多晶陶瓷材料晶粒的面积—周长关系
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摘要
在关于多晶陶瓷力学性能与显微结构关系的研究中,平均晶粒尺寸往往被作为一个关键的显微结构参数得到学者们的普遍重视；在功能陶瓷材料领域,平均晶粒尺寸也经常被用作研究晶界效应对各项性能参数影响规律的一个重要参数。然而必须指出的是,在同一个多晶陶瓷样品中不同晶粒的尺寸差别很大,大小晶粒之间的尺寸差别往往在一个甚至几个数量级以上。在所有相关的研究报道中,晶粒尺寸却都仅仅是采用了一个平均值,而忽略了材料中实际存在的晶粒尺寸的统计分布效应。此外,迄今为止关于多晶陶瓷烧结过程的研究一般都是以观察晶粒平均尺寸的变化为基础进行的,关于烧结过程中晶粒形状变化的研究报道极为罕见。另一方面,从大量文献报道的烧结致密的多晶陶瓷晶粒形貌照片看,理想的正六边形晶粒也十分少见。因此,探求一个新的显微结构参数研究陶瓷材料结构与性能关系,建立一种表征晶粒形状的技术并将其应用于陶瓷烧结研究具有很强的理论意义和实用价值。
本文对BaTiO3系PTCR材料、立方ZrO2和无铅陶瓷三个系统分别在不同的烧结温度下保温不同时间条件下的晶粒生长过程和表面晶粒形貌进行了观察。从统计学角度证实,对于给定的材料,在同一烧结制度下,其表面晶粒的周长(P)与面积(A)的平方根之比P/A0.5值较晶粒尺寸离散性小,能够更加准确、可靠地描述晶粒形貌。确认烧结致密的单相多晶陶瓷材料表面上的晶粒具有一个基本恒定的P/A0.5值。
其次,在以上观测的基础上,将晶粒的P/A0.5值作为晶粒形状的一个表征参数。通过分析P/A0.5值的变化过程所得到的晶粒形状的变化过程,初步考察这一参数研究材料的烧结行为尤其是晶粒生长过程所发挥的作用。
最后,测量了立方ZrO2陶瓷的晶界电导活化能Egb。结果发现：晶粒P/A0.5和Egb两个参数表现出相反的变化趋势。这两个参数之间存在的对应关系似乎说明晶粒形状参数的变化可以反映出导致材料晶界电性能变化的显微结构特征。在研究晶界效应方面,P/0.5值的变化规律可望揭示材料显微结构对材料性能的影响规律。
For the studies of the relationship between the mechanical properties and microstructure in polycrystalline ceramics, the average grain size was often used as a key micro-structural parameter and therefore received scholars'widespread attention. On the studies of functional ceramic materials, the average grain size was also used as an important parameter to analyze the impact of grain boundary effects on various performance parameters. However, it must be noted that, in the same polycrystalline ceramic samples, the sizes of different grains were widely distributed and varied greatly. Size difference during the grains was often above one or even several orders of magnitude. But in all relevant research reports, Just an average was widely used as grain size, while the statistical distribution effect of grain size actually existing in the materials was always ignored. Besides, so far, the studies on polycrystalline ceramic sintering process have been generally based on the observations of the changes in the average size of grain. And studies on the changes of grain shape during the sintering have been reported extremely rare. On the other hand, Photos of grain morphology in dense polycrystalline ceramics, which were reported in a large number of the literature, showed that the ideal grain shape of regular hexagon was very rare. So it is of theoretical and practical values to explore a new micro-structural parameter using research the relationship between structure and properties of ceramic materials, to establish a new technology characterizing grain shapes and apply to ceramic sintering.
In this thesis, grain growth process and surface grain morphology during the three systems of BaTiO3-PTCR materials, cubic ZrO2 and lead-free ceramics were observed under the conditions of different sintering temperatures and different holding times. From the statistical point of view, it was confirmed that for a given material, at the same sintering system, the ratio of P/A0.5on the perimeter (P) and the square root of area(A) about the surface grain had smaller discrete than the corresponding average grain size, could more accurately and credibly descript the grain morphology. It finally confirmed that the surface grains of dense single-phase polycrystalline ceramic materials had a constant P/A0.5 value.
