at the grain boundaries if the crystal orientations of the adjacent grains are not the same, which in turn results in light scattering. Unfortunately, reliable experimental data on Δ *n *for 3Y-TZP is not readily available. By comparing the tetragonal unit cell of zirconia to monoclinic and cubic lattices, Krell et al. predicted that the maximum Δ *n *_{max }value for 3Y-TZP should lie between 0.035 and 0.050. Assuming the 3Y-TZP grains are randomly orientated, the average birefringence can be estimated by Δ *n *_{ave }= 3/2Δ *n *_{max }. This theoretical prediction is in line with the experimentally determined Δ *n *_{max }= 0.030 for 4.5Y-TZP reported by French et al. . Thus, a range of Δ *n *_{ave }= 0.020–0.033 appears appropriate to cover the possible variations in birefringence of 3Y-TZP.