High heat flux laser testing of HfB2 cylinders

L. Larrimbe°, M. Pettinà+, K. Nikbin+, E. Jones§, A.P. Katz§, C. Hawkins*, J. DeCerbo*,

P. Brown*, L. Vandeperre°

° Centre for Advanced Structural Ceramics & Department of Materials, Imperial College

London, South Kensington Campus, London SW7 2AZ, United Kingdom

+ Centre for Advanced Structural Ceramics & Department of Mechanical Engineering, Imperial

College London, South Kensington Campus, London SW7 2AZ, United Kingdom

*Defence Science and Technology Laboratory, Porton Down, Salisbury SP4 0JQ, United

Kingdom

§Materials and Manufacturing Directorate, Air Force Research Laboratory, Wright Patterson Air

Force Base, Dayton, Ohio, United States of America.

Abstract

Hafnium diboride (HfB2) is one of a family of ultra-high temperature ceramics (UHTCs)

which are being considered for application in environments with a substantial heat flux such as

hypersonic flight. In order to characterise transitions in the material response with heat flux and

therefore predict the in-service behaviour of UHTCs, a range of tests were conducted in which

small cylindrical bars of HfB2 were laser heated using heat fluxes from 25 to 100 MW m-2. After

testing, the external damage as well as damage observable in cross-sections through the cylinders

was characterised using photography, optical and scanning electron microscopy (SEM).

Experimental results were compared with finite element (FE) modelling of the heat flow,

temperature distribution and phase transition. Heat flux rather than total deposited heat was found

to be the strongest determinant of the way in which damage develops in samples; for lower heat

fluxes the main damage mechanism is oxidation, progressing to oxidation induced melting and

finally, at the highest heat fluxes, substantial ablation by melting irrespective of oxidation. The

agreement between calculations and experimental observations indicates that such calculations

can be used with confidence to guide the design of components.

Keywords: Ultra-high temperature ceramics (UHTCs), HfB2, laser testing, oxidation, melting

Introduction

Current research in hypersonic flight aims to deliver vehicles which can operate at much

higher speeds and altitudes compared to present day equivalents. The aerodynamic heating and

shock wave interactions associated with hypersonic flight put stringent requirements on the

materials used which have to withstand high stresses, high temperatures and reactive

environments while not showing rapid ablation of the aero structure [1].

Zirconium and hafnium diborides (ZrB2 and HfB2) belong to the family of materials

known as ultra-high temperature ceramics (UHTCs) [2]. They are potential candidates for the

sharp leading edges of hypersonic vehicles due to the combination of properties they offer, such

as high melting points, good oxidation resistance, excellent thermal conductivity, high strength

and hardness and good chemical stability [3]–[5]. Sharp edge designs have the potential to

improve vehicle manoeuvrability. The temperature at the leading edge during flight increases as

the radius of the tip of the leading edge decreases. By increasing the thermal conductivity of the

leading edge material, the heat can be dissipated more efficiently over a wider area, reducing the

overall temperature of the leading edge [6][7]. Because of their properties listed above, UHTCs

are excellent candidates for the leading edge material.

Compared to the number of publications relating to ZrB2, the literature on monolithic

HfB2 is quite limited. Nevertheless, the latter is a stronger candidate when selecting UHTCs due

to its higher thermal conductivity, 1.7 times that of ZrB2 [2], and a lower mass gain when exposed

to air across all temperature ranges which indicates a better oxidation resistance than ZrB2 [8].

To evaluate the performance of UHTCs, some of the most important criteria are thermal

stress and oxidation resistance [9]. Actually, oxidation under hypersonic flow conditions and

environmental degradation are extensively recognized as key life-limiting factors for leading-

edge applications [10]. Oxidation changes the bulk and surface properties of UHTC materials, as

oxides have lower thermal conductivities and lower emittances than virgin UHTC materials, and

consequently, are less able to dissipate heat by conduction into the interior or radiation back to

the environment.

