A Harkati

D Boutagouga

E Harkati

A Bezazi

F Scarpa

M Ouisse

In-plane elastic constants of a new curved cell walls honeycomb concept

Keywords: honeycomb, homogenization, curvature walls, elasticity moduli, auxetic, refined model Cell wall length Elastic strain energy cell. α: curvature ratio

This paper is focused on the identification of the in-plane elastic constants of a new design of auxetic (negative Poisson's ratio) honeycomb configuration with curved cell walls by using analytical and numerical homogenization techniques. The sensitivity of the elastic constants is determined against the various cell geometry parameters. Good agreement between the analytical and numerical simulations is observed. We show that the specific curved wall honeycomb configuration proposed in this paper possesses a high in-plane shear compliance, tailored anisotropy and the possibility of inducing a negative Poisson's ratio behaviour in baseline honeycomb configurations that would have otherwise positive inplane Poisson's ratios.

Introduction

Low density cellular materials are mainly used as a lightweight core rigid and high strength sandwich structures. The physical properties of these materials depend on their constituent phase, geometry and spatial arrangement of the solid [START_REF] Gibson | Cellular solids structure and properties[END_REF]. This type of porous structure has several applications in the civil and military fields that require both rigidity and lightweight characteristics. An example of cellular material used as lightweight core is the corrugated paper honeycomb [START_REF] Pohl | Strengthened corrugated paper honeycomb for application in structural elements[END_REF], which can be used as a base material in lightweight and low-cost sandwich elements. The moduli of elasticity, the shear and compression strengths have been determined in that work both experimentally and analytically, showing that the mechanics of the impregnated material are more consistent than the ones of nonimpregnated cellular solids. It is therefore interesting to evaluate their mechanical properties and predict their behaviour under specific loading and environments. Several research studies on such systems have been carried out in recent years, particularly about tailored two-dimensional honeycombs. Asymptotic homogenization constitutes a means to replace full-scale simulations for predicting the equivalent mechanical properties of the lattices [START_REF] Harkati | In-plane elasticity of a multi re-entrant auxetic honeycomb Composite[END_REF][START_REF] Harkati | The Elastic Uniaxial Properties of a Center Symmetric Honeycomb with Curved Cell Walls: Effect of Density and Curvature[END_REF][START_REF] Bezazi | Novel centre symmetric honeycomb composite structure[END_REF][START_REF] Bezazi | In-plane mechanical and thermal conductivity properties of a rectangular-hexagonal honeycomb structure[END_REF][START_REF] Silva | The effects of non-periodic microstructure on the elastic properties of two-dimensional cellular solids[END_REF][START_REF] Grima | Honeycomb composites with auxetic out-of-plane characteristics[END_REF][9].

The term auxetics indicates structures and materials with negative Poisson's ratio characteristics.

Evans and al. [START_REF] Evans | Molecular network design[END_REF] have been the first to use this term (from the word ''auxetos", i.e. 'may be subjected to increase'). In most cases, the Poisson's ratio of cellular structures is positive, i.e. the material undergoes a contraction along the direction perpendicular to one of the load applications. However, a negative value of the Poisson's ratio means that the material would laterally expand when stretched, leading to an increase of its volume [START_REF] Whitty | Towards the design of sandwich panel composites with enhanced mechanical and thermal properties by variation of the in-plane Poisson's ratios[END_REF][START_REF] Pozniak | Anomalous deformation of auxetic constrained square[END_REF][START_REF] Lim | Auxetic materials and structures[END_REF]. A class of foams that exhibited negative Poisson's ratios has been manufactured and presented for the first time by Lakes [START_REF] Lakes | Foam structures with a negative Poisson's ratio[END_REF] back in 1987.

The first model of re-entrant structures with a negative Poisson's ratio was introduced back in 1985 by Almgren [START_REF] Almgren | An isotropic three-dimensional structure with Poisson's ratio=-1[END_REF]. The structure was first made in 2 D before being extended to 3D. That pattern, which may be applied to different geometric structures such as rods, hinges, and springs led to the development of structures that show macroscopic isotropic elastic properties though anisotropic in their microscopic details. Lira and al. [START_REF] Lira | Transverse elastic shear of auxetic multi re-entrant honeycombs[END_REF] described the out-of-plane shear properties of the multi re-entrant honeycomb configurations. The transverse shear strength properties of zero-Poisson's ratio honeycombs have been described in [START_REF] Scarpa | On the transverse shear modulus of negative Poisson's ratio honeycomb structures[END_REF]. The transverse shear modulus of honeycombs with negative Poisson's ratio coefficients in the plane have been determined using numerical simulations by [START_REF] Nkansah | Modelling the mechanical properties of an auxeticmolecular network[END_REF].

The mechanics of re-entrant and centre-symmetric honeycomb configurations has been described using various analytical models, which have been essentially based on the hypothesis that the behaviour of individual beams or ribs of the cell can be described by elastic engineering beams, specific sets of boundary conditions and different cell walls mechanisms (stretching/hinging/bending [START_REF] Gibson | Failure surfaces for cellular materials under multiaxial loads-I[END_REF]). When loaded on a plane, the honeycomb-shaped cells may be subjected to bending or stretching of their walls, as well as the rotations of the connecting junctions (nodes). Several researchers have developed mathematical models based on these mechanisms. Gibson and Ashby [START_REF] Gibson | Cellular solids structure and properties[END_REF] and Gibson and al. [19] developed a 2-D model assuming a beam-like bending of the cell walls. Nkansah and Hutchinson [START_REF] Nkansah | Modelling the mechanical properties of an auxeticmolecular network[END_REF] however showed that models solely based on bending tend to misrepresent the inplane elastic constants of honeycombs for small (positive and/or negative) cell angles. In order to improve the bending-based models, Gibson et al [START_REF] Gibson | Failure surfaces for cellular materials under multiaxial loads-I[END_REF] and Masters and Evans [START_REF] Masters | Models for the elastic deformation of honeycombs[END_REF] incorporated the phenomena of stretching and rotation of the cell walls. Earlier studies focused on the regular hexagonal honeycomb used as the base material for sandwich panels. In-plane properties are widely studied to improve knowledge of the mechanical behaviour of cellular materials. Advances in shell theories and increasing computational power have improved the models already described by elementary theories. Numerous numerical homogenization techniques have been proposed for modelling network materials (see Arabnejad and Pasini [21]). A comprehensive review about homogenization methods applied to honeycomb structures was presented in [START_REF] Lira | Transverse shear modulus of SILICOMB cellular structures[END_REF] but did not report the effect of the curvature of the wall at the junctions. Within the last two decades, the availability of faster and more sophisticated manufacturing techniques has pushed the development of new cell geometries to meet the needs of technological users.

Works from Harkati et al. [START_REF] Harkati | The Elastic Uniaxial Properties of a Center Symmetric Honeycomb with Curved Cell Walls: Effect of Density and Curvature[END_REF] and Balawi and Abot [START_REF] Balawi | A refined model for the effective in-plane elastic moduli of hexagonal honeycombs[END_REF] have proposed a general analytical model to predict the elastic moduli applied to a hexagonal cell with curved walls. The model has allowed the parametrization of the elastic modulus and relative density as a function of the radius of curvature and other cell geometry characteristics. The model takes into account the effects of bending, shear and axial deformations of the cell ribs along the two principal directions of the plane, and especially confirmed that the curvature of the walls does not have the same effect along each direction. Malek and Gibson [START_REF] Malek | Effective elastic properties of periodic hexagonal honeycombs[END_REF] have studied the elastic behaviour of periodic hexagonal honeycombs over a wide range of relative densities and cell geometries by taking into account nodes at the intersection of vertical and inclined elements. This work is based on the methodologies and results presented in Refs. [START_REF] Harkati | In-plane elasticity of a multi re-entrant auxetic honeycomb Composite[END_REF][START_REF] Harkati | The Elastic Uniaxial Properties of a Center Symmetric Honeycomb with Curved Cell Walls: Effect of Density and Curvature[END_REF][START_REF] Bezazi | Novel centre symmetric honeycomb composite structure[END_REF][START_REF] Bezazi | In-plane mechanical and thermal conductivity properties of a rectangular-hexagonal honeycomb structure[END_REF]. The main novelties introduced here consist in the determination of the in-plane shear modulus (G 12 ) by analytical means, and the development of a refined model that imposes geometric constraints to avoid the contact of the curved walls during deformation. The models are validated using three-dimensional Finite Element models including asymptotic homogenization conditions. The variation of the Poisson's ratio versus the radius of curvature ratio (r / l) for three honeycomb configurations (straight walls, multireentrant and the one described here) and the evolution of the anisotropy versus the curvature ratio of the walls has been identified and discussed. The curved wall honeycomb cell configuration described by these models shows a very high degree of compliance, especially in terms of shear deformation.

Quite importantly, the tailoring of the radius of curvature shows that it is possible to control the degree of anisotropy and the development of auxeticity in baseline honeycomb configurations (i.e., with straight walls) that would normally exhibit a positive Poisson's ratio behavior.

Theoretical analysis

Refined analytical model

The analytical model developed here is based on Castigliano's theorem. The honeycomb cell walls are considered as beam elements and simultaneously subjected to three types of loading (bending, membrane and shear -Fig. 1). In order to avoid contacts and intersections of the cell walls during the deformation the condition below is applied:

(1)

  2 sin 2 1 2 cos a l r     
According to elastic beam theory, the elastic strain energy U is expressed as [START_REF] Harkati | The Elastic Uniaxial Properties of a Center Symmetric Honeycomb with Curved Cell Walls: Effect of Density and Curvature[END_REF]:

(2)

2 2 2 * 0 2 2 2 l M N T N M T U U U U dx EA EI GA             
Where N is the axial internal force, T is the shear internal force and M is the internal bending moment.

