Iterative Regularity and Parent-Offspring Growth Mold of Stable Grain Array in Bismuth Silicate Micro-Crystals

Bismuth silicate micro-crystals with grain array structure were prepared by sintering method under atmosphere pressure. The samples were characterized for structural and surface morphological properties by X-ray diffraction (XRD) and Environmental scanning electron microscopy (ESEM). The result shows that stable grain arrays grow by iterative mode. If a stable grain array eliminates, a new stable grain array will generate. In a stable parent array, an offspring array may generate after the corresponding partial elimination of its parent array. If one part of an offspring array stops growing, it will be as a new parent array, and then its offspring grain array will create. The sum of the lengths of an offspring array and the corresponding eliminated part of its parent array is equal to the length of the next eliminated part of its parent array. It means the growth rate of an offspring array is equal to that of the corresponding survived part of its parent array. There is a highly correlation between grain array length and average grain line spacing. It means that larger average grain line spacing corresponds to the stable grain array with lager length. When average grain line spacing increases 1μm, the corresponding array length will increase approximately 7.6μm.


Introduction
In the phase diagram of Bi 2 O 3 -SiO 2 system, there are three stoichiometric phases existing in the different molar ratio [1,2].Among these phases, the two phases, Bi 12 SiO 20 and Bi 4 Si 3 O 12 are outstanding materials for important applications in various fields.In particular, Bi 4 Si 3 O 12 has ever-increasing interest as new scintillating material [1][2][3].Bismuth germanate (Bi 4 Ge 3 O 12 ) is an excellent scintillators which is widely used in medicine, geological exploration, nuclear physics and high energy physics [4][5][6].Bi 4 Si 3 O 12 resembles Bi 4 Ge 3 O 12 in many aspects including physical, optical and scintillation characteristics [7].Due to the heaviness, fast response, large radiation hardness and lower cost, Bi 4 Si 3 O 12 may be one of the promising candidate materials for an alternative to Bi 4 Ge 3 O 12 in some fields [7,8].However, the complete phase relation and crystallizing behavior of Bi 2 O 3 -SiO 2 system are still not explicit [1][2][3].There are relatively few papers on the crystallizing behavior of Bi 4 Si 3 O 12 [9][10][11].Till now there has been no paper on the highly ordered grain array structure of Bi 4 Si 3 O 12 crystalline phase.
Previously, we have studied the characteristics of grain size trends and correlation characteristic in highly ordered bismuth silicate micro-crystals [12].We also analyzed grain orientation distribution and the influence of grain deviation angle on development of the grain line structure [13].Grain array structure formed by grain lines of Bi 4 Si 3 O 12 micro-crystals needs further study.This paper concerns the growth regularity of stable grain array structure of Bi 4 Si 3 O 12 micro-crystals.

Experimental
Starting materials were Bi 2 O 3 (monoclinic) powder (Analytical reagent, Tianjin No.3 Chemical Plant, Tianjin, P. R. China) and SiO 2 powder (Analytical reagent, Huzhou Chemical Reagent Factory, Zhejiang, P. R. China).Bi 2 O 3 and SiO 2 were mixed in mole ratio of 1:1, and then milled for 3 hours in ethanol at room temperature [14,15].The mixture was dried under the infrared ray light (60W).The dried powders were heated at a heating rate of 10°C /min to 800°C and held at 800°C for 3 hours in an Al 2 O 3 crucible covered with a lid in air.The samples were cooled to the room temperature at a rate of 30°C /min.(XRD shows that the raw Bi 2 O 3 powder was monoclinic and the raw SiO 2 powder was amorphous.) The crystal phases of the sintering samples were identified with X-ray Diffractometry (XRD, D/max 2200PC, Cuk α irradiation, Rigaku, Japan).The morphology of the crystal surface was observed by Environmental Scanning Electron Microscopy (ESEM, Quanta 200, Philips-FET, Holland).

Iterative growth of stable grain array
Fig. 2 shows the micrograph of highly ordered Bi 4 Si 3 O 12 grain arrays.According to the previous research [12,13], the exposed crystal faces are {204} faces.When the {124} faces of grains meet with the similar plane of other two neighbor grains on the same side of a line, the {124} faces of neighbor grains bond together, and highly ordered grain line is formed.A grain line is formed with pairs of grains on both side of the line [12,13].So Line 1 and 2 are two grain lines formed with pairs of grains.The grain line spacing λ is defined as the internal width between two adjacent grain lines.The λ-value between two grain lines remains unchanged in their growth process.A group of grain lines resembling Line 1 and 2 is called a stable grain array.From Fig. 2, stable grain array M has more than eight grain lines (include Line 1 and 2).The growth direction of stable grain array is labeled with white arrow.It can be see that stable grain array M and N have the same growth direction.In Fig. 2, it can be found that the boundaries of neighboring grains in each line disappeared.The boundaries between neighboring grain lines approximately disappeared.It is also shows that there is wavy boundary between neighboring stable grain arrays (M and N).The inserted sketch map of Fig. 2 expresses grain distribution of a grain line tip [12].With the continuous decreasing of grain size, pairs of grains form an approximately elliptic top micrograph.The elliptic tops of these grain lines in a stable grain array can be form wavy boundary.
Fig. 3 shows the micrograph of stable grain arrays at low magnification.From Fig. 2 and Fig. 3, stable grain arrays grow by iterative method.If a stable grain array eliminates, a new stable grain array will generate rapidly.If the new stable grain array eliminates after a growth stage, the other newer grain array will grow.It is described as the iterative growth regularity.For instance, there are three stable grain arrays ( A, B and C) in Fig. 3.The iterative growth relationship of them is A→B→C.

