Effects of grain size and porosity on strength of Li2TiO3 tritium breeding pebbles and its grain growth behavior

Accepted Manuscript Effects of grain size and porosity on strength of Li2TiO3 tritium breeding pebbles and its grain growth behavior Maoqiao Xiang, Yingchun Zhang, Yun Zhang, Chaofu Wang, Wei Liu, Yonghong Yu PII:

S0022-3115(16)30938-2

DOI:

10.1016/j.jnucmat.2016.10.027

Reference:

NUMA 49964

To appear in:

Journal of Nuclear Materials

Received Date: 8 May 2016 Revised Date:

4 September 2016

Accepted Date: 13 October 2016

Please cite this article as: M. Xiang, Y. Zhang, Y. Zhang, C. Wang, W. Liu, Y. Yu, Effects of grain size and porosity on strength of Li2TiO3 tritium breeding pebbles and its grain growth behavior, Journal of Nuclear Materials (2016), doi: 10.1016/j.jnucmat.2016.10.027. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT TITLE AND ABSTRACT PAGE

Effects of grain size and porosity on strength of Li2TiO3 tritium breeding pebbles and its grain growth behavior

Maoqiao Xiang a, Yingchun Zhang *a, Yun Zhang a, Chaofu Wang a, Wei Liu a,

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Yonghong Yu b a School of Materials Science and Engineering, University of Science and Technology Beijing, 30 Xueyuan Road, Haidian District, Beijing 100083, P.R. China.

b Department of Physics, Renmin University of China, Beijing, 100872, P.R. China.

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Abstract

Tons of Li2TiO3 tritium breeding pebbles will be filled in the blanket for

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obtaining tritium fuel. In this work, isothermal sintering was carried out to study the grain growth behavior of the Li2TiO3 pebbles fabricated by agarose method. The grain growth

exponent

(n) and

the activation

energy (Q) calculated

by the

phenomenological kinetic equation were 2 and 435.65 kJ/mol, respectively. The grain growth was controlled by vapor transport (p = 2S/r). In addition, effects of porosity

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and grain-size on the strength of Li2TiO3 pebbles were investigated. The strength was affected by the grain size and the porosity of Li2TiO3 pebbles, and high strength (about 72 MPa) depended partly on achieving the optimum balance between the

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porosity (about 10 %) and grain size (about 2 µm).

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Keywords: Tritium breeder; Li2TiO3; Grain size; Porosity; Strength.

1

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1. Introduction Deuterium–tritium fusion energy, one of the most potential new energy sources, is developed to deal with the current energy crisis. However, tritium, an important fusion fuel, is scarce in nature. Hence, the tritium breeding blanket in fusion reactor

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was designed to produce tritium by neutron irradiation of lithium materials. The blanket mainly consists of tritium breeders, neutron multipliers and structural materials. Li2TiO3 ceramic pebbles have been considered as one the most potential candidate for tritium breeders [1–3]. Various techniques were developed for obtaining

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about 1 mm Li2TiO3 pebbles, such as wet process [4–6], machinery rolling method [7,8], and graphite bed process [9,10]. In addition, presently, the in-pile and

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out-of-pile irradiation experiments show that the tritium release is a complex process involving the tritium diffusion in grains and grain boundary, interaction with irradiation defects, and etc. [2,11]. Bertone [12] indicates that the tritium release was dependent on a characteristic crystal size (G), desorption rate constant (k) and diffusion coefficient (D), and when the Gk > 10D, the bulk diffusion controlled the

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tritium release. Recently, Kopasz and et al. [13], Xiao and et al. [14] proved that the grain size largely determines whether tritium release is limited by diffusion or desorption, i.e., the smaller grain size, the higher the probability that reactions on the

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grain surface will determine the release rate [11]. Therefore, so far, there is a usual requirement for the average grain size of tritium breeders, i.e. below 10 µm. However, it is worth mentioning that during the long-term operation of the pebbles, the high

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temperature and magnetic fields would increase the grain size [15,16], which would affect the tritium release. Besides grain size, the Li2TiO3 breeders also should have spherical shape (0.25–1

mm diameter), about 85 % TD (theoretical density), about10 % open porosity, high crush load, and etc. [17–19]. Crush load is another crucial parameter for the tritium breeder as tons of the pebbles will be filled in the blanket. Once the pebbles were broken or pulverized, the transportation pathways of tritium and sweep-gas would be blocked, resulting local hot spots and affecting the overall thermomechanical response of the pebble bed. Hence, high crush load is needed for Li2TiO3 pebbles. Generally, 2

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the strength of the pebbles is dependent on its grain size and porosity, i.e., the strength increases with a decrease in either porosity or grain size. Nevertheless, in ceramics, the porosity and grain size are correlative. Low porosity is usually gained at the cost of grain growth. Hence, for a pebble, high strength depends partly on achieving the

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optimum balance between porosity and grain size [20]. Currently, almost all the published papers were focused on developing or optimizing the fabrication process of the Li2TiO3 pebbles. However, the microstructure of Li2TiO3 pebbles was not investigated systematically. Moreover, low

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available study in literature refers to the grain growth dynamics of Li2TiO3 pebbles and quantitative relation of grain size, porosity, and crush load of the Li2TiO3 pebbles.

