zirconium hydride precipitation and dissolution kinetics in ......zirconium / zirconium hydride...

Zirconium hydride precipitation and dissolutionkinetics in zirconium alloys

E. Lacroix1,2, P.-C. Simon2, A. T. Motta2 and J. D. Almer3

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1: Framatome, Lynchburg, VA, USA2: Pennsylvania State University, PA, USA3: Argonne National Laboratory, Lemont, IL, USA

19th International Symposium on Zirconium in the Nuclear Industry

Manchester, UK, May 22nd, 2019

• Background

• Experiments

• Model development

• Conclusions

Outline

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– Hydride hysteresis understanding

– How can hydrogen behavior be studied?

– How can we incorporate the experimental

data obtained to create the HNGD model

Background:Hydride hysteresis understanding

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Model

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Zirconium / zirconium hydride hysteresis

4

0

50

100

150

200

250

0 50 100 150 200 250 300 350 400 450

Hyd

roge

n c

on

ten

t in

so

lid s

olu

tio

n (

wt.

pp

m)

Temperature (°C)

Hydride precipitation behavior by region

TSSD

TSSP

Precipitation

Dissolution

if hydrides are present

PrecipitationHydride nucleation and growth

E. Lacroix, A. T. Motta, J.D. Almer "Experimental determination of zirconium hydride precipitation and dissolution in zirconium alloy", Journal of Nuclear Materials, 509 (2018) 162-167.

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z

5

Terminal solid solubility for precipitation and dissolution


603 wt.ppm

400 wt.ppm

541 wt.ppm

z

6

hydrides

Dissolved Hydrogen

Dissolution Temperature


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Dissolved hydrogen

Precipitation Temperature

hydrides


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How was the hydride

behavior studied?

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Experimental Setup at Beamline 1 at APS

Load Frame

Clam shell

furnaceSample

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z

Diffraction patterns

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Peak intensityPeak position

Peak width

volume fractionStress

Size of the crystal size

Integration of diffraction data

Raw data

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Differential Scanning Calorimetry(DSC)

CoolingSystem

Heating system and sample holder

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Nucleation and Dissolution

kinetics measurement using

Synchrotron X-ray diffraction

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Nucleation and Dissolution kinetics:hypothesis

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• First order kinetics in the form:

𝑑𝐶𝑆𝑆𝑑𝑡

= −𝐾 ⋅ 𝐶𝑆𝑆 − 𝐶𝑒𝑞

• Differentiating:

𝐾 = −Δ𝐶𝑆𝑆

(𝐶𝑆𝑆−𝐶𝑒𝑞)Δ𝑡

• K is the kinetic constant, following an Arrhenius law:

𝐾 = 𝐾0 ⋅ exp −𝐸𝑝𝑘𝐵𝑇

𝐶𝑆𝑆 is the hydrogen content in solid solution (wt.ppm)𝐶𝑒𝑞 is the hydrogen content in solid solution at equilibrium (wt.ppm)

𝐾0 is the pre-exponential factor (𝑠−1)𝐸𝑝 is the activation energy of the process (eV/atom)

𝑘𝐵 is the Boltzmann constant𝑇 is the temperature (K)

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Studying hydrogen behavior in Zr

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• I: 𝑇𝑆𝑆P, 𝑇𝑆𝑆𝐷 (dynamic)

• II: 𝑇𝑆𝑆D (equilibrium)

• III: Dissolution rateNucleation rate

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𝐾 = −Δ𝐶𝑆𝑆

(𝐶𝑆𝑆−𝐶𝑒𝑞)Δ𝑡


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• Nucleation Kinetics

•𝑑𝐶𝑆𝑆

𝑑𝑡= −𝐾𝑁(𝐶𝑆𝑆 − 𝑇𝑆𝑆𝑃)

• 𝐾𝑁 =−Δ𝐶𝑆𝑆

Δ𝑡 𝐶𝑆𝑆−𝑇𝑆𝑆𝑃

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• Dissolution Kinetics

•𝑑𝐶𝑆𝑆

𝑑𝑡= −𝐾𝐷(𝐶𝑆𝑆 − 𝑇𝑆𝑆𝐷)

• 𝐾𝐷 =−Δ𝐶𝑆𝑆

Δ𝑡 𝐶𝑆𝑆−𝑇𝑆𝑆𝐷

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Growth kinetics measurement

using DSC

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Differential Scanning Calorimetry

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350 ℃320 ℃305 ℃300 ℃290 ℃280 ℃

𝑥(𝑡) =Δ𝐻 𝑡

Δ𝐻𝑡𝑜𝑡=

𝐶𝑃𝑃(𝑡)

𝐶0 − 𝑇𝑆𝑆𝐷(𝑡)

𝑥 = 1 − exp − 𝐾𝐺𝑡𝑝

Growth Kinetics Parameter

Depends on the growth

regime

𝐾𝐺 = 𝐾𝐺0 ⋅ exp −

𝐸𝐺𝑘𝐵𝑇

Avrami Parameter

Dimensionality of the growth.

