The intensity of neutrons Bragg diffracted from the back face of a 9 mm thick slab-shaped Si(111) analyzer crystal has been measured experimentally at the ORNL double crystal diffractometer and calculated theoretically. The back-face rocking curve of a strain-free perfect crystal contains two symmetrical peaks which become asymmetrical under an ultrasmall static deformation strain (bending with a radius of tens of km). The asymmetry is shown to be a sensitive measure of both the magnitude and direction of bending. [S0031-9007 (98)06594-6] PACS numbers: 62.20. -x, 61.12.ExThe high transparency of silicon for thermal neutrons creates a unique opportunity to study total Bragg diffraction from a thick crystal (with the thickness T ϳ 1 cm). Such experiments cannot be done with conventional x-ray radiation which cannot penetrate to the back face of a thick crystal. This property of neutron radiation was originally used by C. G. Shull in the early 1970s to measure separately the front-face (FF), back-face (BF), and end-face Bragg reflections from a thick Si crystal by scanning a narrow cadmium slit across the exiting beam [1,2]. However, all of these experiments were carried out in the conditions when the crystal under study was set up at a chosen angle of incidence, u u B , or slightly deviated from the exact Bragg angle, u B , and did not move while the detector was scanned across the diffracted beam.The angular dependence of the intensity of BF reflection, I BF ͑u 2 u B ͒, on u was measured for the first time at the ORNL Bonse-Hart double crystal diffractometer (DCD) [3]. In that experiment the short plate of the Si(111) analyzer channel-cut crystal 3 was covered by Cd, as shown in Fig. 1, to block the FF reflected beam and measure only the BF reflection from the long plate. The incident four-bounce neutron beam (wavelength l 2.59 Å, u B 24.4 ± ) was formed by a sequence of reflections from the single-bounce premonochromator, followed by a triple-bounce channel-cut monochromator crystal (see Fig. 1). The intensity of the experimental BF rocking curve (BFRC), normalized by the peak intensity of the FF reflection, is shown in Fig. 2 (open circles) as a function of the dimensionless angular parameter of dynamical diffraction theory, y ͑u 2 u B ͒͞du B , where du B b c e 2W jF S jNl 2 ͞p sin u B is the half-width of the Darwin plateau, b c is the atomic coherent scattering length, e 2W is the Debye-Waller factor, F S is the structure factor, and N is the number of unit cells per unit volume (in our case u 2 u B 1 arc sec corresponds to y 1.2). The BFRC (Fig. 2) contains two sharp peaks at y 62.2 and a deep minimum at y 0, in contrast to the FF rocking curve (FFRC) from a perfect crystal which has one peak at y 0.The BFRC can be derived from the classical dynamical diffraction theory using the condition (see, e.g., in [4]) that the intensity partially transmitted into a transparent crystal in the vicinity of the Bragg angle can be written as 1 2 R D ͑y͒, where R D ͑y͒ is the Darwin reflectivity function [5]Thus, inside the...