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For obtaining an efficient, stable and safe tritium breeding blanket, more specific quantitative relations of these factors are needed. Therefore, in this paper, an attempt was made to clarify the grain growth behavior and mechanism of Li2TiO3 pebbles. We tried to understand and quantify the effects of the porosity and grain-size on the strength of Li2TiO3 pebbles.

2.1 Experiment

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2. Material and Methods

Analytical reagent (A.R.) grade Li2CO3 and TiO2 were raw materials and

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purchased from Sinopharm Chemical Reagent Co., Ltd. The Li2TiO3 green pebble was fabricated by agarose method, which is an efficient manufacturing process for mass production. Fig. 1 shows the schematic diagram of agarose method. Firstly, the

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Li2TiO3 powders were obtained by Li2CO3 and TiO2 solid state reaction (molar ratio 1:1) at 750 oC in air. Secondly, the Li2TiO3 powders, agarose, and deionized water were mixed (dimethyl silicon oil bath 100 oC) with stirring to obtain ceramic slurry. Thirdly, the ceramic slurry was dropped into oil through a nozzle, and green Li2TiO3 pebbles were obtained by the surface tension and solidification of the agarose. Finally, the green Li2TiO3 pebbles were cleaned and sintered at different temperatures (1000, 1050, 1100, and 1150 oC) for different hours (1, 3, 5, and 7h). 2.2 Characterization Techniques Crystal structure was investigated by an X-ray diffractometer (D/Max-RB Rigaku, 3

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Japan). Density was measured by Archimedes’ principle using deionized water as immersion medium. Microstructures were observed by scanning electron microscope (SEM, JSM-6480LV JEOL, Japan). Grain sizes (50 pebbles for each batch and more than 200 grains of each pebble) of the etched cross section were examined by image

was obtained as

= 1. 56 , where

,

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analysis software (Nano Measure 1.2) from SEM images. The average grain size,

is the average grain-boundary intercept length

of a series of random lines on the micrographs [21]. Crush loads (F) of 50 pebbles for each batch were measured by a ceramic strength measuring machine (CDW-5

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Changchun Aowei Inc., China) in air at room temperature. Strength of a pebble is affected by flaws, sphericity and diameter. All the sintered pebbles were annealed at

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800 oC for 2 h to release the residual stresses. Before testing, the annealed pebbles were screened and evaluated for minimizing the size effect, i.e., crush load increases with increase in pebble size. And the sphericity (Dmax/Dmin) of 50 pebbles with serial numbers for each batch was measured by image analysis software (Nano Measure 1.2). It is worth mentioning that, for a pebble, the Dmax, Dmin, and surface

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morphology depend on its projection on the image of the microscopy. In this experiment, indeed strength (σ) of a pebble was expressed as a maximum load per unit area, i.e., σ = 4F/

, where D is the nominal diameter of the tested pebble for

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eliminating the size effects. For each batch, the σ was the average strength of 50 pebbles. 3. Theory

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3.1 The grain growth kinetics The phenomenological kinetic equation can be represented by the form [22, 23]:

−

=

t exp(−Q/RT)

(1)

where G is the average grain size at the time t; G0 is the initial grain size; the n value is the kinetic grain growth exponent; K0 is a constant; Q is the apparent activation energy; R is the gas constant; and T is the absolute temperature. This equation has been successfully used to study the grain growth of ZnO [24], BaTiO3 [25], Al2O3 [26], and etc.. In order to obtain n, equation (1) can be rewritten: 4

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ln =

! ln" +

! ln

−(

$

%&

)

(2)

The n can be determined from the slope of the ln G vs. ln t line. In order to obtain the Q, the equation (1) can be rewritten: ln

'( )

$

! = ln

−( )

(3)

%&

/t) vs. 104/T.