• 2.5 for platelets

• 3 for spheres, 1 for

needles

ASTM standard E2070

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99%(𝑥, 𝑡)

(𝑥, 𝑡)

(𝑥, 𝑡)

ASTM standard E2070

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Time Temperature Transformation diagram

Tem

per

atu

re

Time to reach 99% of reaction

Diffusion reaction, 𝐾𝐺𝑅

Phase transformation reaction, 𝐾𝐺𝐷

𝑇𝑑

1

𝐾=

1

𝐾𝐺𝐷 +

1

𝐾𝐺𝑅

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undExperiment repeated to obtain TTT

Model development

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Model Summary

0

50

100

150

200

250

0 50 100 150 200 250 300 350 400 450

Hyd

roge

n c

on

ten

t in

so

lid s

olu

tio

n (

wt.

pp

m)

Temperature (°C)

Hydride precipitation behavior by region

TSSD

TSSP

Dissolution

if hydrides are present

Hydride nucleation and growth

𝑥 = exp −𝐾𝐷𝑡

Nucleation: 𝑥 = 1 − exp(−KNt)

Growth: 𝑥 = 1 − exp − 𝐾𝐺𝑡𝑝

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Model Results

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Synchrotron Experiment Simulation


z Hold time: 41 days

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157⁰C 454⁰C

1”

64 wt.ppm of Hydrogen

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A. Sawatzky, Hydrogen in Zircaloy-2: its distribution and heat of transport, Journal of Nuclear Materials 2 (1960) 321{328.

Conclusions

▪ Synchrotron X-ray diffraction was successfully used to

measure nucleation, and dissolution kinetics of hydrides.

▪ DSC was successfully used to measure hydride growth

kinetics and to obtain a Time-Temperature-Transformation

diagram for hydride precipitation.

▪ A hydrogen precipitation and dissolution model was created

based on a new approach and showed good agreement with

experimental data.

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Acknowledgement

▪ DOE-NEUP

▪ Argonne National Laboratory

▪ Penn State Nanofab

▪ Penn State MCL

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Questions

Furnace

Roughing Pump

Diffusion Pump

Gas tankControl Volume

Vacuum chamber

1. Remove oxide from sample using an acid solution

2. Deposit Nickel to prevent further oxidation

3. Introduce hydrogen using gaseous charging method

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Introducing Hydrogen in the zirconium metal

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sugar

1. T0 = Room temperature (RT)

2. T1 > Room temperature → less solid sugar in the water→ more dissolved sugar

3. T2 > T1 → Dissolution Temperature→ Only dissolved sugar

4. T3 < T2 → Precipitation Temperature→ first occurrence of solid sugar

5. T3 hold → Growth of sugar crystals

6. T4 = Room temperatureT

time

T1

T2 T3

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T4

z

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157⁰C 454⁰C

1”

64 wt.ppm of Hydrogen


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• Low temperature to measure only diffusion-driven process

•1

𝐾𝐺=

1

𝐾𝐺𝐷 +

1

𝐾𝐺𝑅

• High temperature was implemented using free energy curves

z

35

Terminal solid solubility for precipitation and dissolution


603 wt.ppm

400 wt.ppm

541 wt.ppm

✓ Show that hydrogen continues to precipitate

below TSSP

z

36

Terminal solid solubility measurement using DSC

300

Temp

H content

TDTP

K. Une and S. Ishimoto, “Dissolution and precipitation behavior of hydrides in Zircaloy-2 and high Fe Zircaloy,” Journal of Nuclear

Materials, vol. 322, pp. 66–72, 2003.

K. Colas, A. Motta, D. M.R., and J. Almer, “Mechanisms of hydride reorientation in Zircaloy-4 studied in situ,” Zirconium in the Nuclear Industry: 17th International Symposium, vol. ASTM STP 1543, pp. 1107–1137, 2014.

TSSPTSSD

0

100

200

300

400

500

600

100 200 300 400 500 600

CS

S(w

t.p

pm

)

Temperature (°C)

TSSP (APS) [5]

TSSD (APS) [5]

TSSP (DSC) [3]

TSSD (DSC) [3]

✓ Show that the TSSP is the nucleation temperature


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• Sample A: 0 MPa• Sample B: 200 MPa

zirconium hydride precipitation and dissolution kinetics in ......zirconium / zirconium hydride...

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