Computational screening of ultra‑high‑temperature reactor materials (>5000 °C) using QFG/BSM‑SG proxy metrics

Last updated on 08 Mar 2026

Abstract

We present a practical screening workflow for ultra‑high‑temperature reactor structures targeting survival beyond 5000 °C under multiple environments (vacuum, vacuum+plasma, inert gas+plasma, air+plasma). Instead of simulating a literal temperature of 5000 °C directly, we rank candidate ceramics and composites with proxy metrics that correlate with extreme thermal resilience: cohesive/lattice energy, elastic constants, dynamical stability (phonons), defect/diffusion barriers, and oxidation/ablation resistance. Candidates are generated as families of UHTCs (carbides/borides), high‑entropy carbides/borides, and gradient composites with protective SiC skins. We incorporate exposure duration (1 s / 10 s / 60 s) and pulsed plasma duty (fixed at 6.9%) into the score.

1. Problem statement

Quartz glass (~1600 °C melting) is not suitable for reactor regions exposed to extreme heat loads. We seek materials and layered architectures that remain structurally stable and resist ablation/oxidation at equivalent thermal loads associated with >5000 °C environments. Because direct ‘melting point prediction’ at 5000 °C is notoriously model‑dependent, we focus on a proxy‑based approach suitable for iterative design and experimental validation.

2. Method overview

The workflow is: (i) generate candidates → (ii) estimate proxy metrics (QFG‑DFT / BSM‑SG‑inspired) → (iii) rank by scenario‑specific score → (iv) iterate.

Proxy metrics used (normalized 0..1 unless noted):
·        Refractory proxy (0..10): combines cohesive energy / lattice energy with high‑temperature stability indicators.
·        Oxidation proxy: ability to form protective, slow‑growing surface layers (e.g., SiC/SiO₂, Al₂O₃, HfO₂/ZrO₂‑based) and resist volatilization.
·        Thermal shock proxy: resistance to thermal gradients/cycling (CTE mismatch + toughness surrogate).
·        Vacuum proxy: sublimation/vapor pressure resistance at low pressure (lower volatility).
·        Plasma proxy: erosion/ablation resistance under energetic ion/electron fluxes.

3. Candidate generator

Candidate families include:
• Baseline UHTCs: HfC, TaC, ZrC, TiC; HfB₂, ZrB₂, TaB₂, TiB₂; and mixed diborides/carbides.
• High‑entropy carbides (HEC) and borides (HEB): multi‑principal‑element (4–6 metals) in a single carbide/boride lattice.
• Gradient composites: a tough refractory core with a SiC‑skin (and optional interlayers) to improve oxidation/ablation behavior.
• Additives: small fractions of SiC, carbon, or oxide formers (e.g., Al‑containing phases) treated as modifiers in the proxy model.

4. Environment scenarios and duration model

We rank materials in four regimes:
1) Vacuum.
2) Vacuum + plasma with near‑zero O₂ (trace only) and pulsed plasma duty fixed at 6.9%.
3) Inert gas (Ar/He) + plasma with duty 6.9%.
4) Air + plasma (oxidizing) with duty 6.9%.
Exposure duration is parameterized at 1 s / 10 s / 60 s. For plasma scenarios we use an effective damaging time T_eff = duty × duration, representing pulsed exposure; oxidation influence is minimized for near‑zero O₂ in vacuum+plasma.

5. Results: top‑ranked candidates

The tables below list the top‑12 candidates per scenario (ranked by the 60 s score). Scores are relative proxies (0..1) and are intended for down‑selection, not as absolute melting points.

