Comprehensive nuclear materials 2 13 properties and characteristics of zrc

Comprehensive nuclear materials 2 13 properties and characteristics of zrc Comprehensive nuclear materials 2 13 properties and characteristics of zrc Comprehensive nuclear materials 2 13 properties and characteristics of zrc Comprehensive nuclear materials 2 13 properties and characteristics of zrc Comprehensive nuclear materials 2 13 properties and characteristics of zrc Comprehensive nuclear materials 2 13 properties and characteristics of zrc Comprehensive nuclear materials 2 13 properties and characteristics of zrc

H F Jackson and W E Lee

Imperial College London, London, UK

ß 2012 Elsevier Ltd All rights reserved.

DBTT Ductile-to-brittle transition temperature

TRISO Tri-structural isotropic (coated fuel particle)

unusual combination of properties that are useful for

refractory applications These carbides combine the

cohesive properties of covalently bonded ceramics

(high melting point, high strength, and hardness) with

the electronic properties of metals (high thermal and

electrical conductivity) Comparative properties of

the refractory transition metal carbides have been

reviewed previously by Schwarzkopf and Kieffer,1

Storms,2 Toth,3 Kosolapova,4 and Upadhyaya.5

A thorough understanding of the thermodynamic andheat transport properties of carbides is limited by apaucity of experimental data as a function ofcomposition

and Chemical Bonding

In the Zr–C system, the monocarbide is the onlyintermetallic phase reported, crystallizing in theface-centered cubic NaCl structure (Fm
3m, spacegroup 225) (Figure 1) Zr atoms form a close-packedlattice, and the smaller C atoms (rC¼ 0.48rZr) fill theoctahedral interstices.3

The ZrCxphase exists over a wide compositionalrange and, as further discussed in Section 2.13.3.1,

is stable with up to 50% vacancies on the carbonsublattice Low-temperature ordered phases havebeen experimentally reported for the Ti–C, V–C,and Nb–C systems, but so far have been suggestedonly via thermodynamic calculations for the Zr–Csystem.6Metallic vacancies comprise at most a fewatomic percent.3

The effect of carbon vacancies on unit cell etry has been investigated extensively (Figure 2),

geom-C

Zr

Figure 1 Rocksalt crystal structure of ZrC x

C/Zr ratio 0.5

Nickel et al.121 Ramqvist8

Baker et al.179 Morrison and Sturgess 50

Shevchenko et al.194

Bukatov et al.69 Storms and Griffin 13 Storms and Wagner 35

Bulychev et al.180

Shevchenko et al.140

Kumashiro et al.123 Christensen 182

Aronson et al.60

Figure 2 ZrC x lattice parameter as a function of the carbon/zirconium ratio x.

with the relationship between room temperature

lat-tice parameter and C/Zr ratio difficult to establish

conclusively Scatter in literature values is a common

theme in the study of transition metal carbides

because of the difficulty of preparing pure specimens

and adequately characterizing them Oxygen and

nitrogen readily substitute for carbon in the lattice,

and their presence is correlated with reduced lattice

parameter On the basis of literature values for a range

of impurity contents, Mitrokhin et al.7 established a

quantitative relationship between the lattice

parame-ter of such oxycarbonitrides and carbon, as well as the

oxygen–nitrogen impurity content:

where x is the C/Zr atomic ratio (0.62 < x < 1) and y

is the (Oþ N)/Zr atomic ratio ( y < 0.3)