Determining the performance of UHTCs at such temperatures (above 2000 ºC) is

challenging and costly owing to the limited availability and complex nature of appropriate test

facilities. However, several testing techniques are available for predicting the in-service

behaviour of HfB2 based compounds. The most common has been the measurement of oxidation

kinetics in a furnace atmosphere under isothermal conditions [4], [11]–[15]. The solar furnace is

also an original procedure for testing ultra-high-temperature ceramics at very high temperature in

air with an exposure time of several minutes [16][17]. There are other methods which, in addition

to high temperature, also impose high heating rates including arcjet testing [18], laser-based

heating, electric heating [19] or oxyacetylene torch testing [20]. The ablation resistance of

UHTCs has been extensively researched by means of arc, plasma or oxyacetylene ablations [21]–

[23]; nevertheless, most of these studies have been largely qualitative in nature as the damage in a

limited number of tests is described without comparison with predictions of expected damage.

Laser testing is a reasonable cost method that uses a laser as the heating source to produce

the desired heat flux [24]. With this technique several samples can be tested within a relatively

brief period of time and therefore a variety of heating profiles can more easily be used. Although

laser testing does not capture all of the conditions of a hypersonic flight it can provide the high

temperatures, high heating rates, and steep thermal gradients relevant to the hypersonic

environment, providing a valuable baseline of material behaviour. Although actual hypersonic

applications of UHTC materials involve complex interactions between the material and the aero

thermodynamic environment, being able to predict the damage in these simple tests is a valuable

starting point for future developments.

This paper describes and discusses the effect of high heat fluxes and exposure time on

damage formation in HfB2 monoliths. The main goals were to document different regimes of

damage formation as a function of the heat flux and to determine whether such transitions can be

modelled efficiently using finite difference/finite element techniques.

Experimental

Production of samples for laser testing

Billets of HfB2 with a diameter of 30 mm and a height of 50 mm were produced by spark

plasma sintering (SPS) of a commercial HfB2 powder (H.C. Starck and Treibacher, Germany)

without additives. Processing was carried under a pressure of 50 MPa. From 450 °C to 1700 °C,

a heating rate of 50 °C min-1 was used, decreasing to 25 °C min-1 above 1700 °C. The total

heating profile included one isothermal hold at 1700 °C for 10 minutes and a final dwelling of 15

minutes at the desired sintering temperature of 2150 °C. Cylindrical samples with a diameter of

10 mm and a height of 20 mm were cut from these billets by wire electro-discharge machining

(EDM) for laser testing.

Test set-up and procedure

Samples were held horizontally in a custom made holder, supported by alumina spheres

(Figure 1a). High heat flux evaluation of HfB2 monoliths were conducted using a continuous high

power fibre laser (Model YLS-10000C, 10 kW multimode, IPG Photonics, Oxford, MA, USA)

focussed to a flattened beam profile over the entire front of the sample. Despite this, experimental

evidence of the damage pattern after the tests indicates that the illuminated region was smaller

than the full circular area of the sample. This has been accounted for in the simulation by

applying the heat flux over a smaller area rather than the whole top surface.

The temperature of the back of the sample was monitored with a type K thermocouple,

shown in Figure 1b. Two types of pyrometer were used to measure the front face temperature.

The first was a two colour pyrometer, CWA (LHMEL, Dayton, OH, USA), operating at 694 and

850 nm. The second was a four colour pyrometer, A4C (LHMEL, Dayton, OH, USA), operating

at 8 µm, 4 µm, 500 nm and 1100 nm. Air was blown over the sample to aid the removal of any

gaseous species. The air flow was not expected to be strong enough to blow molten material off

the sample. The calibration of the pyrometers was done using a blackbody at a known

temperature. This blackbody had a known radiance and so the signal/radiance scale factor could

be determined, which was later used to estimate the surface temperature. The detector voltage

signal was fitted to the known temperature using the Sakuma-Hattori equation with three

coefficients determined by the calibration.

