This XML syntax is working:

$  HolidayWorkID = "<Field Type='Number'    Name='HolidayWorkID'    DisplayName='HolidayWorkID    Group='Holidays' />" 

But this doesn’t working:

$  HolidayReportMonth = "<Field Type='Calculated'                                      Name='HolidayReportMonth'                                      DisplayName='CustomMonth'                                      Group='Holidays'                                      ResultType='Text'                                     <FieldRefs>                                         <FieldRef Name='HolidayDateFrom' />                                     </FieldRefs>                                     <Formula>=MONTH([HolidayDateFrom])</Formula>                                  />" 

Error message is:

Exception calling “AddFieldAsXml” with “3” argument(s): “Name cannot begin with the ‘<‘ character, hexadecimal value 0x3C. Line 2, position 10.”