In general, lattice parameter increases with C/Zr

ratio, with evidence for an increase and a decrease as

C content increases above approximately ZrC0.8

toward ZrC1.0 Ramqvist8qualitatively explained the

peak in lattice parameter versus C/Zr ratio as being

due to competing influences on lattice size: expansion

with increasing carbon content due to the increased

space required to accommodate interstitials, and

con-traction due to the increased bond strength

The nature of chemical bonding in ZrCx is not

fully understood, and electronic structure

investiga-tions have sought to establish the relative influences

of covalent, metallic, and ionic contributions Carbon

s- and p-orbitals and zirconium d-orbitals participate

in bonding and contribute to strong metal–nonmetal

bonding and octahedral coordination.9 Other

authors10emphasize the interstitial nature of carbon

in the ZrC structure and the donation of electrons

from carbon to metal, strengthening Zr–Zr bonds

Lye and Logothetis11 proposed that some charge

transfer from carbon to metal occurs and that carbon

stabilizes the carbide structure by contributing

bonding states Hollox12and Storms and Griffin13

suggest that, depending on the carbide, lattice

sta-bility decreases with increasing carbon content if

antibonding states become filled; this is consistent

with observed hardness and melting temperature

measurements for ZrCx The electronic structure

of ZrC must be placed in context with the properties

of Groups IV, V, and VI transition metal carbides,

and the interested reader is referred to the

compar-ative reviews seen earlier

2127 K, contributing to the assessment of low carbonsolubility Solubility of Zr in C is taken as nil.Figure 4shows the results of experimental phasediagram studies superimposed on the assessed dia-gram Phase boundaries of the ZrC phase were estab-lished via ceramography by Farr,18Sara and Doloff,19Sara et al.,20 Sara,15 and Rudy et al.,21 while Stormsand Griffin13 used C and Zr activity values deter-mined during a Knudsen effusion study Rudy et al.21prepared mixtures of Zr, ZrH2, or graphite with ZrCand determined ZrCx solidus temperatures andZrC–C eutectic temperature via differential thermalanalysis (DTA), ceramography, or melting in a Piranifurnace As described by Rudy and Progulski,22 thePirani technique subjects a bar specimen with acentral blackbody hole to resistance heating; melting

is determined by the temperature at which liquidforms in the blackbody hole The technique is noted

to be most precise for isothermal transformations (i.e.,congruent melting or eutectic), as the sample oftencollapses or the blackbody hole closes before theliquidus is reached Sara15 prepared zirconium car-bides having various C/Zr ratios from mixtures ofZrH2 and graphite to determine melting tempera-tures and the congruent melting temperature andcomposition Adelsberg et al.23performed ceramogra-phy on C–Zr diffusion couples to contribute datapoints to the low-carbon liquidus line; ZrC–C eutec-tic temperature was also determined by ceramogra-phy Zotov and Kotel’nikov24placed ZrCxbars with

a radial hole under axial loading and resistanceheating; fracture of the sample at the temperature

at which the hole melted determined ZrCx solidus.For the ZrC0.88 sample, at least, their value is

Liquid + ZrCx

Liquid + ZrCx Liquid

C/Zr ratio

~ZrC 0 85

α-Zr + ZrCx β-Zr + ZrCx

ZrCx

ZrCx+ C

Figure 3 Zr–C phase diagram, as assessed by Fernandez-Guillermet.14

ZrC phase boundary, ceramography ZrC–C eutectic composition, ceramography lsothermally molten

Incipient melting Quenched, liquid observed Specimen collapsed during melting

By DTA Liquidus by chemical analysis

C solubility in Zr at Zr–ZrC eutectic

Bhatt et al.25 Zr–ZrC eutectic temp

ZrC–C eutectic, Ceramography/specimen rupture Specimen ruptured during melting

ZrC–C eutectic temperature

ZrC phase boundaries, activity vs C/Zr

Rudy et al.,21 Rudy 16

by ceramography DTA/ceramography

ZrC phase boundary, lattice parameter vs C/Zr

Adelsberg et al.26

Storms and Griffin 13

Zotov and Kotel’nikov 24

Figure 4 Experimental phase diagram studies compared with the assessed diagram.

anomalously high Heating the sample in an effusion

cell, Bhatt et al.25 determined Zr–ZrC eutectic

tem-perature by an optical pyrometric ‘spot technique.’

2.13.3.2 Enthalpy of Formation

Other properties on which the current phase diagram

is based include enthalpy of formation, enthalpy

increment or heat content, specific heat capacity

(Cp), and activity of C and Zr in ZrC Standard

enthalpy of formation, H

f, of ZrCx as a function

of the C/Zr ratio is plotted inFigure 5 A quadratic

fit to the reviewed data is provided by

Hf¼ 2:03  105

x2 5:04  105

x  9:92  104 ½2

where x is the C/Zr ratio and Hf is in units of

joules per mole Within the compositional range,

H

f is most negative at the stoichiometric

composi-tion and the recommended value is197 kJ mol1.26

Toth3 attributes this to decreasing ZrCx bond

strength with removal of C from the lattice

2.13.3.3 Enthalpy and Heat Capacity

Enthalpy increment of ZrCx with respect to

298 K (HT– H298) is plotted as a function of

tempera-ture inFigure 6and as a function of C/Zr ratio at

1600 K in Figure 7 Storms and Griffin report the

following equation to fit the experimental values of

Mezaki et al.,27 Levinson,28 Kantor and Fomichev,29and Turchanin and Fesenko30:

