http://help.infragistics.com/doc/WPF/2013.2/CLR4.0/?page=xamZoombar_Getting_Started_with_xamZoombar.html

If you used the ZoomChangingEvent, you could interrogate the sender's Range as the initial position and the attribute's NewRange value.  You would then know the initial range and the new range.  Then you would have to determine if the difference between the NewRange's Minimum and Maximum value was less than you wanted to allow.  At that point you could cancel the event or more likely you could set the NewRange values, calculating the appropriate values depending on whether the Minimum or Maximum values had changed.  You would probably want some notification that the width of the thumb is being restricted.

The following code may be helpful to you.

void zoombarA_ZoomChanging(object sender, ZoomChangeEventArgs e)

{

     Range currRange = (sender as XamZoombar).Range;

     Range newRange = e.NewRange;

     double minDif = .1;

     if ((Math.Round(newRange.Maximum, 5) - Math.Round(newRange.Minimum, 5)) < minDif)

     {               

          //e.Cancel = true;

          if (Math.Round(newRange.Maximum, 5) != Math.Round(currRange.Maximum,5) )

          {                    

              newRange.Maximum = Math.Round(newRange.Minimum + minDif,5);

          }

          else

          {                   

              newRange.Minimum = Math.Round(newRange.Maximum - minDif, 5);

          }

    }                

} 

Please let me know if you have any questions.