The first learning outcome of the ABET EC 2000 accreditation criteria, Criterion 3 (a), states that, "Engineering programs must demonstrate that their graduates have an ability to apply knowledge of mathematics, science and engineering appropriate to the discipline." This requires that students either have, or develop an ability, to transfer previously acquired knowledge and skills to new engineering learning situations and applications. One important subject area taught in chemistry that requires this type of "transfer" to the engineering domain is the conceptual knowledge of the phase behavior of liquids, solids, and gases learned in earlier chemistry classes. In fact, it is an area that is applied to a broad set of phenomena in the disciplines of chemical, mechanical, aero, and materials engineering. In the field of materials engineering the knowledge of relationships between liquid and solid phase behavior as a function of composition and temperature is used to understand the formation and evolution of materials' microstructures that is used to predict and engineer a material's properties. This work addresses the question, "How does prior knowledge of solution behavior and conceptual knowledge of solution equilibrium from chemistry affect transfer of learning for understanding and using phase diagrams in materials engineering?" To answer this question, two-tier concept quizzes were developed and given to students before and after instruction on concepts and applications of phase diagrams for understanding and control of microstructure. The results showed limited gains in pre and post instruction testing of solution concepts for a typical liquid-solid system taught in chemistry, water and salt, due to misconceptions about solution definitions and equilibrium behavior. The inability to apply a consistent conceptual model to different situations indicated persistent misconceptions and shallow or surface knowledge characteristic of a novice learner with near transfer ability. However, students given a concept quiz on solid-solid solution behavior, taught in materials engineering with phase diagrams, had more than 80% correct answers from two-tier questions about a phase diagram. However, they explained their answers with a consistent model which did not refer to atomic level processes. The second-tier explanations indicated that chemistry solubility concepts were answered with an atomic level approach, which often had misconceptions. In contrast, phase diagram questions were answered using phase diagram concepts without referring to atomic level processes. Thus, there was an inability to achieve the backward-reaching far transfer (from past science courses) of conceptual knowledge to bridge the atomic world of chemistry with the macroscopic continuum world of phase diagrams in materials engineering. This demonstrates that there are opportunities for improved pedagogy to extend the novice process of near transfer to a pathway toward an expert's deeper conceptual knowledge and far transfer ability needed to bridge conceptual understanding of phase behavior across domains of science and engineering.