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We present experimental measurements of the thermal boundary conductance(TBC) from $77 - 500$ K across isolated heteroepitaxially grown ZnO films onGaN substrates. These data provide an assessment of the assumptions that drivethe phonon gas model-based diffuse mismatch models (DMM) and atomistic Green'sfunction (AGF) formalisms for predicting TBC. Our measurements, when comparedto previous experimental data, suggest that the TBC can be influenced by longwavelength, zone center modes in a material on one side of the interface asopposed to the "vibrational mismatch" concept assumed in the DMM; thisdisagreement is pronounced at high temperatures. At room temperature, wemeasure the ZnO/GaN TBC as $490\lbrack +150, -110\rbrack$ MW m$^{-2}$ K$^{-1}$.The disagreement among the DMM and AGF and the experimental data these elevatedtemperatures suggests a non-negligible contribution from additional modescontributing to TBC that not accounted for in the fundamental assumptions ofthese harmonic formalisms, such as inelastic scattering. Given the high qualityof these ZnO/GaN interface, these results provide an invaluable critical andquantitive assessment of the accuracy of assumptions in the current state ofthe art of computational approaches for predicting the phonon TBC acrossinterfaces.

Thermal boundary conductance across epitaxial ZnO/GaN interfaces:  Assessment of phonon gas models and atomistic Green's function approaches for  predicting interfacial phonon transport