In (2) E is the material's Young's Modulus, G is the shear modulus, A is the cross-section area, A* is the shear reduced area, I is the area moment of inertia and l is the beam length.

The displacement of a beam under the influence of a force P may be expressed as

. P U u   
The mathematical formulation of the expressions providing the modules E 1 , E 2 , v 12 and v 21 are detailed in previous Authors' paper [START_REF] Harkati | In-plane elasticity of a multi re-entrant auxetic honeycomb Composite[END_REF]. The equations are recalled here with E s the elastic modulus of the base material.

(3)

1 1 cos 2 (1 sin ) 1 sin 2 cos             s E E u With:  a/l (4)           2 3 2 1 2 2 2 1 3 6 (
v u                                                                                                 
For a regular cell  (Gibson and Ashby's advanced equation for honeycomb [START_REF] Gibson | Cellular solids structure and properties[END_REF])

 

1 2 2 2 12 5 3 cos 1 ( sin ) sin 1 (cot 1 ) s E E v                  
The apparent modulus in direction 2 writes

(6) 2 2 sin 2 cos 1 cos 2 (1 sin ) s E E u             with (7)           3 2 1 2 2 2 3 6 (
u                                                                                                  
Also, in this case, by imposing  = 0 we obtain the result related to a regular hexagonal cell:

(8)     2 3 2 2 12 5 3 sin 1 cos 1 tan 1 s E E v                 
The Poisson's ratio of the honeycomb is provided by the following expression :

(9)                3 2 1 2 2 6(1 )
v v                                                                                                     
v                                                                                      
Finally, the Poisson's ratio   can be calculated as: E v E  

Shear modulus

Because of symmetry, there is no relative motion between points A, B and C when the honeycomb is sheared (see Fig. 2). The shear deflection u c is due to the horizontal displacement of point A, and bending of beam AD and its rotation through the angle  at around A point [START_REF] Gibson | Cellular solids structure and properties[END_REF].

The rotation angle  can be then expressed by the following formula: [START_REF] Whitty | Towards the design of sandwich panel composites with enhanced mechanical and thermal properties by variation of the in-plane Poisson's ratios[END_REF]  

)

r l u r r l l                                                 
The shear displacement u c (shearing deflection) can be presented as:

(13)   2 3 2 2 48 2 2 sin c Fa l u u a EI l r r              
The shear strain   is given by:

(14)       2 3 12 2 2 2 sin 2 cos 24 sin 2 cos 2 2 sin c u Fa l u a a l r EI a l r l r r                        
One can then calculate the shear stress :

(15) 2 ( cos 2 (1 sin )) F b l r      
After mathematical manipulations and using non-dimensional parameters, one can obtain the expression of G 12 :

(16)

12 12 G    (17)         3 12 2 2 sin 2 cos 1 cos 2 1 sin 1 2 1 2 2 sin s G t E l u                                   
For  = 0 one can obtain the value the in-plane shear modulus of a regular hexagonal honeycomb [START_REF] Gibson | Cellular solids structure and properties[END_REF]:

(18)      3 12 2 sin 2 1 cos s G t E l              

Finite element modelling

In order to validate the results found by the analytical approach, numerical models based on finite elements method were developed using the ABAQUS commercial code [START_REF]ABAQUS, version CEA 6.10-1 reference manuals-Dassault Systemes[END_REF]. The models developed here are based on studies and simulations performed by several authors [1-6, 16, 26, 27]. The first model considers full-scale honeycomb assemblies of 53 mesh cells with quadratic beam elements (8304 elements -3 nodes quadra tic beams in a plane), while the second one involves the use of 68 mesh cells with 69904 shells elements with 4 nodes and 6 degrees of freedom per node (S4R). The different meshes correspond to different numerical convergence reached by using beam and shell elements when simulating the five elastic constants. The simulation of a tensile stress along the 1-direction provides the elastic modulus

Results and discussion

Effect of the curvature on the uniaxial moduli E 1 and E 2

The variation of the relative elastic modulus (E 1 /E S ) as a function of the internal angle of the cell  for different values of the ratio of the wall curvature radius   r/l  (0, 0.1, 0.2 to 0.6) is shown in figure 4. In this case the non-dimensional geometrical parameters β=a/l and t/l are fixed and equal to 1 and 0.05 respectively. The nondimensional modulus E 1 /E S decreases with the increase of  and reaches a maximum value for θ between -14 and -3 degrees; this is valid for every cell wall curvature ratio considered. The increase of θ leads to the decrease of E 1 /E S until a minimum value for every honeycomb configuration here considered, and the maximum values all correspond to values of θ close to zero. The maximum value of E 1 /E S for cells with curvature is typically located in the negative range of its internal angles, and it decreases with increasing angles. Increased radius of curvature ratios from r/l = 0 to r/l = 0.6 extend the range of the internal angles of cell  and the auxetic behaviour only occurs when  > -5 degrees. Reducing r to zero, one can obtain the in-plane Young's modulus for the classical centre symmetric configuration.

For a zero-wall curvature ratio the value of E 1 /E S is respectively 3.33 and 3.72 times greater than for  equal to 0.1 and 0.6 for      0.05. This shows that as the radius of curvature increases the cell walls become more and more flexible. Hexagonal regular honeycomb configurations have higher

Young's modulus (E 1 /E S ) than topologies with or without curvature, especially within the

   interval

By fixing the non-dimensional geometrical parameters constant (β = 1 and  = 0.05), the variation of the non-dimensional elasticity modulus of (E 2 /E s ) with the wall curvature ratio is quasi-parabolic (Figure 5), particularly for internal positive cell angles. Moreover, E 2 /E s reaches its maximum for  equal to 30 degrees in all the honeycomb cells studied here. The highest values are obtained for  equal to zero, which corresponds to a conventional hexagonal cell. The flexibility of the cells is proportional to the radius of curvature of the cell walls when the honeycomb is loaded along the 2 direction. Furthermore, the re-entrant cell without curvature (see [START_REF] Pohl | Strengthened corrugated paper honeycomb for application in structural elements[END_REF]) is more rigid since it has E 2 /E s higher than the one proposed in this work (with curvature).

Effect of the curvature on the Poisson's ratios ( 12 and  21 )

The variation of the Poisson's ratios with the curvature ratio of the cell wall and the internal cell angle is shown in Figure 6. One can notice the decrease of  12 when the wall curvature ratio increases. ratio is quasi-parabolic (Figure 9) especially for conventional cell configurations, and the shear modulus decreases by a factor of 3 when wall curvature ratios change from 0 to 0.6. This may constitute disadvantage for structural applications for which a high shear modulus in the plane is required. However, this is a potentially useful feature for compliance-based applications, such as morphing skin with high shear deformability [START_REF] Hohe | Effective mechanical behavior of hyperelastic honeycombs and twodimensional model foams at finite strain[END_REF][START_REF] Jopek | Effective mechanical properties of concentric cylindrical composites with auxetic phase[END_REF]. Moreover, the variation of the in-plane shear modulus versus the constitutive geometry parameters shows that the re-entrant cell without rounding (multi-re-entrant [START_REF] Harkati | In-plane elasticity of a multi re-entrant auxetic honeycomb Composite[END_REF]) features higher shear stiffnesses than those from the curved wall cells described in this work, but lower than those exhibited by a conventional hexagonal cell.

Comparison between analytical model and Finite Element simulations

Table 1 summarizes the analytical and numerical results related to the uniaxial constants (Young's moduli and Poisson's ratio) for two curvature values (r/l = 2/30, r/l = 10/30) and for different cell configurations (auxetic and conventional). The results are all quite close, nevertheless the FE ones are slightly higher. Moreover, it is also worth of notice that the FE results obtained using the beam elements are closer to the analytical ones than those obtained by using shells (relative errors of 4.80%

for shell elements and 4.46 % for beams ones -Table 1). In the case of the Poissons' ratios the maximum discrepancy is 5.24 % when using shell elements, and 3.74 % for the case of beams.

For the normalised shear modulus G 12 /Es (Fig 11 ), a maximum error of about 4.0 % was found between the numerical simulation and the values of equation (Eq. 21) of the analytical calculation.

The G 12 /Es increase with the increase of  from -30 to 30 degrees.

This confirms the ability of the analytical approach to estimate the mechanical properties of the cellular structure at a very low computational cost.

The effect of the curvature of walls (r/l) on the anisotropy

The effect of the curvature on the anisotropy of the honeycomb is important, especially for zero-cell angles (i.e., vertical ribs). For  equals to 0° and an increase of the curvature ratio  from 0 to 0.30, a very sharp 85% drop of the anisotropy (E 1 /E 2 ) is observed, after which the variation is slower until  equal to . A less dramatic change in the anisotropy of the honeycomb is however obtained for honeycombs with a cell angle of  = +30°, with a loss of 45% when the parameter  passes from 0 to 0.6. Unlike the previous two configurations, a 400% increase in anisotropy is noted for a negative angle  of -30° (auxetic behaviour).

Conclusions

The aim of this work is to understand the effect of the internal angles and curvature of the cell wall on the mechanical behaviour of a new honeycomb cell design using an analytical framework and finite element modelling. In addition, the mechanical properties of the cellular structure were evaluated by introducing the effects of bending and transverse shear and axial forces.

