This schist has two hornblende generations and these small quartz crystals formed on hornblende in some parts of the rock. I want to know what the texture is it.
There are very distinctive recrystallisation textures in the large quartz grains e.g triple point with 120o angle boundaries. You can see some modification of the hbl edge (to a sawtooth) in some cases to accommodate this between the two phases. However where the hbl grain still has a straight edge the recrystallised qtz grains simply have a boundary perpendicular to the hbl grain. This gives the (potentially misleading) appearance of "growing out from the hbl".
The hornblende seem pretty randomly oriented in this pic, is there a fabric in the rock in general, ie preferential alignment of the hornblende or any other evidence for metamorphism. My suggestion would be this is what has caused the recrystallisation, and that the big qtz grains have resulted from the large hbl localising stress during the deformation.
In my opinion there is a typical result of synmetamorphic recrystallization and segregation. Afanitic basaltic texture of surrounding matrix contains Hbl + Pl + Ep, thus typical for amphibolites but significant addition of Qtz suggests rather tuffitic protolith. Therefore, I suggest local increase of silicate terigenic material, which underwent recrystallization due to amphibolite facies metamorphism.
It will be helpful to check chemical zonation of Hbl blasts.
That is a beautiful photomicrograph. I am sorry, but I am unaware of any name for that texture.
The recrystallized quartz crystals (noted by Richard J.M. Taylor and Maksymillian Twyrdy) are not ubiquitous around each of the idioblastic hornblende laths near the center of the slide. For example those in the lower right and upper left portions of the slide are devoid of the quartz. Another that extends to the right, in an "east-northeast" direction shows the quartz on only one side, but not on the other.
I do not know what caused the phenomenon, but based on what is visible would GUESS that a quartz-rich hydrothermal fluid may have invaded the rock under stress and sufficiently elevated T,P conditions to deposit, and induce the recrystallization of, the quartz. Do you see that anywhere else in that, or any other, slide?
I would like to highlight your good observation Wallach Joe: only west /northwest sides of Hbl blasts are surrounded by quartz. That suggests either top-to-the-WSW shearing or this view as a part of larger-scale fold (quartz will concentrate in the hinge zones in this view). Is this rock folded or not? Any foliation might be found under microscope or in meso-scale?
This rock is not folded but was under tensile forces and the first generation Hbls are boudinaged. The second generation Hbls crossed the fist ones and show no bouninage. I wnder these quartz grew by recrystallization under metamorphic conditions or by a fluid after metamorphism?
Pure silica solubility depends only on the temperature of fluid and peaks about 340oC, thus you should check the precipitation temperature of the second generation of Hbl (if really so). Hydrothermal fluid occurrence is often reflected by other precipitated minerals e.g. Fe-oxides and calcite etc. If you'll find those assemblages as veins, fracture fillings, you'll sure about the quartz origin as well. Precipitation temperature of Hbl grains might be estimated by analyzing of Hbl + Pl thermometer after Plyusnina (1982).
To my opinion the rock belongs to hornblende epidote schist, and not to amphibolite, though foliation is weakly expressed in the figure and seems to run diagonally from the right (SE) to the left (NW). You are mentioning extensional structures and this is probably the reason for opening of transversal micro-fracture which was subsequently filled with quartz (probably exolved from the rock itself), which grew perpendicular on the hornblende porphyroblasts. The triple-junctions of the grains indicate crystallization in stable conditions. In addition to quartz, it seems that some albite is present as well. Slightly damaged hornblende porphyroblasts (seen in the centre of the figure) could indicate tension approximately along foliation and growth of quartz on hornblende in this direction. The microfracture seems to open along transversally oriented Hb porphyroblasts, while the ones oriented along foliation and the grains away from the microfracture have no quartz along their prisms.
I agree with Richard about the texture, i.e., triple points with 120° angle boundaries. The question is how to interpret it. If this rock underwent some kind of shearing/deformation, I don´t think this is recognisable in this picture. It doesn´t mean that the rock underwent no deformation but at least this cannot be interpreted from quartz textures, which are more likely to represent post-deformation recrystallization/recovery processes. Dinamically recrystallized quartz would show evidences of BLG, SGR or GBM and the textures that are observable here. Perhaps you should compare the microstructures of other minerals and the fabric of the whole rock to constrain posible deformation processes.