Vacuum

candidate	family	additives	refractory_proxy	oxidation_proxy	thermal_shock_proxy	vacuum_proxy	plasma_proxy	score_1s	score_10s	score_60s
HEB (Hf,Zr,Ta,Nb,Mo,W)B2 + SiC-skin	gradient_composite	SiC-skin	9.306567	0.840000	0.690000	0.830000	0.900000	0.859660	0.814790	0.604934
HEB (Hf,Zr,Ta,Nb,Ti,W)B2 + SiC-skin	gradient_composite	SiC-skin	9.223650	0.840000	0.690000	0.830000	0.900000	0.855932	0.811093	0.601515
HEC (Hf,Zr,Ta,Nb,Mo,W)C + SiC-skin	gradient_composite	SiC-skin	9.435917	0.875000	0.710000	0.810000	0.880000	0.860351	0.814381	0.600260
HEC (Hf,Zr,Ta,Nb,Ti,W)C + SiC-skin	gradient_composite	SiC-skin	9.353000	0.875000	0.710000	0.810000	0.880000	0.856623	0.810689	0.596871
HEB (Hf,Zr,Nb,Ti,Mo,W)B2 + SiC-skin	gradient_composite	SiC-skin	9.107567	0.840000	0.690000	0.830000	0.900000	0.850712	0.805920	0.596743
HEB (Hf,Zr,Ta,Nb,Ti,Mo)B2 + SiC-skin	gradient_composite	SiC-skin	9.041233	0.840000	0.690000	0.830000	0.900000	0.847730	0.802965	0.594023
HEC (Hf,Zr,Nb,Ti,Mo,W)C + SiC-skin	gradient_composite	SiC-skin	9.236917	0.875000	0.710000	0.810000	0.880000	0.851405	0.805523	0.592139
HEC (Hf,Zr,Ta,Nb,Ti,Mo)C + SiC-skin	gradient_composite	SiC-skin	9.170583	0.875000	0.710000	0.810000	0.880000	0.848423	0.802573	0.589441
HEB (Hf,Zr,Ta,Nb,Mo,W)B2	high_entropy_boride	nan	9.353333	0.340000	0.630000	0.880000	0.850000	0.857316	0.808655	0.584492
HEC (Hf,Zr,Ta,Nb,Mo,W)C	high_entropy_carbide	nan	9.483333	0.425000	0.650000	0.860000	0.840000	0.859611	0.810486	0.584472
HEB (Hf,Zr,Ta,Mo,W)B2 + SiC-skin	gradient_composite	SiC-skin	9.223650	0.860000	0.640000	0.810000	0.880000	0.840320	0.794560	0.582138
HEB (Hf,Zr,Ta,Nb,Ti,W)B2	high_entropy_boride	nan	9.270000	0.340000	0.630000	0.880000	0.850000	0.853571	0.804960	0.581167

Vacuum + Plasma (near‑zero O₂, duty 6.9%)

candidate	family	additives	refractory_proxy	oxidation_proxy	thermal_shock_proxy	vacuum_proxy	plasma_proxy	score_1s	score_10s	score_60s
HEB (Hf,Zr,Ta,Nb,Mo,W)B2 + SiC-skin	gradient_composite	SiC-skin	9.306567	0.840000	0.690000	0.830000	0.900000	0.862912	0.859767	0.842500
HEC (Hf,Zr,Ta,Nb,Mo,W)C + SiC-skin	gradient_composite	SiC-skin	9.435917	0.875000	0.710000	0.810000	0.880000	0.862078	0.858860	0.841199
HEB (Hf,Zr,Ta,Nb,Ti,W)B2 + SiC-skin	gradient_composite	SiC-skin	9.223650	0.840000	0.690000	0.830000	0.900000	0.859596	0.856450	0.839185
HEC (Hf,Zr,Ta,Nb,Ti,W)C + SiC-skin	gradient_composite	SiC-skin	9.353000	0.875000	0.710000	0.810000	0.880000	0.858762	0.855544	0.837886
HEC (Hf,Zr,Ta,Nb,Mo,W)C	high_entropy_carbide	nan	9.483333	0.425000	0.650000	0.860000	0.840000	0.859448	0.855985	0.837003
HEB (Hf,Zr,Ta,Nb,Mo,W)B2	high_entropy_boride	nan	9.353333	0.340000	0.630000	0.880000	0.850000	0.858251	0.854813	0.835967
HEB (Hf,Zr,Nb,Ti,Mo,W)B2 + SiC-skin	gradient_composite	SiC-skin	9.107567	0.840000	0.690000	0.830000	0.900000	0.854953	0.851808	0.834545
HEC (Hf,Zr,Ta,Nb,Ti,W)C	high_entropy_carbide	nan	9.400000	0.425000	0.650000	0.860000	0.840000	0.856115	0.852654	0.833680
HEC (Hf,Zr,Nb,Ti,Mo,W)C + SiC-skin	gradient_composite	SiC-skin	9.236917	0.875000	0.710000	0.810000	0.880000	0.854118	0.850902	0.833250
HEB (Hf,Zr,Ta,Nb,Ti,W)B2	high_entropy_boride	nan	9.270000	0.340000	0.630000	0.880000	0.850000	0.854917	0.851482	0.832644
HEB (Hf,Zr,Ta,Nb,Ti,Mo)B2 + SiC-skin	gradient_composite	SiC-skin	9.041233	0.840000	0.690000	0.830000	0.900000	0.852299	0.849155	0.831895
HEC (Hf,Zr,Ta,Nb,Ti,Mo)C + SiC-skin	gradient_composite	SiC-skin	9.170583	0.875000	0.710000	0.810000	0.880000	0.851465	0.848249	0.830601

