Center for Materials Research, Norfolk State University, Norfolk, VA, 23504, USA.
Birck Nanotechnology Center, Department of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, 47907, USA.
Sci Rep. 2017 May 17;7(1):2040. doi: 10.1038/s41598-017-01544-3.
Kirchhoff's law of thermal radiation, relating emissivity and absorptance is commonly formulated for opaque bodies in thermodynamic equilibrium with the environment. However, in many systems of practical importance, both assumptions are often not satisfied. We revisit the century-old law and examine the limits of its applicability in an example of Er:YAG and Er:YLF dielectric crystals-potential radiation converters for thermophotovoltaic applications. The (80 at.%) Er:YAG crystal is opaque between 1.45 μm and 1.64 μm. In this spectral range, its absorptance α(λ) is spectrally flat and differentiates from unity only by a small amount of reflection. The shape of the emissivity spectrum ɛ(λ) closely matches that of absorptance α(λ), implying that the Kirchhoff's law can adequately describe thermal radiation of opaque bodies, even if thermodynamic equilibrium is not satisfied. The (20 at.%) Er:YLF crystal had smaller size, lower concentration of Er ions, and it was not opaque. Nevertheless, its spectrum of emissivity had almost the same shape (between 1.45 μm and 1.62 μm) as the absorptance derived from the transmission measurements. Our results are consistent with the conclusion that the Kirchhoff's law of thermal radiation can be extended (with caution) to not-opaque bodies away from the thermodynamic equilibrium.
基尔霍夫热辐射定律，涉及发射率和吸收率，通常针对与环境处于热力学平衡的不透明体进行公式化。然而，在许多实际重要的系统中，这两个假设通常都不满足。我们重新审视这个有百年历史的定律，并以 Er:YAG 和 Er:YLF 介电晶体为例，研究其在热光伏应用中作为潜在辐射转换器的适用性限制。（80 原子%）的 Er:YAG 晶体在 1.45μm 和 1.64μm 之间是不透明的。在这个光谱范围内，其吸收率α(λ)是光谱平坦的，仅与小量反射相区别。发射率光谱ɛ(λ)的形状与吸收率α(λ)非常匹配，这意味着即使不满足热力学平衡，基尔霍夫热辐射定律也可以充分描述不透明体的热辐射。（20 原子%）的 Er:YLF 晶体具有较小的尺寸、较低的 Er 离子浓度，且不是不透明的。然而，其发射率光谱在 1.45μm 和 1.62μm 之间与从透射测量得出的吸收率具有几乎相同的形状。我们的结果与以下结论一致，即热辐射的基尔霍夫定律可以（谨慎地）扩展到远离热力学平衡的非不透明体。
