Amorphization of ceramic materials by ion beam irradiation

Materials Science and Engineering A253 (1998) 106 – 113

Amorphization of ceramic materials by ion beam irradiation L.M. Wang a,*, S.X. Wang a, W.L. Gong b, R.C. Ewing a, W.J. Weber c a

Department of Nuclear Engineering and Radiological Sciences, Uni6ersity of Michigan, 2355 Bonisteel Boule6ard, Ann Arbor, MI 48109, USA b Department of Earth and Planetary Sciences, Uni6ersity of New Mexico, Albuquerque, NM 87131, USA c Pacific Northwest National Laboratory, P.O. Box 999, Richland, WA 99352, USA

Abstract Ion-beam-induced amorphization of a wide variety of ceramic materials has been investigated using in situ TEM with 1.5 MeV Kr + or Xe + ions at temperatures between 20 and 1000 K. Except for a few ‘amorphization resistant’ materials which usually have simple crystal structures, most ceramic materials under study amorphized after a fraction of a dpa (displacement per atom) at cryogenic temperatures. In general, critical amorphization dose increases with the irradiation temperature at a rate determined by the kinetics of the amorphization and crystallization processes. Based on a cascade quenching model and an analysis on the structural resistance to recrystallization, a semiempirical parameter which can easily be calculated from both structural and chemical parameters of a material, has been developed to predict the susceptibility of ceramics to amorphization. The calculated results for over ten phases in the Al2O3 –MgO–SiO2 system agree quite well with the experimental data. The results for phases in the Al2O3 –MgO –SiO2 system have also suggested a parallel in the kinetics between ion-beam-induced amorphization and glass formation. The critical amorphization temperature, above which irradiation-induced amorphization cannot be completed, is found to be closely related to the glass transition temperature. The ratio between glass transition and melting temperatures can also be used to predict the susceptibility of a ceramic material to amorphization, equivalent to the Debye temperature criterion. © 1998 Elsevier Science S.A. All rights reserved. Keywords: Ion irradiation; Amorphization; Ceramic; Glass transition; Debye temperature

1. Introduction Ceramic materials, especially complex ceramic materials, are in general, susceptible to irradiation-induced amorphization [1,2]. The relative susceptibility of crystalline ceramic phases to amorphization depends on the structure, bond-type and strength, as well as the thermodynamic stability of the phase. Despite over two decades of effort, a universal model for predicting the susceptibility of ceramic materials to irradiation-induced-amorphization has not been developed mainly because the data base has been too small. Following an extensive study on a-decay-induced metamictization (amorphization) in natural minerals [3,4], we have conducted detailed investigations on ion-beam-induced amorphization of numerous ceramic materials [5,6]. In this paper, we first summarize the results of these * Corresponding author. Tel.: +1 734 6478530; fax: + 1 734 6478531; e-mail: [email protected]

studies, and then use recent results from phases in the Al2O3 –MgO–SiO2 system to demonstrate a parallel in the kinetics between ion-beam-induced amorphization and classical glass formation. We also present the recent development on the criteria for irradiation-induced amorphization of ceramics and compare these criteria to previous models.

2. Experimental procedures The materials covered in our study includes a wide variety of structure-types [6–8] (e.g. olivine [9,10], spinel [11], apatite [12], zircon [13], monazite [14] and perovskite [15,16]) and compositions (e.g. oxides, silicates and phosphates). The critical amorphization doses and the temperature dependence (20–1000 K) have been determined for these materials by in situ transmission electron microscopy (TEM) during the ion irradiation using the HVEM-Tandem Facility at Argonne

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L.M. Wang et al. / Materials Science and Engineering A253 (1998) 106–113

National Laboratory [17]. Ex-situ cross-sectional and high-resolution TEM have been performed after low and intermediate doses to study the amorphization process in detail. Recently, phases in the MgO –Al2O3 – SiO2 ternary system were selected for study to compare the existing glass formation data. These phases include: MgO (periclase), a-Al2O3 (corundum), SiO2 (quartz), MgSiO3 (enstatite), Al2SiO5 (three polymorphs: sillimanite, andalusite and kyanite), 3Al2O3 · 2SiO2 (mullite), Mg3Al2Si3O12 (pyrope), and Mg2Al4Si5O18 (cordierite). These phases were irradiated with 1.5 MeV Xe + at a dose rate of 8.5 ×1011 ions cm − 2 s − 1 during the in situ TEM study.

