**2. Chemical tempering**

values, since the increase in these parameters enhanced the stress relaxation process, which hinders the effect of higher ion interdiffusion. Although few porcelains with high leucite content have no strengthening response to ion exchange process, most dental porcelains can be strengthened and significant increases in fracture toughness (up to around 150%) have been reported. The same level of increase in flexural strength has been observed, but the variability of fracture stress also increases due to the relative small thickness of compressive layer and the decreasing resistance curve effect. The lower reliability is counterbalanced by significant increases of the resistance to slow crack growth phenomenon, leading to higher strength retention after long lifetimes even at low levels of fracture probability. Therefore, it is expected that the application of chemical tempering (strengthening by ion exchange) can improve the

**Keywords:** Bioceramics, dental porcelain, ion exchange, chemical tempering,

Dental porcelains have been used in dental restorations due to their good qualities, including high color stability, high resistance to stain, good biocompatibility, low thermal conductivity, high wear resistance, and capacity to mimic dental structures [1–3]. Notwithstanding, disadvantages of these restorations include high susceptibility to fracture, risk of debonding, and microleakage [4–6]. For feldspathic porcelain onlays placed in posterior teeth after 6 years, the observed cumulative survival rate was ~60%, with bulk fracture in 16% of the restorations [7]. The reported clinical success rate for maxillary anterior porcelain veneers after 10 years was 64%, and main reasons for failure were fracture (11%) and large marginal defects (20%) [2]. Similar behavior was also observed for posterior feldspathic porcelain inlays, and marginal defects and fracture were 22% and 11% of the restorations, respectively, after an 8-year period

The high susceptibility to fracture of porcelain restorations is caused by their brittle nature, that is, their low capability to absorb strain energy due to an external loading before fast crack propagation occurs. The resistance to crack propagation can be quantified by the fracture

From Griffith's energy failure criterion, the term*σ f.c*1/2 is constant, which implies that strength

) is not constant and varies inversely with the square root of critical flaw size (*c*1/2). Further‐

(1)

is fracture stress, and c is crack size that results in fracture.

*KY c Ic <sup>f</sup>* =× × s

lifetime of dental porcelain restorations.

strength, toughening, lifetime

**1. Introduction**

166 Ion Exchange - Studies and Applications

of clinical assessment [8].

toughness (*KIc*) which is given by [9,10]:

where, *Y* is a geometrical constant, σ<sup>f</sup>

(*σf*

Chemical tempering is a strengthening or toughening treatment by ion exchange process that introduces a residual compressive stress layer on the surface of glassy materials that hinders the crack propagation and increases the material resistance to fracture. In this treatment, alkali ions of the glass are removed and exchanged by other larger alkali ions from an external source at a temperature sufficiently high to promote ion interdiffusion. Figure 1 shows the sizes of different alkali ions. The most applied alkali ion pair for strengthening is the Na+ /K+ , but other pairs are also exchangeable, like Li+ by Na+ and K+ by Rb+ , depending on the glass composition [21,22].

**Figure 1.** Pauling's calculated ionic diameters for alkali metals. Data from [21]

An usual practice is to make an ion exchange treatment in sodium-containing aluminosilicate glasses with a melt of KNO3 salt, at a temperature between the melting point of salt and the glass transition temperature (Tg) of the glass. During the process, Na+ ions diffuse out from the glass into the salt and simultaneously the diffusion of K+ ions from the salt into the glass takes place, with equal and coupled counterdiffusing ion fluxes (JNa+ = JK+) to maintain the eletro‐ neutrality (Figure 2) [23].

