ZIRCONIUM DIBORIDE SHOCK SYNTHESIS V. N. Leitsin, M.A. Dmitrieva, I.V. Kobral.

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

Computer Simulation ConceptComputer Simulation Concept

44

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.


5

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


66

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:


7

,11

qq

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


8

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


9

),()/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.


10

.

,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


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.


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

ZIRCONIUM DIBORIDE SHOCK SYNTHESIS V. N. Leitsin, M.A. Dmitrieva, I.V. Kobral.

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