3. Results

3.1. Summary of results from our pre6ious study The results of our previous studies can be briefly summarized as follows: (1) Multi-cation, complex structure-types are more easily amorphized than closepacked, simple structures. Except for a few amorphization ‘resistant’ phases (e.g. MgAl2O4), most multi-cation ceramics amorphized after a damage level of a fraction of one displacement per atom (dpa) at room temperature or below, while simple ceramics, such as MgO, ZrO2 and UO2, cannot be amorphized even at 20 K (near liquid helium temperature). The general trend in this regard is in agreement with a model based on the topology of the structures, as recently applied by Hobbs [18]; (2) materials with the same crystal structure but different chemical compositions can show substantial differences in the susceptibility to amorphization due to differences in the bond-type and strength (i.e. silicates vs. phosphates). Although the ionicity criterion [19] can often correctly predict the amorphization of ceramics with the similar crystal structures, it fails when there are large differences between the structures; (3) with a few exceptions (i.e. coesite [20] and Tl-containing high temperature superconductors [16]), the critical amorphization dose, Dc, increases with the irradiation temperature due to a competition from a thermally-enhanced recovery process [21]. Dc approaches infinity at a critical temperature, Tc. A material which is more resistant to amorphization usually has a lower Tc. Near Tc, irradiation may induce a nano-scale polygonization [22], again, due to the competition between amorphization and crystallization processes; (4) for complex ceramics, amorphization by direct impact within the displacement cascade (or subcascade) occurs even with high energy (1 –1.5 MeV) Kr + or Xe + ions which produce many smaller subcascades (2 – 5 nm in dimensions), instead of a single large cascade in the region of study [23,24]. These results have provided a rather large data base for

107

a better understanding of the amorphization process in ceramics and for the extended development of a universal model for predicting the susceptibility of ceramic materials to ion-beam-induced amorphization.

3.2. Results from the phases in the MgO– Al2O3 –SiO2 ternary system The effects of irradiation temperature on the critical amorphization dose, Dc, for six phases in the MgO– Al2O3 –SiO2 system are shown in Fig. 1. The amorphization doses in Fig. 1 are represented by En, the energy deposition by nuclear collision and the uncertainty of the measured dose is within 9 5%. MgO was irradiated at both room temperature and 20 K to doses much higher than the upper limit of vertical scale in Fig. 1, and no amorphization was observed at both temperatures. The critical amorphization dose at room temperature has been commonly used to evaluate the susceptibility of a material to amorphization. The increasing order of amorphization doses (En in eV atom − 1), or the decreasing order of susceptibility to amorphization, of the phases according to this criterion is: quartz (11)“ cordierite (16.9)“enstatite (26.3)“sillimanite, kyanite, andalusite, mullite (40–42)“ pyrope (58.9)“forsterite (65)“ a-alumina (\ 2000)“spinel (\2800)“MgO ( ). The differences in the amorphization doses among these materials are more apparent at elevated temperatures. At temperatures higher than the critical amorphization temperature, Tc, amorphization cannot occur due to enhanced thermal annealing. Tc can be calculated from a model developed by Weber et al. [13]

Fig. 1. Temperature dependence of amorphization dose of 1.5 MeV Xe + irradiation for indicated phases in the MgO – Al2O3 –SiO2 system.