**Figure 2.** Schematics of (a) before and (b) after ion exchange process in dental glassy porcelain. J – ion flux

During the ion exchange process, concentration gradients of K+ and Na+ are formed at the region near the glass surface that can be described by the Fick's second law, given by [22–26]:

$$\mathbf{C}\_{\rm x} = \left(\mathbf{C}\_{\rm S} - \mathbf{C}\_{0}\right) \left[\mathbf{1} - \text{erf}\left(\frac{\mathbf{x}}{2\sqrt{\tilde{D} \cdot t}}\right)\right] + \mathbf{C}\_{0} \tag{2}$$

where, *Cx* is the ion concentration at depth *x* (from surface) after ion exchange time *t*, *C*0 is the initial ion concentration in glass, erf(z) is the Gaussian error function, and *Ď* is the interdiffu‐ sion coefficient given by:

$$\tilde{D} = \frac{D\_{\text{Na}} \cdot D\_{\text{K}}}{D\_{\text{Na}} N\_{\text{Na}} + D\_{\text{K}} N\_{\text{K}}} \tag{3}$$

where, *Ni* is fractional concentration of alkali ion *i* and *Di* is its self-diffusion coefficient in mixed-alkali glass compositions, which increases exponentially with temperature by:

$$D = D\_0 \exp\left(-\frac{Q\_d}{kT}\right) \tag{4}$$

where, *D*0 is preexponential factor, *Qd* is activation energy for diffusion, *k* is Boltzmann's constant and *T* is temperature. Figure 3a shows examples of K+ concentration profiles after ion exchange at different time or temperature.

3

During the ion exchange process, concentration gradients of K+ and Na+ 1 are formed at the 2 region near the glass surface that can be described by the Fick's second law, given by [22–

*<sup>x</sup> <sup>C</sup> <sup>C</sup> <sup>C</sup> erf <sup>x</sup> <sup>S</sup>*

4 (2)

5 where, *Cx* is the ion concentration at depth *x* (from surface) after ion exchange time *t*, *C*0 is 6 the initial ion concentration in glass, erf(z) is the Gaussian error function, and *Ď* is the

*<sup>D</sup> <sup>D</sup> <sup>D</sup>*

~

8 (3)

9 where, *Ni* is fractional concentration of alkali ion *i* and *Di* is its self-diffusion coefficient in

*<sup>Q</sup> <sup>D</sup> <sup>D</sup> <sup>d</sup>* exp <sup>0</sup> 11 (4)

10 mixed-alkali glass compositions, which increases exponentially with temperature by:

 

<sup>0</sup> <sup>~</sup> <sup>0</sup>

*Na Na K K Na K D N D N*

> 

 

2

1 *C*

 

*kT*

*D t*

 

 

Running Title

7 interdiffusion coefficient given by:

14 ion exchange at different time or temperature.

3 26]:

15

place, with equal and coupled counterdiffusing ion fluxes (JNa+ = JK+) to maintain the eletro‐

**Figure 2.** Schematics of (a) before and (b) after ion exchange process in dental glassy porcelain. J – ion flux

region near the glass surface that can be described by the Fick's second law, given by [22–26]:

é ù æ ö

where, *Cx* is the ion concentration at depth *x* (from surface) after ion exchange time *t*, *C*0 is the initial ion concentration in glass, erf(z) is the Gaussian error function, and *Ď* is the interdiffu‐

> *Na K Na Na K K*

*D N DN* <sup>×</sup> <sup>=</sup> <sup>+</sup>

mixed-alkali glass compositions, which increases exponentially with temperature by:

<sup>0</sup> exp *D D Qd*

æ ö = -ç ÷

*kT*

where, *D*0 is preexponential factor, *Qd* is activation energy for diffusion, *k* is Boltzmann's

*D D <sup>D</sup>*

is fractional concentration of alkali ion *i* and *Di*

constant and *T* is temperature. Figure 3a shows examples of K+

exchange at different time or temperature.

( 0 0 ) 1

*D t*

ë û è ø <sup>×</sup> % (2)

% (3)

*<sup>x</sup> C C C erf <sup>C</sup>*

=- - + ê ú ç ÷

and Na+ are formed at the

is its self-diffusion coefficient in

concentration profiles after ion

è ø (4)

During the ion exchange process, concentration gradients of K+

2 *x S*

neutrality (Figure 2) [23].