Secondly, on the basis of above observations, the PIA0.s value of surface grains was proposed as a parameter to characterize the grain shapes. By analyzing the changes of P/A0.5 values during sintering process, the corresponding grain shapes was obtained. This made foundation for the parameter to be used in the studies of sintering behavior of materials, especially in grain growth process.
Finally, grain boundary conductance activation energy Egb was measured in cubic ZrO2 ceramics. It was found that, PIA0.5 and the corresponding Egb showed opposite trends. The corresponding relationship between these two parameters seemed to indicate that the changes of grain shapes'parameter could reflect the character of the microstructure resulted in the changes of electrical properties of grain boundaries. In the research on Grain boundary effects, the changes of P/A0.5 value were expected to reveal the relationship between microstructure and the material properties.
本文对BaTiO3系PTCR材料、立方ZrO2和无铅陶瓷三个系统分别在不同的烧结温度下保温不同时间条件下的晶粒生长过程和表面晶粒形貌进行了观察。从统计学角度证实,对于给定的材料,在同一烧结制度下,其表面晶粒的周长(P)与面积(A)的平方根之比P/A0.5值较晶粒尺寸离散性小,能够更加准确、可靠地描述晶粒形貌。确认烧结致密的单相多晶陶瓷材料表面上的晶粒具有一个基本恒定的P/A0.5值。
其次,在以上观测的基础上,将晶粒的P/A0.5值作为晶粒形状的一个表征参数。通过分析P/A0.5值的变化过程所得到的晶粒形状的变化过程,初步考察这一参数研究材料的烧结行为尤其是晶粒生长过程所发挥的作用。
最后,测量了立方ZrO2陶瓷的晶界电导活化能Egb。结果发现：晶粒P/A0.5和Egb两个参数表现出相反的变化趋势。这两个参数之间存在的对应关系似乎说明晶粒形状参数的变化可以反映出导致材料晶界电性能变化的显微结构特征。在研究晶界效应方面,P/0.5值的变化规律可望揭示材料显微结构对材料性能的影响规律。
For the studies of the relationship between the mechanical properties and microstructure in polycrystalline ceramics, the average grain size was often used as a key micro-structural parameter and therefore received scholars'widespread attention. On the studies of functional ceramic materials, the average grain size was also used as an important parameter to analyze the impact of grain boundary effects on various performance parameters. However, it must be noted that, in the same polycrystalline ceramic samples, the sizes of different grains were widely distributed and varied greatly. Size difference during the grains was often above one or even several orders of magnitude. But in all relevant research reports, Just an average was widely used as grain size, while the statistical distribution effect of grain size actually existing in the materials was always ignored. Besides, so far, the studies on polycrystalline ceramic sintering process have been generally based on the observations of the changes in the average size of grain. And studies on the changes of grain shape during the sintering have been reported extremely rare. On the other hand, Photos of grain morphology in dense polycrystalline ceramics, which were reported in a large number of the literature, showed that the ideal grain shape of regular hexagon was very rare. So it is of theoretical and practical values to explore a new micro-structural parameter using research the relationship between structure and properties of ceramic materials, to establish a new technology characterizing grain shapes and apply to ceramic sintering.
In this thesis, grain growth process and surface grain morphology during the three systems of BaTiO3-PTCR materials, cubic ZrO2 and lead-free ceramics were observed under the conditions of different sintering temperatures and different holding times. From the statistical point of view, it was confirmed that for a given material, at the same sintering system, the ratio of P/A0.5on the perimeter (P) and the square root of area(A) about the surface grain had smaller discrete than the corresponding average grain size, could more accurately and credibly descript the grain morphology. It finally confirmed that the surface grains of dense single-phase polycrystalline ceramic materials had a constant P/A0.5 value.
Secondly, on the basis of above observations, the PIA0.s value of surface grains was proposed as a parameter to characterize the grain shapes. By analyzing the changes of P/A0.5 values during sintering process, the corresponding grain shapes was obtained. This made foundation for the parameter to be used in the studies of sintering behavior of materials, especially in grain growth process.
