Structures of exfoliated single layers of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">WS</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">MoS</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">MoSe</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>in aqueous suspension

Single layers of the transition-metal dichalcogenides ${\mathrm{WS}}_{2},$ ${\mathrm{MoS}}_{2},$ and ${\mathrm{MoSe}}_{2}$ were formed as aqueous suspensions by lithium intercalation and exfoliation of crystalline powders and examined by x-ray diffraction and x-ray absorption fine structure (XAFS) spectroscopy. The two-dimensional characteristics of these systems were readily apparent through the absence of any (hkl) peaks $(l\ensuremath{\ne}0)$ and in the strong asymmetry of the $(\mathrm{hk}0)$ peaks in the diffraction patterns. Indexing the diffraction patterns with rectangular unit cells revealed the diselenide as the most distorted from the hexagonal structures of the parent materials, with the Mo atoms forming a ``zigzag'' structure which is also corrugated perpendicular to the layers. Mo K-edge and W L3-edge XAFS analysis using ${\mathrm{WTe}}_{2}$-related structural models enabled the determination of the short, intermediate, and long metal-metal near-neighbor distances with the shortest metal-metal distances contracted approximately 0.4 \AA{} compared to parent reference materials. Shifts in the Mo K-absorption-edge energy in ${\mathrm{MoSe}}_{2}$ correlated with changing Se-Se interactions. Combining the XAFS and diffraction results enabled an estimation of the layer puckering and atomic positions in three-dimensional models of the unit cells. Selenium K-edge XAFS also identified two selenium-oxygen scattering paths from water or ${\mathrm{OH}}^{\ensuremath{-}}$ ions coordinating the layers of exfoliated ${\mathrm{MoSe}}_{2}.$