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The Q can be calculated from the gradient of the Arrhenius plot of ln ( 3.2 The diameter, porosity, and grain size influence of the strength

In terms of spherical tritium breeders, many factors can affect the crush load,

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such as, diameter, sphericity, flaw structure, temperature, humidity and atmosphere. Generally, the strength increases with a decrease in either porosity or grain size.

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Equations relating the strengths of ceramic materials to their grain size have been put forward by Knudsen [27] who modified the Orowan equation [28] and Petch equation [29], and he proposed that the relation between strength and grain size could be represented by the form σ=*

+,

(4)

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where σ is the strength, and G is the grain size, and k and a are empirical constants. As for the influence of pore, Duckworthl expressed the semilogarithmic relation [30]: σ = σ - +./

(5)

where σ is calculated strength of a similar nonporous body, and b is an empirical

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constant, and P is specimen porosity. As we all know, the porosity usually decreases with the increase of grain size. A quantitative equation was proposed to describe both

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porosity and grain size influence on the strength [27]: σ=*

+, +./

-

(6)

These equations have been widely used to study the strength of TiB2 [31], ZnO [32], nanocrystalline materials [33], oxide and no-oxide ceramics [34], B4C [35], Al2O3 [36] and MgO ceramics [37]. 4. Results and discussion 4.1. Macro morphology and phase analysis Fig. 2 shows the picture and the SEM image of the representative Li2TiO3 pebbles sintered at 1050 oC for 3h. The average sphericity of 50 pebbles was about 1.03. 5

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Ideally, the sphericity should be 1.00. However, before complete solidification some pebbles gathered together inevitably leading to deformation. The average diameter was about 1.0 mm. Fig. 3 shows the XRD patters of the synthetic Li2TiO3 powder (750 oC) and the Li2TiO3 pebbles sintered at different temperatures, and they all were

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pure β-Li2TiO3 phase (space group 15, C2/c, , JCPDS# 33-0831). The lattice slightly increased as the sintering temperature increased from 1000 to 1100 oC, which was agreed with the previous paper [38].

4.2 Microstructures and grain growth kinetics of Li2TiO3 pebbles.

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Fig. 4 shows the SEM micrographs of the Li2TiO3 pebbles sintered at 1000, 1050, and 1100 oC for 1, 3, 5 and 7 h at each of these temperatures. And Fig. 5 summarized

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the grain sizes and the porosities of these pebbles. As can be seen from Fig. 4, the average grain sizes increased gradually from 0.89 µm to 10.05 µm as the sintering temperature and time increased, expecting from Eq. (2). In addition, the pore sizes also increased. The porosity of these pebbles decreased from 15.49 % to 10.78 %. In terms of the sintering of ceramics, the driving force for grain growth and densification

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derives from the decline of the system energy. The system obtained greater force as the temperature increased, leading to grain growth and densification. Hence, the slope of grain sizes in Fig. 5 slightly increased as the sintering temperature increased.

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However, as for the pebbles sintered at 1100 oC for 7h, the porosity increased slightly. The increased pore size and the number of pores located in the grains can be responsible for the increased porosity. For Fig. 4c (4), almost all of the pores located

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inside grains. At higher sintering temperature and longer sintering time, the grain boundary moving increased resulting in the inside pores. Fig. 6 shows the plot of ln G vs. ln t of Li2TiO3 pebbles. These data were analyzed by the linear regression method. The table 1 shows the calculated n. The slopes are equal to 0.5, i.e. n = 2, suggesting that during sintering the grain growth of Li2TiO3 pebble can be expressed by −

= * exp(− 0 ⁄12) × " . Generally, n = 2 represents the normal grain

growth for a pure, ideal single phase and fully dense system, and the grain growth was controlled by grain boundary migration. The driving force for grain boundary migration is the variation of chemical potential gradient, leading to the well known 6

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result that grain boundaries migrate toward their center of curvature. Apparently, in this experiment, the pebbles were not fully dense pebbles (Fig. 4). In practice, microstructural and compositional parameters (pore size and distribution, extent of solid second phases, the level of dopants and their segregation, texture) can affect the

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controlling mechanism [39]. According to previous reports [39,40], there are some mechanisms for the different n (Table 2). Compared with the n values in table 2, the grain growth of Li2TiO3 pebbles was controlled by vapor transport (p = 2S/r, p= the pressure; S = surface energy; r = the principal radii of curvature of the grain /t) vs. 104/T. The Q can be calculated from

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boundary). Fig. 7 shows the plot of ln (

the gradient of the plot. The dispersion in the plot of ln (

/t) vs. 104/T at

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temperatures was because the grain growth does not correspond to the specific value of grain growth exponent [23]. The calculated Q values and lnK0 are shown in table 1. The Q values obtained by the concatenate multi-date mode linear fit were 412.37, 435.659 and 403.229 kJ/mol corresponding to the n values of 1.89, 2.00 and 1.85, respectively. However, the activation energies for grain growth in Li2TiO3 ceramic