Table 1 gives an overview of the test conditions used. The laser power was either ramped

up in 15 s to 25 MW m-2 followed by immediate transition to the desired level between 25 and

100 MW m-2 or slowly increased with intermediate dwells as shown in Figure 2. Heat flux was

determined previously by sampling the beam in real time using a beam splitter of known

transmittance. The split beam was then imaged on a spinning spectralon plate. This was

calibrated prior to experimentation against the main beam passing through beam expander and

into a calorimeter. Beam diameter was determined from the spectralon plate and calibrated

against a short exposure on a plexiglass target. The tests were conducted in two phases, several

months apart. Four different heat fluxes were studied: 25, 50, 75 and 100 MW m-2.

Characterization of the samples

After testing, all samples were photographed. Typically three photographs were taken:

one of the front of the sample, one of the back of the sample and one of the top of the sample. A

set of measurements was made on the sides of the sample: (i) the height, measured from the

bottom, where the absence of white discoloration indicates no oxidation had occurred, (ii) the

remaining height of the sample and (iii) the undamaged height of the sample in as far as this

could be judged by visual inspection of the edge of the sample. For further observations the

samples were cut in half longitudinally using a slow speed diamond saw (15 LC, Buehler,

Germany) and the obtained cross sections prepared by grinding and polishing down to 1 µm. The

cross sections were then characterized using scanning electron microscopy (SEM, Jeol JSM 6010

LA, Japan).

Finite element model

In order to establish whether the conditions of the test could be reproduced by calculation

and therefore allow the interpretation of the results to be improved, the temperature distribution

in the sample was calculated for an axisymmetric model using the implicit solver implemented in

Abaqus/Standard (Abaqus v6.11-2, Simulia, USA). It was assumed that the laser heat flux was

fully absorbed by the front surface and that all exposed surfaces radiate heat to a 300 K

environment with an emissivity of 1. The surfaces not being illuminated were also assumed to

transfer heat to the environment by convection. An exchange coefficient of 200 W m-2 K-1 was

chosen to account for air being blown over the sample [30]. Convection was neglected for the top

surface as it was difficult to judge what an appropriate reservoir temperature would be. However,

this is not expected to have much influence on the results since radiation dominates at high

temperatures. Consistent with what was observed experimentally, the heat flux in the FE model

was applied over an area of 6 mm diameter rather than on the whole top surface.

First-order axisymmetric CAX4T elements were chosen as the analysis is fully coupled in

temperature and displacement. A structured uniform mesh of 0.2 mm elements was generated for

this model, giving a total number of 2500 elements and ensuring results that are reasonably

accurate for the purpose of this study as confirmed with a sensitivity analysis. Figure 3 shows a

schematic of the FE model after meshing and highlights the thermodynamic assumptions

presented earlier, where ‘R’ and ‘C’ stand for radiative and convective thermal exchange,

respectively.

Since diborides oxidise when exposed to air at high temperature, the oxidation of the

material was incorporated in the model as a user subroutine (USDFLD) which uses a parabolic

growth law and an Arrhenius expression to account for temperature differences. The latter was

calibrated using experiments in which oxidation was carried out in a simple air furnace on small

bars. Starting from a parabolic kinetics law:

x=√K p t (1)

where x is the thickness of the oxide layer formed, t is time and K p is the parabolic kinetic

constant, expressed in mm2 s-1 , it was possible to derive an expression to calculate oxide growth

incrementally:

dx=K p

2 xdt (2)

For each element in the model, Eq. 2 was evaluated at every time increment in the user

subroutine based on the actual element temperature. When the sum of oxide growth increments

reached the distance of the element from the closest surface, the material properties were changed

to those of HfO2 and the element was marked as oxidised. Further details on the methodology are

reported elsewhere [29]. Melting was also incorporated in the user subroutine by simple

comparison with the respective melting point of HfO2 or HfB2 depending on whether or not the

material had previously been oxidised. Key outputs from the model were the temperature

distribution, the regions which were expected to be oxidised and the areas where melting was

expected. All material properties used in the simulations were given as a function of temperature

and material state. Room temperature properties for HfB2 and HfO2 are summarised in Table 2.