168 Ion Exchange - Studies and Applications

sion coefficient given by:

where, *Ni*

16 **Fig. 3.** Normalized potassium concentration profiles (Equation 2) (a), and normalized 17 residual stress profile (b) in dental glassy porcelain after ion exchange process **Figure 3.** Normalized potassium concentration profiles (Equation 2) (a), and normalized residual stress profile (b) in dental glassy porcelain after ion exchange process

The bigger K+ ions that replace Na+ 18 ions tend to cause material expansion (known as ion 19 stuffing) in the exchanged surface layer, which is restricted by the non-ion exchanged glass 20 region. This situation, when the ion exchange is carried out at a temperature lower than the 21 Tg of glass, generates a residual compressive stress field parallel to the surface in the K-rich The bigger K+ ions that replace Na+ ions tend to cause material expansion (known as ion stuffing) in the exchanged surface layer, which is restricted by the non-ion exchanged glass region. This situation, when the ion exchange is carried out at a temperature lower than the Tg of glass, generates a residual compressive stress field parallel to the surface in the K-rich layer. This layer has a gradient of compressive stress similar to the potassium concentration gradient, that is, the compressive stress is high at the surface and decreases with the increase in distance from surface. In order to counterbalance the net stress state, a residual tensile stress field is generated below the compressive layer (Figure 3b).

The residual compressive stress layer adds a toughening contribution, *KRC*, which hinders crack propagation, leading to an increase in the fracture toughness in ion exchanged glass, *KIc,IE*, by:

$$\mathbf{K}\_{\ \perp \mathbf{c}, l\mathbf{E}} = \mathbf{K}\_0 + \mathbf{K}\_{\mathbf{R}\mathbf{C}} \tag{5}$$

where, *K*0 is the fracture toughness of unreinforced glass. The higher *KIc* leads to a higher fracture stress, if a flaw size *c* is unaltered (Equation 1). Therefore, the generation of a surface compressive layer by ion exchange can result in the increase in fracture toughness and strength of glasses and porcelains.

The toughening effect depends on the thickness of compressive layer, known as case depth (Figure 3b), especially when the glass contains deep surface flaws. Because of the relative slow ion exchange rate, the case depths varying from few tens to hundreds of micrometers have been reported, depending on the ion exchange parameters, including time (up to hundreds of hours of treatment have been reported), temperature, salt composition, exchangeable ionic pair, and glass composition [22,26,27].

An effect that can lower the strengthening rate by the ion exchange process is the stress relaxation that can occur during this process, leading to a reduction in the magnitude of residual compressive stress [27]. Stress relaxation occurs by viscous flow of the glass and can be described by the Maxwell's model given by [28,29]:

$$
\sigma = \sigma\_0 \exp\left(\frac{G \cdot t}{\eta}\right) \tag{6}
$$

where, *σ* is the remaining stress at time *t*, *σ*0 is initial stress, and *G* and *η* are shear modulus and viscosity of glass, respectively. Since *η* decreases strongly with temperature, the rate of stress relaxation is more rapid with the increase in temperature.

The chemical tempering has been applied to strengthen cockpit windows for aircrafts, high speed train windshields, photocopier scanner glass, display windows in mobile personal electronic devices, compact disks for portable hard drives, high-end ophthalmic glasses, and glass items for drug delivery [22,26]. Advantageous characteristics of chemical tempering include: possibility to strengthen complex geometries and thin components (thickness of up to around 100 μm), which are difficult in thermal tempering; higher compressive stress level on the surface compared to thermal tempering; low level of internal residual tensile stress, with less fragmentation and explosion-like fracture propagation; and did not cause optical distortion. Disadvantageous characteristics include: limited to alkali-containing glasses; shallow depth of residual compressive stress layer (case depth); generation of corrosive alkalicontaining salt residue; and high cost when long time of ion exchange is applied [22,26].