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based on the temperature dependence of amorphization doses:

temperatures [26]:

ln (1−D0/Dc)= C −Ea/kT

where h0 is a temperature-independent coeficient and Q is the activation energy. Ea in Eq. (1) and Q in Eq. (2) may be related because they are both activation energies for kinetic processes involving structural rearrangement of the amorphous phase. The activation energy (Ea) in Eq. (1) represents the energy barrier for recrystallization during irradiation. The higher the activation energy for recrystallization, the easier the material may be amorphized by the ion beam, especially at elevated temperatures. Thus, the material is more susceptible to amorphization. The activation energy Q in Eq. (2) represents the energy barrier to viscous flow. The higher the activation energy for viscous flow, the easier a glass may be made by quenching. If irradiation-induced amorphization is the result of processes similar to liquid quenching, the two activation energies should be related. The activation energies for dynamic annealing during irradiation can be calculated by applying Eq. (1) to the experimental data presented in Fig. 1. The viscosity data from [27] have been used to calculate the activation energies for the viscous flow, through Eq. (2), for different compositions in the MgO–SiO2 and Al2O3 –SiO2 binary systems. The variations of these two activation energies with the composition are plotted in Fig. 2(a) and (b) for the two binary systems. Three features can be noted in Fig. 2(a) and (b): (1) Both activation energies decrease with increasing Al2O3 or MgO content, which indicates that increasing Al2O3 or MgO content lowers the viscosity and leads to easier annealing; (2) The decreases in both activation energies show a parallel trend. This suggests that the ion irradiation-induced amorphization can be related to the ease of viscous flow of the melts; (3) The activation energy for viscous flow is 50 times greater than that of the radiation-enhanced annealing activation energy. The differences in the values of the two activation energies are probably due to the different scales represented in Eqs. (1) and (2) for the two different processes. For viscous flow, the activation energy, Q, represents the energy barrier for the movement of molecular groups. For the process during irradiation, the activation energy, Ea, represents the energy barrier to epitaxial recrystallization, which only requires atomic-scale rearrangement. In this analysis, the absolute value for the activation energy is not important; however, of critical importance is the variation of these two activation energies with the chemical composition which reveals a parallel trend between glass formation and ion-beam-induced amorphization. In these two binary systems, the ease of glass formation and the susceptibility to ion-beam-induced amorphization both decrease with the increasing Al2O3 or MgO content.

(1)

where Dc is the amorphization dose at temperature T in Kelvin; D0 is the amorphization dose extrapolated to T =0 K; C is a constant at a given dose rate; Ea is the activation energy for an irradiation-enhanced annealing process; k is Boltzmann’s constant. The critical temperatures (Tc) calculated using this model are: quartz (1400 K), sillimanite (1375 K), kyanite (1281 K), cordierite (983 K), andalusite (982 K), pyrope (868 K), enstatite (797 K), mullite (595 K), forsterite (497 K) and alumina (123 K), spinel (20 K), MgO (B 20 K). Materials with a higher Tc are more susceptible to ion-beam-induced amorphization than these with a lower Tc in a wider temperature range. Note, for the MgO – SiO2 and Al2O3 –SiO2 binary systems, the susceptibility of phases to ion-beaminduced amorphization decreases with the increasing Al2O3 or MgO content.

4. Discussion

4.1. Comparison with glass formation Heavy ion (with masses comparable to the target atoms) irradiation-induced amorphization of ceramics, especially multi-cation complex ceramics, can occur directly in the displacement cascade. The cascade evolution, in a certain way, is an analogue to the liquid quenching process [19,25]. During the initial collision, a region of disorder is created inside the cascade. The cascade region may be identified as a hot, molten zone. The energy within a cascade dissipates rapidly to the surrounding matrix. Through a process which lasts for only  10 ps, the molten zone returns to a solid state. This resembles a rapid quenching process, with a cooling rate of 1015 K s − 1 [25]. In metallic materials, where the annealing rate is usually high, there might only be a few isolated point defects remaining after cooling of the cascade. However, in ceramic materials, where annealing rate is much lower, part of the disorder inside the cascade may be ‘frozen in’ leaving a small amorphous volume. The accumulation of these small amorphous volumes at higher ion doses eventually leads to the amorphization of the entire crystalline phase. Because the cascade quenching process may resemble glass formation by liquid quenching, we have investigated the properties related to glass formation, such as viscosity, to examine the susceptibility of various phases to irradiation-induced amorphization. In many glass-forming systems, the viscosity, h, fits an Arrhenius-type equation over a certain range of

h= h0 exp (Q/RT)

