稀土掺杂氧化铝恒速无压烧结行为及作用机理研究
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摘要
高温结构陶瓷是未来航空、航天发动机的关键材料,氧化铝-稀土系陶瓷熔点高达1700℃以上,备受人们关注,但是通过无压烧结工艺来制备此类材料,仍然存在很多问题,如烧结过程中均一性显微结构的形成,致密度的提高以及力学性能改善等,为了实现显微结构均一,力学性能优良的此类材料的无压烧结制备,有必要就其烧结行为进行研究。
本论文以α-Al_2O_3以及纳米γ-Al_2O_3为原料,研究了稀土掺杂(RE=La、Ce、Nd、Gd、Eu、Y、Dy)氧化铝在恒速无压烧结条件下的烧结行为、膨胀行为、相变过程的影响及作用机理;建立了纯α-Al_2O_3低升温速率条件下的主烧结曲线,并研究了其烧结过程中的热行为。
以全期烧结模型为基础建立了两种粒度分布的α-Al_2O_3低升温速率条件下(低于5℃/min)的主烧结曲线。α-Al_2O_3主烧结曲线对烧结路径不敏感,烧结体的相对密度仅是时间和温度的函数,利用主烧结曲线得到的密度和Archimedes法实测密度吻合,证明了所建立主烧结曲线的有效性,因此可以对陶瓷烧结过程的致密化行为和最终密度进行预测;烧结体显微结构的演变与其密度变化密切相关,利用主烧结曲线可以预测氧化铝陶瓷烧结过程中显微结构的演化;同时主烧结曲线提供了一种计算烧结激活能的新方法,200-500nm和2-3μm两种粒度氧化铝低升温速率烧结条件下的烧结激活能分别为1035和1148kJ/mol,大于高升温速率条件下得到的值。
为了研究α-Al_2O_3恒速无压烧结过程中的热行为,对200-500nm原始粉以及10-20目的造粒后颗粒烧结过程中热力学函数进行了研究。研究表明烧结过程是一个吸热过程,相同升温速率条件下,造粒后颗粒烧结过程中的热焓要低于原始粉;两种颗粒低升温速率烧结过程中的热焓要大于高升温速率条件,这与烧结激活能的变化趋势相一致;通过直接法计算了样品的定压比热容C_p(单位为Jg~(-1)K~(-1)),发现随温度的升高,样品比热容不断增加,对两种样品1273.5K之前的比热容数据进行多项式拟合得到:200-500nm(C_p=2.70177-0.01187×T+1.35929×10~(-5)×T~2,拟合优度为0.99),10-20目(C_p=1.34048-0.00354×T+3.2239×10~(-6)×T~2,拟合优度为0.98);三种速率升温过程中,各种样品的热焓、熵以及吉布斯自由能的绝对值均在不断增加,表明样品的烧结过程是不可逆过程,以热力学函数不等式表示为dS>0或dG<0。
稀土掺杂α-Al_2O_3烧结行为研究发现,稀土与氧化铝固相反应产生三种结构化合物-重稀土为石榴石结构RE_3Al_5O_(12)(RE=Y,Dy),轻稀土为磁铅石结构REAl_(11)O_(18)(RE=Nd,La,Ce)和钙钛矿结构AIREO_3(RE=Eu,Gd);与未掺杂样品相比,稀土掺杂均提高了样品收缩开始的对应温度,其中,Nd掺杂样品提高了近200℃;掺杂促进了致密化(La除外),其中Eu掺杂样品的收缩率比未掺杂样品提高了近3个百分点,掺杂抑制了颗粒粗化(La效果最明显),基体颗粒未出现异常长大,La和Nd掺杂样品中发现了长轴状及板状颗粒,主要是部分游离晶界的高迁移率使基体离子在某些基面发生优先偏聚引起;掺钕样品的透射电镜研究表明,当Nd离子在晶界处形成过饱和状态,就会产生第二相沉淀,主要分布于基体颗粒的交接处;掺杂后样品以沿晶断裂模式为主,主要是稀土氧化物与其它氧化物的共存弱化了氧化铝的界面结合强度,然而这种晶界强度的降低对氧化铝断裂韧性的影响是有限的。
膨胀行为研究发现无论是坯体收缩前还是烧结体,其平均线膨胀系数均}JI于稀土掺杂得到较大提高;对于坯体样品,Nd掺杂样品最大为8.59×10~(-6)/℃,而未掺杂样品为6.78×10~(-6)/℃,轻稀土元素相对于重稀土元素,更有利于提高氧化铝坯体的热膨胀系数;对于烧结体,Eu掺杂样品最大为10.1×1010~(-6)/℃,而未掺杂样品为7.54×10~(-6)/℃,轻、重稀十对其影响差别不明显,基体中新物相的形成以及空位的增多是热膨胀系数增大的主要原因;根据复合体的热膨胀系数规律可以判定REAl_(11)O_(18)(RE=La,Ce,Nd),REAlO_3(RE=Gd,Eu),RE_3A_(15)O_(12)(RE=Y,Dy)三类结构化合物的热膨胀系数均要高于刚玉结构氧化铝。
稀上掺杂及未掺杂纳米γ-Al_2O_3的烧结曲线分为R1(相变为主),R2(烧结致密化)两个阶段,掺杂抑制了其致密化;各种样品R1阶段相对密度变化值高于理论计算值,主要是相转变过程伴随有颗粒重排过程,不同掺杂对其影响存在差别;掺杂有效延长了样品中处于临界尺寸的θ相晶粒转变为α相形核粒了的时间;相变过程中,不同热处理条件下氧化铝的红外吸收谱存在差异,主要是由于不同物相的O~(2-)的密堆积方式和Al~(3+)的填充方式的不同影响了Al-O键的振动;La掺杂与未掺杂样品相同温度下对应红外特征吸收带400-1000cm~(-1)波数范围(Al-O键的振动吸收)吸收峰存在较大差别,证明了La~(3+)的引入改变了基体中Al~(3+)和O~(2-)周围的电子组态;La掺杂有效延迟了γ→α相转变过程中各中间相的出现,这主要是由于化合物LaAlO_3的产生(900-950℃之间)抑制了O~(2-)和Al~(3+)的扩散,从而提高了相变温度,不同稀土作用效果不同,主要是不同稀土对基体中Al~(3+)由四面体间隙位置向八面体间隙位置迁移速率的影响不同造成的。
