Grain Orientation Distribution and Development of Grain Line in Highly Ordered Bi 4 Si 3 O 12 Micro-Crystals

Bismuth silicate (Bi4Si3O12) micro-crystals with a grain line structure were grown by a sintering method under atmosphere pressure. The as-grown products were studied using Xray diffraction (XRD) and Environmental scanning electron microscopy (ESEM). The grain orientation law was tested by the One-Sample Kolmogorov-Smirnov (K-S) test. The result shows Bi4Si3O12 grains are always distributed in pairs on both sides of a stable line. On one side of a line, the angle between grain orientation and the growth direction of the line obeys the normal distribution. It indicates that the grains on one side have almost the same orientation. The range of mean angle on one side is from 53.9o to 68.9o in a stable line. There is a highly positive correlation between mean angle and mean growth rate on one side of a stable line. If a mean angle on one side exceeds the maximum mean angle of a stable line, the highly ordered structure on the opposite side will be destroyed. However, the elimination process on the destructed side has no effect on the highly ordered structure on the other side. There are two kinds of grain line creation. One originates from a defect on one side of a line, and the other originates from the boundary between neighboring lines.


Introduction
Compounds in the Bi 2 O 3 -SiO 2 system are interesting materials due to their optical and electrical properties, which confer them a wide variety of potential applications.From a structural point of view, the compounds have three crystalline phases with different Bi 2 O 3 :SiO 2 molar ratio, such as Bi 12 SiO 20 , Bi 4 Si 3 O 12 and Bi 2 SiO 5 [1,2].Because of the complexity of the Bi 2 O 3 -SiO 2 system, complete phase relations and the crystallizing behavior of the system are still not explicit [1][2][3].
Bismuth germanate (Bi 4 Ge 3 O 12 ) is one of the excellent scintillators used in X-ray or γ-ray detection.It is also an important component in positron emission tomography (PET) and electromagnetic calorimeters [4][5][6].Recently, Bi 4 Si 3 O 12 has ever-increasing interest as a new scintillating material.It resembles Bi 4 Ge 3 O 12 in many respects 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 respects [7,8].To our knowledge, some papers have investigated Bi 4 Si 3 O 12 single crystal growth by Bridgman method [7][8][9][10][11].Up to now, no paper reports grain orientation law in a highly ordered Bi 4 Si 3 O 12 grain line structure.Also no paper discusses the development characteristic of Bi 4 Si 3 O 12 grain line growth.
In our earlier research, we investigated grain size distribution, grain size trends and correlation analysis of highly ordered grain line structure in Bi 4 Si 3 O 12 micro-crystals [12][13][14].There is still no good explanation for the Bi 4 Si 3 O 12 grain line structure and it needs further study.In this article, characteristics of the grain deviation angle distribution are reported.The elimination and creation of grain lines are analyzed.

Experimental Procedures
Raw materials were Bi 2 O 3 (monoclinic) powder (analytical reagent, Tianjin No. 3 Chemical Plant, Tianjin, China) and SiO 2 (amorphous) powder (analytical reagent, Huzhou Chemical Reagent Plant, Zhejiang, China), and were both tested by X-ray diffraction.Bi 2 O 3 and SiO 2 were mixed in equivalent mole ratio, and then milled for 3 hrs in ethanol at room temperature.Then the mixture was treated by infrared drying (60 W).The dried powder was heated at a heating rate of 10°C/min to 800°C and held at this temperature for 3 hrs in an Al 2 O 3 crucible covered with a lid in air.The samples were cooled to room temperature at a rate of 30°C/min.
The crystalline phases for the prepared crystals were identified with an X-ray diffractometer (XRD, D/max 2200PC, CuK irradiation, Rigaku, Japan).The morphology of the crystals was observed by an environmental scanning electron microscopy (ESEM, Quanta 200, Philips-FEI, Holland).

XRD patterns
The XRD pattern of the sintered Bi 2 O 3 -SiO 2 sample is shown in Fig. 1.Eulytite with a chemical formulation of Bi 4 Si 3 O 12 is determined to be the crystal structure (JCPDS Card No. 35-1007).This structure is identified as the isometric system 43 I d , Z=4.The structure can be considered as the reciprocal linkage of [SiO 4 ] tetrahedrons and [BiO 6 ] octahedrons in three dimensions [12].