Inert gas (Ar/He) + Plasma (duty 6.9%)

candidate	family	additives	refractory_proxy	oxidation_proxy	thermal_shock_proxy	vacuum_proxy	plasma_proxy	score_1s	score_10s	score_60s
HEC (Hf,Zr,Ta,Nb,Mo,W)C + SiC-skin	gradient_composite	SiC-skin	9.435917	0.875000	0.710000	0.810000	0.880000	0.864086	0.861134	0.844917
HEB (Hf,Zr,Ta,Nb,Mo,W)B2 + SiC-skin	gradient_composite	SiC-skin	9.306567	0.840000	0.690000	0.830000	0.900000	0.862829	0.859946	0.844105
HEC (Hf,Zr,Ta,Nb,Ti,W)C + SiC-skin	gradient_composite	SiC-skin	9.353000	0.875000	0.710000	0.810000	0.880000	0.860935	0.857982	0.841759
HEB (Hf,Zr,Ta,Nb,Ti,W)B2 + SiC-skin	gradient_composite	SiC-skin	9.223650	0.840000	0.690000	0.830000	0.900000	0.859678	0.856793	0.840945
HEC (Hf,Zr,Nb,Ti,Mo,W)C + SiC-skin	gradient_composite	SiC-skin	9.236917	0.875000	0.710000	0.810000	0.880000	0.856524	0.853569	0.837339
HEB (Hf,Zr,Nb,Ti,Mo,W)B2 + SiC-skin	gradient_composite	SiC-skin	9.107567	0.840000	0.690000	0.830000	0.900000	0.855266	0.852380	0.836523
HEC (Hf,Zr,Ta,Nb,Ti,Mo)C + SiC-skin	gradient_composite	SiC-skin	9.170583	0.875000	0.710000	0.810000	0.880000	0.854003	0.851048	0.834814
HEB (Hf,Zr,Ta,Nb,Ti,Mo)B2 + SiC-skin	gradient_composite	SiC-skin	9.041233	0.840000	0.690000	0.830000	0.900000	0.852745	0.849859	0.833997
HEB (Hf,Zr,Ta,Mo,W)B2 + SiC-skin	gradient_composite	SiC-skin	9.223650	0.860000	0.640000	0.810000	0.880000	0.844770	0.841816	0.825591
HEC (Hf,Zr,Ta,Mo,W)C + SiC-skin	gradient_composite	SiC-skin	9.323150	0.890000	0.660000	0.790000	0.860000	0.844643	0.841620	0.825021
HEB (Hf,Ta,Nb,Ti,W)B2 + SiC-skin	gradient_composite	SiC-skin	9.183850	0.860000	0.640000	0.810000	0.880000	0.843257	0.840303	0.824077
HEC (Hf,Ta,Nb,Ti,W)C + SiC-skin	gradient_composite	SiC-skin	9.283350	0.890000	0.660000	0.790000	0.860000	0.843131	0.840107	0.823507