The high-temperature structural ceramics, as the key materials, can be used as turbine blades for the shuttle in the future. The alumina doped with the rare earth having the melting point higher than 1700℃attracted much attention widely. However, there were still many problems about its preparation through pressureless sintering process, such as the formation of uniform structure, the increase of the density and the strength, et al. To prepare this kind of material with uniform structure and excellent strength through pressureless sintering process, it is necessary to investigate its sintering behavior.
The pressureless sintering behaviors, thermal expansion behaviors, phase transformation process and the working mechanism at constant heating rates were investigated forα-Al_2O_3 and nanometerγ-Al_2O_3 doped with the rare earth (RE= La, Ce, Nd, Gd, Eu, Y, Dy). Otherwise, the master sintering curves (MSC) were constructed at low heating rates as well as the thermal behaviors were investigated for pureα-Al_2O_3.
The MSC of 200-500nm and 2-3μmα-Al_2O_3 were constructed based on the combined-stage sintering model only at low constant heating rates lower than 5℃/min. In this condition, the sintering activation energies evaluated based on the MSC theory were 1035 and 1148 kJ/mol for 200-500nm and 2-3μm samples respectively, which were greater than that obtained at higher heating rates reported in other works. This phenomenan may be induced by the surface diffusion in the low temperature stage. The densities measured by Archimedes method for the samples undergoing different heating history agreed with that determined by the MSC. The results showed that the master sintering curve, in which the sintered density uniquely relies on the integral of a temperature function versus time, is insensitive to the heating path. Quantitative image analysis was used to characterize the sintered microstructure as a function of the time-temperature sintering conditions, and to verify the linkage between sintered density and microstructure. The results demonstrated how MSC theory can be applied to design a reproducible process to fabricate controlled density and microstructure ceramics undergoing the heating history with low heating rates.