The results found showed that curved walls had a significant effect on the elastic properties of cellular structures:

The moduli of elasticity E 1 , E 2 and G 12 decrease with increasing radius of curvature.

The behaviour of the cell becomes less anisotropic when the relative curvature of the walls increases except for the negative internal angles.

The consideration of different deformation mechanisms (bending-shear-stretching) tends to reduce the effective modulus of elasticity in the plane of the honeycombs.

The behaviour becomes less auxetic with the growth of the radius of curvature r for negative internal angles.

The shear modulus reduces with increasing radius of curvature and reaches its maximum value for the cell angle of +30°.

The modulus of elasticity E 1 is maximum for an internal angle and radius of zero curvature (vertical walls).

The Poisson's ratio  12 values decrease with increasing radius of curvature for both configurations.

The elastic constants of the lattice with curved walls and calculated via the analytical model show a significant increase of the in-plane compliance compared to the classical regular hexagonal honeycomb [1] [30].

This study also highlights the difference in terms of results when using different classes of elements in finite element simulations for these honeycomb structures. The presence of curvature also makes it possible to design configurations with a positive Poisson's ratio even for the internal angles of the negative cells and makes this honeycomb design attractive for specific mechanical applications.

Figure 1 :

 1 Figure 1: Honeycomb architectures a): Present work b): Previous Authors' work [5] c): regular hexagonal

Figure 2 :

 2 Figure 2: Deformation induced by cell wall bending and rotation -Force distribution to evaluate G 12 .

E 1

 1 Figure 3.c.

Figure 3 :

 3 Figure 3: Numerical model description. (a) and (b) Boundary conditions taken in the simulation of the tensile along direction 1 and 2 respectively. (c) Boundary condition taken in order to determine G 12 . (d) REV

Figure 4 :

 4 Figure 4: Normalized effective elastic modulus in 1-direction E 1 / Es versus cell angle for different normalized radius of curvature ratios (   ).

Figure 5 :

 5 Figure 5: Normalized effective elastic modulus in 2-direction E 2 /Es versus cell angle for different normalized radius of curvature (   )

  It is also important to observe that the curvature causes a widening of the conventional behaviour of the cell (i.e., positive Poisson's ratio), even for negative internal angles. The maximum value of the Poisson's ratios ( 12 ) corresponds to a regular hexagonal cell (, and it is equal to 9.49 and -10.54 respectively for  equal to 3 and -3 degrees Cells without curvature [2] lead to  12 values equal to 8.51 and -9.01 respectively, for  equal to 2 and -2 degrees. The cell with the curved base walls presented in this work shows however positive and the negative values for  12 equal to 7.40 and -7.84 in the cases of r/l of 0.1, and for  equal to 2 and -7 degrees respectively.

Figure 6 :

 6 Figure 6: Poisson's ratio  12 versus cell angle for different normalized radius of curvature for   ).

Figure 7 Figure 7 :

 77 Figure 7 shows the evolution of the Poisson's ratio   versus the internal cell angle for different curvature ratios α from 0.1 to 0.6, with an increment of 0.1. The   values decrease with increasing radius of curvature for every honeycomb configuration considered here, with and without the curved walls. Classical honeycombs can have a negative Poisson's ratio from smaller negative values of  reach the minimum of   (-0.33) to for  = -30 o . The maximum positive Poisson's ratio is however equal to 0.96 for  = 30 o . It is important to note that the configuration without the corner is practically similar to the classical configuration, however the honeycomb cell with curved corners shows a

Figure 8 . 12 Figure 9

 8129 Figure 8. Poisson's ratio  12 versus curvature radius ratio (  r/l) for the three configurations ( equal to   and  degrees

Figure 9 :

 9 Figure 9: Normalized effective shear modulus G 12 /Es versus cell angle for different normalized radius of curvature (   ).

Figure 10

 10 Figure10shows a surface map of the normalized shear modulus G 12 /Es as a function of the two parameters  and . It can also be noticed that the difference in values of the shear modulus between the two configurations (auxetic and conventional) is almost 3 times. The auxetic design is therefore more flexible than the one with positive angles, with a maximum value of the shear modulus occurring when the cell angle is of 30 ° and the curvature ratio assumes the value of 0.8.

Figure 10 :

 10 Figure 10: 3D representation of an analytical simulation of the shear modulus G 12 /E s versus cell angle  for different normalized radius α for (a/l, =t/l 

Figure 11 :

 11 Figure 11: Normalized shear modulus G 12 /Es versus cell angle for normalized radius of curvature   (Predicted by refined model and FEA).

Figure 12 :

 12 Figure 12 : The evolution of the anisotropy versus the curvature ratio of walls (r/l).

Acknowledgements

The Authors would like to acknowledge the Directorat General For Scientific Research and Technological Development (DGRSDT) -Algeria for supporting the project.


Ph.D Fangnao Xiao

Thierry Barriere

Gang Cheng

Qiang Miao
email: miaoqiang@nuaa.edu.cn

; Shizhong

Wei ; Shiwei Zuo; Liujie Xu

Shizhong Wei

Shiwei Zuo

Zhimin Huang

Liujie Xu

particles dispersion-strengthened tungsten alloy through

Keywords: Hydrothermal process, Ammonium tungsten bronze, In situ oxide dispersion strengthening, Zirconia, Spark plasma sintering Hydrothermal process, Ammonium tungsten bronze, In situ oxide dispersion strengthening, Zirconia, Spark plasma sintering

Research on preparation process for the in situ nanosized Zr(Y)O2 particles dispersion-

Introduction

Over the past years, oxide particles (such as ZrO 2 , La 2 O 3 , and Y 2 O 3 ) dispersion-strengthened tungsten alloys (ODS-W) are used as plasma facing material in future fusion reactors owing to their high melting point, high-temperature antiwear high-temperature strength and high-thermal conductivity [START_REF] Wang | A comparative study of several constitutive models for powder metallurgy tungsten at elevated temperature[END_REF][START_REF] Wei | Review on Research Progress of Steel and Iron Wear-Resistant Materials[END_REF][START_REF] Xiao | Hydrothermal synthesis of nanoplates assembled hierarchical h-WO 3 microspheres and phase evolution in preparing cubic Zr (Y) O 2 -doped tungsten powders[END_REF][START_REF] Xie | Achieving high strength/ductility in bulk W-Zr-Y 2 O 3 alloy plate with hybrid microstructure[END_REF]. With the development of increasingly accurate and netshape powder metallurgy manufacturing processing, the mechanical properties of tungsten alloys depend on the quality of tungsten powder to some extent [START_REF] Donoso | Computational study of the industrial synthesis of tungsten powders[END_REF][START_REF] Li | Porous structure uniformity investigation of tungstenmatrix prepared by jet milled and annealed tungsten powder[END_REF][START_REF] Wu | The process and mechanisms for the transformation of coarse grain to nanoscale grain in tungsten by ball milling[END_REF][START_REF] Asachi | A review of current techniques for the evaluation of powder mixing[END_REF][START_REF] Staiger | Particle size distribution measurement and assessment of agglomeration of commercial nanosized ceramic particles[END_REF][START_REF] Senapati | Modeling of viscosity for power plant ash slurry at higher concentrations: effect of solids volume fraction, particle size and hydrodynamic interactions[END_REF]. Mazher Ahmed Yar et al. [START_REF] Yar | Chemically produced nanostructured ODS-lanthanum oxide-tungsten composites sintered by spark plasma[END_REF][START_REF] Yar | Spark plasma sintering of tungsten-yttrium oxide composites from chemically synthesised nanopowders and microstructural characterization[END_REF] reported the W-Y 2 O 3 and La 2 O 3 powder through solid-liquid doping method using ammonium paratungstate (APT) as materials. The doped powders consisted of significant particle aggregates, resulting in heterogeneous distribution of oxide particles. Belgacem Mamen et al. [START_REF] Mamen | Experimental and numerical analysis of the particle size effect on the densification behaviour of metal injection moulded tungsten parts during sintering[END_REF] revealed that particle size of powders affected the densification behaviour and sintering stress of tungsten specimens during solid state sintering.

To improve the quality of tungsten powders for preparing high-performance tungsten products, over the past several years, the liquid-liquid (L-L) doping techniques, particularly spray drying [START_REF] Zhang | Microstructure and strengthening mechanism of oxide lanthanum dispersion strengthened molybdenum alloy[END_REF][START_REF] Hu | Effect of yttrium doping on the formation and stability of β-tungsten powder[END_REF][START_REF] Lai | Reduction, sintering and mechanical properties of rhenium -tungsten compounds[END_REF][START_REF] Cui | Effect of scandia on tungsten oxide powder reduction process[END_REF][START_REF] Xiao | Microstructure and mechanical properties of W-ZrO 2 alloys by different preparation techniques[END_REF][START_REF] Han | The effect of trace nickel additive and ball milling treatment on the near-full densification behavior of ultrafine tungsten powder[END_REF] and evaporation-precipitation/sol-gel process [START_REF] Dong | Synthesis of nanosized composite powders via a wet chemical process for sintering high performance W-Y 2 O 3 alloy[END_REF][START_REF] Zhao | Thermal shock behavior of W-0.5 wt% Y 2 O 3 alloy prepared via a novel chemical method[END_REF][START_REF] Liu | Nanostructured yttria dispersion-strengthened tungsten synthesised by sol-gel method[END_REF][START_REF] Zhu | Refining mechanisms of arsenic in the hydrogen reduction process of tungsten oxide[END_REF], were introduced to synthesize doped tungsten powders. On the one hand, it can avoid the introduction of detrimental contaminants during the mixing process of doping phase and tungsten powder. On the other hand, it can lead to the doping phase evenly distributed in tungsten powders through the molecular-level mixing. However, the prepared doped tungsten powders also exhibit high degree of agglomeration, such as W-Y 2 O 3 powders [START_REF] Hu | Effect of yttrium doping on the formation and stability of β-tungsten powder[END_REF][START_REF] Zhao | Thermal shock behavior of W-0.5 wt% Y 2 O 3 alloy prepared via a novel chemical method[END_REF], W-Re powders [START_REF] Lai | Reduction, sintering and mechanical properties of rhenium -tungsten compounds[END_REF], W-Sc 2 O 3 powders [START_REF] Cui | Effect of scandia on tungsten oxide powder reduction process[END_REF] and W-As powders [START_REF] Zhu | Refining mechanisms of arsenic in the hydrogen reduction process of tungsten oxide[END_REF].