(2)

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less readily quenched to form a glass. The same is true for MgO. As a network-modifier, MgO decreases the stability of the network. The addition of MgO leads to easier crystallization or more difficult glass formation. MgO favors crystallization more than Al2O3, so MgOenriched phases are more ‘resistant’ to ion-beam-induced amorphization. Comparing the viscosity curves in Fig. 3(a) and (b), adding MgO to SiO2 causes a more abrupt decrease in viscosity than adding Al2O3 to SiO2. This corresponds to the faster increase in critical amorphization dose with the increasing MgO-content than with the Al2O3-content. MgO cannot be amorphized, even when irradiated at a temperature of 20 K. We emphasize that by recognizing a parallel between glass formation and ion-beam-induced amorphization of ceramics, we do not imply that the structures of the amorphous phases produced by the two, still unique, processes are necessarily the same. As reported by Sales et al. [28,29], there are structural differences between the glass state and ion-beam-amorphized states of lead pyrophosphate. Qin and Hobbs [30] have also reported structural differences between vitreous silica and quartz amorphized by electrons and neutrons. There are several major differences between the glass formation by

Fig. 2. The variations of the activation energies for viscous flow and dynamic annealing during irradiation with chemical composition for (a) Al2O3 – SiO2 and (b) MgO–SiO2 system.

The rate of crystallization from a melt is largely affected by viscosity [26]. Indeed, viscosity is a measure of the ease of molecular or structural rearrangement. In Fig. 3(a), the critical doses (in dpa) for ion-beam-induced amorphization (at room temperature and 573 K) are plotted together with the viscosities (at melting temperatures) against the Al2O3 content for the Al2O3 – SiO2 binary system. In Fig. 3(b), the critical amorphization dose at room temperature and the viscosities at melting temperatures are plotted against the MgO content for the MgO – SiO2 binary system. With the change in composition, the amorphization doses show a negative correlation with the viscosities at the melting temperature. This suggests that the rate of molecular rearrangement or the viscosity at the melting temperature can be used as a qualitative indicator for susceptibility to ion irradiation-induced amorphization. As a typical network former, SiO2 is a good glass-former as well as the easiest to amorphize under ion irradiation, and silica has the highest viscosity at its melting point. Al2O3, an intermediate between network-formers and network-modifiers, improves the kinetics of crystallization. Thus, with increasing Al2O3 content, the material is more difficult to amorphize under ion beam and is

Fig. 3. (a) Chemical composition dependence of viscosity (at melting temperature) and critical amorphization doses (at T= 298 and 573 K, respectively) in (a) Al2O3 – SiO2 and (b) MgO – SiO2 binary system.

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quenching and ion-beam-induced amorphization processes (e.g. in quenching rate, local pressure and the degree of local disordering); however, we do note a qualitative similarity in the kinetics of the two amorphization processes.

coordination number); ai is the cation-anion distance; c and d are constants (c= 0.3, d= 0.1). The relationship between S and the critical amorphization dose, Dc, at a certain irradiation temperature, T, is presented in a recent model for the temperature effect on ion-beam-induced amorphization [36].

4.2. Susceptibility to irradiation-induced amorphization Dc = Based on a consideration of glass-forming ability, which emphasizes the structural geometry of the crystalline form [31,32], Hobbs [18,33,34] has evaluated the susceptibility of materials to amorphization according their structural topologies. With this approach, the ease of amorphization is predicted by calculating the structural freedom, f: f = d−C{d − d (d + 1)/2V} − (d −1) (Y/2) −[(p− 1) d − (2p − 3)](Z/p)

(3)

where d is the number of degrees of freedom (= 3); C is the connectivity, which is the number of polytopes common to a vertex; d is the dimensionality of the structural polytope; V is the number of vertices of structural polytope; Y is the fraction of edge-sharing vertices; Z is the fraction of vertices sharing p-sided faces. We have constructed a semi-empirical parameter, S, which is based on both structure and bonding properties of a material, in order to describe the susceptibility to irradiation-induced amorphization of ceramic materials [35]. S consists of three factors: (1) the structural factor, G, of cation polytopes; (2) bond strength, F, based on the field strength; and (3) upward phase transition temperature, Ts, which is a parameter related to the driving force for crystallization. The three factors are summed in the following equation: S = f (Ts) · %xi · Gi · F ci