To study the thermal behaviors during the sintering process forα-Al_2O_3 with the particle size of 200-500nm, the thermodynamics functions of original particles and granulated particles with 10-20 mesh were investigated by DSC, respectively. It was found that the whole sintering process is an endothermic process. At the same heating rates, the enthalpy of the original particles was higher than that of granulated grains. For both of the two kinds of particles, the enthalpy during the sintering at low heating rates was greater than that of high heating rates, which complied with changing trend of the sintering activation energy. The specific heat capacity (c_p, J g~(-1) K~(-1)) of two samples obtained using the direct method increased with the temperature increasing. In the temperature range of room temperature-1273.5K, the relationship of c_p and the temperature can be expressed as certain multinomials: 200-500nm (c_p = 2.70177-0.01187×T+1.35929×10~(-5)×T~2, goodness of fitting was 0.99), 10-20 mesh (c_p = 1.34048 -0.00354×T + 3.2239×10~(-6)×T~2, goodness of fitting was 0.98). The absolute values of enthalpy, entropy and Gibbs energy rised with temperature increasing, which showed that the sintering process was anon-reversible process and could be expressed as dS>0 or dG<0.
Three kinds of structural compounds including garnet-structure RE_3Al_5O_(12)(RE=Y, Dy), magnetoplumite-structure REAl_(11)O_(18)(RE=Nd, La, Ce) and perovskite-structure AIREO_3 (RE=Eu, Gd) came into being due to the solid reaction ofα-Al_2O_3 with the corresponding rare earth oxide during the sintering process. The initial shrinking temperatures for the doped samples were enhanced compared with the pure alumina, which for the Nd-doped sample was about 200℃higher than that of the un-doped specimen. The rare-earth dopants (La excluded) promoted the overall densification and inhibited the particle coarsing (La showing the stronger effect) without abnomal grain growth. The shrinkage of the Eu-doped sample was 3% higher than that of the un-doped specimen. There were some lathlike alumina grains in Nd- and La- doped specimens, which could be attributed to the preferential segregation of ions to some basal planes due to the higher mobility of some dissociative boundaries. In addition, it was found that the secondary phase precipitates occurred due to the supersaturation of Nd~(3+) at grain boundaries, which located predominantly at grain triple points. The fracture mode of intergranular dominated in the RE-doped samples, which could be ascribed to a weakened interface bonding as a result of the coexistence of rare-earth oxides and other oxides. However, the reduced grain boundary cohesion in RE-doped alumina is expected to have only a limited effect on fracture toughness.
The average line expansion coefficients of the green compacts (α_g) before its shrinking and the sintered body (as) were enhanced by RE doping. For the green compact, theα_G, of Nd-doped specimen was 8.59×10~(-6)/℃, whereas, which was 6.78×10~(-6) /℃for un-doped sample, it was found that the light RE was more strongly than the heavy RE did for enhancingα_G For the sintered body, theα_S of Eu-doped specimen was 10.1×10~(-6)/℃, nevertheless, which was 7.54×10~(-6) /℃for the un-doped sample, it was found that the differences of light RE and heavy RE for enhancingα_S were little. The main factors causing the enhancedα_S were the formation of new compounds and the increasing vacancies due to the doping rare earth. According to the rule of the expansion coefficients for composites, it could be concluded that theα_S of REAl_(11)O_(18)(RE=La, Ce, Nd), REAlO_3(RE= Gd, Eu) and RE_3A_(15)O_(12)(RE=Y, Dy) were higher than that of the corundum-structure alumina.
The sintering curves could be divided into two regimes of R1 (associated with the phase transition ofγ→αand R2 (densification ofα-Al_2O_3) for both RE-doped and un-doped nanometerγ-Al_2O_3. It was found that the RE doping inhibited the overall densification. An enhanced Rl relative density change, over and above that expected for the phase transitionγ→α, was brought about by particle re-arrangement (influenced by the doped RE) during the transformation. It was found that the time needed for performing the transformation of oneθ-crystallite of critical size to oneα-nucleus was lengthened significantly by the RE doping compared with the pure sample. The oxygen sublattice and the occupying interstitial sites of Al~(3+) for different alumina polymorphs were different, which would influence the vibration of Al-O bonds and further affected the IR spectra. The adsorption bands in the range of 400-1000cm~(-1) (characteristic bands of A-O vibration) for La-doped samples differenated greatly from that of un-doped specimens undergoing the same sintering process, which proved that the ionicity of Al~(3+) and O~(2-) were changed significantly due to the La dopant. The presence of LaAlO_3 precipitates (in the temperature range of 900-950℃) would block diffusion of O~(2-) and Al~(3+), which would retard the formation of the transition alumina effectively during the phase transitionγ→αand then enhancing phase transition temperature. It was found that the effect of doped RE for enhancing the ending temperature of phase transition was different, which could be attributed to the differences of them on influencing the migration rates of Al~(3+) from tetrahedral interstitial sites to octahedral interstitial sites.