A large number of studies have shown that the physical and chemical characteristics of the precursor powder, the phase evolution process and the evolution of mechanisms affected the resultant reduced powders [START_REF] Liu | Recovery of tungsten carbides to prepare the ultrafine WC-Co composite powder by two-step reduction process[END_REF][START_REF] Schubert | Production and characterization of hydrogen-reduced submicron tungsten powders. Part II: Controlled decomposition of APT and hydrogen reduction of the oxides[END_REF][START_REF] Hong | Fabrication of W-20 wt % Cu composite nanopowder and sintered alloy with high thermal conductivity[END_REF][START_REF] Yoon | Microstructure and sintering behavior of W-Cu nanocomposite powder produced by thermo-chemical process[END_REF][START_REF] Wu | Preparation of ultrafine tungsten powders by in-situ hydrogen reduction of nano-needle violet tungsten oxide[END_REF][START_REF] Zeiler | On the reduction of NS-doped tungsten blue oxide-Part I: Literature review[END_REF][START_REF] Wu | Crystal growth of tungsten during hydrogen reduction of tungsten oxide at high temperature[END_REF]. Hu Yazhou et al. and Hong Seong-Hyeon et al. [START_REF] Hu | Effect of yttrium doping on the formation and stability of β-tungsten powder[END_REF][START_REF] Hong | Fabrication of W-20 wt % Cu composite nanopowder and sintered alloy with high thermal conductivity[END_REF] synthesized the spherical doped precursor W-Y 2 O 3 and W-Cu powders through spray drying method, respectively. The resultant doped tungsten powders were composed of solid agglomerates. Yoon Eui-Sik et al. [START_REF] Yoon | Microstructure and sintering behavior of W-Cu nanocomposite powder produced by thermo-chemical process[END_REF] reported the H 2 reduction behavior of powders can be significantly affected by the microstructure and composition of tungsten powders. Wu Chonghu et al. [START_REF] Wu | Preparation of ultrafine tungsten powders by in-situ hydrogen reduction of nano-needle violet tungsten oxide[END_REF] pointed out that tungsten blue oxide (WO 2.72 , WO 2.90 , W 20 O 58 or (NH 4 ) х •WO 3 ) would be an ideal materials for preparing ultrafine tungsten alloy powders through dry hydrogen reduction. It was reported that the physical properties of tungsten powder would be determined by different transition sequences from tungsten blue oxide to W to some extent, which depend on the operating conditions (reduction temperature, holding time and H 2 O partial pressure) [START_REF] Zeiler | On the reduction of NS-doped tungsten blue oxide-Part I: Literature review[END_REF][START_REF] Wu | Crystal growth of tungsten during hydrogen reduction of tungsten oxide at high temperature[END_REF].

Among tungsten blue oxide, the metastable phases of hexagonal ammonium tungsten bronze (NH 4 ) х •WO 3 (HATB) have attracted a lot of attention during the last decades [START_REF] Guo | Simple route to (NH 4 ) x WO 3 nanorods for near infrared absorption[END_REF][START_REF] Szilágyi | Phase transformations of ammonium tungsten bronzes[END_REF]. Due to their special channel structures, large specific surface area and high-activity, they are used in catalytic detectors, color development devices and gas sensors [START_REF] Guo | Simple route to (NH 4 ) x WO 3 nanorods for near infrared absorption[END_REF][START_REF] Szilágyi | Phase transformations of ammonium tungsten bronzes[END_REF][START_REF] Szilágyi | In situ HT-XRD Study on the Formation of Hexagonal Ammonium Tungsten Bronze by Partial Reduction of Ammonium Paratungstate Tetrahydrate[END_REF]. They are also preferred materials for producing tungsten filaments in the lighting, extremely hard and refractory metal industry [START_REF] Szilágyi | Phase transformations of ammonium tungsten bronzes[END_REF][START_REF] Lassner | Tungsten: properties, chemistry, technology of the element, alloys, and chemical compounds[END_REF][START_REF] Bartha | Special issue on the chemistry of non-sag tungsten[END_REF].

According to the above analysis mentioned, the doped HATB with high-dispersity synthesized through liquid-liquid doping technique would be expected to produce high-quality doped tungsten powders and alloys. In this work, the nanosized Zr(Y)O 2 particles uniformly distributed in the tungsten alloys are fabricated through the novel composite hydrothermal method and spark plasma sintering process.

Composite hydrothermal method and reaction mechanism for preparing highly dispersed doped α-HATB is deeply investigated in detail. Through optimized hydrogen reduction process of doped α-HATB, the fine doped tungsten powders particles are obtained and have a narrower size distribution. Moreover, the phase composition and morphology evolution are investigated. After sintering, the nanosized Zr(Y)O 2 particles uniformly distributed in the developed tungsten alloy are realized, which are considerably smaller than those in the state-of-the-art review. Our approach can readily be adapted to manufactured nanosized Zr(Y)O 2 particles dispersion-strengthened W and 92.25W-4.9Ni-2.1Fe-0.75ZrO 2 through the proposed liquid-liquid doping and hot isostatic pressing processes.

Experimental methods

Composition of samples

The compositions of doped tungsten powders were listed in Table 1

Preparation of composite powders and alloys

In this research, the W-Zr(Y)O 2 powders were synthesized through composite hydrothermal method, which distinguishes from the multiple step hydrothermal method [START_REF] Xiao | Hydrothermal synthesis of nanoplates assembled hierarchical h-WO 3 microspheres and phase evolution in preparing cubic Zr (Y) O 2 -doped tungsten powders[END_REF][START_REF] Cui | Study on preparation and properties of molybdenum alloys reinforced by nano-sized ZrO 2 particles[END_REF][START_REF] Wang | Microstructure and preparation of an ultra-fine-grained W-Al 2 O 3 composite via hydrothermal synthesis and spark plasma sintering[END_REF]. Firstly, the raw materials, which are commercial ZrOCl forming the resultant solution. Finally, this solution was placed in a stainless-steel autoclave at 120 °C. After the reaction was completed, the autoclave was cooled down to 25 °C. The reaction products were dried and then the doped precursor powders were synthesized. After that, the precursor powder was calcined in air or reduction with hydrogen gas flow rate of 6 l.min -1 at different temperature, forming the resultant doped powders.

The reduced powders were loaded into a graphite mold (grade SS, 1.85g/cm 3 )

with an inner diameter of 20 mm by manual operation and then were densified using spark plasma sintering (SPS) processes using various sintering conditions in SPS furnace (SPS-20T-10-4) manufactured by Shanghai Chenhua Technology Co., Ltd.

Measurement, experimental procedures and analysis

The reaction process of precursor powders during calcination were studied through Thermogravimetric Analysis (TGA) and Differential Scanning Calorimeter (DSC) using a NETZSCH STA 409 PC/PG thermal analyzer. The composition, crystallite size and full width at half maxima (FWHM) of powders were determined using X-ray diffraction analyses combined with the JADE 5.0 software. The morphology evolution and chemical composition were investigated using a scanning electron microscope (SEM), electron dispersive spectroscopy (EDS), backscattered electron (BSE) and high-resolution transmission electron microscopy (HR-TEM).

Laser diffraction particle size analyzer (Mastersizer-2000) was used to determine the particle-size distribution (PSD) dispersed in ethanol. The specific surface area (SSA) and d BET sizes of doped powders was described as [START_REF] Liao | Particle size characterization of ultrafine tungsten powder[END_REF]:

The distribution slope parameter, S w , was calculated from the measured particle size by Eq. ( 1) [START_REF] Staiger | Particle size distribution measurement and assessment of agglomeration of commercial nanosized ceramic particles[END_REF]. The coefficient of uniformity, C u, is defined by Eq. ( 2) [START_REF] Senapati | Modeling of viscosity for power plant ash slurry at higher concentrations: effect of solids volume fraction, particle size and hydrodynamic interactions[END_REF].

S
C u = d 60 /d 10 (2)
where d 60 is the particle sizes at 60% of the cumulative volume percentage.

The span value (Ψ) is calculated using Eq. (3) [START_REF] Li | Particle size distribution control and related properties improvements of tungsten powders by fluidized bed jet milling[END_REF]:

Ψ = (d 90 -d 10 ) / 2 d 50 (3)
where d 50 is the particle sizes at 50% of the cumulative volume percentage and is regarded as mean particle size.