S298 S0of 33.3 J mol1.Heat capacity of ZrCx is plotted as a function oftemperature in Figure 8and as a function of C/Zrratio at 298 K inFigure 9 Heat capacity is equal tothe first derivative of enthalpy with temperature, andthe function recommended by Storms and Griffin13is

to quantify the entropy of mixing introduced bycarbon vacancies High-temperature drop calorimetry

Langmuir vaporization Same, Knudsen effusion

Same, Knudsen effusion Mah, 188

combustion calorimetry

Baker et al.,179

combustion calorimetry Equation [2]

Coffman et al.,38 Langmuir vaporization

C/Zr ratio 54⫻ 10 3

Westrum and Feick (1963), ZrC0.96Levinson (1965), ZrC0.958Storms and Griffin (1973), ZrC0.96

Figure 6 Enthalpy of ZrC x as a function of temperature.

Temperature (K)

Neel et al.,32 ZrC0.92

Mezaki et al.,32 ZrC0.986Westrum and Feick, 31 ZrC0.927Levinson, 28 ZrC0.958

Storms and Griffin, 13 ZrC0.96Petrova and Chekhovskoi, 34 ZrC1.04Kantor and Fomichev, 29 ZrC 1.0

Figure 9 Heat capacity at 298 K as a function of C/Zr ratio.

measurements were made on ZrC0.92–1by Neel et al.,32

Mezaki et al.,27Levinson,28Bolgar et al.,33Kantor and

Fomichev,29and Turchanin and Fesenko.30Petrova and

Chekhovskoi34 determined heat capacity, using a

pulsed electric current method to measure thermal

diffusivity Storms and Wagner35 used the laser flash

method to measure thermal diffusivity for ZrC0.64–1at

300 K and estimated Cpfor these compositions, using a

known value for ZrC0.9631 and by assuming a curve

parallel to that established for NbCx as a function

of C/Nb ratio.36 Heat capacity increases sharply

between 0 and 500 K, saturates, then begins to increase

more rapidly near the melting point Both

room-temperature heat capacity and high-room-temperature

enthalpy increase with C/Zr ratio in the homogeneity

range Room-temperature heat capacity of ZrC0.96 is

38 J mol1K1.31,35

2.13.3.4 Vaporization

Vapor pressures have been established by Langmuir

vaporization of C-saturated ZrC and by Knudsen

effusion studies of ZrC in equilibrium with graphite

These are plotted in Figure 10 Langmuir studies

are internally consistent, but give higher pressures

than for the Knudsen method Pollock37and Coffman

et al.38assumed the congruent evaporation composition

to be stoichiometric, that is, equal evaporation ratesfor Zr and C However, Langmuir evaporation ofZrC0.74–0.96 by Nikol’skaya et al.39 found the con-gruently evaporating composition to lie in the rangeZrC0.8–0.87, decreasing with increasing temperaturebetween 2300 and 3100 K Vidale40computed Zr and

C vapor pressures from tabulated H and S functions for

Zr(g)and C(s),Hf for ZrC of196.6 kJ mol1, and

Hvap for ZrC of 608 kJ mol1, with the predictionconsistent with Knudsen data Evaporation rate as afunction of temperature is plotted inFigure 11 Stan-dard enthalpy of vaporization of ZrC at 298 K hasbeen reported as1520 kJ mol1for Langmuir studiesand805 kJ mol1for Knudsen studies.37,38

Storms and Griffin13 coupled Knudsen effusionfrom TaC cells with mass spectrometry between

1800 and 2500 K to determine the Zr activity ofZrC0.55–‘‘1.97’’ by comparing ion currents from pure

Zr with those of the carbide Carbon activity wasobtained via a Gibbs–Duhem integration; activity ofboth as a function of C/Zr ratio at 2100 K is plotted

Coffman et al.,38 Langmuir

Coffman et al.,38 Langmuir Vidale, 40 thermochemical calculations

Vidale, 40 thermochemical calculations Storms, 2 thermochemical calculations

4.6 ⫻ 10 −4

Figure 10 Vapor pressures of C and Zr as a function of temperature.

