We have observed a distinctive quantization-related behavior in the LLaMA3/3.1-70B models that is absent in both the LLaMA2-70B and LLaMA3/3.1-8B/405B models. Quantization is a crucial technique for deploying large language models (LLMs) efficiently. Among various bit widths and representations for weights and activations, the 8-bit integer weight and 8-bit integer activation (W8A8) configuration is particularly popular due to its widespread hardware support. However, the impact of W8A8 post-training quantization on model accuracy remains contentious. While several studies have suggested calibrating either weights or activations to mitigate accuracy degradation, a comprehensive solution has yet to be identified. In this paper, we empirically investigate multiple LLMs featured on an open LLM leaderboard, discovering that the LLaMA3-70B model series have a unique accuracy degradation behavior with W8A8 per-channel post-training quantization. In contrast, other model series such as LLaMA2, LLaMA3-8B, Qwen, Mixtral, Mistral, Phi-3, and Falcon demonstrate robust performance with W8A8, sometimes surpassing their FP16 counterparts. Contrary to previous assertions attributing degradation to the large dynamic range of activations, our findings indicate that the weight distribution of the LLaMA3-70B is the primary factor behind the vulnerability. By meticulously analyzing the distinct characteristics of weight distributions across Transformer blocks, we propose a mixed strategy with less than 3% of the layers enabling finer W8A8 quantization granularity, while the remaining 97% of layers retain the per-channel configuration. As a result, the average accuracy of LLaMA3-70B-W8A8 is increased from 45.5% to 73.4% (just 0.7% shy of LLaMA3-70B-FP16) across eight reasoning tasks. Notably, our method requires neither calibration nor fine-tuning.