本论文以α-Al_2O_3以及纳米γ-Al_2O_3为原料,研究了稀土掺杂(RE=La、Ce、Nd、Gd、Eu、Y、Dy)氧化铝在恒速无压烧结条件下的烧结行为、膨胀行为、相变过程的影响及作用机理;建立了纯α-Al_2O_3低升温速率条件下的主烧结曲线,并研究了其烧结过程中的热行为。
以全期烧结模型为基础建立了两种粒度分布的α-Al_2O_3低升温速率条件下(低于5℃/min)的主烧结曲线。α-Al_2O_3主烧结曲线对烧结路径不敏感,烧结体的相对密度仅是时间和温度的函数,利用主烧结曲线得到的密度和Archimedes法实测密度吻合,证明了所建立主烧结曲线的有效性,因此可以对陶瓷烧结过程的致密化行为和最终密度进行预测;烧结体显微结构的演变与其密度变化密切相关,利用主烧结曲线可以预测氧化铝陶瓷烧结过程中显微结构的演化;同时主烧结曲线提供了一种计算烧结激活能的新方法,200-500nm和2-3μm两种粒度氧化铝低升温速率烧结条件下的烧结激活能分别为1035和1148kJ/mol,大于高升温速率条件下得到的值。
为了研究α-Al_2O_3恒速无压烧结过程中的热行为,对200-500nm原始粉以及10-20目的造粒后颗粒烧结过程中热力学函数进行了研究。研究表明烧结过程是一个吸热过程,相同升温速率条件下,造粒后颗粒烧结过程中的热焓要低于原始粉;两种颗粒低升温速率烧结过程中的热焓要大于高升温速率条件,这与烧结激活能的变化趋势相一致;通过直接法计算了样品的定压比热容C_p(单位为Jg~(-1)K~(-1)),发现随温度的升高,样品比热容不断增加,对两种样品1273.5K之前的比热容数据进行多项式拟合得到:200-500nm(C_p=2.70177-0.01187×T+1.35929×10~(-5)×T~2,拟合优度为0.99),10-20目(C_p=1.34048-0.00354×T+3.2239×10~(-6)×T~2,拟合优度为0.98);三种速率升温过程中,各种样品的热焓、熵以及吉布斯自由能的绝对值均在不断增加,表明样品的烧结过程是不可逆过程,以热力学函数不等式表示为dS>0或dG<0。
稀土掺杂α-Al_2O_3烧结行为研究发现,稀土与氧化铝固相反应产生三种结构化合物-重稀土为石榴石结构RE_3Al_5O_(12)(RE=Y,Dy),轻稀土为磁铅石结构REAl_(11)O_(18)(RE=Nd,La,Ce)和钙钛矿结构AIREO_3(RE=Eu,Gd);与未掺杂样品相比,稀土掺杂均提高了样品收缩开始的对应温度,其中,Nd掺杂样品提高了近200℃;掺杂促进了致密化(La除外),其中Eu掺杂样品的收缩率比未掺杂样品提高了近3个百分点,掺杂抑制了颗粒粗化(La效果最明显),基体颗粒未出现异常长大,La和Nd掺杂样品中发现了长轴状及板状颗粒,主要是部分游离晶界的高迁移率使基体离子在某些基面发生优先偏聚引起;掺钕样品的透射电镜研究表明,当Nd离子在晶界处形成过饱和状态,就会产生第二相沉淀,主要分布于基体颗粒的交接处;掺杂后样品以沿晶断裂模式为主,主要是稀土氧化物与其它氧化物的共存弱化了氧化铝的界面结合强度,然而这种晶界强度的降低对氧化铝断裂韧性的影响是有限的。
膨胀行为研究发现无论是坯体收缩前还是烧结体,其平均线膨胀系数均}JI于稀土掺杂得到较大提高;对于坯体样品,Nd掺杂样品最大为8.59×10~(-6)/℃,而未掺杂样品为6.78×10~(-6)/℃,轻稀土元素相对于重稀土元素,更有利于提高氧化铝坯体的热膨胀系数;对于烧结体,Eu掺杂样品最大为10.1×1010~(-6)/℃,而未掺杂样品为7.54×10~(-6)/℃,轻、重稀十对其影响差别不明显,基体中新物相的形成以及空位的增多是热膨胀系数增大的主要原因;根据复合体的热膨胀系数规律可以判定REAl_(11)O_(18)(RE=La,Ce,Nd),REAlO_3(RE=Gd,Eu),RE_3A_(15)O_(12)(RE=Y,Dy)三类结构化合物的热膨胀系数均要高于刚玉结构氧化铝。
稀上掺杂及未掺杂纳米γ-Al_2O_3的烧结曲线分为R1(相变为主),R2(烧结致密化)两个阶段,掺杂抑制了其致密化;各种样品R1阶段相对密度变化值高于理论计算值,主要是相转变过程伴随有颗粒重排过程,不同掺杂对其影响存在差别;掺杂有效延长了样品中处于临界尺寸的θ相晶粒转变为α相形核粒了的时间;相变过程中,不同热处理条件下氧化铝的红外吸收谱存在差异,主要是由于不同物相的O~(2-)的密堆积方式和Al~(3+)的填充方式的不同影响了Al-O键的振动;La掺杂与未掺杂样品相同温度下对应红外特征吸收带400-1000cm~(-1)波数范围(Al-O键的振动吸收)吸收峰存在较大差别,证明了La~(3+)的引入改变了基体中Al~(3+)和O~(2-)周围的电子组态;La掺杂有效延迟了γ→α相转变过程中各中间相的出现,这主要是由于化合物LaAlO_3的产生(900-950℃之间)抑制了O~(2-)和Al~(3+)的扩散,从而提高了相变温度,不同稀土作用效果不同,主要是不同稀土对基体中Al~(3+)由四面体间隙位置向八面体间隙位置迁移速率的影响不同造成的。
The high-temperature structural ceramics, as the key materials, can be used as turbine blades for the shuttle in the future. The alumina doped with the rare earth having the melting point higher than 1700℃attracted much attention widely. However, there were still many problems about its preparation through pressureless sintering process, such as the formation of uniform structure, the increase of the density and the strength, et al. To prepare this kind of material with uniform structure and excellent strength through pressureless sintering process, it is necessary to investigate its sintering behavior.