in Figure 12 Activity of Zr exceeds that of C for

carbon-deficient compositions up to the cross-over

composition at 2100 K of ZrC0.89 The change in Zr

activity with C/Zr ratio is most rapid at high-carbon

compositions and becomes near-constant as the

com-position drops below approximately ZrC0.8 Partial

standard molar enthalpies of vaporization for Zr

and C as a function of C/Zr ratio are plotted in

Figure 13 Total enthalpies obtained by Pollock37

and Coffman et al.38 are consistent with the values

of Storms and Griffin.13 Partial enthalpy of Zr

decreases monotonically as C is removed from the

lattice Partial enthalpy of C exceeds that of Zr for

most of the homogeneity range, approaching that of

Zr at a composition of ZrC0.99

2.13.4.1 Thermal Conductivity

It is appropriate to discuss thermal and electrical

conductivity as coupled phenomena Thermal

con-ductivity is considered a sum of phonon and electron

contributions to conductivity The phonon

contribu-tion to thermal conductivity should decrease with

temperature, as atomic vibrations inhibit phonon

transport The contribution to thermal conductivitydue to electrons is calculated by the Wiedemann–Franz law,41according to

where keis the electronic thermal conductivity, L isthe Lorentz constant (2.44 108WO K2

), T isabsolute temperature, andr is electrical resistivity.Generally, electrical resistivity of metals increaseswith temperature; in transition metal carbides, elec-tron thermal conductivity increases with tempera-ture At low temperatures heat is mainly conducted

by phonons, which are scattered strongly by duction electrons.42–44 At intermediate tempera-tures, both electrons and phonons contribute tothermal conductivity, but in the transition metalcarbides the electronic component is dominant.Phonon scattering by carbon vacancies becomesimportant above about 50 K, contributing to adecrease in thermal conductivity with increasingtemperature At high temperatures, thermal conduc-tivity increases approximately linearly with temper-ature The temperature dependence of electronicthermal conductivity is plotted in Figure 14; thiswas computed from the Wiedemann–Franz law and

a linear fit to the electrical resistivity measurements

of Taylor45and Grossman46:r ¼ 0:79T þ 36:3

Experimental measurements of thermal

conduc-tivity of ZrC as a function of temperature between

1.8 and 3400 K are also plotted in Figure 14.The overall trend is a steep increase of thermal con-ductivity with temperature up to 50 K, followed by aslight decrease in an intermediate temperature range

(up to 100–1000 K) and then a more gradual increase

up to the melting temperature Room-temperature

thermal conductivity has been reported between 20

and 40 W m1K1, meeting or exceeding that of Zr

metal.47A source of experimental scatter in thermal

conductivity is sample porosity, which is not always

reported by authors

Room temperature thermal conductivity is also a

strong function of C/Zr ratio (Figure 15) Storms

and Wagner35 measured thermal diffusivity of

hot-pressed ZrC0.64–1(0.01–0.1 wt% O) by the laser flash

method,48 computing thermal conductivity from

sample density and heat capacity according to

where k is thermal conductivity (W m1K1), a is

thermal diffusivity (m2s1), d is density of the sample

(kg m3), and Cp is heat capacity ( J kg1K1) As

described in Section 2.13.3.4, Cpwas available for

ZrC0.96but not for other compositions and Cpversus

x was estimated by assuming that it was parallel to

that of NbCx A maximum room temperature

ther-mal conductivity of 45 W m1K1 occurs at

near-stoichiometric compositions, with a steep drop-off

as carbon atoms are removed from the lattice Further

reduction of the C/Zr ratio below approximately

ZrC0.9 has little effect on thermal conductivity,which approaches a constant value of 10 W m1K1.From a fit to literature electrical resistivity measure-ments and the Wiedemann–Franz law, Storms andWagner calculated the composition dependence ofthe electronic component of thermal conductivity as

ke¼ 1:05  103 0:00382 þ 1

55þ 950ð1  xÞ

½7where x is the C/Zr ratio, and a Lorenz number of3.5 108V2K2was used (by assuming that the ther-mal conductivity in the low-carbon region was entirelyelectronic) By taking the difference between theirexperimentally measured thermal conductivities andtheir calculated electronic thermal conductivities,Storms and Wagner expressed the phonon thermal con-ductivity as a function of composition by the equation

kp ¼ 0:007

where x is the C/Zr ratio As plotted in Figure 15,electronic thermal conductivity is dominant for highlynonstoichiometric ZrCx, while lattice or phononconductivity makes a larger contribution in near-stoichiometric ZrCx The effect of a decrease in C/Zrratio is proposed by Avgustinik et al.49 to reduce the