The agglomeration factor (F ag ) was calculated as shown in Eq. ( 4) [START_REF] Staiger | Particle size distribution measurement and assessment of agglomeration of commercial nanosized ceramic particles[END_REF]:

F ag = d 50 /d BET ( 4
)
where d 50 is the average diameter of the powders.

The densities of the alloys were determined using by Archimedes' principle. The relative densities were obtained by using the apparent volume mass divided by the theoretical value of 19.18 g/cm 3 . Vickers hardness test was made using 200 g indented load and a dwell time of 20 seconds. The average hardness value is performed with 10 randomly selected sample specimens.

Results and discussion

Reaction mechanism of precursor powders

Considering different polytungstate species could exist in aqueous solutions of different acidities (Fig. 1) [START_REF] Xiao | Microstructure and mechanical properties of W-ZrO 2 alloys by different preparation techniques[END_REF], in order to obtain optimal doping effect, the existence forms and reaction mechanisms of polytungstate ions in aqueous solutions were analyzed.

When

+2H 2 O+OH -=2(H 3 W 6 O 21 ) 3- (H 3 W 6 O 21 ) 3- Pseudo-AMT pH>6 (H 3 W 6 O 21 ) 3-+2OH -= (HW 6 O 21 ) 5-+2H 2 O (HW 6 O 21 ) 5- Paratungstate pH>9 (HW 6 O 21 ) 5-+3H 2 O+7OH -=6(HWO 4 ) -+H + +7OH -=6WO 4 2- +7H + +7OH - WO 4 2-
Tungstate ion

Synthesis and analysis of precursor powders

As shown in Fig. 2 a), the undoped precursor powder is composed of radiant microspheres with an average size less than 5 µm. The inset in Fig. 2 a) shows these microspheres are composed of circular or lamellar substances. Containing a small account of (Zr, Y) substances exists of hydrothermal system, the complete microspheres are destroyed into loose cotton-like powder particles, see Fig. 2 b).

XRD patterns of precursor powders, as shown in Fig. 2 c), show that the sharp peaks can be observed, indicating that the synthesized precursor powder exhibits the high-degree crystallinity. All these diffraction peaks can be indexed as hexagonal (NH 4 ) 0.33 •WO 3 •(α-HATB, PDF# 42-0452), which agree with the patterns of α-HATB in elsewhere [START_REF] Szilágyi | Phase transformations of ammonium tungsten bronzes[END_REF]. From the XRD patterns, it can be seen that no any other phases containing Zr and Y elements were detected. Though, ZrOCl 2 •8H 2 O dissolves in strong acid solutions, the hydrolysis of ZrOCl 2 •8H 2 O in aqueous solution still occurs and the Cl -ions in the outer sphere of the ionic complex are replaced by OH -groups (Eq. ( 5)) [START_REF] Yao | Synthesis and characteristics of nanocrystalline YSZ powder by polyethylene glycol assisted coprecipitation combined with azeotropic-distillation process and its electrical conductivity[END_REF].

{[Zr 4 (OH) 8 •16H 2 O] 8+ 8Cl -} + 4H 2 O = {[Zr 4 (OH) 8 •16H 2 O] 8+ 8OH -} + 8HCl↑ (5)
Then the [Zr 4 (OH) 8 16H 2 O] 8+ can react with the hydroxyl ions and form Zr(OH) 4 sols [START_REF] Guo | Thermal, spectroscopic and X-ray diffractional analyses of zirconium hydroxides precipitated at low pH values[END_REF][START_REF] Glushkova | Specific features in the behavior of amorphous zirconium hydroxide: I. Sol-gel processes in the synthesis of zirconia[END_REF]. As the Zr(OH) 4 sols is amorphous, these aren't detectable in doped precursor [START_REF] Guo | Thermal, spectroscopic and X-ray diffractional analyses of zirconium hydroxides precipitated at low pH values[END_REF].

The morphology of the doped precursor was investigated by TEM observation, see Fig. 2 d). A detailed examination reveals that the precursor consists of nanoplate coalescence. The diameter of the synthesized nanoplates is less than 15 nm and their length is less than 100 nm. From the inset in Fig. 2 d), the lattice spacing of hexagonal (NH 4 ) 0.33 WO 3 •H 2 O is 3.841 Å and identified as the (002) plane. These results indicate the growth of nanoplates along the c-axis direction [START_REF] Glushkova | Specific features in the behavior of amorphous zirconium hydroxide: I. Sol-gel processes in the synthesis of zirconia[END_REF]. In this regard, the possible formation mechanism of (NH 4 ) 0.33 WO The overall reaction was given in the Eq. ( 8).

( six-membered rings by sharing equatorial oxygen in the ab plane (001) (Fig. 3) [START_REF] Miao | Large scale hydrothermal synthesis of monodisperse hexagonal WO 3 Nanowire and the growth mechanism[END_REF].

In this structure, tungsten atoms are bound to six oxygen atoms in an octahedral coordination. Each oxygen atom is shared by two octahedrons, which are arranged in layers. This finding indicates that numerous hexagonal and trigonal tunnels are distributed in the [001] crystal direction. However, these rings usually stack by sharing the axial oxygen in the c axis [001] and form hexagonal prism (Fig. 3).

During nucleation, these primary precipitated crystals from the crystal cell can be generated as a regular hexagonal prism. In the hydrothermal reaction system, the presence of a certain concentration of NH 4 + ions contributes to occupying the hexagonal tunnels (Fig. 3) [START_REF] Zhan | A solvothermal route for the synthesis of ammonium tungsten bronze[END_REF][START_REF] Clark | An NMR Study of Ionic Motion in Ammonium Tungsten Bronze[END_REF], and then leads to the accelerated growth of hexagonal-prism WO 3 along the [001] direction and the formation of hierarchical (NH 4 ) 0.33 WO 3 •H 2 O nanoplates. The nanoplates self-assemble together to form microspheres to reduce the high surface energy [START_REF] Cao | Hydrothermal synthesis, characterization and gas sensing properties of the WO 3 nanofibers[END_REF]. However, it may be due to the addition of doped ions (Zr 4+ , Y 3+ and Cl -) into hydrothermal system, the breakage of order between the positive and negative charge destroys the self-assemble process, leading to the transformation of agglomerated microspheres into relatively dispersed cotton-like precursor.

Morphology and phase evolution of doped powders during calcination

The TGA and DSC curves of α-HATB were presented in Fig. 4 a). When increasing the temperature to 230 °C, the weight loss may be caused by the loss of surface-adsorbed water at 90 °C and structural water elimination at 175 -260 °C in the DSC curve (peaks 1 and 2) [START_REF] Huo | Synthesis and mixed conductivity of ammonium tungsten bronze with tunneling structures[END_REF].

From 260 °C to 383°C, a small variation of weight loss was observed. This would be owing to the degassing of NH 3 molecules due to the partial (NH 4 ) 0.33 WO 3 •H 2 O decomposition. However, it was reported that α-HATB powder can be produced after calcining APT at 400 °C under hydrogen atmosphere [START_REF] Fouad | Characterization of ammonium tungsten bronze [(NH 4 ) 0.33 WO 3 ] in the thermal decomposition course of ammonium paratungstate[END_REF], so the degassing of NH 3 below 400 °C was unexpected. Up to 430 °C, an obvious weight loss occurs quickly. This may be due to the partial NH 3 molecular rearrangement occurred in a solid state chemical equilibrium reaction, causing partial NH 3 molecules to transfer to the surface of α-HATB particles and then leading to the complete decomposition of (NH 4 ) 0.33 WO 3 •H 2 O•H 2 O. However, it's not like that the flat horizontal TGA line at above 430°C, it can also be seen that the exothermic peak 3 could be observed at 500°C in DSC results. This indicated a phase transition, see Fig.

Phase and morphology evolution of reduced powders

The XRD patterns of the reduced H 0.5 powders obtained directly from doped precursor by the hydrogen reduction at 500 ~ 950 °C are shown in Fig. 5. The reduced powders were hereafter abbreviated as RP samples in Fig. 5. Some characteristic (b) (a) parameters of the H 0.5 powder prepared through different reduction processes were listed in Table 3. From the XRD patterns of the powder reduced at 500 °C, it can be seen that the powder mainly consists of hexagonal (NH 4 ) 0.42 WO 3 (β-HATB) phase.

No m-WO 3 peaks can be indexed. All the diffraction peaks of β-HATB agree well with the standard data file (PDF#42-0451, a=0.7359 nm, b=0.7359 nm, c=0.7544 nm), which is also in consistent with the patterns of β-HATB in elsewhere [START_REF] Szilágyi | Phase transformations of ammonium tungsten bronzes[END_REF]. Generally speaking, under high temperature (i.e. above 430°C), the hexagonal structure collapses due to the release of the NH 3 . However, in reductive atmosphere, these anoxic environments hinder the formation of m-WO 3 and promote the occurrence of the β-HATB. However, the structure of β-HATB was disputed [START_REF] Szilágyi | Phase transformations of ammonium tungsten bronzes[END_REF]. As so far, there This finding indicates that the nucleation and growth of WO 2.0 and α-W phases from the precursor occur at reduction temperature of 550 -650 °C. Moreover, detailed examination shows that there are three weak diffraction peaks at 35.59° (004), at 43.97° (211) and 69.7° (321), respectively. All these peaks correspond to β-W phase (PDF#47-1319). Hu et al. [START_REF] Hu | Effect of yttrium doping on the formation and stability of β-tungsten powder[END_REF] reported that the β-W phase transformed into α-W at 520 -625 °C. It indicates that in this current research, the transformation temperature of β-W into α-W increases, which may be due to the addition of containing (Zr, Y) phase.