Properties used for molten material are essentially the same as those used for HfB2, with the

exception of elastic modulus and heat capacity. To account for the reduced mechanical properties

of the molten material an elastic modulus of 0.5 GPa was used, which is 2 to 3 orders of

magnitude less than that of HfB2 and HfO2. Heat capacity of the melt has been estimated to be

525 J kg-1 K-1 using the software CALPHAD [25].

Results

Oxidation and limited melting

Figure 4 shows the samples exposed to 25 MW m-2 for between 30 and 480 seconds. The

laser power was ramped in a stepwise fashion for the samples of the first series, whereas a

standard ramp was used for the second series. For short durations (up to 60 s), the samples

experienced little damage: there was only a thin dusting of oxide and small areas of damage

caused by melting. The pitting in the photographs of the top surfaces confirms that the laser did

not heat the entire surface homogeneously but heated a smaller area resulting in localized

melting.

The cross section of the sample exposed for 60 seconds clearly confirms that melting did

occur in a localized region as seen in Figure 5a. A comparison between a homogeneously spread

heat input and a more concentrated one using the model indicates that such limited melting is a

consequence of the more limited area over which the laser heat is deposited. As the exposure

times were increased, the oxide started to cover the entire sample. As shown in Figure 6, the rate

at which this was expected to happen by the model agrees well with experimental observations.

Another prediction by the model born out in the experiments is that for this heat flux, the

progression of the molten zone is largely determined by the progression of oxidation. The shape

of the molten zone therefore depends strongly on the temperature distribution with a much thicker

oxide layer near the top of the sample, where the material is hotter and oxidation is faster, which

thins down substantially away from the top surface as the material is colder and hence oxidation

slows down. The cross section of the sample exposed for 480 seconds, shown in Figure 5b,

demonstrates that this prediction is also reflected in the experiments; an oxide layer has covered

the entire sample at the top evolving to a thinner ribbon near the edges. The distortion of material

near the top towards the right hand side, which during the test was pointing downwards, shows

clear signs that the material was molten at some stage during the test and was flowing down.

Limited melting

Figure 7 shows photographs of samples exposed to 50 MW m-2 for various times as well

as predictions of the damage pattern. The first thing to note is the growth of the oxide layer from

the top of the sample towards the bottom with exposure duration, again predicted rather well by

the finite element calculation (see Figure 8).

The most obvious difference with the results for 25 MW m-2 is that the molten zone

penetrated the sample to a more substantial depth irrespective of oxidation, i.e. the progression of

melting into the sample was not a consequence of oxidation alone but a consequence of direct

melting of the HfB2 before the material could oxidise. The penetration into the sample with higher

heat flux was still limited: only about 3 mm of the 20 mm of the sample melted. Samples tested

up to 120 seconds suggest that the melt did not flow much owing to gravity, but by 240 seconds

the molten material started to flow. The predictions of the damage explain why it took so long for

the melt to flow: by focusing the laser energy slightly more in the center of the sample, the

molten zone actually takes on a cup shape which contains it and stops it from flowing down to

one side. However, due to oxidation these walls eventually melt allowing the melt to flow. That

this is indeed the main reason for the containment of the melt is clear when the cross sections of

the samples, shown in Figure 9, are considered: at 30 seconds exposure the dense zone, which is

believed to have been liquid at temperature, is clearly contained in a cup of material, Figure 9a.

Even at 60 seconds, the contrast suggests that there is still some containment, Figure 9b, whereas

at 240 seconds the melt was flowing and has torn during solidification, Figure 9c.

Melt removal

Samples exposed to the highest heat fluxes (75 and 100 MW m -2) are shown in Figure 10.