Grain deviation angle distribution
An ESEM micrograph of highly ordered Bi 4 Si 3 O 12 micro-crystals is shown in Fig. 2. It is obvious that a typical grain line structure is exhibited.The grains grow in pairs on both sides of a grain line.The grain line formed by pairs of grains is called a stable line.Grain lines A, B, C, D, E and F grow along the parallel directions (as demonstrated by a group of white arrows 'P' in Fig. 2).A group of stable lines can be described as an array.According to previous research [12][13][14], the exposed crystal faces are {204} faces.When the {124} faces of grains meet with the similar plane of other two neighboring grains on the same side of a line, the {124} faces of neighboring grains bond together, and the highly ordered structure is formed.The grain line spacing λ is defined as the internal width between two adjacent lines in Fig. 2. It can be found that the λ values are not equal.Although the maximum spacing is almost three times higher than the minimum one, the growth directions of Line A-F are parallel to each other.Tab.I Descriptive statistics of grain deviation angles of Lines A-F presented in Fig. 2 ('L' corresponds to the angle on the left side of a line; 'R' corresponds to the angle on the right side) represents the maximum value between two means on both sides of a line ) 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, Angle 1 is the grain deviation angle between the orientation of a grain on the left side and the growth direction of Line A. Angle 2 is the grain deviation angle between the orientation of a grain on the right side and the growth direction of Line A. Angle1 and Angle 2 are two grain deviation angles of a pair of grains.30-40 pairs of grains in each line were measured to determine the angle distribution in the highly ordered structure.
Tab.I shows the basic descriptive parameters (mean, standard deviation, max, min, difference percentage) of the angles in Lines A-F.Compared with two mean angles on both sides of a line, the difference percentage is from 0.3% to 13.2%.The data shows that there is a small difference for the angle distribution between both sides of each line.The range of mean angle on one side of a line is from 53.9º to 68.9º.The standard deviation is from 2.3º to 6.1º.The difference between the maximum mean angle and minimum mean angle is 15º.The range of the mean angle may be the growth condition of a stable grain line.Fig. 3a -f show the grain deviation angle distribution histograms and the fitting curves of the grains on each side in Lines A-F.The angle distribution on one side of a line is wondrously close to the normal distribution.In order to strictly examine the distribution of the angle data, the One-Sample K-S test tests if it may reasonably be assumed that this angle distribution reflects an underlying normal distribution [15].The angle distribution on each side is tested by the One-Sample K-S test.
Tab. II P values of the One-Sample K-S Test ('L' corresponds to the left side; 'Right' corresponds to the right side) In Tab.II, the P values on both sides in Line A-F are 0.43 and 0.66, 0.98 and 0.86, 0.66 and 0.75, 0.33 and 0.51, 0.92 and 0.91, 0.18 and 0.54 respectively, which are all larger than the significance level of 0.05.The result indicates the angle distribution on each side of a line is the normal distribution.The characteristic of the normal distribution shows that the grains on one side of a line have almost the same orientation.The wonderful crystal habit is a further benefit to the formation of a highly ordered Bi 4 Si 3 O 12 grain line structure.

Correlation between mean angle and mean grain size
Fig. 5 shows the curves of mean angles and mean grain sizes on both sides of the lines, in which grain size 'l' is the distance between two intersection points of the crystal faces {204} and {024} in Fig. 2. The curves show a relationship between the mean angle and 0.43 0.66 0.98 0.86 0.66 0.75 0.33 0.51 0.92 0.91 0.18 0.54 mean grain size on one side.In order to further investigate this relation, statistical methods are used to calculate Pearson's correlation coefficient (R) between them.The value of R is such that -1≤R≤+1.The + and -signs are used for positive linear correlations and negative linear correlations, respectively.By calculation, the correlation coefficient (R) value is +0.83.The data shows that there is a highly positive correlation between the mean angle and mean grain size on one side of a stable line.On one side of a line, as mean angle is larger, the mean grain size is also larger.In other words, as the mean angle is larger, mean growth rate is also larger on the same side.
Fig. 5 Curves of mean angles and mean grain sizes on both sides of the lines ( AL, BL, CL, EL, DL, FL correspond to the left side of Lines A-F respectively; AR-FR correspond to the right side of Lines A-F; R is the correlation coefficient between the mean angle and mean grain size.)

Elimination and creation of a grain line
Fig. 6 shows the partial elimination of one existing grain line.The white arrow represents the growth direction of Line K. In the initial stage, grains distribute in pairs, and there is a highly ordered grain line structure.Unlike Lines A-F in Fig. 2, the left grain mean deviation angle is 86° and the right grain mean deviation angle is 73° in Line K. Mean angles on both sides are all larger than the maximum mean angle (68.9°) of a stable line.So the growth process of Line K is unstable.Left grains have a history of weak development, corresponding to smaller grain sizes.In the end, the highly ordered structure is destroyed on the left side of the line.After partial elimination of Line K, the new grain on the left side is very small, and the grains on both sides don't distribute in pairs.Angle 1 represents an angle on the left side before partial elimination.Angles 2 and 3 represent two angles on the right side before and after partial elimination, respectively.Although the highly orderly structure on the left side is eliminated, the structure on the right side still remains highly ordered.It is found that if the mean angle on one side exceeds the maximum mean angle (68.9°) of a stable line, the grains on the opposite side cannot form a highly orderly structure.The growth of grain line L is similar to that of grain line K in the later stage.In region A, the grains don't form a highly ordered grain line structure.In region B, the grain boundaries and the boundaries between lines almost disappear.

Fig. 3
Fig. 3 Grain deviation angle distribution histogram on both sides of each line (Lines A-F) in Fig.2 ('Left' corresponds to angles on the left side of the line; 'Right' corresponds to angles on the right side)

Fig. 4
Fig.4 Grain deviation angle distribution histogram of all lines (A-F) in Fig.2

Fig. 4
Fig.4shows the grain deviation angle distribution histogram of the crystallites in all lines (A-F).The angle distribution obeys the normal distribution by the K-S test (P=0.17>0.05).The mean of all angles is about 61.1º and the standard deviation is about 5.9º.The scope of the angles is roughly from 42.3º to 75.6º and mainly in 55º-68º.The mean angle on each side of each line is nearly close to the mean angle of all lines based on the data in Tab.I.

Fig. 6
Fig.6 Elimination of the grain line on one side