First of all: Thanks for your very fast and helpful response.

I copied actually only the partition, not the whole disk: /dd_rescue 
--force -r1 /dev/sdd1 /dev/sdc1/
The cause for this is that I don't have enough space left on another 
device to store a whole copy of the faulty disk. I thought it would be 
possible, like in some examples I found with google, that you can rescue 
a partition directly.

/file -s /dev/sdc1/ says:
//dev/sdc1: data/

The disks look like this (/fdisk -l/):
/Disk /dev/sdc: 3000.6 GB, 3000592982016 bytes, 5860533168 sectors//
//Units = Sektoren of 1 * 512 = 512 bytes//
//Sector size (logical/physical): 512 bytes / 4096 bytes//
//I/O size (minimum/optimal): 4096 bytes / 4096 bytes//
//Disk identifier: 0xcba506ee//
//
//   Gerät  boot.     Anfang        Ende     Blöcke   Id System//
///dev/sdc1             256   732566645   366283195   83 Linux//
//
//Disk /dev/sdd: 2000.4 GB, 2000397852160 bytes, 3907027055 sectors//
//Units = Sektoren of 1 * 512 = 512 bytes//
//Sector size (logical/physical): 512 bytes / 512 bytes//
//I/O size (minimum/optimal): 512 bytes / 512 bytes//
//Disk identifier: 0x3c34826b//
//
//   Gerät  boot.     Anfang        Ende     Blöcke   Id System//
///dev/sdd1              63  3907024064  1953512001   83 Linux/

If it is not possible to rescue the partition this way I will have to 
extend my to RAID5 so that I can put the copy of the faulty disk on this 
one, like Michael explained in his answer. I just hoped that I can avoid 
this, because it would save me more than 100EUR.

As last information: The content of this copy is not totally lost, 
actually only the last few files I have added. All the other stuff is 
already stored on the RAID5, only the latest stuff is not contained in 
this backup. So I don't loose everything if something goes wrong (at 
least one thing :-) ).

Kind regards,
Benedikt