ZIRCONIUM DIBORIDE SHOCK SYNTHESIS
V. N. Leitsin, M.A. Dmitrieva, I.V. Kobral
2
Powder layer structurePowder layer structure
y
zx
a
b
a d0
b
a
W, J
t, мксtimp
x – main direction
Reactive cell
timp=0.1÷1μc
Pf, Па
x
V=a×a×b=(V1+V2+V3)(1+П0)=const
3
State parameters of powder medium behind shock pulse front
,}/)1(4/])1({[
2/])1([
2/122fpimpfpf
fpfimpf
bDvbDa
bDavU
,UDP fpf 001
,1 0 fppf UDD ,22fUW
impimpffp vvbaD 5.011
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а0
b0 c
0 2
da
300
1;
2 1
db
3
0
12 .
2 1
dc
а b
Real material (а), Nesterenko model (b)
The porous medium is simulated by a The porous medium is simulated by a modified Nesterenko single-pore model modified Nesterenko single-pore model with a nondeformable central core.with a nondeformable central core.
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specific energy, WD, dissipating in the surroundings of a pore at the collapse stage
;1
1;
1
,1ln,3
2
01
01
00
10
xx
xxHxHxHWs
TD
at further stages, energy is expended to disrupt the boundary layers of particles implementing non-stationary compacting mode mechanisms
Wk=W-WD
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The mechanical loading of powder The mechanical loading of powder mixture can increase the reactionary mixture can increase the reactionary ability of reactive componentsability of reactive components
1. Plastic deformation:
,ln3
2PP
0s
sTminsl
,ρρ1
Hv
ρ
ρ36,0P
0s
02s
N
iiiiTi ;ρmθσA
11
N
iiibi ;ρmWA
12
2. Fracture of surface layers:
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,11
x
T
xTTf
t
Tc slslsT
sssl
,x
Tvc
x
T
xTTf
t
Tc lll
llllsT
llll
,,0 xTTTt sl
.0,,,0
x
T
x
TnbxTTTx ls
fls
The law of conservation of energy
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Volumetric heat transfer coefficient 32Pr25.0 vcCCv 321109.1
7247
101772472
6111112
7247
61111121
зS
Skeleton thermal conductivity
1.0,1
1.0,2
31
23
2
k
kS
l з
TS
Sf oT
Heat sources:
Qt
z
t
Aq i
iv
Heat losses:
ips
ipsi
m
v
TT
TTQtq,0
,
,0
0
mm
mm t
tt
m =0,7 мкс
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),()/exp(0 zRTEkt
za
,10 nbkkPre-exponent
Change in the reactivity ,*0 iiia APPHEE
Condition of reactive equivalence ,0
0 RT
E
RT
Ea
,1 1 nmzz φ(z)=0,5z-1 The kinetic function
The exothermal conversion macrokinetics is supposed to be a multilevel reactionary cell model coordinated with the power law of reactionary diffusion.
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.
,21
,
TCPP
ETT
CCP
PPP
Tafжf
плaabbtk
жftkж
,0
,
v
vK
Pж
,1180 222 dK
Porous pressure
0exp(Еμ /RT),
Viscosity of the melt
Filtration of liquid phase obeys the Darcy law
Permeability coefficient
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0.6 0.7 0.8 0.9
10
100
1000
m ax
/ M
Dependence of the relative viscosity of slurry on the relative number density of solid particles
The peculiar behaviour of the powder materials that do not form a solid sceleton in the process of physicochemical transformations may manifest itself in their specific reaction to the increase in the intensity of mechanical impact. The achievement of effective viscosity of a critical value is considered as a criterion of powder support instability - the change of internal friction mechanism - the viscoplastic compaction of hard deformed powder body of the given type will yield to a nonlinear viscoplastic flow of concentrated slurry of interacting particles, which is characterised by a higher flow velocity and the termination of the process of reactive component mechanical activation.
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0.1
0.2
0.3
0.4
0.5C
b 2b
1
2
3
4
1
2
34
B
Zr
10 12 14 16 18 20
0
0.2
0.4
0.6
0.8
Р , ГПа
1
2
34
Zr + 2 B =ZrB2+QParticles size d= 50 m
Initial porosity П0 = 0,4 Concentration inhomogeneity parameter b/a = 1,1÷1,4;
Initial temperature T0 = 500 K
Shock pulse parameters Pf= 3÷20 ГПа, timp=0.1 мкс
1 – b/a=1.1; 2 – b/a=1.2; 3 – b/a=1.3; 4 – b/a=1.4.
0.2
0.25
0.3
0.35
0.4
b 2b
B
Zr
C ,
0
40
80
120
160
b 2b
1
2
3
4
E a , êÄ æ/ì î ë ü
Curve 1 – critical values of activation energy; curve 2 – Pf= 3 GPa; curve 3 – Pf=5 GPa; curve 4 – Pf=7 GPa
The distribution of local values of activation energy
The distribution of component concentration through the thickness of initial compact
,*0 iiia APPHEE
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ConclusionConclusion
The data presented suggest that the degree of mechanical activation of Zr-B mixture reactive components play the key role in the satisfaction of the conditions of shock initiation of chemical transformations. For the macroscopically heterogeneous powder mixture, shock initiation is possible in the areas with an excess of refractory component.
The change of internal friction mechanism is key feature of zirconium diboride shock synthesis
Thank You for Your attention
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