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have not been reported previously, so it is difficult for us to make a comparison. 4.3 Porosity and grain size influences on the strength of Li2TiO3 pebble Crush load is another important parameter for the breeders. Fig. 8 shows strength versus (vs.) grain size (Fig. 8 (a)) and strength vs. porosity (Fig. 8 (b)) of these

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Li2TiO3 pebbles sintered at 1000, 1050, and 1100 oC for 1, 3, 5, and 7 h at each temperature. As can be seen from Fig. 8, the pebble with small grain size and low

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porosity had higher strength, expecting from Eqs. (5) and (6). In the field of ceramic failure, grain boundaries, intrinsic defects on the microstructural level, are regarded as nucleation sites for micro-cracks [27]. Pores, processing defects, act as stress concentrators. In most cases, the pores and grain size can affect the strength through fracture energy, fracture toughness and flaw geometry size [27]. For the fine grained materials with low porosity and fine pores, they had high fracture energy and small flaw geometry size, leading to high strength. Conversely, for materials with abnormal grains and big pores usually exhibit low strength. Nevertheless, low porosity is obtained usually at the cost of considerable grain growth. Hence, high strength 7

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depends partly on achieving the optimum balance between the porosity and grain size. As can be seen from Fig. 8, the strength increased with the decrease of grain size except the grain size of 0.89 µm. The intrinsic defects and porosity may be responsible for this result. The high porosity can be responsible for the decline. Fig. 9

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shows the plot of ln G vs. ln σ. The slope of these data obtained by the linear regression method was 0.12, suggesting that the grain size-strength (Eq. 4) can be expressed by ln 5 = 4.33 − 0.12ln . When the grain sizes increased from 1.84 to 3.36 µm corresponding to the porosity from 15.02 to 13.08 %, the strength reached a

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short plateau (about 72 MPa). Roux et al. [41] measured the rupture strength of Li2TiO3 pellets (fabricated by 150 MPa cold isostatic pressing and sintered at 1050 oC)

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with 82% TD and 1 ~ 2 µm grain size, and the strength was 100.54 MPa. The different microstructures of the Li2TiO3 pebbles and pellets can be responsible for this disparity. For ceramic materials, microstructure (such as size, shape, orientation) has an obvious influence on the mechanical property.

From the porosity-strength curves (Fig. 8 and Fig. 10), the strength increased with

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the increase of porosity except the porosity of 15.49 %. Apparently, it was not agreed with the reality and the Eq. (5) which indicates strength will increase with decreasing of porosity. Hence, we fitted these data by the linear regression method with fix slope,

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and the best linear fitting porosity-strength can be expressed by ln 5 = 4.1 − 0.019. However, the linear correlation was weak, and these data had large discreteness. Roux et al. [38] reported that the porosity-strength relation of the Li2TiO3 pellets can be

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expressed by 5 = 170(1 − 2.279) . The microstructure, surface condition and stressed state of the pebble might account for the difference. Besides, we had tried to fit the strength, porosity, and grain-size data of the Li2TiO3 pebbles sintered at different temperatures for different time with the Eq.6. However, we found theses data had no convergence. The fracture strength of ceramics is very sensitive to flaws and varies unpredictably from component to component, even if a set of nominally identical specimens are tested under the same conditions [32]. Generally, the failure usually originates from pre-existing defects, i.e., intrinsic defects (grain boundaries as nucleation sites for micro-cracks) and processing defects (pores, and inclusions as 8

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stress concentrators) [42–44]. And the interaction between defects is sensitive to the details of their geometrical arrangement [32]. Therefore, it is very difficult to create a precise and comprehensive equation to describe the grain size-porosity-strength relation with one equation [45]. However, the accumulation of these data is very

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important for obtaining the optimal grain size and porosity for the tritium breeder. 5. Conclusion

The grain growth behavior of Li2TiO3 pebble fabricated by the agarose method was studied by the phenomenological kinetic equation. It was controlled by vapor

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transport (p = 2S/r). The grain growth equation can be expressed by

−

=

* exp(− 0 ⁄12) × ", and the Q and lnk were 435.65 kJ/mol and 40.94 at 1050 oC,

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respectively. The effects of the porosity and grain-size on the strength Li2TiO3 pebbles were investigated. High strength depends partly on achieving the optimum balance between porosity and grain size. In this experiment, the strength decreased with the increase of grain size. The strength reached a plateau (about 72 MPa) in the grain size range from 1.84 to 3.36 µm corresponding to the porosity from 15.02 to 13.08 %. The

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grain size-strength relation could be expressed by Eq. 4; however, the porosity-strength relation and the porosity-grain size-strength relation of the Li2TiO3 pebbles fabricated by the agarose method could not be expressed by Eq. 5 and Eq. 6.