(4)

i

in which, Gi = Fi =

 

1 n · sh Ci nT

2

z1 · z2 a 2i

f (Ts)=

1 , T ds

where Ts is the phase transition temperature (K); xi is the mole fraction of ith cation (anions are not counted); Ci is connectivity, which is the number of polytopes shared at one corner anion and equals the coordination number of the anion; nsh is the number of shared polytope corners; nT is the number of total polytope corners for one cation; z1 and z2 are effective electrostatic charges (equal to the charge of cation divided by



1 ln (DC) · 2 · A ln [(Tm − Tc)/(Tm − T)]



(5)

where DC is the detection limit for the crystalline fraction remaining in a thin foil at Dc. Thus, Dc is actually the critical dose needed for producing an amorphous fraction and equals (1− DC) instead of complete amorphization. A is the cross-sectional area of the cumulative displacement cylinder caused by one incident ion; Tm is the melting temperature, Tc is the critical temperature above which amorphization will not occur under irradiation, which varies with the ion mass, energy and the target mass. The derivation of Eq. (5) assumes that radiation-induced amorphization is produced by accumulating an amorphous fraction. By least square refinement of the experimental data according to Eq. (5), Tc can be calculated. The Tc values obtained according to Eq. (5) are similar to those obtained using Eq. (1). The relation of S to Tc is: S= A/(Tm − Tc)

(6)

where A is a constant that is mainly dependent on the cascade size. From Eqs. (5) and (6), the amorphization dose, Dc, at low temperatures is expected to be approximately: S= A · exp(B/Dc)

(7)

where both A and B are constants. Using energy deposition, En (Ev atom − 1), instead ion cm − 2 for the critical dose, we can replace Dc with En. The S value obtained with Eq. (7) can then be regarded as a normalized value for the critical amorphization dose. With Eqs. (6) and (7), S can be determined experimentally either through Tc or Dc at low temperatures. The normalized critical amorphization doses (i.e. experimental S values obtained with Eq. (7)) for the phases used in this study are compared with the S values calculated from Eq. (4) in Fig. 4. The correlations are quite good.

4.3. Comparison with the Debye temperature criterion From a thermodynamic perspective, solid-state amorphization (or the c–a transformation) is analogous to melting [37–39]. In particular, Lam and Okamoto’s model [40,41] supports a generalized phenomenological form of the Lindemann melting criterion, which leads to an interpretation of the c–a transformation as defect-induced melting of metastable crystals by consider-

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that all the amorphous phases have a similar Debye temperature. However for the 20 ceramic materials studied, B50% of the predictions are correct using this assumption. Garoche and Bigot have extended Lindermann’s formula for melting to include the amorphous state by considering Tg as the melting temperature of the amorphous phase and given the following relationship [43]: Tg/Tm = u 2a/u 2c

Fig. 4. Comparison of S values with the normalized critical amorphization dose [A exp(B/En)] at room temperature.

ing static atomic displacements as a measure of chemical and topological disorder in the solid. In imperfect crystals, atomic defects create significant static displacements, msta, in addition to displacements resulting from thermal vibrations, mvib. The c – a transformation in such crystals is interpreted as melting which occurs when the sum of the dynamic and static mean-square displacements, m 2sta +m 2vib, reaches a critical value, m 2cri. For Debye solids, the scaling relationship can be expressed as: Td/Tm =u 2d/u 2c =Gd/Gc =(1 −m 2sta/m 2vib),