The molten material has flown away and significant bubbles and craters are observed in the SEM

images (Figure 11). At such elevated heat fluxes, the rapid, total melting of the sample surface

cannot be avoided and the melt is removed easily. Since this exposes new material to the

incoming heat flux, the entire sample is expected to melt as time progresses and the residual life

of the sample will depend solely on the amount of remaining material. Despite melt flow not

being accounted for in the model, for the short exposures used, the depth of melting is still

reasonably predicted.

Temperature measurements

A comparison between measured temperatures and calculated ones for 25 and 50 MW m-2

applied heat flux is shown in Figure 12 a and b, respectively. As can be seen, it is clear that the

back face temperature was reasonably predicted even during cooling. Nevertheless, the front

temperature was more difficult to judge due to the large difference in temperature between the

centre and the edge of the samples in the model which was even more substantial for the sample

exposed to 50 MW m-2 (around 2000 ºC). This observation was attributed to the assumed heat

flux distribution in the model in which the laser energy was applied over an area of 6 mm

diameter and not on the whole top surface, according to the experimental observations of the

cross sections of the samples after testing. The weighted average of the surface temperature

predictions, however, seemed to agree with the range of temperatures measured by the different

pyrometers.

The dissimilarities between calculations and experimental values observed on Figure 12

could have also been a consequence of HfO2 formation. The growth of an oxide layer whose

radiative properties are different could affect the pyrometer measurement; Moreover, HfO2 is

transparent to a range of wavelengths [31], and hence some of the measured temperatures might

in fact stem from below the surface. Not all of the measurements of the pyrometers are shown in

Figure 12 because some wavelengths did not give actual signal below certain temperatures while

other gave poor results above critical temperatures (around 2500 ºC). One possible explanation

for this could be that off-gassed material given off during heating interfered with the detection of

certain wavelengths by the pyrometer.

Discussion

As discussed in the previous section, following the post-test characterization of the HfB2

cylinders and the analysis of the model predictions, four damage regimes can be identified

depending on the heat flux applied to the sample (see Table 3).

At moderate levels of applied heat flux, not covered in this work [20], temperatures below

the melting points of both HfB2 and HfO2 are expected. As a result, oxidation is the only

damaging mechanism and the lifetime of the component will be determined by its kinetics. The

HfO2 layer formed is brittle and porous and may chip off while in service leaving fresh HfB2

material exposed to further attack, increasing the oxidation and degradation of the configuration.

In fact, this rupture of the oxide scale is a critical issue of UHTCs for applications in extreme

environments. Moreover, as shown in Table 2, thermal properties of the oxide are significantly

different from those of the non-oxide. This incoherence between oxide scale and unaltered

material will impact on the efficiency of thermal radiation and heat dissipation to the

environment.

As the heat flux increases, temperature also increases. At 25 MW m-2 the predicted

temperature is expected not to exceed the melting point of HfB2 but to be above that of HfO2,

which has been shown to correlate well with the experiments. Therefore, melting is induced by

oxidation and the long term stability at this heat flux probably depends entirely on the progress of

that oxidation, which controls the damage in the component.

For higher heat fluxes of 50 MW m-2 some HfB2 melts, though remains confined to the

surface of the sample for the particular geometry tested in this work. In fact, the cup-like shape of

solid material shown in Figure 9a partly contains the molten material and prevents it from

flowing.

For heat fluxes above 50 MW m-2, the containment of the melt becomes impossible due to

complete melting of the entire top surface (see Figure 11). Moreover, the increased temperature

makes the molten material more fluid, accelerating its removal from the surface under the effect

of gravity. The material underneath is left exposed to the heat flux; it melts and is immediately

removed. Hence, the amount of material left to melt is what determines the residual life of the

component.