Korshunov et al.,186 sintered ZrC0.97, 20% porosity, thermal diffusivity

Neel et al.,32 sintered ZrC0.92

’ radial heat flowShaffer and Hasselman, 54 hot-pressed rod, 10% porosity, linear heat flow Same, hot-pressed sphere, thermal diffusivity

Taylor, 45 hot-pressed ZrC0.93 and ZrC1.05, 5% porosity, radial heat flow Grossman, 46 hot pressed ZrC1.02 and ZrC1.042’ 0.3 wt% free C, linear heat flow Radosevich and williams, 42,43 single crystal ZrC0.88

’ linear heat flowMorrison and Sturgess, 50 hot-pressed ZrC0.924

’ 0.6 wt% O, laser flash

Zotov et al.,196 sintered ZrC0.98

’ 3–7% porosity, axial and radial heat flowElectron component of thermal conductivity, calculated from electrical resistivity measurements of Taylor 45 and Grossman 46

L’vov et al.,187 hot-pressed ZrC0.79

’ 5–12% porosity, 1.1 wt% free C, linear heat flow

Fedorov and Aleinikov, 183 sintered ZrC0.96

’ 12–16%porosity, radial heat flow

Temperature (K) 0

connectivity of the lattice while introducing vacancies

and increasing the concentration of nonlocalized

elec-trons The net effect is an increase in phonon scattering

and a decrease in conductivity with deviation from

stoichiometry

Storms and Wagner also studied the effect on

thermal conductivity of tripling the oxygen content

in ZrC0.64–0.682 from 0.042 to 0.125–0.13 wt% They

found that thermal conductivity was affected little by

varying oxygen content in the low-carbon region but

asserted that 0.6 wt% O in ZrC0.92450 produced a

more noticeable effect They suggested that

impuri-ties which substitute for carbon (i.e., O or N) reduce

the vacancy concentration and have the same effect

on thermal conductivity as an increase in C/Zr ratio

The effect of impurities on thermal conductivity

is correspondingly more pronounced for ZrC0.9–1.0

Too few measurements of well-characterized

near-stoichiometric samples are available to assess this

phenomenon more conclusively

Neshpor et al.51measured room-temperature

ther-mal conductivity of 85–95% dense sintered ZrC0.6–0.9

containing 1.4 wt% nitrogen by a steady-state

heat-flow method, repeating this study with Avgustinik

et al.49 after decreasing N content to 0.05 wt%

Other room-temperature measurements by heat

flow or thermal diffusivity measurements42,49–55 are

consistent with the trend established by Storms andWagner, but by covering only one composition, orcompositions only below the drop-off at ZrC0.9, theindividual studies fail to capture the true trend.2.13.4.2 Electrical Resistivity

Electrical resistivity of ZrCxis plotted as a function oftemperature inFigure 16 Room temperature resistivityranges from 60 to 200mO cm, depending on C/Zr ratioand microstructure In an intermediate temperaturerange from approximately 100 to 2000 K, resistivityincreases linearly with temperature.45,46,56,57 Modine

et al.58 measured resistivity of single crystal ZrCx(x ¼ 0.89, 0.93, and 0.98) between 4 and 1000 K.The authors deemed the data well represented bythe Bloch–Gruneisen model for temperature depen-dence of resistivity of metals, with resistivity varying

as T5at low temperatures (4 –100 K) and linearly atintermediate temperatures At a high enough tem-perature (1000–2000 K), resistivity deviates fromlinear behavior and tends to saturate at a constantvalue which decreases with C/Zr ratio The higher-temperature measurements on single-crystal ZrC0.93

of Hinrichs et al.59 are consistent with the trendestablished for single crystal ZrC0.93at lower tem-peratures by Modine et al (Figure 16)

C/Zr ratio

0.6 0

Same, electronic thermal conductivity (fit)

Same, phonon thermal conductivity (fit)

Figure 15 Room-temperature thermal conductivity of ZrC x as a function of C/Zr ratio.

