Correlation Between Grain Deviation Angles and the Partial Ordering Transformation of Grain Line in Bi 4 Si 3 O 12 Micro-crystals

Bismuth silicate micro-crystals with grain line 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 Bi4Si3O12 grains are always distributed in pairs on both sides of a complete grain line. There is highly positive correlation between grain deviation angles on both sides of a stable complete line. Although the grains distribute in pairs, there is zero correlation between grain angles on both sides of an unstable complete line. By the reduction of grain angle on one side, grain sizes on the side gradually decrease. After adjustment, grain angles have highly positive correlation and the line turns stable. If there is disordered structure on one side of a line and ordered structure on the other side, the disordered structure may turn to highly ordered structure. The partial ordering transformation on the disordered side has no effect on the structure on the other side. While the growth directions of the grains on one side of a line face to a disordered grain distribution zone, the line loses the characteristic of grain growth in pairs.


Introduction
There are three compounds with different molar ratio in the binary system of Bi 2 O 3 -SiO 2 system [1,2] .Among these compounds, Bi 4 Si 3 O 12 has ever-increasing interest as new scintillating material [3,4] .Bismuth germanate (Bi 4 Ge 3 O 12 ) is an excellent and conventional scintillators which is widely used in medicine, geological exploration, nuclear physics and high energy physics [5][6][7] .Bismuth silicate (Bi 4 Si 3 O 12 ) resembles Bi 4 Ge 3 O 12 in many respects including physical, optical and scintillation properties [8] .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 [9,10] .To our knowledge, the complete phase relation and crystallizing behavior of Bi 2 O 3 -SiO 2 system are still not explicit [3,[10][11][12] .
Papers on the grain line structure of Bi 4 Si 3 O 12 micro-crystals are relatively few.
In our earlier researches [3,[13][14][15] , we have investigated grain size distribution, grain size correlation, grain deviation angle distribution and growth defects of highly ordered grain line structure in Bi 4 Si 3 O 12 micro-crystals.In this paper, the characteristics of grain angle correlation are reported.The partial ordering transformation and abnormal growth of grain line are analyzed.

Experimental Procedure 2.1 Preparation of BSO crystals
The starting materials were Bi 2 O 3 (monoclinic) powder and SiO 2 powder.Bi 2 O 3 and SiO 2 were mixed in equal mole ratio and then milled for 3 hrs in ethanol at room temperature.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 hrs 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.)

Characterization of the prepared crystals
The crystalline 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).

Grain line structure of Bi 4 Si 3 O 12 micro-crystals
Fig. 2 shows ESEM picture of the highly ordered Bi 4 Si 3 O 12 micro-crystals.The grains grow in pairs on both sides of grain line.Grain line formed by pairs of grains is called as complete grain line.There is highly ordered structure on each side of a complete grain line.Grain lines A, B, C, D, E and F are complete lines.They grow along the parallel directions (labeled with the arrows 'P').Grain line G is an incomplete line and grows along the direction (labeled with the arrow 'q').According to the previous research [13][14][15] , 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, the {124} faces of neighbor grains bond together, and the highly ordered structure is formed.

Correlation analysis of grain angles on both sides
In Fig. 2, grain orientation goes along the ray through two intersection points of crystal faces {204} and {024} of a grain.The grain deviation angle is defined as the angle between grain orientation and the growth direction of a line.For example, Angle1 and Angle 2 are two grain deviation angles of a pair of grains.The range of mean angle on one side of a complete line is from 53.9º to 68.9º [14] .
The correlation coefficient (R), measures the strength and the direction of a linear relationship between two variables.The mathematical formula for computing R between grain angles on both sides is: Here α L and α R are grain angles on left and right sides respectively, and n is the number of pairs of crystal grains in one line.The value of R is such that -1≤R≤+1.The + andsigns are used for positive linear correlations and negative linear correlations, respectively.The correlation coefficients between grain angles on both sides in the lines (Line A-F) were analyzed (in Table.I).
From Tab.I, R values are all greater than or equal to 0.7, show that there is a highly positive correlation between grain angles on both sides of each complete line (Line A-F).The data shows a relationship between grain angles on both sides of a stable complete line, such as value for left grain angle are larger, value for right grain angle is also larger.Grain size l in Fig. 2 is the distance between two intersection points of the crystal faces {204} and {024}.In our previous work [13] , it had been deduced that there is a highly positive correlation between grain sizes on both sides of each line (A-E).So grain angle and grain size on both sides all have positive correlation characteristic.The wonderful phenomenon is zero correlation between grain sizes on both sides of Line F [13] , and grain angle have highly positive correlation.The reason is explained that the grow direction of Line G deviate from that of Line F. The grains on left side of Line F may obtain more solute and grow gradually lager while grain angle remains highly correlation.From Table II, the R values of grain angles and sizes before Line J creation are all less than 0.3.It indicates that angle and size all haven't correlation characteristic before new line J creation.Although Line I is a complete line, it is unstable before new line J creation.By the reduction of grain angle on right side of Line I, grain size on the side gradually decrease [14] .The decreased process may leads to large boundary between two neighbor lines and new line J creation.Unstable Line I may be the main reason of new grain line creation.

Creation of new grain line
Tab. II The correlation coefficients between grain angles (and grain sizes) on both sides of Line I, respectively ('before' and 'after' are corresponding to before and after Line J creation).