Simple estimations via FE modelling have proven to be reasonably accurate and can help

identify how test parameters affect performance. Back face temperature predictions show fair

agreement with measurements. There is a clear difference between the calculated front face

temperatures and the experimental results possibly because the pyrometers cannot measure the

large thermal gradient across the front surface. Nevertheless, it can be concluded that the

weighted average of the calculated front face temperature values matches quite well with the

range of measurements obtained from the pyrometers.

Finally, it is important to notice that the quantification of the heat fluxes and identification

of different damage regimes are only valid for the sample geometry and dimensions considered

here. If the sample was shorter, for example, all damage regimes would be brought down in heat

flux, whereas a different geometry would result in a different temperature distribution in the

sample and hence a different damage pattern. This is where the modelling can support the

experimental work, predicting temperature and damage distribution in the sample and helping

find the most suitable design while reducing the number of laboratory tests to be performed.

Conclusions

Laser testing of HfB2 monoliths was carried out in order to predict the behaviour of this

UHTC under conditions of high heat flux. Samples were tested in air at four different heat fluxes,

25, 50, 75 and 100 MW m-2 for various exposures times. A finite element model which simulated

the same conditions of experimental tests was developed. The damage patterns can be

summarised as follows: for moderate heat fluxes (not tested here) it is expected that only

oxidation will occur. For heat fluxes of 25 MW m-2 the temperature is not high enough to melt

HfB2 but is above the HfO2 melting point. Therefore, melting of the oxide will occur and hence

degradation rates are controlled by the oxidation kinetics. At higher heat fluxes (25-50  MW m-2)

limited melting of the HfB2 will also occur. If the melt can be contained – e.g. as observed in the

experiments here because the molten zone remains enclosed in a cup-like shape of solid material

– damage remains limited to the surface layer. As the heat flux increases (> 50 MW m-2), the

surface fully melts making it impossible to contain the melt which flows away under the effect of

gravity leaving fresh material underneath exposed to the laser beam. At this point the only

resistance offered by the sample is the time needed to ablate it completely. While these different

stages in damage formation can be expected to occur for all sample sizes, the sample shape is

very important in determining the actual values of the heat flux for damage regime transitions.

This shows the importance of relatively straightforward modelling to be carried out in parallel

with experiments to aid the interpretation of the results and to build confidence in predictability

of the damage for other circumstances.

Acknowledgements

LL and LV thank the Defence Science and Technology Laboratory of the UK for the

financial support for the third phase of the UHTC project under contract DSTLX-1000085784,

and the Engineering and Physical Sciences Research Council of the UK for the financial support

from the Material Systems for Extreme Environments grant (EP/K008749/2). MP and KN thank

the UK’s Defence Science and Technology Laboratory for providing the financial support for the

modelling work under contract number DSTLX-1000064072. The laser testing was performed

under a Project Arrangement between the United States of America Department of Defense and

the United Kingdom of Great Britain and Northern Ireland Ministry of Defence.

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ZrB2 and HfB2 from room temperature to 1300 K,” J. Less Common Met., 18 [2] 149–157

(1969).

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during high temperature oxidation of ZrN ceramics”, J. Eur. Ceram. Soc. (2015).

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coefficient of polycrystalline alumina”, J. Mater Sci, 28 [8] 2079-208 (1993).

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Figure captions

Figure 1. Laser test set-up: (a) Front face; (b) Back face and thermocouple.

Figure 2. (a) standard and (b) complex ramp for increasing the laser power from zero to the

desired level.

Figure 3. Schematic showing the structured uniform mesh chosen for this work. Taking

advantage of symmetry, an axisymmetric section of the sample was modelled, resulting in a total

number of 2500 elements. Thermodynamic assumptions are also indicated in the figure, where

‘R’ and ‘C’ stand for radiative and convective thermal exchange, respectively. Radiation only is

acting on the top surface, whereas both radiation and convection are acting on the side and

bottom of the sample.