When heating the doped powder to 750 °C, the WO 2 peaks become weaker, whereas peaks of the α-W become stronger. Up to 800 °C, the WO 2 completely disappears and the powder consists of the α-W phase as shown Fig. 5 b). However, the peak intensities of the α-W phase are still weaker compared to powders reduced at 850 °C and 900 °C, respectively. With heated to 900 °C, the peak intensities of the α-W powder remain almost unchanged compared with those of the powder reduced at 950 °C, indicating that the doped powder reduced at 900 °C has complete crystallinity.

As a result of the above analysis as listed in Table 3, α-HATB is reduced to W in the range of 500 -900 °C through the reduction sequence of α-HATB→ β-HATB→W 29 O 58 →WO 2 →(β-W) α-W. It's worth noting that among these phase transitions, the phase transitions of HATB→WO 2.9 and WO 2.9 →WO 2 , is very fast and the overall transition rate of HATB→W is limited by WO 2 → W [START_REF] Wu | Crystal growth of tungsten during hydrogen reduction of tungsten oxide at high temperature[END_REF]. Increasing the temperature to 650 °C, a little change in the morphology is observed, see Fig. 6 b). However, combined on the XRD result, close examination reveals that the powder is composed of agglomerates, consisting of nanosized tungsten or tungsten oxide crystals. Observations in the micro-morphology don't reveal differences in their actual crystalline structure. With increasing temperature up to 750 °C, the doped powder consists of nanosized particles as shown in Fig. 6 c). The nanosized particles are distinguishable as marked by the white square. This is enhanced due to the chemical vapor transport (CVT), causing the formation of distinct, nanosized and single crystals [START_REF] Wu | Preparation of ultrafine tungsten powders by in-situ hydrogen reduction of nano-needle violet tungsten oxide[END_REF]. Increasing the temperature to 800 °C provokes that the α-W powder exhibits two different particle morphologies due to grain growth: the ratio of rod length to mill diameter is about 5 and equiaxed flaky particles with a mean particle size of the order of 0.93 μm as shown in Fig. 6 d) and Table 3

Analysis of phase and morphology of the W-Zr(Y)O 2 powders

XRD patterns of doped tungsten powders prepared through the reduction process of 500 °C (1.5h) + 900 °C (2h) have been compared plotted in Fig. 7. The characteristic parameters of these powders were summarized in Table 4, such as crystallite size, specific surface area, full width at half maximum and the parameters of PSD.

As the tiny amount of Zr(Y)O 2 (the doping amount is less than 0.75%) was doped in powders, no diffraction peaks of containing (Zr, Y) phases can be found. 4. The comparison of the FWHM of five powders reveals a slight increase in peak broadening with increasing in Zr(Y)O 2 content as shown in Fig. 7 and Table 4, which were mainly caused by the fine particle size [START_REF] Xiao | Hydrothermal synthesis of nanoplates assembled hierarchical h-WO 3 microspheres and phase evolution in preparing cubic Zr (Y) O 2 -doped tungsten powders[END_REF][START_REF] Kurlov | Oxidation of tungsten carbide powders in air[END_REF]. The undoped W powder particles having a polyhedral shape, see Fig. 8a). The surface of particle is smooth. However, the surface of the nearly spherical doped W powder particles is rough compared with that of undoped W particles. Moreover, compared to the undoped powder, the distinguishable quantitative comparison of particle profile indicates a low degree of agglomeration. Detailed examination shows that the surfaces of the doped powder particles exhibit some white nanosized substances, see inset in the Fig. 8 d) (arrow A in inset).

The EDS results reveals that the atomic ratio of Zr(Y) to O was in a ½ molar ratio, as shown in Fig. 8 e). It indicates that these nanosized substances are mainly Zr(Y)O 2 . From Fig. 8 f), it can be also seen that as Zr(Y)O 2 content increases, the crystalline size and the mean particle size [d 50 ] both decrease firstly and then increase slightly. However, the crystalline size of the four powders is about 15-20 times less than the mean particles size, see Table 4). Crystalline structural details were revealed by TEM and HR-TEM observations conducted on the H 0.5 powder sample. The observation of the nanosized particles shows nearly-spherical morphology in Fig. 10 a). The statistical distribution of the particle size histogram is based on 300 particles from different TEM images, see Fig. 10 b). The diameters of more than 90% of particles range from 6 nm to 50 nm with the average particle size of 28 nm.

The crystal planes correspond to the (110) planes of α-W shown by the HR-TEM image in Fig. 10 c). The measured lattice spacing is about 2.313 Å. As shown in Fig. 10 d

Zr Y

Clustering ZrO 2 and Y 2 O 3 is the premise of forming stabilised ZrO 2 phase [START_REF] Sotomayor | Influence of powder particle size distribution on rheological properties of 316 L powder injection moulding feedstocks[END_REF]. So it is easy to understand that the doping process described in the experimental section for synthesis of the precursor powders was used to obtain containing Zr and Y phase close together. distribution and the powders with S w value between 4 and 5, are usual process conditions used as raw materials for manufacturing non-defective injected components by Powder Injection Moulding Process [START_REF] Staiger | Particle size distribution measurement and assessment of agglomeration of commercial nanosized ceramic particles[END_REF][START_REF] German | Injection Molding of Metals and Ceramics[END_REF][START_REF] Sotomayor | Influence of powder particle size distribution on rheological properties of 316 L powder injection moulding feedstocks[END_REF]. On the contrary, the lower the C u value, the narrower the particle sizes-distribution [START_REF] Senapati | Modeling of viscosity for power plant ash slurry at higher concentrations: effect of solids volume fraction, particle size and hydrodynamic interactions[END_REF]. Thus, the value of C u reduces from 3.06 to 2.30, indicating the narrower PSD. It can be also confirmed by the reduced value of Ψ from 1.18 to 0.86 [START_REF] Li | Particle size distribution control and related properties improvements of tungsten powders by fluidized bed jet milling[END_REF]. It's worth noting that the reduced values of C u and Ψ show a non linear variation, this is due to that the different Zr(Y)O 2 doping amount results in the different refinement effect. Excessive Zr(Y)O 2 would cause the agglomerates' formation of refined particles [START_REF] Xiao | A hybrid microstructure design strategy achieving W-ZrO 2 (Y) alloy with high compressive strength and critical failure strain[END_REF]. However, as listed in Table 4, the agglomeration factors (F ag ) of the doped powders, indicating the agglomerate state, are less than 3, which means the particles were little agglomerated [START_REF] Bowen | Particle size distribution measurement from millimeters to nanometers and from rods to platelets[END_REF].

Microstructure of alloys

The effect of sintering temperature on microstructure of the W-0.25 wt. % Zr(Y)O 2 alloy produced by spark plasma sintering process with various final temperatures from innovative developed powder was investigated. As through fracture surfaces, oxide particle cannot be obviously observed, the SEM images of the etched microstructure, are presented as shown in Fig. 13(a-d). Fig. 13 a) shows the plenty of necks and interconnected pores in the samples. After sintering at 1900 °C, the grain size slightly increases from 1.5 μm to 2.2 μm, which may result from the accelerated diffusion process due to the combined effects of higher pressure and high temperature.

However, after sintering at 2000 °C, the grains size and relative density increased rapidly. It indicates the rapid densification of the tungsten powder in the temperature range of 1900~2000 °C under 30 MPa, in which the change trend of grain size and density matched well with the case of micro-hardness inflection-point. The average grain size of alloy sintering at 2000 °C is 4.7 μm, smaller than that of pure tungsten (8.5 μm) [START_REF] Wang | Effect of ZrO2 content on microstructure and mechanical properties of W alloys fabricated by spark plasma sintering[END_REF]) under the same sintering process, suggesting that oxide particles cause the refinement effect on grain growth of high temperature sintering process. Further increasing temperature to 2100 °C, the grain size and density continuously increase and the average grain size reaches the value of 6.3 μm.

