## Structure and charge density waves of blue bronze

Variable temperature constant current STM measurements in the figure, the “apparent” surface structure changes as the temperature is lowered from 300K to 100K. At 300K only one periodic structure is present on the (20) surface,with lattice vectors ** 1** = 1.2 nm and

**= 0.76 nm. The modulus of the lattice vector**

*b***(see inset in fig.**

*b***A**) agrees with the corresponding X-ray diffraction-determined lattice parameter in the bulk of 0.756 nm. The modulus of vector

**matches the known bulk distance between (112) planes, and the angle between vectors**

*1***1**and

**b**also agree with the bulk angle. At 140K (below the Peierls transition), two periodic structures are evident from peak splitting in the FFT, Fig.

**B**. One structure has the lattice parameters of the atomic structure at 300K, consistent with the small change in bulk lattice parameters (<1%) in this temperature range. The second structure is smaller (vector

**= 1.2 nm, vector**

*1***= 0.71 nm) with slightly different angles between the surface unit vectors. Lowering the temperature down to 100K results in vanishing of FFT peak splitting (fig.**

*b***C**) indicating the transition from incommensurate to commensurate CDW.

We attribute this structure to the CDWs on the surface. The corrugation associated with the CDW is not distinguished in the profile, but the effect of the additional intensity at the atomic sites is clear. The superposition of the two results in an underlying low frequency component with a period 11 times that of the lattice. This represents a lattice mismatch of about 9%, which agrees with bulk measurements (~ 9% at 140K). The separation of the two lattices is evident (on Fig. **E**) and illustrates mismatch on the order of 10% along the ** b** direction and almost commensurate alignment along the

**+**

*a***+ 2**

*b***direction.**

*c*