<p>This study investigates the orientation relationships (ORs) within the microstructure of hot-dip galvannealed coating layers. The orientation relationships between ζ(FeZn₁₃) and Γ₁(Fe₃Zn₁₀) phases are examined in detail. Mn–Si transformation-induced plasticity (TRIP) steels with different galvannealing times were used as samples. Transmission electron microscopy (TEM) was employed to analyze the coating layer microstructure, confirming the presence of ζ(FeZn₁₃), Γ₁(Fe₃Zn₁₀), Γ₂(Fe₁₁Zn₃₉), δ(Fe_0.64Zn_10.48), and α-ferrite phases. The ORs between ζ(FeZn₁₃) and Γ₁(Fe₃Zn₁₀) were characterized using TEM analysis. Based on the TEM results, the following conclusions were drawn: (1) A cube-on-cube orientation relationship was identified at the α-ferrite/Γ₁(Fe₃Zn₁₀) and α-ferrite/Γ₂(Fe₁₁Zn₃₉) interfaces. Additional ORs at the α-ferrite/Γ₂(Fe₁₁Zn₃₉) interface include (001)_α//<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13632_2025_1249_Article_IEq1.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\({\left(1\overline{1 }2\right)}_{\Gamma 2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mfenced close=")" open="("> <mn>1</mn> <mover> <mn>1</mn> <mo>¯</mo> </mover> <mn>2</mn> </mfenced> <mrow> <mi mathvariant="normal">Γ</mi> <mn>2</mn> </mrow> </msub> </math></EquationSource> </InlineEquation>,<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13632_2025_1249_Article_IEq2.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">\({\left[1\overline{1 }0\right]}_{{\upalpha }}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mfenced close="]" open="["> <mn>1</mn> <mover> <mn>1</mn> <mo>¯</mo> </mover> <mn>0</mn> </mfenced> <mi mathvariant="normal">α</mi> </msub> </math></EquationSource> </InlineEquation>//<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13632_2025_1249_Article_IEq3.gif" Format="GIF" Height="25" Rendition="HTML" Resolution="72" Type="Linedraw" Width="100" /> </InlineMediaObject> <EquationSource Format="TEX">\({\left[5\overline{55 }\right]}_{\upzeta }, {\left[\overline{2 }00\right]}_{{\upalpha }}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mfenced close="]" open="["> <mn>5</mn> <mover> <mn>55</mn> <mo>¯</mo> </mover> </mfenced> <mi mathvariant="normal">ζ</mi> </msub> <mo>,</mo> <msub> <mfenced close="]" open="["> <mover> <mn>2</mn> <mo>¯</mo> </mover> <mn>00</mn> </mfenced> <mi mathvariant="normal">α</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>//<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13632_2025_1249_Article_IEq4.gif" Format="GIF" Height="25" Rendition="HTML" Resolution="72" Type="Linedraw" Width="100" /> </InlineMediaObject> <EquationSource Format="TEX">\({\left[\overline{3 }\overline{3 }\overline{9 }\right]}_{\upzeta }, {\left[\overline{1 }\overline{1 }0\right]}_{{\upalpha }}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mfenced close="]" open="["> <mover> <mn>3</mn> <mo>¯</mo> </mover> <mover> <mn>3</mn> <mo>¯</mo> </mover> <mover> <mn>9</mn> <mo>¯</mo> </mover> </mfenced> <mi mathvariant="normal">ζ</mi> </msub> <mo>,</mo> <msub> <mfenced close="]" open="["> <mover> <mn>1</mn> <mo>¯</mo> </mover> <mover> <mn>1</mn> <mo>¯</mo> </mover> <mn>0</mn> </mfenced> <mi mathvariant="normal">α</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>//<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13632_2025_1249_Article_IEq5.gif" Format="GIF" Height="25" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\({\left[\overline{6 }\overline{6 }0\right]}_{\upzeta }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mfenced close="]" open="["> <mover> <mn>6</mn> <mo>¯</mo> </mover> <mover> <mn>6</mn> <mo>¯</mo> </mover> <mn>0</mn> </mfenced> <mi mathvariant="normal">ζ</mi> </msub> </math></EquationSource> </InlineEquation>. (2) Various ORs at the ζ(FeZn₁₃)/Γ₁(Fe₃Zn₁₀) interface were identified, including (101)_Γ1//<InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13632_2025_1249_Article_IEq6.gif" Format="GIF" Height="25" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="TEX">\({\left(15\overline{2 }\right)}_{\upzeta }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mfenced close=")" open="("> <mn>15</mn> <mover> <mn>2</mn> <mo>¯</mo> </mover> </mfenced> <mi mathvariant="normal">ζ</mi> </msub> </math></EquationSource> </InlineEquation>, (234)_Γ1//(130)_ζ, and (412)_Γ1//(102)_ζ. (3) ORs at the Γ₂(Fe₁₁Zn₃₉)/δ(Fe_0.64Zn_10.48) interface, such as (111)_Γ2//(111)_δ and (111)_Γ2//(101)_δ, were observed in the galvannealed coating layers.</p>