The curves of grain size and relative density obtained by SPS with various final temperature were plotted in Fig. 14 a). It is worth noting that in the etched microstructure, a lot of white particles were observed. These white particles are Zr(Y)O 2 particles confirmed by the EDS analysis using the same methodology and the same case study as F. N. Xiao et al. [START_REF] Xiao | Microstructure and mechanical properties of W-ZrO 2 alloys by different preparation techniques[END_REF]. The PSD of Zr(Y)O 2 of the corresponding alloy manufactured by via SPS sintering, at 2000 °C for 5 minutes in Fig. 14 b). These results confirm that more than 95% of particles are less than 500 nm with an average particle size of 250 nm. Among these Zr(Y)O 2 particles, some larger oxide particles are located at or near the grain boundaries (marked by white arrows in Fig. 13 c), which induced stress/strain concentrations as the starting points of possible cracks and reduce the fracture toughness of material [START_REF] Liu | Nanostructured high-strength molybdenum alloys with unprecedented tensile ductility[END_REF]. However, as shown from the inset in Fig. 13 c), lots of nanosized oxide particles as marked by red arrows are homogeneously distributed within the grains. In fact, in standard TEM observation as shown in Fig. 14 c) (indicated by solid arrows), a large number of particles were found in grains. HR-TEM images based selected area electron diffraction pattern (SAEDP) from selected area under the red box in Fig. 14 c) reveal the white particles were obtained in the presence of cubic phase of nanocrystalline ZrO 2 , which may be caused by the diffusion of Y element into containing Zr phase during high-sintering temperature. These particles can generate, hinder and then accumulate dislocations during the deformation process. The particles exhibit a good bonding with the tungsten phase. However, there are no coherent relationship between tungsten phase and oxide phase, see Fig. 14 d). Ultrafine and nanosized Zr(Y)O 2 particles dispersed in current tungsten alloy may be due to the high quality doped powder prepared by composite hydrothermal method. The powder particles surfaces are covered each of the white substances, see Fig. 8 d). Sintered under 1800 °C, these white substances have the similar size as the oxide particles as shown Fig. 13 b). With increasing sintering temperature to 1900 °C, the nanosized white substances agglomerate slowly. The same case can be found in references [START_REF] Wang | Microstructure and preparation of an ultra-fine-grained W-Al 2 O 3 composite via hydrothermal synthesis and spark plasma sintering[END_REF][START_REF] Wang | Effect of ZrO2 content on microstructure and mechanical properties of W alloys fabricated by spark plasma sintering[END_REF][START_REF] Li | Fabrication and mechanical properties of tungsten alloys reinforced with c-ZrO 2 particles[END_REF]. Moreover, the content of oxide particle also affects the eventual oxide particle size. In references [START_REF] Li | Fabrication and mechanical properties of tungsten alloys reinforced with c-ZrO 2 particles[END_REF][START_REF] Wang | Preparation, microstructure, and constitutive equation of W-0.25 wt% Al 2 O 3 alloy[END_REF], the effect of oxide particle content on microstructure of the ODS-W alloy through different processes was investigated.

Therefore, it can be confirmed that larger particles are formed by the aggregation of small particles at high temperature sintering.

The initial oxide particle size in doped tungsten powders, mainly deponds upon the doping techniques. SPS, HIP and sintering in vertical direction (VD) processes regarded as a rapid sintering process, can reveal the initial oxide particle size in doped tungsten powders to some extent. Wang et al. [START_REF] Wang | Microstructure and preparation of an ultra-fine-grained W-Al 2 O 3 composite via hydrothermal synthesis and spark plasma sintering[END_REF][START_REF] Wang | Effect of ZrO2 content on microstructure and mechanical properties of W alloys fabricated by spark plasma sintering[END_REF] prepared the W-ZrO 2 and W-Al 2 O 3 alloys through separately hydrothermal method combined with SPS sintering process. Due to the serious agglomeration of precursor powder, Al 2 O 3 and ZrO 2 can not be evenly distributed in powders. It leads that coarse and adhesive oxide particles (areas marked by a red circle) and reaches to value of 3 μm in alloy as shown in Fig. 15 a) and b). It indicates that using separately hydrothermal method cannot obtain the ultrafine and uniformly distributed oxide particle in powders compared to the proposed methods in this current research. In this case study, W-ZrO 2 powder were manufactured by azeotropic distillation method, followed by the vertical direction, the ZrO 2 particles still reach the value of 1.0 μm, which may result from agglomerated W-ZrO 2 powders [START_REF] Wang | Microstructure and preparation of an ultra-fine-grained W-Al 2 O 3 composite via hydrothermal synthesis and spark plasma sintering[END_REF][START_REF] Xiao | Preparation, microstructure, and properties of tungsten alloys reinforced by ZrO 2 particles[END_REF].

A novel fabricated method was developed to elaborate W-Zr(Y)O 2 alloy and was compared of the tradionnal methods to produce some oxide dispersion-strengthened tungsten alloys manufacturing by fast sintering processes, as listed in Table 5. These alloys listed in Table 5 were prepared via other liquid-liquid, liquid-solid or solid-solid (mechanical alloying) doping methods, respectively.

Seen from Table 5, using liquid-liquid doping processes, can achieve smaller oxide particle compared to conventional mechanical alloying. However, the average particle size of alloys through the liquid-liquid methods, which are different from the proposed method, still reach up to 1.5 μm, 3.5 μm and 3.6 μm, respectively. For mechanical alloying of ODS-W powders, the refinement effect on oxide particle size is limited to some extent even through doping nanosized oxide particles [START_REF] Muñoz | La 2 O 3 -reinforced W and W-V alloys produced by hot isostatic pressing[END_REF][START_REF] Ki | Fabrication of high temperature oxides dispersion strengthened tungsten composites by spark plasma sintering process[END_REF].

Angel Muñoz et al. [START_REF] Muñoz | La 2 O 3 -reinforced W and W-V alloys produced by hot isostatic pressing[END_REF] prepared the W-La 2 O 3 powder using nanosized La 2 O 3 particles ranging from 10 to 50 nm in size as raw material. However, the large adsorption effect of nanosized oxide particles leads to the formation of particle aggregations even after ball-milling for 30 hours [START_REF] Ki | Fabrication of high temperature oxides dispersion strengthened tungsten composites by spark plasma sintering process[END_REF]. For the liquid-solid doping processes, they are usually expected to obtain smaller oxide particles size. However, in the W-La 2 O 3 alloys prepared through SPS process and sintering in the vertical direction, respectively [START_REF] Yar | Chemically produced nanostructured ODS-lanthanum oxide-tungsten composites sintered by spark plasma[END_REF][START_REF] Shen | Microstructure of a commercial W-1% La2O3 alloy[END_REF], both La 2 O 3 particles exceeding 2 μm. Yar M.A. et al.

prepared the nanosized Y 2 O 3 particle reinforced tungsten alloy through liquid-solid doping processes [START_REF] Yar | Spark plasma sintering of tungsten-yttrium oxide composites from chemically synthesised nanopowders and microstructural characterization[END_REF], oxide particles were non-uniformly distributed into the tungsten matrix due to the reaction occurred only at the surfaces of APT as shown in Based on the above analysis, doped tungsten powders were prepared combined with composite hydrothermal method and mechanical alloying process. Then, through SPS and HIP processes, respectively, W-ZrO 2 and 92.25W-4.9Ni-2.1Fe-0.75ZrO 2 alloys were fabricated as shown in Fig. 16 a), b) and c). Seen from the inset in Fig. 16 a), a lots of nanosized particles are evenly distributed into the tungsten matrix. In Fig.

  . Five kinds of doped tungsten powders consist of the following types: with 0 wt% Zr(Y)O 2 , 0.25 wt% Zr(Y)O 2 , 0.5 wt% Zr(Y)O 2 , 0.75 wt% Zr(Y)O 2 and 5 wt% Zr(Y)O 2 , respectively. The H 5.0 sample was used to investigate the composition of doped powder through X-ray diffraction (XRD) analysis.

(

  Fig. 2 (a) and (b) SEM images of the undoped and doped precursor powders, (c) XRD patterns of doped precursor powder and (d) TEM image of the H 0.75 doped precursor.

Fig. 3

 3 Fig. 3 Schematic diagram of morphology evolution mechanism of (NH 4 ) 0.33 WO 3 •H 2 O precursor.

Fig. 4 (

 4 Fig. 4 (a) The TGA and DSC curves of the decomposition of the H 0.5 precursor powder and (b) XRD patterns of doped powder after calcination at different temperature for 2 h.

  are two different PDF# cards assigned to it. They are (NH 4 ) 0.06 WO 3 •(H 2 O) 0.11 (PDF#15-0217) and (NH 4 ) 0.42 WO 3 •H 2 O (PDF# 42-0451), respectively. When the temperature increases to 550 °C, the weaker intensities of W 20 O 58 peaks indicate that a tiny amount of β-HATB powder transform into W 20 O 58 powder. When heated to 650 °C, the patterns of powder significantly have changed compared to the previous two powders. β-HATB and W 20 O 58 phases are disappeared. The powder mainly consists of WO 2.0 and W phase. Three peaks of W phase can be observed at 40.26° (110), 58.27° (200) and 73.19° (211) corresponding to the α-W phase (PDF#04-0806).

Fig. 5 (

 5 Fig. 5 (a) XRD patterns of tungsten powders reduced at 550-750 °C for 1.5 h and (b) XRD patterns of tungsten powder reduced at 800 -950 °C for 2 h.

Fig. 6 a

 6 ), b), c) and (a) (b)d). The doped powder reduced at 550 °C has the similar morphology with that of calcined powder, which also preserves the morphology of precursor powder.

Fig. 6

 6 Fig. 6 Change of particle morphologies of doped powders obtained by different reduction processes at varying temperature: (a) 550 °C, (b) 650 °C, (c) 750 °C and (d) 800 °C, respectively.

  Thus, 5% wt Zr(Y)O 2 was designed to determine the composition of doped tungsten powder. The XRD patterns of H 5.0 powder indicate that the doped tungsten powders consist of α-W and cubic ZrO 2 (c-ZrO 2 ). With the increase in Zr(Y)O 2 content to 0.5 wt%, the tungsten particles are refined gradually through SEM observation as shown in Fig. 8. The refinement effect can also be confirmed by the reduced crystallite size and d BET as listed in Table

Fig. 7

 7 Fig. 7 XRD patterns of five doped powders after reduction at 900 °C for 2 h.

  To analyze the distribution of W and the doping phase Zr(Y)O 2 , EDS mapping was conducted on W-0.75% Zr(Y)O 2 powder as shown in Fig.9. The W and Zr elements have more obvious signal strength compared to Y element with law Y content in powder, see Fig.9 d). This would be owing to the tiny Y content in powder.Moreover, Zr and Y coexist in same W particles, suggesting Zr(Y)O 2 is uniformly distributed in doped powder, see Fig.9(b-d).