The resistivity of single crystals exceeds that of

polycrystals up to 2200–2500 K where the former

begins to saturate; resistivity of polycrystalline ZrCx

saturates only near the melting temperature, although

few measurements have been made in this

tempera-ture range The effects of free carbon and oxygen/

nitrogen impurities on resistivity have not been

explored Measurements on pyrolytic ZrCx53 lie in

the same range as those of other polycrystalline

speci-mens, but a detailed study of the effects of grain size,

texture, porosity, and other microstructural factors

on electrical resistivity is needed

Room temperature electrical resistivity as a

function of C/Zr ratio is plotted inFigure 17

Resis-tivity is lowest for near-stoichiometric compositions

and increases with deviation from stoichiometry

A decrease in C/Zr ratio increases the concentration

of carbon vacancies, which scatter conduction electrons

Storms and Wagner35 fit the available experimental

data to the formula

55þ 950ð1  xÞ

½9

wherer is electrical resistivity (mO cm) and x is C/Zr

ratio, which is plotted inFigure 17

2.13.4.3 Thermal ExpansionThermal expansion has been investigated vialow- and high-temperature X-ray diffraction,60–67neutron diffraction,68 and dilatometry.32,54,57,69–74ElongationðL=L298Þ and linear coefficient of ther-mal expansion (CTE) are plotted as a function

of temperature with respect to 298 K inFigures 18and 19, respectively Elongation results are gener-ally consistent between lattice parameter and dila-tometric methods, diverging at high temperatures.Scatter is magnified on the CTE versus T curve,which is akin to the second derivative of lengthversus T experimental data Elongation is fairlylinear, permitting authors to report a mean CTEover various temperature ranges; slope increasesslightly with temperature, consistent with anobserved rising CTE with temperature Increase inCTE is more pronounced at temperatures up to

500 K with a more modest increase at higher perature, although more lower-temperature valuesare needed to fully understand this behavior Atsubambient temperatures, elongation (or contrac-tion, as the reference temperature is 298 K) is non-linear with temperature

tem-CTE values with respect to 298 K lie in therange (5–7) 106K1, but the degree of scatter

50 100

Taylor,45 hot-pressed ZrC0.93, 6% porosity, 0.3 wt% free C

Neshpor et al.,51 ZrC 0.63–0.9, 5–15% porosity, 1.4 wt% N

Neshpor et al.,56 ZrC 1.0, 0.3 wt% free C

Samsonov et al.57

Neshpor et al.,53 pyrolytic ZrC0.92Petrov et al.,191 sintered ZrC1.08’ 12.6% porosity, 1.14 wt% free CModine et al.,58 single crystal ZrC0.93

Hinrichs et al.,59 single crystal ZrC0.93Grossman, 46 hot-pressed ZrC 1.02–1.04, 2–8% porosity

Figure 16 Electrical resistivity of ZrC x as a function of temperature.

precludes a more precise recommended value.

Thermal expansion coefficient at 1273 K as a

func-tion of C/Zr ratio is plotted inFigure 20, where a

trend of increasing CTE with deviation from

stoichiometry can be seen This composition dence of CTE confirms the general picture ofdecreasing bond strength as C atoms are removedfrom the lattice.5

depen-C/Z ratio

Taylor, 45 hot-pressed

Neshpor et al.,51 sintered, 5–15% porosity

Neshpor et al.,56 sintered, 5–8% porosity Stroms & Wagner,35 least-squares fit to reviewed data

Temperature (K)

Temperature (K)

2.13.4.4 Diffusion

The results of diffusion studies are summarized in

Table 1 The temperature dependence of diffusion

coefficient conforms to an Arrhenius relationship,according to

Temperature (K) 0

Leipold and Nielsen,72 hot-pressed ZrC0.85

Fridlender and Neshpor, 70 pyrolytic ZrC0.994Caputo, 181 pyrolytic ZrC0.8–1.0

Bukatov et al.,69 hot-pressed ZrC0.966’ 6% porSamsonov et al.57

Richardson,66 arc-melted Miccioli and Shaffer, 73 sintered ZrC0.946Houska,62 hot-pressed ZrC0.95

Krikorian et al.,63 ZrC0.97Shaffer and Hasselman, 54 hot-pressed, 8.8% por Elliott and Kempter, 61 ZrC0.957 powder

Figure 19 Linear coefficient of thermal expansion (CTE) of ZrC x as a function of temperature.

