三维各向异性热导率张量在热反射测量中的可辨识性：单表面极限与全张量恢复

中文摘要 AI 辅助

具有完全各向异性热导率的材料在先进应用中广泛使用，因此需要对其热导率张量进行专门表征。此类张量包含六个独立分量：三个对角热导率和三个非对角耦合项。然而，单表面热反射测量能否唯一确定任意张量仍不清楚。在此，我们通过推导一个Schur等价热导率矩阵来回答这个问题，该矩阵在平面换能器/基底配置中再现单表面热响应。这一等价性确立了内在的非唯一性，该非唯一性无法通过改变频率、延迟时间、光束几何或空间偏移来消除。我们还证明，基于灵敏度矩阵奇异值分解（SVD）的参数可辨识性测试本身无法排除完全各向异性热导率张量重建中的全局等价解。通过将系统分析与数值验证相结合，我们为全张量表征提供了选择信号和测量方向的指导。我们表明，三个相互正交的表面为全张量恢复提供互补信息。这些发现界定了单表面测量的极限，并建立了通往完全各向异性热导率张量表征的系统路径。

英文摘要

Materials with full anisotropic thermal conductivity tensors are widely used in advanced applications, creating a need for dedicated characterization. Such tensors contain six independent components: three diagonal conductivities and three non-zero off-diagonal couplings. However, whether thermoreflectance measurements on a single crystalline orientation can uniquely determine an arbitrary tensor remains unclear. Here, we show that every fully anisotropic thermal-conductivity tensor admits a Schur-equivalent tensor with zero cross-plane couplings ($k_{xz}=k_{yz}=0$). The two tensors produce identical surface thermal responses, and this equivalence persists as frequency, delay time, beam geometry, and spatial offset vary. We further demonstrate that parameter-identifiability assessments based on heuristic interpretations of sensitivity trends or singular-value decomposition (SVD) of the sensitivity matrix cannot, by themselves, rule out globally equivalent solutions in fully anisotropic systems. Combining systematic analysis with numerical validation, we provide guidance on selecting signals and measurement orientations for full-tensor characterization. Specifically, measurements at three mutually orthogonal crystallographic orientations provide complementary information for full-tensor recovery. These findings clarify the limits of single-surface measurements and establish a systematic approach to characterizing fully anisotropic thermal-conductivity tensors.

发表机构

• Department of Mechanical Engineering and Materials Science, University of Pittsburgh（匹兹堡大学机械工程和材料科学系）

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