(8)

where Td is the temperature at which the defective crystal becomes destabilized when (m 2sta +m 2vib) \m 2cri; ud and uc are the Debye temperatures for the defective and perfect crystals, respectively; Gd and Gc are the average shear elastic constants of the defective and perfect crystals. As DHd =DHa (u 2c −u 2d)/(u 2c −u 2a), where DHd is the enthalpy increase in the defective crystal and DHa is the difference between the amorphous and crystalline state, respectively, it is clear that DHd =DHa whenever the defective crystal is driven to a critical state of disorder where its Debye temperature becomes equal to that of the amorphous phase. Thus, (uc −ua) can be used to precisely predict amorphization susceptibility of materials upon energetic particle irradiation [40]. A material can be expected to be more susceptible to defect-induced amorphization when (uc −ua) is small. This prediction is confirmed by some available measurements on intermetallics such as made by Xu et al. [42]. However, the Debye temperature criterion for predicting the amorphization susceptibility is difficult in application, because there are limited data on the Debye temperatures of the amorphous phases. One may use the Debye temperatures of the crystalline state to predict the amorphization susceptibility by assuming

(9)

Comparing Eq. (9) to the Debye temperature criterion, (uc − ua), we note that both Tg/Tm and (Tm −Tg) are excellent parameters for predicting the amorphization susceptibility of a crystalline phase if the Debye temperature criterion is correct. Whenever (uc −ua) is small, u 2a − u 2c is large, as is Tg/Tm according to Eq. (9). When Tg B Tm, which is true for most of the cases, a larger Tg/Tm corresponds to a smaller (Tm −Tg). The major advantage of replacing (uc − ua) with Tg/Tm or (Tm − Tg) for predicting the amorphization susceptibility is that for many ceramics both Tm and Tg are readily available. Table 1 shows that (Tm − Tg) and Tg/Tm are excellent parameters for the prediction of amorphization susceptibility. In this case, the critical amorphization temperature, Tc, is used as a measure of the amorphization susceptibility. The higher the Tc, the more susceptible a material is to amorphization. This is even valid at low temperatures because for most materials the curves for critical amorphization dose (adjusted to dpa) do not cross each other with increasing temperature, i.e. a material which requires a lower dose for amorphization at low temperatures (room temperature or below) usually shows a higher Tc as well. Another value of using Tc instead of Dc at cryo- or room temperatures for comparison is that for many phases the Dc value is so close at low temperatures that the uncertainty in the displacement energy may cause a change in the relative ranking. The prediction of amorphization susceptibility with (Tm − Tg) and Tg/Tm is consistent with the experimental measurements, as well as with the predictions made by the S values [35]. It should be noted that both Tc and Tg are kinetically related parameters. Tg may increase with the cooling rate and Tc depends critically on the irradiation conditions (e.g. increases with the increasing dose rate and ion mass) [44]. However, they both seem to approach an upper limit with increased cooling rate or dose rate. Generally, the Tc values measured by in situ TEM during ion irradiations are a little below the reported Tg values. The calorimetrically determined Tg can thus be considered to be the upper limit of the Tc that can be reached for irradiation-induced amorphization. Another limitation of the Debye temperature criterion is exemplified by the comparison of the (uc −ua) data with experimental results for the silica poly-

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Table 1 Comparison of the Tg/Tm criterion with the critical amorphization temperature, Tc, and the S values Materials

Tg (K)

Tm (K)

Tg/Tm

(Tm−Tg)

Tc (K)

S

SiO2 (quartz) GeO2 (rutile) Mg2Al4Si5O18 Al2SiO5 CaAl2O4 Al6Si2O13 MgSiO3 Mg2SiO4 Al2O3 MgAl2O4 MgO

1480 980 1118 1047a 1003 961a 874 672a

1700 1350 1740 1818 1873 1920 1830 2163 2345 2408 3125

0.87 0.73 0.64 0.58 0.53 0.50 0.48 0.31

220 370 622 771 870 959 956 1491

52.52

0.02

2358

1400 920 985 900 758 616 780 550 123 100 B20

50a

36.94 31.94 31.04 30.47 22.48 15.42 15.32 7.68

Most Tg data were from Richet and Bottinga [46,47], and Bottinga et al. [48]. Calculated from existing high-temperature viscosity data from Urbain et al. [49]; Bansal and Doremus [50]. These calculated values may contain relatively larger errors. a

morphs. The (uc − ua) value for quartz is 67; for coesite, 172; and for stishovite, 721. These data predict a reversal of susceptibility to amorphization if the Debye temperature criterion is applied. The importance of the thermodynamic metastability on amorphization has been illustrated by recent studies on solid-state amorphization of coesite which experience thermodynamic melting below its glass transition temperature [20,45]. The same limitation applies when Tg/Tm is used as a criterion for predicting the susceptibility to amorphization.