C/Zr ratio 0.6

Lepie, 96 pyrolytic Elliott and Kempter, 61 powder

where T is absolute temperature, R is the gas constant,

Q is the activation energy for diffusion (kJ mol1), and

D0 is a preexponential factor having the same units

as D, the diffusion coefficient, (cm2s1)

Diffusion of carbon ina-Zr (hcp) and b-Zr (bcc)

has been investigated through diffusion of14C tracer

deposited onto Zr75–79and by the rate of ZrC layer

growth on Zr in contact with graphite.23,79

Self-diffusion of C in ZrCxhas been determined by

tracer diffusion.80–83The study by Andrievskii et al.83

provides the only reported value for self-diffusion of

Zr in ZrC,which was found to be independent of C/Zr

ratio Activation energy for C self-diffusion in ZrCx

increased with decreasing C/Zr ratio, while diffusion

coefficient at a given temperature increased with

increasing C/Zr ratio However, O (0.16–0.19 wt%)

and N (0.27–0.55 wt%) impurity content was

substan-tial and varied for different samples No further studies

of C self-diffusion in ZrCxas a function of C/Zr ratio

are available to clarify differences between C

self-diffusion in pure ZrCxversus oxycarbonitride phases

Carbon and zirconium self-diffusion in ZrC is

slower than the inter-diffusion of C in Zr, with

cor-respondingly higher preexponential factors and

acti-vation energies Pavlinov and Bykov77remarked that

the activation energy for C diffusion in Zr was close

to that of Zr self-diffusion in Zr As for self-diffusion,

Zr diffuses much slower than C, which may be stood in terms of the interstitial nature of C in ZrC:the smaller C atom is able to diffuse via either ther-mal metal vacancies or interstitial sites, the latterdwarfing the former in most cases

under-Matzke84 proposed three potential mechanismsfor C self-diffusion in ZrC First, a C atom mayjump along h110i directions to its nearest neighborvacant C octahedral interstitial site, which, according

to the author, requires a large lattice strain and themovement of two Zr atoms Second, a C atom mayjump along h111i directions to its nearest neighborvacant C octahedral interstitial site via an unoccu-pied tetrahedral interstice, requiring lower strainenergy Third, a C atom may jump to a vacant octa-hedral site via a thermal metal vacancy The authorproposes that this divacancy mechanism requires thelowest energy, close to the activation energy for gen-eration of a metal vacancy

The operative diffusion mechanism depends on theC/Zr ratio Upadhyaya5suggested that carbon diffu-sion in near-stoichiometric compositions occurs viathermal metal vacancies, while jumps via tetrahedralinterstices are favored at higher carbon vacancy con-centration No adequate explanations are availablefor the composition dependence of activation energy

of C in ZrC, or the composition independence of that

Table 1 Diffusion parameters for ZrC

D 0 (cm2s1) Activation

energy (kJ mol1)

Temperature range (K)

a Zotov and Tsedilkin, 75 14 C tracer diffusion.

b Agarwala and Paul, 76 14 C tracer diffusion on Zr rod, vacuum.

c Pavlinov and Bykov, 77 ZrI4/ 14 C-ZrI4diffusion couple, vacuum.

d Andrievskii et al., 78 14 C tracer diffusion on ZrI 4 , vacuum.

e Ushakov et al., 79 rate of ZrC layer growth on alternating ZrI4and graphite pellets stacked in Mo crucible, vacuum.

f

Adelsberg et al.,23rate of ZrC layer growth on Zr bar melted in graphite crucible, vacuum.

g Andrievskii et al., 80 14 C tracer diffusion on hot-pressed ZrC0.96, He atmosphere.

h

Sarian and Criscione,8114C tracer diffusion on single crystal and arc-melted ZrC 0.965 , vacuum.

i Andrievskii et al., 82 14 C tracer diffusion on hot-pressed ZrC0.85, Ar atmosphere.

j Andrievskii et al., 83 14 C tracer diffusion on hot-pressed ZrC0.97(Zr self-diffusion composition-independent from ZrC0.84–0.97).