Parent and offspring mold
According to Fig. 3, stable grain array A has four eliminations.The first, the second and the third eliminations of the array are partial eliminations on its left side.After the first elimination, a new array A 1 generates, and the survived part of array A on the right side continuously grows.After a growth stage, with the simultaneous elimination of array A 1 and the second partial elimination of array A, array A 2 creates immediately.When array A 2 eliminates, array A also finishes its third partial elimination.After their eliminations, array A 3 creates.Finally, there are three small arrays (A 1 , A 2 and A 3 ) successively grow out.From the growth relationship, array A is called as parental array and three smaller arrays are called as offspring arrays.An offspring array may generate from a partial elimination of its parent, or an elimination of previous offspring array and a partial elimination of its parent.After the fourth elimination of array A, its survived part disappears completely.
In a stable array, a group of grain lines (don't partially eliminate in midway) simultaneously create, grow, eliminate, and the length of them are same.Thus the length of the stable array is equal to the length of every grain line.The phenomenon means the growth rates of the grain lines are same in a stable array.
In the Fig. 3, L 1 , L 2 , L 3 and L 4 are four lengths of array A (correspond to four eliminations).l 1 , l 2 and l 3 are the lengths of array A 1 , A 2 and A 3 ( l 1 isn't labeled in the Fig. 3 ).It can be found that the sum of the offspring array A 1 length (l 1 ) and the first eliminated part length of its parent (L 1 ) is equal to the second elimination part length of parent array (L 2 ).The mathematic relation is expressed as: L 1 + l 1 =L 2. It means that the growth rate of array A 1 is same to that of the survived part of its parent array after the first elimination.The similar relations can be discovered as: L 2 + l 2 = L 3, L 3 + l 3 = L 4 .These mathematic relations show that the sum of the lengths of an offspring array and the corresponding elimination part of its parent is equal to the length of the next eliminated part of the parent array.In the other words, the growth rate of an offspring array is equal to that of its survived parent array.Thus, the relation of the array lengths can be expressed as: Here is the serial number of parent array elimination.L i is the elimination part length of parent array; L i+1 is the length of the next elimination part of parent array; l i is the offspring array length.
In array C of Fig. 3, these two offspring arrays C 1 and C 2 successively generate after partial eliminations of array C. The very interesting thing is that the newer offspring array C 21 grows out after the partial elimination of the offspring array C 2 (as a parent array in the process).It indicated the parent array and offspring array are a set of relative concept, and not fixed.If an offspring array stops growing, its offspring array will create.So, the parentoffspring characteristics is inherited.

Correlation between array length and grain line spacing
In Tab.I, the average λ-values measured in the arrays of Fig. 3 are listed.This table also summarizes the corresponding maximum and minimum spacing (λ max and λ min ) measured from the corresponding arrays in Fig. 3, indicating the lower and upper limits of the allowable spacing range.It can be found that the maximum spacing is approximately triple of the minimum one in a stable array.Fig. 4 shows the relation plot between grain array length and average grain line spacing ( λ ).Relationship between them is highly linear correlation and the correlation coefficient R is 0.98.It shows that larger average grain line spacing corresponds to stable grain array with lager length.When average grain line spacing increases 1μm, the corresponding array length will ascend approximately 7.6 μm.

Development of grain array structure
Fig. 5 shows the macro-morphology of highly ordered Bi 4 Si 3 O 12 micro-crystals.According to the morphology development characteristics, it is observed there are three regions (P, Q and R) in Fig. 5.In region Q, stable grain array growth corresponds to the iterative regularity and parent-offspring relation.In region P and R, grain arrays grow along with change directions.Grain arrays turn on right in region R, and those turn on left in region P.There are some branch points labeled by white circles.From these branch points, grain arrays begin the change processes of their growth directions.1. Stable grain arrays grow in successive step.If a stable grain array eliminates, a new stable grain array will generate.

Fig. 1
Fig.1 shows the X-ray diffraction pattern of the phase appeared on the surface of the sample.It is clear from the analysis that the surface phase is Bi 4 Si 3 O 12 (JCPDS card No. 35-1007).Bi 4 Si 3 O 12 has the eulytite structure with point group 43 m.The structure can be considered as the reciprocal linkage of [SiO 4 ] tetrahedron and [BiO 6 ] octahedron in the space.

Fig. 2 .
Fig. 2. ESEM micrograph of highly ordered Bi 4 Si 3 O 12 grain arrays (the inserted sketch map shows the grain distribution of a grain line top [12])

Fig. 4 .
Fig. 4. The relation plot of grain array length and average grain line spacing ' λ '

Fig. 5 .
Fig. 5.The macro-morphology of highly ordered Bi 4 Si 3 O 12 micro-crystals parent array.It means the growth rate of offspring array is equal to that of the corresponding survived part of its parent array.
Statistic data of grain line spacing