The pressureless sintering behaviors, thermal expansion behaviors, phase transformation process and the working mechanism at constant heating rates were investigated forα-Al_2O_3 and nanometerγ-Al_2O_3 doped with the rare earth (RE= La, Ce, Nd, Gd, Eu, Y, Dy). Otherwise, the master sintering curves (MSC) were constructed at low heating rates as well as the thermal behaviors were investigated for pureα-Al_2O_3.
The MSC of 200-500nm and 2-3μmα-Al_2O_3 were constructed based on the combined-stage sintering model only at low constant heating rates lower than 5℃/min. In this condition, the sintering activation energies evaluated based on the MSC theory were 1035 and 1148 kJ/mol for 200-500nm and 2-3μm samples respectively, which were greater than that obtained at higher heating rates reported in other works. This phenomenan may be induced by the surface diffusion in the low temperature stage. The densities measured by Archimedes method for the samples undergoing different heating history agreed with that determined by the MSC. The results showed that the master sintering curve, in which the sintered density uniquely relies on the integral of a temperature function versus time, is insensitive to the heating path. Quantitative image analysis was used to characterize the sintered microstructure as a function of the time-temperature sintering conditions, and to verify the linkage between sintered density and microstructure. The results demonstrated how MSC theory can be applied to design a reproducible process to fabricate controlled density and microstructure ceramics undergoing the heating history with low heating rates.
To study the thermal behaviors during the sintering process forα-Al_2O_3 with the particle size of 200-500nm, the thermodynamics functions of original particles and granulated particles with 10-20 mesh were investigated by DSC, respectively. It was found that the whole sintering process is an endothermic process. At the same heating rates, the enthalpy of the original particles was higher than that of granulated grains. For both of the two kinds of particles, the enthalpy during the sintering at low heating rates was greater than that of high heating rates, which complied with changing trend of the sintering activation energy. The specific heat capacity (c_p, J g~(-1) K~(-1)) of two samples obtained using the direct method increased with the temperature increasing. In the temperature range of room temperature-1273.5K, the relationship of c_p and the temperature can be expressed as certain multinomials: 200-500nm (c_p = 2.70177-0.01187×T+1.35929×10~(-5)×T~2, goodness of fitting was 0.99), 10-20 mesh (c_p = 1.34048 -0.00354×T + 3.2239×10~(-6)×T~2, goodness of fitting was 0.98). The absolute values of enthalpy, entropy and Gibbs energy rised with temperature increasing, which showed that the sintering process was anon-reversible process and could be expressed as dS>0 or dG<0.