of Zr Other properties (formation enthalpy,

hard-ness) indicate a decrease in bond strength as the

C/Zr ratio decreases, which would suggest that

dif-fusion would be enhanced as well This stands in

opposition to measured activation energies for the

diffusion of C in ZrC0.84–0.97, which increased with

deviation from stoichiometry.83 As for Zr diffusion,

Upadyaya5 suggested that two effects in operation

when the C/Zr ratio decreases, a decrease in the

energy required to form thermal metal vacancies,

and an increase in the energy required for metal

vacancy motion due to the decreased interatomic

distance, cancel each other out

Further discussion of diffusion mechanisms in

the context of mechanical creep are considered in

Section 2.13.5.6

Transition metal carbides have found application in

abrasive and cutting tools, where their high hardness

and high melting points may be exploited Extreme

brittleness has so far limited their use in

ambient-temperature structural applications, but at high

temperatures, carbides have been shown to deform

plastically on slip systems analogous to fcc metals

A sufficient number of independent slip systems are

available so that polycrystalline ZrC can be made

ductile

2.13.5.1 Elastic Properties

Room-temperature elastic constants of ZrCxare

sum-marized in Table 2 Chang and Graham85 measured

elastic constants of two single-crystal rods, ZrC0.94with

[100] orientation and ZrC0.89 with [110] orientation,

by an ultrasonic method from 4 to 298 K Constants c11

and c44decrease, while c12increases over this

tempera-ture range, none by more than a few percent

Polycrys-talline isotropic elastic moduli were computed from

these single crystal measurements

Young’s modulus has been measured via dynamic

methods54,72,86–89,95 during the course of

indenta-tion90or loading in a four-point bend91configuration

Typical room-temperature values for

near-stoichio-metric ZrC range between 380 and 420 GPa Young’s

modulus as a function of temperature is plotted

inFigure 21and as a function of the C/Zr ratio at

room temperature in Figure 22 Young’s modulus

decreases linearly with temperature, decreasing

more rapidly above 0.5T , as plastic deformation is

favored Avgustinik et al.87 found both Young’s andshear moduli to decrease with decreasing C/Zr ratio,which they attribute to a corresponding decrease

in the average bond strength as C is removed fromthe lattice

2.13.5.2 HardnessTypical room-temperature mechanical propertiesare summarized inTable 3 Measurements of micro-indentation hardness of ZrCx are prevalent in theliterature Hardness as a function of temperature isplotted in Figure 23and as a function of the C/Zrratio at room temperature in Figure 24 Room-temperature hardness ranges from 20 to 34 GPa(2000–3300 kgfmm2) Hardness decreases withincreasing test temperature, dropping to approxi-mately 0.5 GPa (49 kgfmm2) at 1800 K Room-temperature hardness decreases with decreasingC/Zr ratio Scatter in room-temperature measure-ments may be due to the variety of proceduresreported (Knoop or Vickers indenter, 50–500 gload), which may not be in accordance with standardtest methods.109,110 Hardness may be affected bysample microstructure, including porosity, grainmorphology, and secondary phases Residual stressespresent in ion-beam deposited or pyrolytic ZrCcoatings53,107 tend to inflate hardness, while freecarbon reduces hardness.107,111

Table 2 Typical room-temperature elastic properties

h,i

Shear modulus (GPa)

Bulk modulus (GPa) 229  25 a,d,f,k

Poisson’s ratio 0.197  0.023 a,d,f,j

a Chang and Graham, 85 single crystal [ 100 ] ZrC0.94and [ 110 ] ZrC 0.89 , respectively.

b Shaffer and Hasselman, 54 hot-pressed, 3.4% porosity.

c

Leipold and Nielsen,72hot-pressed ZrC 0.77–0.84 , 1.6–2.5% free C, <5% porosity.

d Brown and Kempter, 86 hot-pressed ZrC0.964, 3% porosity.

e Avgustinik et al., 87 sintered ZrC 0.95 , 5–10% porosity.

f Baranov et al., 88 sintered ZrC0.96, 6% porosity.

g

Travushkin et al.,89ZrC 0.92

h Warren, 90 sintered ZrC0.95, 8% porosity.

i

Zubarev et al.,91die-extruded ZrC 1.0

j Shaffer et al., 92 hot-pressed, 4.5% porosity.

k

Ajami and MacCrone,93calculated from pressure–volume equation of state fit to high-pressure experiments of Champion and Drickamer.94