Acknowledgements The authors thank Professor R.H. Doremus of Rensselaer Polytechnic Institute for valuable discussions on glass formation, the staff of the HVEM-Tandem Facility at Argonne National Laboratory for assistance during the ion irradiation and in situ TEM. This work was supported by DOE/BES grant DE-FG02-97ER45656 (UM) and DE-AC06-76RLO-1830 (PNNL).

References 5. Conclusions 1. Ceramic materials with complex structures and compositions are generally susceptible to ion-beaminduced amorphization. 2. In general, critical amorphization dose increases with the irradiation temperature at a rate determined by the kinetics of the amorphization and crystallization processes. 3. Based on results obtained from phases in the Al2O3 –MgO– SiO2 system, ion-beam-induced amorphization of ceramic materials is a process kinetically parallel to glass formation by quenching from a melt. 4. A semiempirical parameter, S, which can easily be calculated from both structural and chemical parameters of a material, has been developed as a relative measure of susceptibility to amorphization. 5. The ratio or difference between the glass transition and melting temperatures (Tg/Tm or Tm − Tg) is equivalent to the Debye temperature difference used in Lam and Okamoto’s model [38,40]. Thus, Tg/Tm (or Tm − Tg) can be used to predict susceptibility to amorphization.

[1] H. Matzke, Radiat. Eff. 64 (1982) 3. [2] L.W. Hobbs, F.W. Clinard, S.J. Zinkle, R.C. Ewing, J. Nucl. Mater. 216 (1994) 291. [3] R.C. Ewing, B.C. Chakoumakos, G.R. Lumpkin, T. Murakami, MRS Bull. 12 (4) (1987) 58. [4] R.C. Ewing, Nucl. Instrum. Methods B91 (1994) 22. [5] L.M. Wang, R.C. Ewing, MRS Bull. 17 (5) (1992) 38. [6] R.C. Ewing, L.M. Wang, W.J. Weber, Mater. Res. Soc. Symp. Proc. 373 (1995) 347. [7] L.M. Wang, R.K. Eby, J. Janeczek, R.C. Ewing, Nucl. Instrum. Methods B59/60 (1991) 395. [8] R.K. Eby, R.C. Ewing, R.C. Birtcher, J. Mater. Res. 7 (1992) 3080. [9] L.M. Wang, R.C. Ewing, Mater. Res. Soc. Symp. Proc. 235 (1992) 333. [10] L.M. Wang, W.L. Gong, R.C. Ewing, Mater. Res. Soc. Symp. Proc. 321 (1994) 405. [11] L.M. Wang, W.L. Gong, N. Bordes, R.C. Ewing, in: J.S. Williams, R.G. Elliman, M.C. Ridgway (Eds.), Ion Beam Modification of Materials, Elsevier, 1996, p. 1073. [12] L.M. Wang, M. Cameron, J.W. Weber, in: P.W. Brown, B. Constantz (Eds.), Hydroxyapatite and Related Materials, CRC Press, 1994, p. 243. [13] W.J. Weber, R.C. Ewing, L.M. Wang, J. Mater. Res. 9 (1994) 688. [14] A. Meldrum, L.M. Wang, R.C. Ewing, Nucl. Instrum. Methods B116 (1996) 220. [15] L.M. Wang, A.Y. Wu, R.C. Ewing, Mater. Res. Soc. Symp. Proc. 268 (1992) 343.