Three kinds of structural compounds including garnet-structure RE_3Al_5O_(12)(RE=Y, Dy), magnetoplumite-structure REAl_(11)O_(18)(RE=Nd, La, Ce) and perovskite-structure AIREO_3 (RE=Eu, Gd) came into being due to the solid reaction ofα-Al_2O_3 with the corresponding rare earth oxide during the sintering process. The initial shrinking temperatures for the doped samples were enhanced compared with the pure alumina, which for the Nd-doped sample was about 200℃higher than that of the un-doped specimen. The rare-earth dopants (La excluded) promoted the overall densification and inhibited the particle coarsing (La showing the stronger effect) without abnomal grain growth. The shrinkage of the Eu-doped sample was 3% higher than that of the un-doped specimen. There were some lathlike alumina grains in Nd- and La- doped specimens, which could be attributed to the preferential segregation of ions to some basal planes due to the higher mobility of some dissociative boundaries. In addition, it was found that the secondary phase precipitates occurred due to the supersaturation of Nd~(3+) at grain boundaries, which located predominantly at grain triple points. The fracture mode of intergranular dominated in the RE-doped samples, which could be ascribed to a weakened interface bonding as a result of the coexistence of rare-earth oxides and other oxides. However, the reduced grain boundary cohesion in RE-doped alumina is expected to have only a limited effect on fracture toughness.
The average line expansion coefficients of the green compacts (α_g) before its shrinking and the sintered body (as) were enhanced by RE doping. For the green compact, theα_G, of Nd-doped specimen was 8.59×10~(-6)/℃, whereas, which was 6.78×10~(-6) /℃for un-doped sample, it was found that the light RE was more strongly than the heavy RE did for enhancingα_G For the sintered body, theα_S of Eu-doped specimen was 10.1×10~(-6)/℃, nevertheless, which was 7.54×10~(-6) /℃for the un-doped sample, it was found that the differences of light RE and heavy RE for enhancingα_S were little. The main factors causing the enhancedα_S were the formation of new compounds and the increasing vacancies due to the doping rare earth. According to the rule of the expansion coefficients for composites, it could be concluded that theα_S of REAl_(11)O_(18)(RE=La, Ce, Nd), REAlO_3(RE= Gd, Eu) and RE_3A_(15)O_(12)(RE=Y, Dy) were higher than that of the corundum-structure alumina.
The sintering curves could be divided into two regimes of R1 (associated with the phase transition ofγ→αand R2 (densification ofα-Al_2O_3) for both RE-doped and un-doped nanometerγ-Al_2O_3. It was found that the RE doping inhibited the overall densification. An enhanced Rl relative density change, over and above that expected for the phase transitionγ→α, was brought about by particle re-arrangement (influenced by the doped RE) during the transformation. It was found that the time needed for performing the transformation of oneθ-crystallite of critical size to oneα-nucleus was lengthened significantly by the RE doping compared with the pure sample. The oxygen sublattice and the occupying interstitial sites of Al~(3+) for different alumina polymorphs were different, which would influence the vibration of Al-O bonds and further affected the IR spectra. The adsorption bands in the range of 400-1000cm~(-1) (characteristic bands of A-O vibration) for La-doped samples differenated greatly from that of un-doped specimens undergoing the same sintering process, which proved that the ionicity of Al~(3+) and O~(2-) were changed significantly due to the La dopant. The presence of LaAlO_3 precipitates (in the temperature range of 900-950℃) would block diffusion of O~(2-) and Al~(3+), which would retard the formation of the transition alumina effectively during the phase transitionγ→αand then enhancing phase transition temperature. It was found that the effect of doped RE for enhancing the ending temperature of phase transition was different, which could be attributed to the differences of them on influencing the migration rates of Al~(3+) from tetrahedral interstitial sites to octahedral interstitial sites.
引文
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