Figure 4. Photographs of the samples tested at 25 MW m -2 different times as well as predicted

damage at the end of the dwell at maximum powder where light grey is molten material, black is

oxidation and dark grey is unaltered HfB2: (a) 30 s; (b) 60 s; (c) 120 s and (c) 480 s.

Figure 5. Cross-sections of samples tested at 25 MW m-2 (a) 60 s and (b) 480 s.

Figure 6. Predictions and experimental observations of height of the sample not covered in a thin

layer of oxide.

Figure 7. Photographs of the samples tested at 50 MW m -2 different times as well as predicted

damage at the end of the dwell at maximum powder where light grey is molten material, black is

oxidation and dark grey is unaltered HfB2: (a) 10 s; (b) 30 s; (c) 60 s; (d) 120 s and (e) 240 s.

Figure 8. Predictions and experimental observations of height of the sample not covered in a thin

layer of oxide.

Figure 9. Composite SEM micrographs of the cross section of samples exposed to 50 MW m -2 for

(a) 30 s, (b) 60 s and (c) 240 s.

Figure 10. Photographs of the samples tested at 75 and 100 MW m-2 as well as predicted damage

at the end of the dwell at maximum powder where light grey is molten material, black is

oxidation and dark grey is unaltered HfB2; (a) 6.75 s at 75 MW m-2 and (b) 5 s at 100 MW m-2.

Figure 11. Cross sections of the samples exposed to 75 and 100 MW m -2: (a) 6.75 s at 75 MW m-2

and (b) 5 s at 100 MW m-2.

Figure 12. Measurements of experimental and calculated front and back face temperatures and

the weighted average of the front face temperatures: (a) Sample exposed to 25 MW m-2 and (b)

sample exposed to 50 MW m-2.

Tables

Table 1. Overview of tests conducted.

SeriesSample

number*

Ramp

(s)Type

Heat flux (MW m-

2)

Dwell

(s)

First 1.6 55 Complex ramp rate 25 30

First 1.13 55 Complex ramp rate 25 60

Second 2.10 15 Standard ramp rate 25 120

Second 2.19 15 Standard ramp rate 25 480

First 1.2 15 Standard ramp rate 50 5

First 1.7 15 Standard ramp rate 50 10

First 1.11 15 Standard ramp rate 50 20

First 1.18 15 Standard ramp rate 50 30

Second 2.15 15 Standard ramp rate 50 20

Second 2.11 15 Standard ramp rate 50 30

Second 2.5 15 Standard ramp rate 50 60

Second 2.14 15 Standard ramp rate 50 120

Second 2.8 15 Standard ramp rate 50 240

First 1.12 15 Standard ramp rate 75 3.3

First 1.8 15 Standard ramp rate 75 6.75

First 1.1 15 Standard ramp rate 100 5

*1 refers to samples from the first phase; 2 refers to samples from the second phase.

Table 2. Overview of room temperature material properties used for HfB2 and HfO2.

Property Unit HfB2 HfO2 Source

Melting temperature K 3653 ± 20 3085 [26,27]

Density kg dm-3 10.5 9.68 *

Elastic modulus GPa 502 ± 0.7 62 [28,*]

Poisson’s ratio −¿ 0.152 0.23 [28,*]

Thermal conductivity W m-1 K-1 112 ± 5 1.2 ± 0.2 *

Thermal expansion coeff. K-1 6.58 ± 0.01·10-6 4.5·10-6 *

Specific heat J kg-1 K-1 244 348 [25]

Temperature dependence of properties is accounted for in the simulation. Readers can find more

data on material properties in the references provided. Properties for molten material are

essentially the same as those used for HfB2, with the exception of elastic modulus and heat

capacity, chosen as 500 MPa and 525 J kg-1 K-1 respectively. (*) denotes a property measurement

derived at Imperial College London.

Table 3. Damage regimes identified.

Damage

regimeObservations

Moderate fluxes Oxidation

< 25 MW m-2 Oxidation induced melting

25-50 MW m-2 Limited melting

> 50 MW m-2 Melt removal-ablation