Finally, grain boundary conductance activation energy Egb was measured in cubic ZrO2 ceramics. It was found that, PIA0.5 and the corresponding Egb showed opposite trends. The corresponding relationship between these two parameters seemed to indicate that the changes of grain shapes'parameter could reflect the character of the microstructure resulted in the changes of electrical properties of grain boundaries. In the research on Grain boundary effects, the changes of P/A0.5 value were expected to reveal the relationship between microstructure and the material properties.
引文
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[2]陶杰,姚正军,薛烽.材料科学基础[M].北京：化学工业出版社,2006：69-82
[3]徐晓红.材料概论[M].北京：高等教育出版社,2006：76-61
[4]周志朝,杨辉等.无机材料显微结构分析[M].杭州：浙江大学出版社,2000：325-325
[5]陆佩文.硅酸盐物理化学[M].南京：东南大学出版社,1991：298-299
[6]金格瑞W D.陶瓷导论[M].北京：中国建筑工业出版社,1982：236-254
[7]熊兆贤.陶瓷材料的分形研究[M].北京：科学出版社,2000：69-69
[8]果世驹.粉末烧结理论[M].北京：冶金工业出版社,1998：68-84
[9]Balod J. B. Grain growth of the lime and periclase phases in a synthetic dolomite [J], Journal of the American Ceramics,1998, V11(9):720-725
[10]Harker H. H, Tse K.Y. Grain growth of ZnO in ninary ZnO-V2O5 ceramics [J]. Journal of Materials Science,2003, V38:2367-2372
[11]布鲁克理查德J编.清华大学新型陶瓷与精细工艺国家重点实验室译.陶瓷工艺[M].北京：科学出版社,1998：115-116
[12]姚永红,高峰,洪荣子等.钛酸铋钠基无铅压电陶瓷晶粒生长机制的研究[J].压电与声光,2008,V30(4)：474-476
[13]Gusak A.M, Tu K.N. Thery of normal grain growth in normalized size space [J]. Acta Mater,2003, V51:3895-3904
[14]Green D.J.. An Introduction to the Mechanical Properties of Ceramics [M]. London:Cambridge University Press,1998,V43:74-78
[15]Mukhopadhyay A.K., Datta S.K. and Chakraborty D. On the microhardness of silicon nitride and sialon ceramics[J]. Journal of the European Ceramic Society,1990, V18:303-311
[16]徐庭献等.电子陶瓷材料[M].天津：天津大学出版社,1993：26-29
[17]Waser R. and Hagenbeck R.. Grain boundary in dielectric and mixed-conducting ceramics[J]. Acta Materialia,2000, V48:797-825
[18]Khoruzhii O.V, Kourtchatov S.Yu. and Likjanskii V.V. New model of equiaxed grain growth in irradiated UO2[J]. Nucl. Mater,1999, V65:112-116
[19]Han J., Mantas P.Q. and Senors A.M.R.. Grain growth in Mn-doped ZnO[J]. Ceram. Soc.,2000, V20:2753-2758
[20]孙允午.统计学：数据的搜集、整理和分析[M].上海：上海财经大学出版社,2009.67-104-169：56-57
[21]梁前德.基础统计[M].北京：高等教育出版社,2009.213-248-237：47-156
[22]吴喜之.统计学：从概念到数据分析[M].北京：高等教育出版社,2008.88-103-128：145-178
[23]董云展.统计学[M].北京：高等教育出版社,2008.164-158：78-131
[24]Kingery W.D, Bowen H.K. and Uhlmann D.R. Introduction to Ceramics[M]. New York: The Second Edition. John Wiley & Sons,1976,26:341-352
[25]Aoki M, Chiang Y.M, Kosacki I, etal. Solute segregation and grain-boundary impedance in high-purity stabilized zirconia [J]. Am Ceram Soc,1996, V79:1169-1180
[26]Ma N, Dregia S.A, Wang Y. Solute segregation transition and drag force on grain boundaries[J]. Acta Materialia,2003, V51(13):3687-3700
[27]Liu F, Yang G.C, Reiner Kirchheim. Overall effects of initial melt undercooling, solute segregation and grain boundary energy on the grain size of as-solidified Ni-based alloys[J]. Journal of Crystal Growth,2004, V264(1-3):392-399
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