A sharp broken piece of a hard substance' can be termed as -

• Shard (Noun)
English Meaning: A sharp broken piece of a hard substance.
Bangla Meaning: (প্রাচীন প্রয়োগ তবে মালী ও প্রত্নতাত্ত্বিকরা এখনো ব্যবহার করে থাকেন) মাটির পাত্রের ভাঙা টুকরা; খোলামকুচি।

Synonyms: Fragment (খণ্ড; টুকরা), Sliver (ধারালো টুকরা), Piece (খণ্ড; অংশভাগ), Splinter (ছোট ছোট কুচি), Particle (ক্ষুদ্র কণা)। 
Antonyms: Chunk (পুরু খণ্ড বা টুকরা), Slab (পুরু মসৃণ খণ্ড), Hunk (মোটা খণ্ড; প্রস্থ; বড় টুকরো). Core, (মূল) Entirely (সম্পূর্ণরূপে)। 

Other Forms: 
Example Sentence: 

1. Saying that shards of broken glass are razor sharp is an understatement.
2. One shard of glass ripped his hand and another across his forehead.

Options,
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Source: Website Lecture & Cambridge Dictionary.