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. 2017 Dec 11;7:17337. doi: 10.1038/s41598-017-17654-x

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© The Author(s) 2017

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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(a) Change in length of the first (ΔL₁) and second (ΔL₂) tempering steps and their difference versus temperature for a medium carbon steel. (b) Non-isothermal double tempering plot displaying the derivative of the difference between the change in length for the first and second tempering steps with respect to temperature (d(ΔL₁–ΔL₂)/dT) versus non-isothermal tempering temperature. Both tempering steps were conducted at a heating rate of 2 °C/min. Dotted lines indicate temperatures where tempering reactions of interest occur.