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Acknowledgements

This work has been financially supported by the National Natural Science Foundation of China (No. 51372017), International Thermonuclear Experimental

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Reactor (ITER) Project of China (No. 2014GB123000) and National Magnetic Confinement Fusion Energy Research Project (No. 2015GB121006).

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Figure captions Fig. 1. The schematic diagram of agarose method for fabricating Li2TiO3 pebbles. Fig. 2. The picture (a) and the SEM image (b) of the Li2TiO3 pebbles sintered at 1050 o

C for 3h.

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Fig. 3. XRD patters of the synthetic Li2TiO3 powder (750 oC) and the sintered Li2TiO3 pebbles.

Fig. 4. SEM micrographs of Li2TiO3 pebbles sintered at different temperatures for different time: (a) 1000 oC, (b) 1050 oC, (c) 1100 oC, (1) 1h, (2) 3h, (3) 5h, (4) 7h.

temperatures for different time.

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Fig. 6. Plot of ln G vs. ln t of Li2TiO3 pebbles.

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Fig. 5. Grain size and porosity of the Li2TiO3 pebbles sintered at different

Fig. 7. Arrhenius plots corresponding to grain growth exponents: (a) n = 1.85, (b) n = 1.89 and (c) n = 2.

Fig. 8. The grain size and strength of the Li2TiO3 pebbles (a); the porosity and strength of the Li2TiO3 pebbles (b).

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Fig. 9. Plot of ln G vs. ln σ of Li2TiO3 pebbles

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Fig. 10. Plot of P vs. ln σ of Li2TiO3 pebbles.

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Table 1. Kinetic parameters for grain growth of Li2TiO3 pebbles.

lnK

n

Q (kJ/mol)

1000

38.63

1.89

412.37

1050

40.94

2.00

435.65

1100

37.78

1.85

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Temperature (oC)

403.229

Controlling mechanism

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Table 2. Kinetics of grain growth for various mechanisms [39,40].

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Surface diffusion Pore control

n 4

Lattice diffusion

3

Vapour transport (p = const)

3

Vapour transport (p = 2S/r)

2

Pure system

2

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Coalescence of second phase by lattice 3 diffusion

Coalescence of second phase by grain

Boundary

4

boundary diffusion

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Impure

control

Solution of second phase

2

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System

Diffusion through continuous second 3 phase Impurity drag (low solubility)

3

Impurity drag (high solubility)

2

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FIGURES

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Fig. 1. The schematic diagram of agarose method for fabricating Li2TiO3 pebbles.

Fig. 2. The picture (a) and the SEM image (b) of the Li2TiO3 pebbles sintered at 1050 o

C for 3h.

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FIGURES

Fig. 3. XRD patters of the synthetic Li2TiO3 powder (750 oC) and the sintered Li2TiO3

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pebbles.

Fig. 4. SEM micrographs of Li2TiO3 pebbles sintered at different temperatures for different time: (a) 1000 oC, (b) 1050 oC, (c) 1100 oC, (1) 1h, (2) 3h, (3) 5h, (4) 7h.

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FIGURES

Fig. 5. Grain size and porosity of the Li2TiO3 pebbles sintered at different

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temperatures for different time.

Fig. 6. Plot of ln G vs. ln t of Li2TiO3 pebbles.

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FIGURES

Fig. 7. Arrhenius plots corresponding to grain growth exponents: (a) n = 1.85, (b) n =

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1.89 and (c) n = 2.

Fig. 8. The grain size and strength of the Li2TiO3 pebbles (a); the porosity and strength of the Li2TiO3 pebbles (b).

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FIGURES

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Fig. 9. Plot of ln G vs. ln σ of Li2TiO3 pebbles.

Fig. 10. Plot of P vs. ln σ of Li2TiO3 pebbles.

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ACCEPTED MANUSCRIPT AUTHOR INFORMATION

AUTHOR INFORMATION Corresponding Author *

Yingchun Zhang

School of Materials Science and Engineering, University of Science and Technology

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Beijing, 30 Xueyuan Road, Haidian District, Beijing 100083, P.R. China. Fax:

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+86-01062334951; Tel: +86-01062334951; E-mail: [email protected]

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