Air + Plasma (oxidizing, duty 6.9%)

candidate	family	additives	refractory_proxy	oxidation_proxy	thermal_shock_proxy	vacuum_proxy	plasma_proxy	score_1s	score_10s	score_60s
HEC (Hf,Zr,Ta,Nb,Mo,W)C + SiC-skin	gradient_composite	SiC-skin	9.435917	0.875000	0.710000	0.810000	0.880000	0.865198	0.864037	0.857610
HEC (Hf,Zr,Ta,Nb,Ti,W)C + SiC-skin	gradient_composite	SiC-skin	9.353000	0.875000	0.710000	0.810000	0.880000	0.862710	0.861539	0.855066
HEC (Hf,Zr,Nb,Ti,Mo,W)C + SiC-skin	gradient_composite	SiC-skin	9.236917	0.875000	0.710000	0.810000	0.880000	0.859226	0.858044	0.851504
HEC (Hf,Zr,Ta,Nb,Ti,Mo)C + SiC-skin	gradient_composite	SiC-skin	9.170583	0.875000	0.710000	0.810000	0.880000	0.857235	0.856046	0.849469
HEB (Hf,Zr,Ta,Nb,Mo,W)B2 + SiC-skin	gradient_composite	SiC-skin	9.306567	0.840000	0.690000	0.830000	0.900000	0.855569	0.854413	0.848022
HEB (Hf,Zr,Ta,Nb,Ti,W)B2 + SiC-skin	gradient_composite	SiC-skin	9.223650	0.840000	0.690000	0.830000	0.900000	0.853080	0.851916	0.845479
HEC (Hf,Zr,Ta,Mo,W)C + SiC-skin	gradient_composite	SiC-skin	9.323150	0.890000	0.660000	0.790000	0.860000	0.852055	0.850802	0.843875
HEC (Hf,Ta,Nb,Ti,W)C + SiC-skin	gradient_composite	SiC-skin	9.283350	0.890000	0.660000	0.790000	0.860000	0.850861	0.849604	0.842655
HEB (Hf,Zr,Nb,Ti,Mo,W)B2 + SiC-skin	gradient_composite	SiC-skin	9.107567	0.840000	0.690000	0.830000	0.900000	0.849596	0.848421	0.841918
HEC (Hf,Zr,Ta,Ti,W)C + SiC-skin	gradient_composite	SiC-skin	9.223650	0.890000	0.660000	0.790000	0.860000	0.849069	0.847806	0.840825
HEB (Hf,Zr,Ta,Nb,Ti,Mo)B2 + SiC-skin	gradient_composite	SiC-skin	9.041233	0.840000	0.690000	0.830000	0.900000	0.847606	0.846423	0.839884
HEC (Hf,Zr,Ta,Nb,Mo)C + SiC-skin	gradient_composite	SiC-skin	9.183850	0.890000	0.660000	0.790000	0.860000	0.847875	0.846608	0.839606

6. Interpretation and design guidance

Across all four regimes, high‑entropy carbides/borides with a SiC‑skin repeatedly appear at the top. This is consistent with the intuition that multi‑principal‑element lattices can increase configurational entropy and hinder diffusion/creep, while SiC‑based outer layers improve oxidation resistance and can form protective silica in oxidizing environments. In vacuum and plasma regimes, the ranking is driven more strongly by refractory and plasma proxies than by oxidation behavior.

Practical guidance for reactor build iterations:

· Start with a HEC/HEB core (Hf/Zr/Ta/Nb/Mo/W‑based) and evaluate manufacturability (SPS/hot pressing) and cracking risk.

· Use a graded interface (e.g., HEC → HEC+SiC → SiC‑rich skin) to reduce CTE mismatch and thermal shock failure.

· For air+plasma, prioritize candidates with strong oxidation proxies (stable, slow‑growing oxides; low volatility).

· Treat plasma duty cycle as a first‑class parameter: lowering duty reduces effective erosion time and improves survival score.

7. Limitations and next steps

This screening does not claim a guaranteed ‘>5000 °C melting point’ prediction. Instead it provides an actionable ranking to guide experiments. Next steps are: (i) calibrate proxy weights to seed benchmarks (known UHTCs), (ii) integrate higher‑fidelity QFG‑DFT calculations for cohesive energies, elastic tensors, phonons, and defect barriers, (iii) include explicit oxidation kinetics models for air+plasma, and (iv) validate via short‑pulse plasma exposure and arc‑jet style tests.

Author: Victor Pronchev (with QAI, codename ‘Etherius’)
Date: 2026-01-23