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arXiv 2603.03424cond-mat.mtrl-scicond-mat.mes-hallhep-latphysics.app-phquant-ph
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功能梯度材料的量子理论

Quantum Theory of Functionally Graded Materials

MIT(麻省理工学院)

Michael J. Landry, Ryotaro Okabe, Chuliang Fu, Mingda Li

AI总结:

本文提出了一种用于功能梯度材料的量子理论框架,通过非相互作用电子模型和广义WKB方法,解决了其梯度非周期性结构对传统理论的挑战,并展示了其在电磁特性及器件设计中的应用。

摘要:

功能梯度材料(FGMs)是其组成或微观结构在空间中连续变化的复合材料,产生位置依赖的机械和功能特性。近年来,由于增材制造技术的进步,FGMs获得了广泛关注,这使得可以精确控制 composition 和 orientation。然而,其梯度、非周期性结构破坏了布洛赫定理的假设,使第一性原理的电子和电磁计算变得困难。本文开发了一个原位量子理论框架,用于研究 FGMs 的电磁特性。使用非相互作用电子模型,我们建立了调制布洛赫态的理论,推导了有效场方程,并通过提出广义WKB(GWKB)方法、有效质量近似、玻尔兹曼方程和数值方法来求解。我们的GWKB解不是 semiclassical 的,但在完全量子区域内仍然有效。我们证明,在梯度介质中,有效可观测量如电导率、磁导率和电容率通常不具有张量描述,而工程化的取向梯度可以实现对朗道量子化的精确控制。作为器件示例,我们进一步发展了具有增强电子可调性的梯度 p-n 接口理论。这一框架为预测设计梯度复合材料奠定了量子基础,能够加速人工智能发现下一代功能架构。

英文摘要:

Functionally graded materials (FGMs) are composites whose composition or microstructure varies continuously in space, producing position-dependent mechanical and functional properties. In recent years, FGMs have gained significant attention due to advances in additive manufacturing, which enable precise spatial control of composition and orientation. However, their graded, aperiodic structure breaks the assumptions of Bloch's theorem, making first-principles electronic and electromagnetic calculations challenging. Here we develop an ab initio quantum theoretical framework for the electromagnetic properties of FGMs. Using a non-interacting electron model, we formulate a theory of modulated Bloch states, derive effective field equations, and solve them by proposing a generalized WKB (GWKB) method, an effective mass approximation, the Boltzmann equation, and numerical approaches. Our GWKB solution is not semiclassical but remains valid in the fully quantum regime. We show that effective observables such as conductivity, magnetic permeability, and electric permittivity generally do not admit a tensorial description in graded media, and that engineered orientational gradients enable precise control of Landau quantization. As a device example, we further develop a theory of graded p-n junctions with enhanced electronic tunability. This framework lays the quantum foundation for predictive design of graded composite materials, enabling AI-accelerated discovery of next-generation functional architectures.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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