L.M. Wang et al. / Materials Science and Engineering A253 (1998) 106–113 [16] P.P. Newcomer, J.C. Barbour, L.M. Wang, E.L. Venturini, J.F. Kwak, R.C. Ewing, M.L. Miller, B. Morosin, Physica C267 (1996) 243. [17] C.W. Allen, L.L. Funk, E.A. Ryan, S.T. Ockers, Nucl. Instrum. Methods B40/41 (1989) 553. [18] L.W. Hobbs, Nucl. Instrum. Methods B91 (1994) 30. [19] N.M. Naquib, R. Kelly, Radiat. Eff. 25 (1975) 1. [20] W.L. Gong, L.M. Wang, R.C. Ewing, J. Zhang, Phys. Rev. B54 (1996) 3800. [21] L.M. Wang, W.L. Gong, R.C. Ewing, W.J. Weber, Mater. Res. Soc. Symp. Proc. 398 (1996) 233. [22] L.M. Wang, R.C. Birtcher, R.C. Ewing, Nucl. Instrum. Methods B80/81 (1993) 1109. [23] L.M. Wang, M.L. Miller, R.C. Ewing, Ultramicroscopy 51 (1993) 339. [24] L.M. Wang, W.J. Weber, Mater. Res. Soc. Symp. Proc. 373 (1995) 389. [25] T. Diaz de la Rubia, R.S. Averback, H. Hsieh, R. Benedek, J. Mater. Res. 4 (1989) 579. [26] R.H. Doremus, Glass Science, 2nd, Wiley, New York, 1994. [27] N.P. Bansal, R.H. Doremus, Handbook of Glass Properties, Academic Press, New York, 1986. [28] B.C. Sales, J.O. Ramey, L.A. Boatner, J.C. McCallum, Phys. Rev. Lett. 62 (1989) 1138. [29] B.C. Sales, J.O. Ramey, J.C. McCallum, L.A. Boatner, J. NonCryst. Solids 126 (1990) 179. [30] L.C. Qin, L.W. Hobbs, Mater. Res. Soc. Symp. Proc. 373 (1995) 341. [31] A.R. Cooper, Phys. Chem. Glasses 19 (1978) 60.

.

[32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50]

113

P.K. Gupta, J. Am. Ceram. Soc. 76 (1993) 1088. L.W. Hobbs, J. Non-Cryst. Solids 182 (1995) 27. L.W. Hobbs, J. Non-Cryst. Solids 193 (1995) 79. S.X. Wang, L.M. Wang, R.C. Ewing, R.H. Doremus, submitted to J. Non-Cryst. Solids. S.X. Wang, L.M. Wang, R.C. Ewing, Mater. Res. Soc. Symp. Proc. 439 (1997) 619. D. Wolf, P.R. Okamoto, S. Yip, J.F. Lutsko, M. Kluge, J. Mater. Res. 5 (1990) 286. N.Q. Lam, P.R. Okamoto, R. Devanathan, M Meshii, J. Alloys Comp. 194 (1993) 447. H.J. Fetch, Mater. Trans. JIM 36 (1995) 777. N.Q. Lam, P.R. Okamoto, MRS Bull. 18 (1994) 41. N.Q. Lam, P.R. Okamoto, Surf. Coatings Tech. 65 (1994) 7. G. Xu, M. Meshii, P.R. Okamoto, L.E. Rehn, J. Alloys Comp. 194 (1993) 401. P. Garoche, J. Bigot, Phys. Rev. B28 (1983) 6886. W.J. Weber, L.M. Wang, Nucl. Instrum. Methods B91 (1994) 63. P. Richet, Y. Bottinga, Earth Planet, Sci. Lett. 67 (1984) 415. P. Richet, Y. Bottinga, Rev. Geophys. 24 (1986) 1. Y. Bottonga, P. Richet, A. Sipp, Am. Miner. 80 (1995) 305. G. Urbain, Y. Bottinga, P. Richet, Geochim. Cosmochim. Acta 46 (1982) 1061. N.P. Bansal, R.H. Doremus, Handbook of Glass Properties, Academic Press, New York, 1986. W.L. Gong, L.M. Wang, R.C. Ewing, Y. Fei, Phys. Rev. B53 (1996) 2155.

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