Fig. 8 Fig. 9

 89 Fig. 8 Morphologies of doped tungsten powders: (a) Pure W, (b) W-0.25 wt% Zr(Y)O 2 , (c) W-0.5 wt% Zr(Y)O 2 , (d) W-0.75wt% Zr(Y)O 2 , (e) EDS pattern of the nanosized substance of red arrow A and (f) Mean particle size and crystalline size vs. Zr(Y)O 2 contents.

  ), the value of the measured lattice spacing of 3.030 Å agrees well with the (111) lattice spacing of cubic ZrO 2 [d(111)=2.965 Å, PDF#49-1642]. Previous research revealed that the synthesized cubic ZrO 2 may result from the doping process.

Fig. 10 Fig. 11

 1011 Fig. 10 (a) TEM images of the W-0. 5% Zr(Y)O 2 powder, (b) Size distribution of nanosized particles, (c) and (d) HR-TEM images conducted on selected area marked by red and white squares in Fig. 10 a), respectively.

Fig. 12

 12 Fig. 12 PSD parameters of four W-Zr(Y)O 2 powders: (a) Particle sizes at the different cumulative volume percentage vs. Zr(Y)O 2 content and (b) Distribution slope parameter, coefficient of uniformity and span value vs. Zr(Y)O 2 contents.

Fig. 13 .Fig. 14 (

 1314 Fig. 13. Microstructure of alloys produced by different spark plasma sintering processes with various final temperatures: (a) 1800 °C for 5 min, (b) 1900 °C for 5 min, (c) 2000 °C for 5 min and (d) 2100 °C for 5 min.

Fig. 15 d

 15 Fig.15 d). In current research, the oxide particles in tungsten alloy are 0.8-10 times smaller than those in published alloys. Moreover, a large number of the nanosized oxide particles are observed within tungsten grains, see inset in fig.13c), indicating the proposed novel liquid-liquid doping process is the appropriate to reduce the particles size.

Fig. 15 .

 15 Fig.15. Microstructure of alloys reported in published references: (a, b) Powders prepared by a liquid-liquid method coupled with SPS process [61, 67], (c) Powdersprepared by a liquid-solid doping method combined with sintering in vertical direction and hot swaging process[START_REF] Shen | Microstructure of a commercial W-1% La2O3 alloy[END_REF] and (d) Powders prepared by a liquid-solid doping method couple with SPS process[START_REF] Yar | Spark plasma sintering of tungsten-yttrium oxide composites from chemically synthesised nanopowders and microstructural characterization[END_REF].

Table 1

 1 Composition of five kinds of doped tungsten powders.

	Samples	W	ZrO 2	Y 2 O 3
	H 0	100	0	0
	H 0.25	99.718	0.250	0.032
	H 0.50	99.437	0.500	0.063
	H 0.75	99.154	0.750	0.096
	H 5.0	94.370	5.000	0.630

  [START_REF] Wei | Review on Research Progress of Steel and Iron Wear-Resistant Materials[END_REF]

  NH 4 ) 6 H 2 W 12 O 40 •xH 2 O, in distilled water, introduces H 2 W 12 O 40

	(H 2 W 12 O 40 ) 6-+ 6H + + 32H 2 O = 12(H 2 WO 4 •2H 2 O)	(7)
	(a)	(b)
	(c)	(d)
			d (002)
			3.841Å
			h-HATB
			6+ and NH 4	+ ions,
	see next equation Eq. (6).
	(NH 4 ) 6 H 2 W 12 O 40 •xH 2 O = (H 2 W 12 O 40 ) 6-+ 6NH 4	+ + xH 2 O	(6)

[START_REF] Xiao | Hydrothermal synthesis of nanoplates assembled hierarchical h-WO 3 microspheres and phase evolution in preparing cubic Zr (Y) O 2 -doped tungsten powders[END_REF]

•H 2 O nanoplates was proposed. In previous paper of F. N. Xiao and al.

[START_REF] Xiao | Microstructure and mechanical properties of W-ZrO 2 alloys by different preparation techniques[END_REF]

, the dissolution of (At the beginning of reaction, WO 3 •nH 2 O is firstly formed through the hydrothermal reaction of (H 2 W 12 O 40 )

6

-and H + [Eq.

[START_REF] Wu | The process and mechanisms for the transformation of coarse grain to nanoscale grain in tungsten by ball milling[END_REF]

].

  NH 4 ) 6 H 2 W 12 O 40 •xH 2 O + 6HNO 3 = 6NH 4 NO 3 + 12WO 3 •nH 2 O↓ + (8-x) H 2 O (8) WO 3 •nH 2 O is formed from the layers of highly distorted corner-sharing WO 5 (H 2 O) octahedron and interlayer water through hydrogen bonds [40, 41]. The h-WO 3 crystal structure is obtained from hexagonal WO 5 (H 2 O). Based on the previous research of S. Cao and al. [46], WO 5 (H 2 O) octahedrons can form three-and

Table 3

 3 Characteristic parameters of H 0.5 powder prepared through different reduction processes at varying temperature from 550 to 900°C.

	Reduction tempe.	500 °C	650 °C	750 °C 800 °C 850 °C	900 °C
			α-W, β-W,	α-W
	Composition	β-HATB			α-W	α-W	α-W
			WO 2	WO 2
	[d 50 ] /μm	-	-	0.125	0.926	1.12	1.57
	Crystallite size (Å)	218(3)	316(3)	503(3) 662(21) 565(7)	1164(42)
	SSA (m 2 •g -1 )	-	-	3.265	2.765	2.673	0.213

The morphologies of the doped powders obtained by different reduction processes at varying temperature from 550 to 800 °C are shown in

Table 4

 4 Characteristic parameters of the four doped powders reduced at 900 °C for 2h.

		Crystallite		SSA	d BET	d 10 /	d 25 /	d 50 /	d 75 /	d 90 /
	Samp.	sizes(Å)	FWHM	(m 2 •g -1)	(μm)	μm	μm	μm	μm	μm	F ag
	H 0	1404	0.134	0.235 1.32	1.37 1.09 2.76 4.53 6.52 2.09
	H 0.25	1164	0.174	0.289 1.12	0.95 0.85 1.91 2.60 4.15 1.71
	H 0.50	1065	0.176	0.213 1.46	0.81 1.05 1.57 2.52 3.32 1.08
	H 0.75	1099	0.189	0.372 0.83	0.79 1.23 1.73 2.62 3.95 2.08

Table 5

 5 Microstructure and mechanical properties of ODS-W alloys. Powders prepared by proposed novel process combined with mechanical alloying.

	Doping	Sintering		W grain	Oxide particle	Density (g/cm 3 )/	Microhardness
			Alloy					Refs.
	process	Process		size (μm)	size (μm)	Relative density (%)	/Hv
		SPS	W-6vol% Al 2 O 3	3.64	>1.0	-/94.96	347.39	[37]
	L-L	SPS	W-2.5%ZrO 2	4.65	2.5	-/99.6	480	[61]
		VD	W-2.5%ZrO 2	40-80	1.5	-/98.7	-	[63]
		VD	W-La 2 O 3	50	3	-	-	[66]
	L-S a*	SPS	W-0.9wt%La 2 O 3	-	2	17.8/94	406	[11]
		SPS	W-1.0%Y 2 O 3	2.3	Nanosize	17.5/92	423	[12]
		HIP	W-1%La 2 O 3	-	>5	18.9/90.6	-	[68]
	S-S	HIP	W-Ti-0.5%Y 2 O 3	2-5	>1.5	-	-	[69]
		SPS	W-5%HfO 2	11.6	>5	-/94.5	440	[70]
		SPS	W-0.5%Zr(Y)O 2	4.67	0.25	18.44/96.7	472
		SPS b*	W-0.5%Zr(Y)O 2	4.1	<0.1	18.56/97.3	495
	Proposed
	process	HIP b*	W-0.5%Zr(Y)O 2	5.6	0.41	18.29/95.9	467
		HIP b*	92.25W-4.9Ni-	15	0.15	17.49/99.48	442
			2.1Fe-0.75ZrO 2
		a* Using ammonium paratungstate (APT) as tungsten source;
		b*

Acknowledgements

We would like to thank all the researchers who participated in our works discussed in the paper and whose names appear in references.

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

Data will be presumably available for sharing before submission.

grains. Due to long sintering time process, these particles are larger than those in Fig. 16 a). The alloy corresponding to Fig. 16 c) and d), was produced by conventional sintering in hydrogen atmosphere, at 2400 °C for 4h, followed by hot isostatic pressing at 1400 °C for 1h under 250 MPa. Fig. 16 c) and d) shows its microstructure.

Through BSE observation, the average size of the ZrO 2 particle is also about 400 nm, which is smaller than oxide particle in ODS-W alloy reported in those already published results. The microstructure and properties researches have be detailedly presented in latest study of F. N. Xiao and al. [START_REF] Xiao | Uniform nanosized oxide particles dispersion strengthened tungsten alloy fabricated involving hydrothermal method and hot isostatic pressing[END_REF]. (5) Compared to the state of art, through SPS process, over 95% of particles in W-Zr(Y)O 2 alloy are less than 500 nm, which are smaller than those actually performs.

The particles exhibit a good bonding with the tungsten phase. Additionnaly, through milling reduced powders, the Zr(Y)O 2 particle size further decrease. The nanosized particle dispersion strengthened W-Ni-Fe alloy can also be manufactured through HIP process.

Declaration of interest

There are no conflicts to declare.