The partial ordering transformation of grain line
Fig. 5 shows the partial ordering transformation of two grain lines (K and M).The black arrows represent the growth directions of these lines.Compared with Line A-F in Fig. 2, these grains don't distribute in pairs on both sides in initial growth stage of Line K.There are highly ordered structure on right side and disordered structure on the left.So Line K is an incomplete grain line.The disordered structure on the left side of Line K gradually transforms into highly ordered structure.The development from disorder to order on one side is named as a partial ordering transformation.After the ordering transformation, the grains on both sides of Line K distribute in pairs, and Line K turns from incomplete to complete.Angle 3 and 4 represent two angles on right side before and after the ordering transformation, respectively.The mean angles between before and after the ordering transformation have no difference.The partial ordering transformation on one side has no effect on the highly ordered structure on the other side.In Fig. 5, the structure of Line M is similar to that of Line K in the beginning stage.There are highly ordered structure on right side and disordered structure on left side.The difference of these two lines is a new grain line generated from the right side part of Line M. Grain '1' size suddenly decreases in Line M. Grain '2' immediately generates and its growth orientation is same as grain '1'.Grain '2' is the first grain on the right side of new line N. Angle 5 and 6 represent two angles on right side of Line M before and after the ordering transformation on left side.The mean angles on right side of Line M before and after the ordering transformation are 71.9° and 72.3°, respectively.Approximate equality of mean angles shows the angle rule on the right side remains unchanged.Even if new grain line generates from the ordered side part of an incomplete line, the partial ordering transformation on the disordered side have no effect on the structure on the ordered side.

Abnormal growth of grain line
In Fig. 6, grain line S loses the growth characteristic of grain growth in pairs.Grain quantity on the left side is more than that on the right.Although there is ordered structure on both sides, Line S isn't a complete line.On the right side of Line S, the grains growth formation is more regular than that in pairs (in Fig. 2).The mean angle on the right side is 81.5°, more than that in complete grain line.The mean grain size is four times bigger than that in complete line (in Fig. 2).On the left side of Line S, the grains are very weak.The angle of every grain on the left exceeds to 90°.Angle 7 and 8 represent two angles on both sides of Line S. The abnormal growth reason may be the grain growth direction on right side faces to disorder grain zone.In the inserted sketch map of Fig. 6, grain top angle β is defined as the angle between two faces (belong to crystal faces {204}) of a grain top.Fig. 7 shows the distribution histogram of grain top angle in Fig. 6.The top angle distribution obeys the normal distribution by the K-S test (P=0.45>0.05).The mean of top angles is 80.8º and the standard deviation is

Conclusions
Highly ordered Bi 4 Si 3 O 12 micro-crystals with grain line structure were prepared by sintering method at 800°C and normal atmosphere.The structure and growth characteristic were analyzed by XRD and ESEM.The conclusions were drawn as follows: (1) Bi 4 Si 3 O 12 grains are always distributed in pairs on both sides of a complete line.There is highly positive correlation between grain angles on both sides of a stable complete line.The correlation expresses a linear relationship between grain angles on both sides, such as value for left grain angle is larger, value for right grain angle is also larger.
(2) Although the grains distribute in pairs, there is zero correlation between grain angles on both sides of an unstable complete line.By the reduction of grain angle on one side, grain sizes on the side gradually decrease.In the end, grain angles have highly positive correlation and the grain line turns stable.The reduction of angle and size on one side leads to the large boundary appearance and new line creation.
(3) If there is disordered structure on one side of a line and highly ordered structure on the other side, the disordered structure may turn to highly ordered structure.The partial ordering transformation on disordered side has almost no effect on the structure on the other side.
(4) While the growth directions of the grains on one side of a line face to a disordered grain zone, the line may lose the characteristics of grain growth in pairs.These grains on faced side grow perfectly regular than those in pairs.The top angle distribution of these grains obeys the normal distribution and the mean of top angles is 80.8º.

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.

2 l
Tab.I The correlation coefficients between grain angles on both sides in these lines.

Fig. 3 Fig. 3 .
Fig.3 (a) shows one kind of new grain line creation.There is a new grain line J generated from the boundary of adjacent lines (Line H and I).Fig.3 (b) is the partial enlargement of Fig.3 (a).It can be found that the pair of grains (labeled with arrow '1') in Line I have a large change.While their grain angles and sizes on both sides decrease suddenly, grain 'a' generates in the boundary between Line H and I.The next pair of grains ('2') grows rapidly, and hinders grain 'a' growth.The boundary between two neighboring pairs of grains ('1' and '2') disappears entirely.The pairs of grains ('3','4','5','6') grow slowly and their sizes decrease gradually.In the end, grain 'b' and 'c' appear successively.Grain 'b' hasn't obvious growth orientation and grains 'c' seem to grow in pairs.According to Fig 3 (a) and (b), these grains 'a',' b', 'c' constitute the initial form of new grain line J.

Fig. 4
Fig.4shows the mean angle histogram of Line H and I before and after new line J creation.The comparison of mean angles before and after Line J creation shows that mean angle on each side of Line H has little change.The mean angle on the right side of Line I before and after Line J creation remains approximately unchanged.The mean angle on the right side of Line I decreases obviously, and the difference percentages is 9.5%.

Fig. 4 .
Fig. 4. Mean angle histogram of Line H and I. ('Before' and 'After' correspond to before and after new line J creation.'HL' and 'IL' correspond to mean angles on left side of Line H and I, respectively.'HR' and 'IR' correspond to mean angles on right side of Line H and I, respectively).
6º.While the grain growth direction faces to disorder grain zone, the perfect development of grain top and regular outline dimensions are appeared.