The surface atomic structure and the charge-density-wave (CDW) structure in the 1T phase of ${\mathrm{TaSe}}_{2}$, ${\mathrm{TaS}}_{2}$, and ${\mathrm{VSe}}_{2}$ have been studied at 4.2, 77, and 300 K. The response of the scanning tunneling microscope (STM) to the CDW superlattice in 1T-${\mathrm{TaSe}}_{2}$ and 1T-${\mathrm{TaS}}_{2}$ is extremely strong, while in 1T-${\mathrm{VSe}}_{2}$ the CDW generates a much weaker response. In 1T-${\mathrm{TaSe}}_{2}$ and 1T-${\mathrm{TaS}}_{2}$ at 4.2 and 77 K the STM scans show a \ensuremath{\surd}13 ${\mathbf{a}}_{0}$\ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}13 ${\mathbf{a}}_{0}$ pattern characteristic of a triple-q commensurate CDW structure. The atomic lattice and CDW superlattice are simultaneously resolved, but the atomic modulation represents a small fraction of the total STM deflection leading to a substantial variation in the atomic resolution. At 300 K we continue to observe a commensurate \ensuremath{\surd}13 ${\mathbf{a}}_{0}$\ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}13 ${\mathbf{a}}_{0}$ CDW pattern in 1T-${\mathrm{TaSe}}_{2}$ while 1T-${\mathrm{TaS}}_{2}$ shows a modulated two-dimensional structure due to the incommensurate CDW wavelength characteristic of the nearly commensurate phase.The STM scans on 1T-${\mathrm{VSe}}_{2}$ show a 4${\mathbf{a}}_{0}$\ifmmode\times\else\texttimes\fi{}4${\mathbf{a}}_{0}$ CDW superlattice with a pattern that reflects a triple- to double-q transition in the CDW structure and the formation of domains. In 1T-${\mathrm{VSe}}_{2}$ the atomic modulation is dominant with a weak superimposed modulation due to the CDW superlattice. This difference in the strength of the CDW is reflected in the z deflection of the STM and in the effective barrier height as a function of tip-to-surface distance. The STM scans and profiles of z deflection have been analyzed and compared for all three materials. Defects in the CDW structure of 1T-${\mathrm{TaSe}}_{2}$ and 1T-${\mathrm{TaS}}_{2}$ have been observed which create missing CDW maxima and a variable enhancement of the surrounding CDW maxima. These appear to result from defects in the Ta layer rather than in the surface Se or S layer. Defects in the STM scans of 1T-${\mathrm{VSe}}_{2}$ are very localized and appear to be associated with Se-atom vacancies in the surface layer. The STM patterns and response will be reviewed and analyzed in terms of the band structures and Fermi surfaces of the various compounds. Results are also compared to information obtained from electron diffraction.

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